Modelling of an Efficient Dynamic Smart Solar … Photovoltaic Power Grid System ... While the thesis has contributed to the smart solar ... Modelling of an Efficient Dynamic Smart

Modelling of an Efficient Dynamic Smart

Solar Photovoltaic Power Grid System

Balogun Emmanuel Babajide

B.Sc (University of Lagos, Nigeria – UNILAG) (2005)

M.Sc(University of Lagos, Nigeria – UNILAG) (2010)

A Thesis Submitted in Requirement for the Degree of Doctor

of Philosophy (Information Science & Engineering)

at

University of Canberra.

Faculty of Education, Science, Technology and Mathematics

September 2015.

i

Abstract

A smart solar photovoltaic grid system is an advent of innovation coherence of information

and communications technology (ICT) with power systems control engineering via the internet

[1]. This thesis designs and demonstrates a smart solar photovoltaic grid system that is self-

healing, environmental and consumer friendly, but also with the ability to accommodate other

renewable sources of energy generation seamlessly, creating a healthy competitive energy

industry and optimising energy assets efficiency.

This thesis also presents the modelling of an efficient dynamic smart solar photovoltaic power

grid system by exploring the maximum power point tracking efficiency, optimisation of the

smart solar photovoltaic array through modelling and simulation to improve the quality of design

for the solar photovoltaic module. In contrast, over the past decade quite promising results have

been published in literature, most of which have not addressed the basis of the research questions

in this thesis.

The Levenberg-Marquardt and sparse based algorithms have proven to be very effective tools in

helping to improve the quality of design for solar photovoltaic modules, minimising the possible

relative errors in this thesis. Guided by theoretical and analytical reviews in literature, this

research has carefully chosen the MatLab/Simulink software toolbox for modelling and

simulation experiments performed on the static smart solar grid system. The auto-correlation

coefficient results obtained from the modelling experiments give an accuracy of 99% with

negligible mean square error (MSE), root mean square error (RMSE) and standard deviation.

This thesis further explores the design and implementation of a robust real-time online solar

photovoltaic monitoring system, establishing a comparative study of two solar photovoltaic

tracking systems which provide remote access to the harvested energy data. This research made a

landmark innovation in designing and implementing a unique approach for online remote access

solar photovoltaic monitoring systems providing updated information of the energy produced by

the solar photovoltaic module at the site location. In addressing the challenge of online solar

photovoltaic monitoring systems, Darfon online data logger device has been systematically

ii

integrated into the design for a comparative study of the two solar photovoltaic tracking systems

examined in this thesis. The site location for the comparative study of the solar photovoltaic

tracking systems is at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C.

The overall comparative energy output efficiency of the azimuthal-altitude dual-axis over the 450

stationary solar photovoltaic monitoring system as observed at the research location site is about

72% based on the total energy produced, estimated money saved and the amount of CO2

reduction achieved. Similarly, in comparing the total amount of energy produced by the two

solar photovoltaic tracking systems, the overall daily generated energy for the month of July

shows the effectiveness of the azimuthal-altitude tracking systems over the 450 stationary solar

photovoltaic system. It was found that the azimuthal-altitude dual-axis tracking systems were

about 68.43% efficient compared to the 450 stationary solar photovoltaic systems. Lastly, the

overall comparative hourly energy efficiency of the azimuthal-altitude dual-axis over the 450

stationary solar photovoltaic energy system was found to be 74.2% efficient.

Results from this research are quite promising and significant in satisfying the purpose of the

research objectives and questions posed in the thesis. The new algorithms introduced in this

research and the statistical measures applied to the modelling and simulation of a smart static

solar photovoltaic grid system performance outperformed other previous works in reviewed

literature. Based on this new implementation design of the online data logging systems for solar

photovoltaic monitoring, it is possible for the first time to have online on-site information of the

energy produced remotely, fault identification and rectification, maintenance and recovery time

deployed as fast as possible.

The results presented in this research as Internet of things (IoT) on smart solar grid systems are

likely to offer real-life experiences especially both to the existing body of knowledge and the

future solar photovoltaic energy industry irrespective of the study site location for the

comparative solar photovoltaic tracking systems. While the thesis has contributed to the smart

solar photovoltaic grid system, it has also highlighted areas of further research and the need to

investigate more on improving the choice and quality design for solar photovoltaic modules.

Finally, it has also made recommendations for further research in the minimization of the

absolute or relative errors in the quality and design of the smart static solar photovoltaic module.

v

Acknowledgements

This dissertation would have never been written, much less completed without acknowledging

the unmerited mercies, love and favour of the Almighty God for His unfailing grace, strength,

knowledge and wisdom throughout the learning process of my doctoral studies.

I would like to express sincere gratitude to my primary supervisor, Prof. Xu Huang, for his

excellent guidance and counsel, patience, providing insightful comments, valuable contribution

and support over the course of my research. I would also like to thank my co-supervisor A/Prof.

Dat Tran for his encouragement and moral support in every step of this research work. I wish to

express my indebtedness to fellow research colleagues, and all administrative staffs at the

National Kaohsiung University of Applied Sciences, Taiwan, the Republic of China for their

guidance, cooperation and support during my research visit for data collection.

My sincere thanks also go to Mrs Carmela Thambirajah Adisa and family for their timely and

invaluable support at the hour of distress during my study. I would also like to express sincere

gratitude to Dr Abayomi Adeniyi and family for their moral guidance and support. I would like

to thank every member and friends of the Ammish family, especially Dr Ammish Adu and Dr

Joyce Adu for their unflinching and unfailing assistance and encouragement to persevere in

finishing my doctoral research.

I would like to thank Dr Michael S. Adelana and all members of the Deeper Christian Life

Ministry, Australia for their timely and financial support in the period of crisis and ceaseless

prayers supporting me spiritually throughout this study period. I would like to thank my fellow

research mates for their thought-provoking discussions across all works of life, for the

opportunities to work together, and for all the fun in sports, we had in the last three years.

I am indebted to the Lagos State Government Scholarship Board, Nigeria for granting me the

opportunity to undertake this research study at the University of Canberra, Australia for their

financial commitment was invaluable to me in completing my doctoral studies. Special thanks to

all who have crossed my paths during this journey, who has in one way or another been a

blessing contributing to the successful completion of this dissertation.

vi

Last but not the least, I would like to thank my parents, especially my mother for her ceaseless

prayers and mobile calls since I left for this doctoral studies and my beloved wonderful sisters

for their concern on my study progress and unconditional support in taking good care of my dad.

vii

List of Acronyms AADAT Azimuth-Altitude Dual Axis Tracker

ANN Artificial Neural Network

CCD Charge Coupled Device

Cfcs Chlorofluorocarbons

CO2-e Carbondioxide Equivalent

CPV Concentrated Photovoltaic

CR Time Constant

CSP Concentrated Solar Power

CVR Conservation Voltage Reduction

DLS Damped Least-Squares

EPA Environment Protection Agency

EPRI Electric Power Research Institute

FDIR Fault Detection, Isolation And Restoration

GDP Gross Domestic Product

GHG Green House Gases

GM-Estimators Generalized M-Estimators

GNA Gaussian-Newton Algorithm

GPS Global Positioning System

GUI Graphical User Interface

HSAT Horizontal Single Axis Tracker

IAAS Infrastructure As A Service

ICT Information and Communication Technology

IP Internet Protocol

IREAs International Renewable Agencies

ISA International Society Of Automation

ISP Internet Service Providers

IVVCO Integrated Volt-Var Control Optimisation

viii

IoT Internet of Things

LAD Least Absolute Deviation

LDRs Light Dependent Resistors (Or Photo-Resistors),

LMA Levenberg-Marquadt Algorithm

LREs Large Renewable Energy Schemes

LT Local Times

LTS Least Trimmed Squares

MLP Multilayer Perceptron

MPPT Maximum Power Point Tracking

MSE Mean Square Error

NERC CIP North American Electric Reliability Corporation Critical Infrastructure Protection

NIPP National Infrastructure Protection Plan

NIST National Institute Of Standard And Technology

NREAP National Renewable Energy Action Plan

O&M Operations And Maintenance

OLS Ordinary Least Squares

PAAS Platform As A Service

PASAT Polar Aligned Single Axis Tracker

PC Personal Computers

P-I-N Diode Photo-Diode

PLC Programmable Logic Control

PSpice Personal Computer Simulation Program with Integrated Circuit Emphasis

PV Photo-Voltaic

QoS Quality of Service

RBF Radial Basis Function

REAs Renewable Energy Agencies

RECs Renewable Energy Credits

RES Renewable Energy Sources

ix

RETs Renewable Energy Targets

RMSE Root Mean Square Error

RPS Renewable Portfolio Standards

SAAS Software As A Service

SGN Smart Grid Network

SRES Small Renewable Energy Schemes

T&D Transmission And Distribution

TSAT Tilted Single Axis Tracker

TTDAT Tip-Tilt Dual Axis Tracker

UCAAS Unified Communication As A Service

UV UltraVoilet

VSAT Vertical Single Axis Tracker.

WCRE World Council For Renewable Energy

xi

List of Symbols

𝐼𝑝ℎ photo current generator

𝐼𝑜 leakage or reverse saturation current

q electron charge

V solar cell voltage

A ideality factor

k Boltzmann constant

𝑅𝑆 series cell resistance

𝑅𝑠ℎ shunt cell resistance

𝑇𝑎 ambient temperature

𝑤𝑠 wind speed

S solar irradiation

𝐼𝑜𝑟 𝐼𝑜 at reference temperature at 𝑇𝑟 = 301.18K

𝐸𝐺 band gap energy

𝑇𝑟 reference temperature

𝑇 solar cell temperature

𝐼𝑠𝑐𝑟 short circuit current at 𝑇𝑟

𝑘𝑖 short circuit current temperature coefficient

𝑉𝑂𝐶 open circuit voltage

𝑉𝑚𝑝 maximum power voltage

𝐼𝑚𝑝 maximum power current

𝑛𝑝 number of parallel modules

𝑛𝑠 number of series modules

P output power

xiii

List of Publications

Balogun, Emmanuel B., Xu Huang, and Dat Tran. "Efficiency of Sensor Devices Used

in Dynamic Solar Tracking System: Comparative Assessment Parameters

Review." Applied Mechanics and Materials 448 (2014): 1437-1445.

Balogun, Emmanuel B., Xu Huang, and Dat Tran "Solar optimisation based on different

tracking techniques". Proceedings of the 2013 International Conference on Agriculture

Science and Environment Engineering (ICASEE 2013), 19-20 December, Beijing, China.

DEStech Publications, Inc.

Balogun, Emmanuel B., Xu Huang, and Dat Tran. "A Revolution in Green Energy:

Solar Tracking System". Proceedings of the 2013 International Conference & Exhibition

on Clean Energy (ICCE 2013), 9-13 September, Ottawa, Canada.

Balogun, Emmanuel B., Xu Huang, and Dat Tran. "The Prospective Grid: The Smart

Grid Network". Proceedings of the 2014 International Conference & Exhibition on Clean

Energy (ICCE 2014), 20-24 October, Quebec city, Canada.

Balogun, Emmanuel B., Xu Huang, and Dat Tran. "Comparative Study of Different

Artificial Neural Networks Methodologies on Static Solar Photovoltaic Module."

"International Journal of Emerging Technology and Advanced Engineering" Volume 4,

Issue 10, October 2014(ISSN 2250-2459(Online)): 674-685.

Balogun, Emmanuel B., Xu Huang, Dat Tran, Yun-Chuan Lin, Mingyu Liao, and

Michael Adaramola. "Regression estimation modelling techniques on static solar

photovoltaic module" "International Journal of Emerging Technology and Advanced

Engineering" Volume 5, Issue 4, April 2015 (ISSN 2250-2459(Online)): 451-461.


Michael Adaramola. "A robust real-time online comparative monitoring of an azimuthal-

altitude dual axis GST 300 and a 45° fixed solar photovoltaic energy tracking systems."

In SoutheastCon 2015, pp. 1-10. IEEE, 2015.


Michael Adaramola. "Power quality improvement by integration of Distributed

Networks" "International Journal of Emerging Technology and Advanced Engineering"

Volume 5, Issue 7, July 2015 (ISSN 2250-2459(Online)): 465-471.

xv

Table of Contents Abstract .......................................................................................................................................................... i

Certificate of Authorship of Thesis .............................................................................................................. iii

Acknowledgements ....................................................................................................................................... v

List of Acronyms ........................................................................................................................................ vii

List of Symbols ............................................................................................................................................ xi

List of Publications .................................................................................................................................... xiii

List of Tables ............................................................................................................................................. xix

List of Figures ............................................................................................................................................ xxi

Chapter 1 Introduction ................................................................................................................................. 1

1.1 Introduction to the Study ................................................................................................................... 1

1.2 Characteristics of the Term Smart Power Grid ................................................................................. 2

1.3 Smart Power Grid Concept ................................................................................................................ 3

1.4 Evolution in the Power Grid Systems ................................................................................................ 5

1.5 Background and Context .................................................................................................................... 6

1.6 Research Objectives and Questions .................................................................................................... 9

1.6.1 Research Objectives ..................................................................................................................... 9

1.6.2 Research Questions ...................................................................................................................... 9

1.7 Research Methods ............................................................................................................................ 10

1.8 Research Works, Contribution and Justification .............................................................................. 11

1.9 Limitation and Assumptions ............................................................................................................ 13

1.10 The Outline of this Thesis .............................................................................................................. 14

1.11 Conclusion ..................................................................................................................................... 16

Chapter 2 Literature Review ...................................................................................................................... 17

2.1 Introduction ...................................................................................................................................... 17

2.2 Solar Photovoltaic Sensor and Tracking Optimisation Devices ...................................................... 18

2.2.1 Dynamic Characteristics of Solar Photovoltaic Sensors ........................................................... 19

2.2.2 Assessments of Physical Sensor Parameters ............................................................................. 22

2.3 Solar Photovoltaic Tracking Optimisation Techniques ................................................................... 28

2.3.1 Dynamic Single axis Tracking Optimisation ............................................................................ 29

2.3.2 Dynamic Dual- axis Solar Tracker ............................................................................................ 31

xvi

2.4 Smart Solar Power Grid System ...................................................................................................... 33

2.4.1 Smart Solar Photovoltaic Power Grid Network ........................................................................ 33

2.4.2 Concept of the Smart Solar Photovoltaic Grid Network ........................................................... 34

2.4.3 Challenges and Issues on the Smart Solar Photovoltaic Grid System ...................................... 36

2.5 Green Energy Revolution and Policy ............................................................................................... 38

2.5.1 Overview of the State of Evolution ........................................................................................... 38

2.5.2 Determinants of Green Energy Revolution .............................................................................. 41

2.5.3 Impacts of Green Renewable Energy ...................................................................................... 45

2.6 The Prospective Grid: A Smart Grid Network ................................................................................. 48

2.6.1 The Smart Grid Network .......................................................................................................... 48

2.6.2 Conceptual Framework of the Smart Grid Network ................................................................ 50

2.6.3. A Smart Grid Network Policy and Implementation Guidelines .............................................. 52

2.6.4. The Smart Grid Network Challenges ....................................................................................... 53

2.6.5. Benefits of the Smart Grid Network ........................................................................................ 54

2.7 Conclusion ...................................................................................................................................... 55

Chapter 3 Modelling and Simulation Techniques for a Solar Photovoltaic System .................................. 59

3.1 Introduction ...................................................................................................................................... 59

3.2 Static Solar Photovoltaic Modules Modelling and Simulation Performance .................................... 59

3.3 Static Solar Farm Photovoltaic Modules Modelling ........................................................................ 61

3.4 Solar Photovoltaic Module Simplest Model and Parameter Definitions ......................................... 61

3.4.1 Solar Photovoltaic Module Simplest Model ............................................................................. 61

3.4.2 Module Parameter Definitions .................................................................................................. 62

3.5 Proposed Research Methodology..................................................................................................... 65

3.5.1 Neural Network Model ............................................................................................................ 65

3.5.2 Sparse Based Algorithm........................................................................................................... 81

3.6 Conclusion ..................................................................................................................................... 100

Chapter 4 Astronomical and Analytical Derivation for Solar Photovoltaic Tracking Systems ................ 101

4.1 Introduction .................................................................................................................................... 101

4.2 An Astronomy of Dynamic Solar Photovoltaic Tracking System ................................................. 101

4.3 Geometric Modelling Equation Derivations for Dynamic Smart Solar Photovoltaic Systems ..... 104

4.4 Simulink Modelling Approach....................................................................................................... 111

4.5 Simulink Implementation for Smart Solar Photovoltaic Systems .................................................. 112

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4.5.1 Simulink Implementation of a Solar Photovoltaic Module ..................................................... 112

4.5.2 Simulink Implementation of a Static Smart Solar Photovoltaic off-grid model ..................... 117

4.5.3 General Photovoltaic Model Characteristics ........................................................................... 121

4.5.4 Simulink Implementation of Five thousand Solar Photovoltaic Modules .............................. 126

4.6 Conclusion ...................................................................................................................................... 129

Chapter 5 Robust Real-Time Online Solar Photovoltaic Data Monitoring Systems ............................... 131

5.1 Introduction .................................................................................................................................... 131

5.2 An Overview of Robust Real-Time Remote Solar Photovoltaic Monitoring and Tracking Systems

.............................................................................................................................................................. 131

5.3 Robust Real-Time Online Solar Photovoltaic Monitoring Infrastructure ...................................... 133

5.4 Solar Photovoltaic Data Monitoring and Acquisition Energy System ........................................... 137

5.5 Comparative Solar Photovoltaic Tracking Systems under Investigation ....................................... 140

5.6 Data Management and Presentation of a Solar Photovoltaic Tracking System ............................. 145

5.7 Presentation of Results and Discussions ........................................................................................ 148

5.8 Conclusion ...................................................................................................................................... 151

Chapter 6 Conclusion ............................................................................................................................... 153

6.1 Introduction .................................................................................................................................... 153

6.2 Impacts and Conceptualisation Benefits of this Research Study ................................................... 154

6.3 Significance of Classical Modelling Algorithms on solar photovoltaic systems ........................... 155

6.4 Significance of the Simulink Solar Photovoltaic Design Model.................................................... 156

6.5 Benefits of Robust Online Cloud Computing Solar Photovoltaic Tracking Systems .................... 157

6.6 Evaluation of Simulation Smart Solar Photovoltaic Tracking Systems ......................................... 158

6.7 Significance of this Research ......................................................................................................... 159

6.8 Recommendations for Future Research ......................................................................................... 161

Bibliography ............................................................................................................................................. 163

Appendix A .............................................................................................................................................. 173

Thesis Appendices ................................................................................................................................ 173

A.1 Regression Algorithm Model ..................................................................................................... 173

A.2 Real-time online Solar photovoltaic monitoring data ............................................................... 178

xix

List of Tables

Table 1. The existing traditional power grid system compared with the Smart power grid

system …..……………………………………………………………………………….. 6

Table 2. A Summary of sensor assessment parameters…………………………………………... 23

Table 3. Conceptual framework for the smart grid network …..………………………………..... 51

Table 4. Summary of the sub-sections of literature chapter review………………………. 56

Table 5. Parameter definitions used in solar photovoltaic model……………………………........ 62

Table 6. Photovoltaic parameters used in the simulation experiments ……………....................... 76

Table 7. The summary of the experimental results…………………………………...................... 77

Table 8. Comparison of standard error estimates of the static solar photovoltaic module……….. 96

Table 9. Comparison of the MSE and RMSE regression methods of the static solar photovoltaic

module…………………………………………………………………………………… 96

Table 10. The simulated output characteristics at ten different irradiance levels………………….. 127

Table 11. Stationary 450 solar photovoltaic obtained raw data……………………………………. 176

Table 12. Dual-axis solar photovoltaic obtained raw data………………………………………… 193

Table 13. Comparative total energy generated for a month……………………………………….. 211

Table 14. Comparative hourly energy efficiency………………………………………………….. 212

xxi

List of Figures

Figure 1. Smart power grid system characteristics and its capabilities…………………………..… 3

Figure 2. Divisions of smart power grid concept……………………………………………….…. 4

Figure 3. Hybrid smart power grid system………………………………………………………… 5

Figure 4. Frequency characteristic and response of a first-order sensor……………………………. 20

Figure 5. Frequency characteristic with limited upper and lower cut-off frequencies 𝜏 𝑢 and 𝜏 𝐿

are the corresponding time constants……………………………………………………. 20

Figure 6. Responses of sensors with different damping characteristics…………………………… 22

Figure 7. Solar intensity wavelength………………………………………………………………. 26

Figure 8. Horizontal single axis tracking………………………………………………………….. 30

Figure 9. A vertical single axis tracking (VSAT)…………………………………………………. 30

Figure 10. Tilted single axis tracker………………………………………………………………… 31

Figure 11. Dual axis tracker architecture……………………………………………………………. 32

Figure 12. Summary of types of sun trackers……………………………………………………….. 33

Figure 13. A green smart grid network concept…………………………………………………….. 40

Figure 14. Solar PV Global capacity, shares of top 10 countries, 2012 (Global status report)……... 41

Figure 15. A Green energy revolution determinant………………………………………………… 42

Figure 16. Conceptual framework for smart grid network …………………………………………. 52

Figure 17. Parameter indicator for smart grid network policy and implementation…………………. 53

Figure 18. Challenges facing a smart grid network………………………………………………… 55

Figure 19. Static solar farm photovoltaic module…………………………………………………… 61

Figure 20. Simplest model of equivalent circuit solar photovoltaic module………………………… 62

Figure 21. Basic neural network model……………………………………………………………... 66

Figure 22. Radial basis function architecture……………………………………………………….. 68

Figure 23. MLP feed forward neural network………………………………………………………. 71

Figure 24. Training performance for MLP model…………………………………………………... 78

Figure 25. Training state for MLP model…………………………………………………………… 79

Figure 26. Training fit for MLP model……………………………………………………………... 79

Figure 27. Training error histogram for MLP model……………………………………………….. 80

Figure 28. Training regression performance for MLP model………………………………………. 80

xxii

Figure 29. RBF Training window……………………………………………………………….. 81

Figure 30. Dispersion diagram of Pmp vs. S…………………………………………………….. 97

Figure 31. Dispersion diagram of Vmp vs. S……………………………………………………. 97

Figure 32. Dispersion diagram of Imp vs. S……………………………………………………... 98

Figure 33. Dispersion diagram of Vmp vs. S……………………………………………………. 98

Figure 34. Dispersion diagram of Pmp vs. S…………………………………………………….. 99

Figure 35. Dispersion diagram of Imp vs. S……………………………………………………… 99

Figure 36. The Solar tracking elevation and azimuth angles…………………….………………. 102

Figure 37. Geometrical setup of a concentrated solar photovoltaic system using two

mirror-symmetrically disposed on the left (M1) and right (M2)…….…..…………… 105

Figure 38. Euler’s observatory angle compared to altazimuthal coordinate system…………….. 106

Figure 39. Simplest model of an equivalent circuit solar photovoltaic module………………….. 112

Figure 40. PV cell photocurrent, Iph Matlab/Simulink subsystem……………………………….. 114

Figure 41. PV cell photocurrent, Iph Matlab/Simulink masked subsystem………………………. 114

Figure 42. Diode reverse saturation current, Io Matlab/Simulink subsystem…………………… 115

Figure 43. Diode reverse saturation current, Io Matlab/Simulink masked subsystem…………… 115

Figure 44. Simulink model of the characteristics equation of the solar photovoltaic module……. 116

Figure 45. Masked Simulink model of the characteristics equation of the solar photovoltaic

module………………………………………………………………………………… 116

Figure 46. I-V & P-V characteristics of solar photovoltaic module……………………………… 117

Figure 47. A series connection of ten solar photovoltaic modules……………………………….. 119

Figure 48. Masked subsystem of the series connection…………………………………………… 119

Figure 49. Functional block parameter of a solar PV cell………………………………………… 120

Figure 50. Functional block parameter of a solar PV cell………………………………………… 120

Figure 51. Masked subsystem block units of a hundred solar photovoltaic modules……………... 120

Figure 52. Simulink Model of a single block of hundred solar photovoltaic modules…………..... 120

Figure 53. A five thousand series-parallel configurations of solar photovoltaic modules………..... 122

Figure 54. Solar photovoltaic array model for GUI environment of Simulink…………………… 123

Figure 55. I-V Characteristics behaviour of the solar photovoltaic model………………………. 124

Figure 56. P-V characteristics behaviour of the solar photovoltaic model………………………. 124

Figure 57. I-V characteristics of the parallel configuration model………………………………. 125

Figure 58. P-V characteristics of the parallel configuration model……………………………… 125

Figure 59. Masked subsystem for the five thousand solar photovoltaic module………………… 126

Figure 60. Full Simulink model for the five thousand solar photovoltaic modules arrangement... 126

xxiii

Figure 61. Simulation results of the output current, power and voltage against simulation time…. 127

Figure 62. Output power, voltage generated with increased irradiance level……………………... 128

Figure 63. Output current generated with increased irradiance level……………………………... 128

Figure 64. A robust real-time online solar monitoring system at roof building platform…….…… 135

Figure 65. A schematic solar photovoltaic monitoring wiring system architecture…….….…….. 136

Figure 66. Client/server internet architecture……………………………………………………… 137

Figure 67. Client/server intranet architecture……………………………………………………… 137

Figure 68. Real-time solar monitoring and acquisition infrastructure architecture………………. 138

Figure 69. Basic fundamental cloud computing service model…………………………………… 139

Figure 70. Fixed solar energy system installed at a 450 inclination……………………………..... 141

Figure 71. GST 300 tracker deployed at the roof platform……………………………………….. 144

Figure 72. Architectural framework of the GST 300 tracker……………………………………… 145

Figure 73. Graphic User Interface of the remote Darfon data logger…………………………….. 147

Figure 74. An overview of the solar photovoltaic modules installed on roof building…………….. 147

Figure 75. GUI for the 450 stationary solar systems……………………………………………… 148

Figure 76. GUI for the azimuthal-altitude dual solar systems…………………………………… 148

Figure 77. Daily profile of the mean daily total energy for the azimuthal-altitude solar systems... 150

Figure 78. Daily profile of the mean daily total energy for 450 stationary solar systems………... 150

Figure 79. Hourly profile of the mean daily total energy for 450 stationary solar systems………. 151

Figure 80. Hourly profile of the mean daily total energy for the azimuthal-altitude solar systems 151

Figure 81. Ordinary Least Regression algorithm………………………………………………… 174

Figure 82. Logistic Robustfit regression code……………………………………………………. 176

Figure 83. Least Trimmed Squares regression code………………………………………………. 178

Modelling of an Efficient Dynamic Smart Solar Photovoltaic Power Grid System

1

Chapter 1 Introduction

1.1 Introduction to the Study

This research explores one of the fast growing renewable energy sources globally, a smart

solar photovoltaic energy system. This energy system has increased the reliability of

providing a more secure and guaranteed source of power generation in many parts of the

world today. The smart solar photovoltaic energy system has received global research

attention due to the sun’s natural abundance, lack of noise pollution, non-emission of

greenhouse gases (GHG), unlike fossil and coal powered generation sources which affect the

climatic conditions causing global warming. The smart solar photovoltaic energy system is

emerging as a convergence of information and communications technology in electrical

power and control system engineering making it an intelligent energy solution system.

The electrical power grid system is undergoing a transformation driven by a number of

demands. There is an exigent demand for reliability, availability, energy security and

conservation, and environmental compliance in protecting the climate from further

deterioration. In particular, the transformation has been significant in power generation over

the past two decades globally. This is because of the increase in energy demand for industrial

and domestic purposes from the existing traditional power generation which has contributed

immensely to the emission of greenhouse gases, affecting the climate and giving rise to

global warming [2].

As a result of these demands, technological transformations and innovations have been

witnessed in the electrical power generation industry by the birth of this new power grid

system called the "smart power grid system". There are several definitions of the term, "smart

power grid system" but as applied to our research investigations in modelling and simulation

implementation to better improve the optimisation and efficiency of the smart solar power

grid system, are critical for this research. The "smart power grid system" comprises of an

organically intelligent, fully integrated environment involving an end-to-end communication

of tasks, objectives and implementation replacing the traditional power grid system [3]. The

comparative analysis of the output characteristics and efficiency between the static and

dynamic online remote solar photovoltaic power monitoring systems investigation are

significant in real life circumstances to determine the exact energy generated, fault location


2

and detection of the energy system. As a contribution to the existing body of knowledge, it is

closely addressed in this thesis.

1.2 Characteristics of the Term Smart Power Grid

For clarity in our discussion, we present the following characteristics of the smart power grid

[3-5]:

A smart power grid is referred to as a grid that accommodates a wide variety of

generation options, e.g. central, distributed, intermittent, and mobile.

A smart power grid provides an interface between consumer appliances and the

traditional assets in a power system. This implies it encourages a two-way

communication channel for its operational decisions.

A smart power grid is designed to be semi-autonomous enabling much faster

operations when handling interruptions, failures in the power system and

reconfiguration to mitigate contingencies.

A smart power grid optimises the assets of the electrical power system employing

responsive operating protocols along the existing transmission links, thereby

improving the system reliability and forecasting for long-term investments.

A smart power grid refers to a completely modernised electricity delivery system

which monitors, protects and optimises the operation of its interconnected elements

from end to end.

Figure 1 represents the key characteristics of the smart power grid system as highlighted

above. This is fundamental in resolving the increasing complexity of traditional power

grids, growing demand and requirements for significant reliability, better operational

decisions, and most importantly, environmental and energy sustainability.


3

Figure 1. Smart power grid system characteristics and its capabilities

1.3 Smart Power Grid Concept

The concept of the smart power grid system was borne out of the urgency for the reliability of

abundant energy, relatively independent power grid system, energy security, undesirable side

effects such as environmental pollution, and damages to natural environments caused by the

traditional fossil fuel and coal powered generation systems [6]. This fundamental challenge

of controlling the negative effects on climate and ensuring the increasing energy demand is

adequately met, have led to research on these emerging renewable energy sources (RES) of

power generation [5].

Over the years, there has been a remarkable development in research and technological

innovations in renewable energy sources (RES) for power generation. The renewable energy

sources (RES) most exploited are hydro-electric, solar and wind energy. Other emerging

renewable energy sources (RES) are biomass, wave, and tidal energy. The abundance and

availability of these natural renewable energy resources regardless of which part of the world

has enabled the concept of smart power grid systems to thrive irrespective of the engineering

Smart Power Grid

System

Interface Communication

Semi-autonomous

Optimisation of Power System

Assets

Complete Modernised

delivery

Generation Options


4

challenges faced in this new area of power generation [3]. Figure 2 represents the six

divisions of smart power grid concept.

Figure 2. Divisions of Smart power grid concept

The emergence of these renewable energy technologies has brought about transformation in

the reduction of huge capital investments, assets in acquiring electrical power distribution,

and transmission networks, and the civil engineering challenges faced during the construction

and installation of power transmission lines [1, 3, 6]. The initial aspects of these new power

grid systems are fascinating with the development of advanced control and monitoring

algorithms, availability of software engineering tools, testing-verification-validation of

models, and simulation experiments before implementation of the design technology

concepts.

The integration of two or more sources of renewable energy sources (RES) is termed a hybrid

smart power grid system [6]. Figure 3 represents a hybrid smart power grid system.

Smart Power

Grid Concept

Wind Power

Grid System

Hydro-Electric

Power Grid System

Biomass Power Grid

System

Wave Power Grid

System

Tidal Power Grid

System

Solar Power Grid

System


5

Figure 3. Hybrid Smart power grid system

The problems associated with power grid integration of two different power configurations in

a hybrid smart power grid system have been resolved with advanced control and monitoring

systems, the introduction of smart sensor integration, and embedded intelligence encapsulated

components which have enabled a two-way communication link. The ease at which these

grids are integrated through the plug-and-play integration of the different renewable energy

sources (RES), makes the system an intelligent power grid system [6].

1.4 Evolution in the Power Grid Systems

The transformation in the power grid system is inevitably massive as the transition from the

traditional power grid generations are gradually been phased out with smart power grid

systems, or upgraded to a smart power grid system. The existing traditional power grid

systems have about 8% of output generated energy lost through transmission power lines,

huge capital investments in the installation of massive power transmission towers, and

manual delay in restoration of power failures. The smart power grid system is expected to

address most of these shortcomings, providing full visibility, pervasive control and

automation, reliable and efficient systems meeting the demand for services [7, 8].

Table 1 depicts the comparative analysis between the traditional power grid system and the

smart power grid system within the context of the new capabilities, communication and data

management, in-built intelligence and flexibility experienced in the use of IT (information

technology) to optimise monitoring and control of the grid system minimising operational

and maintenance costs. It is observed from Table 1 that the smart grid power system has

advantages over the existing traditional power grid as the smart grid power system involves a

Solar Power Grid

System

Wind Power Grid

System

Hybrid Smart Power Grid System


6

two-way communication process providing access to the exact energy generated and

distributed with other capabilities as highlighted in the table.

Table 1. The existing Traditional power grid system compared with the Smart power grid system [7]

Existing Traditional Power Grid Smart Grid Power System

Electromechanical Digital

One-Way communication Two-Way Communication

Centralised Generation Distributed Generation

Hierarchical Network

Few sensors Sensor Throughout

Blind Self-monitoring

Manual Restoration Self-healing

Failures and Blackouts Adaptive and Islanding

Manual Check Remote Check

Limited Control Pervasive Control

Few Customer Choices Many Customer Choices

1.5 Background and Context

There have been increasing energy demands for constant supply of electricity for both

domestic and industrial purposes. Since inception, the traditional power grid system has

been driven by fossil fuels and coal contributing immensely to the emission of

greenhouse gases (carbon dioxide, chlorofluorocarbons (CFCs), methane, nitrous oxide

and ozone) affecting global changes observed in temperature rises, the climatic condition

of the earth and adverse effects on humans and the planet. The impact of the energy

demand from the traditional power generation has contributed to the present global

warming crisis, changes observed in weather, and climate conditions in the world.

Research developments in smart solar power grid systems have proven that the new

intelligent power grid system would definitely eliminate the problem of emissions of

greenhouse gases in the atmosphere.

The ability to design and model smart solar power grid systems with different software

packages available, optimising the efficiency of the system before implementation and

validating analysed results through modelling and simulation processes, has provided a

cutting edge for the industry. The extent of research work and results achieved thus far


7

has taken the industry to this level with remarkable positive impacts attained in reducing

the effects of global warming and environmental power generation pollution. There is

ongoing research in this field and the results published have been notable both in the

academic environment and in the industry.

This research was spawned out of the need to efficiently and economically utilise the

abundant energy resources from the sun by improving and promoting the smart solar

photovoltaic grid concept. The MatLab/Simulink software tool is employed in this

research for the assessment and optimisation of solar photovoltaic module performance to

achieve the desired maximum power point tracking (MPPT) energy and minimization of

relative errors in the design and quality of solar photovoltaic module production. This

software tool has been employed in various research fields to handle complex non-

linearities, uncertainties and variations in the input parameters in a controlled system.

Unlike, all other renewable sources which are scarce in some parts or regions of the

world, the energy from the sun is universal and in preferential abundance compared to

other renewable sources of energy. Irrespective of its abundance in nature, research has

intensified on different algorithms and approaches in maximising the output efficiency of

the energy generated by solar photovoltaic (PV) modules. The smart solar photovoltaic

power grid system has contributed to rural electrification in many parts of the

undeveloped world because of its availability to the people within that geographical

region, changing the concept of their civilisation and livelihood.

Despite the demonstrated importance for this research investigation, there are several

issues that are of concern. These concerns include a high unpredictable rate in the

production costs and sales of solar photovoltaic modules. As a result, the new smart solar

photovoltaic grid system has been hampered by displacement of interests from private

and corporate people, thereby dampening commitment and investment participation

because of the first cost barrier experienced in connecting to the grid system. The

apparent less competitive solar photovoltaic energy market globally has allowed the price

to be overvalued and variability experienced in the quality of solar photovoltaic

production technology. Another major concern is the level of support and slow rate of

participation by policy decision makers in the industry to alleviate and remove the

financial and institutional burdens faced by solar photovoltaic manufacturers. It has been

observed that the price of the solar photovoltaic module has been experiencing a decline


8

of 4% per annum and future predictions show further price reductions are expected in the

years ahead [9].

As described in more detail in the literature review that follows (chapter 2), this research

considers the different solar photovoltaic tracking techniques for efficiency improvement

to boost the collected energy at different times in the year, irrespective of geographical

locations and conditions. However, within the broad categorisation the solar photovoltaic

tracking techniques, modelling and simulation techniques are classified and analysed in

terms of their performance in the review. While the growing body of literature and

research on the smart solar photovoltaic power grid system indicates an increased interest,

there is little research that specifically investigates efficiency optimisation, minimization

of relative errors in design and quality by using the various algorithms as deployed in this

research. This will be highlighted in chapter 3 and the statistical results thus presented.

Similarly, comparative studies between the two main solar photovoltaic tracking

mechanism modes namely static and dynamic solar photovoltaic tracking systems, have

attracted extensive research. While some of the previous research have focused on the

off-line comparative study of the two solar photovoltaic tracking modes and the

efficiency benefits each of these modes have over the other. This thesis thoroughly

examines through the lens, a robust real-time online solar photovoltaic monitoring system

of the two tracking modes framework. This framework is explained in more detail in

chapter 5. As noted in section 1.3, the smart grid concept needs the support of all

stakeholders, partnership and commitment, especially the government in policy

implementation and regulation, providing necessary subsidies and incentives, promoting

an enabling healthy financial environment and market for the new intelligent power grid

to thrive amidst initial challenges experienced at the establishment of the industry.

This research aims to address the clear gaps observed in the literature reviewed by the

chosen approach in the research methodology in chapters 3, 4 and 5 of this thesis. A

systematic approach and tool have been carefully chosen and developed. Its applicability

across a wide range of parameters in improving the efficiency optimisation of smart solar

photovoltaic grid systems have also been tested and these results are thus presented in this

thesis.


9

1.6 Research Objectives and Questions

1.6.1 Research Objectives

The primary research objective is to examine, using various modelling and simulation

processes to optimise the efficiency of the solar photovoltaic module with the use of the

Matlab/Simulink software package to achieve maximum power point tracking (MPPT).

The second phase of the research comparatively measures the output efficiency of a real-

time robust online solar photovoltaic monitoring system between a static and dynamic

solar photovoltaic installed system establishing the significance of such a monitoring

network approach.

1.6.2 Research Questions

In examining the modelling and simulation of the smart solar photovoltaic power grid

system to achieve the best optimisation efficiency for maximum power point tracking

(MPPT), the following research questions are put forward in the thesis to achieving our

research objectives:

1. Which of the algorithm models can achieve the best maximum power point

tracking (MPPT) using the neural network for smart solar photovoltaic grid

system?

2. Which of the algorithm models can achieve the best maximum power point

tracking (MPPT) using the sparse based regression estimation algorithm to

evaluate the mean square error (MSE) and the root mean square error (RMSE)

for smart solar photovoltaic grid system?

3. What is the comparative output efficiency for the robust real-time online solar

monitoring between the static and dynamic solar photovoltaic tracking systems?

4. What will be the resultant effect of the proposed algorithm model for the

maximum power point tracking (MPPT) on the extraction of available power from

the smart solar photovoltaic system?


10

1.7 Research Methods

In answering the above research questions, the research uses an artificial neural network

(ANN) approach in modelling and simulation on the static solar photovoltaic module

under variable input parameters and conditions. This tool was chosen because of its

capacity to perform nonlinear mathematical and statistical modelling effectively between

dependent and independent variables. A comparative study of two artificial neural

networks was conducted using the Levenberg-Marquardt algorithm to evaluate the

performance and output efficiency within the respective networks. The mean square error

and autocorrelation coefficient parameters were used in the comparison of the two

networks performance under evaluation. These two parameters were chosen to explicitly

analyse in such a way that the best optimal efficiency characteristics for the solar

photovoltaic module are exploited in this thesis. The results are presented on a very large

scale for all operating conditions to confirm the validity of the model.

In addition, this research evaluates three different regression modelling techniques

namely ordinary least squares, logistic robustfit and least trimmed squares respectively.

They are discussed elaborately in this thesis using the sparse based regression estimation

algorithm on the static solar photovoltaic module. The regression modelling techniques

were used to predict on a large scale the most suitable of the three, based on manufacturer

solar photovoltaic parameters to determine the performance, efficiency, and reliability of

these models. The performance evaluation parameters are carried out using the mean

square error (MSE), root mean square error (RMSE), and standard deviation estimate to

determine the maximum power point tracking (MPPT). These were chosen to explicitly

analyse the performance of the solar photovoltaic module for the maximum power point

tracking. The maximum power point tracking current, voltage and power is obtained for

the static solar photovoltaic array in the simulation and modelling experiments.

As part of the research collaborations in this thesis, a robust real-time online solar

photovoltaic monitoring system was carefully designed via cloud computing devices, to

remotely access the solar photovoltaic data information installed on-site over mobile

phones, tablets, PCs and notebooks. The research implementation was deployed at the

National Kaohsiung University of Applied Sciences, Taiwan, R.O.C. We obtained raw

data information comparing the static and dynamic solar photovoltaic tracking systems.

The research reveals that there is a significant increase in the optimisation performance in


11

the comparative data, and on the graphic user interface of the data analysis obtained

between the two measuring solar photovoltaic tracking modes.

1.8 Research Works, Contribution and Justification

The research works related to this thesis are based on three theoretical frameworks

including optimisation, improving the efficiency performance and minimization of errors

in a smart solar photovoltaic module. Hence, it increases the output efficiency of the

maximum power point tracking for the current, voltage and power characteristics. The

three frameworks are described in detail in chapters 3, 4 and 5 of this thesis respectively.

While the frameworks have a strong backbone of research associated with them, the

existing research provides insufficient answers to the research questions in this thesis.

Extensive research works have been undertaken over the years in solar photovoltaic grid

systems, a comparative study between the static and dynamic solar photovoltaic tracking

systems have been critically examined in this research, providing a robust real-time

online exact generated energy data in a real-life scenario is thoroughly examined in this

research. The research investigation has fully established an online solar photovoltaic

monitoring database system for scholars and the industry world. Additionally, the use of a

newly developed solar photovoltaic monitoring real-time data online logger allows this

research to contribute to the existing body of knowledge.

The research investigation on modelling and simulation experiments has made significant

contributions to the existing background knowledge in creating an excellent output

performance for a smart solar photovoltaic module and comparative study of the static

and dynamic solar photovoltaic tracking systems. The optimisation of the efficiency and

maximisation of the power point tracking for the solar photovoltaic module is of immense

value. The established facts in literature have led to the foundation of research in this

area. It is imperative to evaluate on the minimization of the occurrence of relative errors

in solar photovoltaic modules using the statistical measuring parameters such as mean

square error (MSE), root mean square error (RMSE), and the standard deviation of

estimate to better improve the performance of the solar photovoltaic module.

In any case, optimising the efficiency of the solar photovoltaic module is important in

light of the contemporary challenges such as the high-cost price of solar photovoltaic


12

modules, increasing the overall maximum output energy expected from the photovoltaic

module, and the concern over the nonlinear characteristics of the photovoltaic module.

There is a pressing need for government and corporate policy collaboration and support in

solar renewable energy for more intensive research activities on the existing structure,

thereby improving the quality of solar photovoltaic module design. The smart solar

photovoltaic grid policy substantially makes a contribution complementing the existing

traditional grid system in a wider context. The theoretical frameworks of the smart grid

policy provide clean, noise pollution-free power generation, energy security assurance

and environmental friendly grid systems. These have received increased acceptance by

the public, research development and innovation over the last two decades. Government

policies in renewable energy solutions and participation have greatly promoted awareness

by corporate and private individuals of the newly intelligent power grid system.

The outcomes are thus presented in this thesis, the output performance of the simulation

and modelling investigations. The comparative study and analyses of the smart solar

photovoltaic grid system on a very large scale with real solar photovoltaic manufacturer’s

data is conducted. Statistical measures were used for the evaluation of the algorithm

employed in the modelling and simulation techniques in this research. The obtained

online raw data results from the comparative study of the two solar photovoltaic systems

at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C are thus

presented reflecting the merits and disadvantages of the system under investigation.

In summary, this research work makes a significant contribution to both the academic

field of research in smart solar photovoltaic energy and offers a real-life experience for

the future solar photovoltaic energy industry application. The use of MatLab/Simulink

software tool further enhances future investigation in ways to better optimise the

efficiency, improving the performance of the smart solar photovoltaic grid system.

Moreover, robust real-time online solar photovoltaic monitoring systems complement the

findings of the modelling and simulation experiments for further research.


13

1.9 Limitation and Assumptions

A number of limitations and assumptions are introduced in the research methods in

modelling and simulation experiments conducted in this research investigation. For

example, the experiments conducted on modelling and simulation using Levenberg-

Marquardt algorithm and sparse based algorithm, the input parameters of the artificial

neural network were assumed for the neural network training to solve the nonlinear and

implicit general equation for a solar photovoltaic module. In our analyses, the two

assumed input parameters are solar irradiation (S) and the wind speed (ws) respectively.

The solar radiation, S was increased in steps of 10 units from 10 to maximum of 1000

m/s2 and the wind speed, ws was increased in steps of 2 units from 1 to maximum of 20

m/s2. These assumptions often employed in modelling and simulation, predict a regular

pattern and behaviour of the solar photovoltaic system under evaluation. The increment in

steps of units was introduced to improve the simulation performance of the solar

photovoltaic array to justify the variable weather that occur to a real-life scenario in our

simulation experiments and results.

However, in a real-life situation, the results obtained in this research establish a

remarkable correlation difference between the simulated results and real-life raw data

collected. The research investigation conducted on a robust real-time online solar

photovoltaic monitoring system had a challenge broadcasting via the internet at night but

resumes broadcasting in the early hours during daylight. The system has been designed in

such a way that when no irradiation is observed, the system will shut down automatically.

Another drawback experienced during the data collection is the frequent interruption of

the internet service during abnormal weather conditions such as typhoon and torrential

rainfall.

A further limitation in this research investigation acknowledged is that the results

obtained from the robust real-time online solar photovoltaic monitoring system were set

up at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C and is most

valid based on that geographical location but can be inferred anywhere in the world as a

contribution to the existing body of knowledge. The challenge to restoring faults of the

solar photovoltaic monitoring system could take longer time and so, data may not be

accessible during this period. Though data obtained are practically valid for the solar


14

photovoltaic energy industry, its applicability is a challenge due to the variable weather

conditions in other parts of the world.

It is noted in this research that modelling and simulation experiments were established on

the assumption of varying two input variables in a well-defined unit steps increase as

described in Chapter 3 of this thesis. These experiments were carried out with the chosen

algorithms that will help in the optimisation of the efficiency design, minimization of

relative errors in the solar photovoltaic modules. It is expected that this will improve the

quality of production of the solar photovoltaic modules, predictions and forecasting of the

output energy of the system and will provide answers to the research questions posed in

this thesis.

1.10 The Outline of this Thesis

The thesis consists of six chapters and the structure of the thesis is as revealed below:

1. Introduction

2. Literature Review

3. Modelling and Simulation Techniques for a Solar Photovoltaic System

4. Astronomical and Analytical Derivation for Solar Photovoltaic Tracking Systems

5. Robust Real-Time Online Solar Photovoltaic Data Monitoring Systems

6. Conclusion, Discussion and Recommendations

In this preliminary chapter, a background of the study has been provided in which a smart

solar photovoltaic power grid system has been described. Thus, definitions of the term the

smart power grid as it relates to this research and the smart power grid concept were

highlighted. Moreover, the evolution in the power grid system has been described and

comparative analysis between traditional and smart grid power systems were also

emphasized. The background and the context of this research led to the research goals and

questions that formed the basis of this research providing a brief outline of the proposed

methods for the research and importantly, the justification and contribution of this study

were identified. Further, an outline of the limitations and assumptions related to this

research was also included.

The next chapter, literature review, provides a contextual review of related literature and

research investigation into the area of smart solar photovoltaic grid systems, and

optimisation of sun-tracking methods for maximum output examined. Other aspects of the


15

literature covered in this chapter, include energy gains in solar photovoltaic tracking

systems, sun-tracking methods, and classification of sun tracking systems.

In addition, chapter 2 also includes a review of solar photovoltaic energy policies,

benefits and reliability perspectives of the smart grid systems. This chapter as well

presents the concept of the prospective grid, the smart grid network, the conceptual

framework of the smart grid network, smart grid policy and implementation guidelines

and benefits of the smart grid network. This chapter concludes by highlighting the gaps in

the current body of knowledge describing how and where the current study fits in relation

with the existing research.

Chapter 3 primarily focuses on modelling and simulation techniques for a static solar

photovoltaic system employing the Levenberg-Marquardt algorithm on the chosen neural

network model and sparse based algorithms to decide how best to optimise the output

efficiency of the solar photovoltaic module; using different statistical measures to

evaluate the performance on a very large scale to achieve maximum power point tracking

for this research. One section in this chapter focuses on discussion of research results

validity and reliability. Each of the modelling and simulation techniques discussed

provides a clear outline of how the research was undertaken and why. The results

achieved answer the research questions posed as the context of the research investigation

are thus presented.

Chapter 4 examines the astronomy and analytical derivation for solar photovoltaic

tracking systems, tracker definitions and taxonomy, tracker system elements and the

simulink design implementation for the smart solar photovoltaic array model. This

chapter concludes by presenting the results of the simulated models and charts on the

implemented solar photovoltaic array designed in this research.

Chapter 5 provides a detailed analysis of the experimental setup and results of a robust

real-time online comparative study of the static and dynamic solar photovoltaic tracking

energy system at National Kaohsiung University of Applied Sciences, Taiwan, R.O.C.

The research findings address the research questions within the context of the thesis. As

well, the chapter gives a significant contribution to the existing body of knowledge and

research.


16

The last chapter, chapter 6, conclusion and discussion, places the results of this research

within the context of the existing research being described in chapters 2, 3, 4 and 5. A

link was established between this new research with the existing research. The

contributions made in relation to academic knowledge in the optimisation of the output

harvested energy involves the use of statistical measures to evaluate the improvement on

the quality of solar photovoltaic module design. The results obtained from the robust real-

time online comparative monitoring are likely to offer a real-life experience for the future

solar photovoltaic energy industry applications. Additionally, the significance of this

research in the context of the smart grid system is to offer an energy security assurance

and eco-friendly grid system. Suggestions for further research are also provided.

Following the last chapter of this thesis, the reference list and appendix is included. The

reference list in the thesis includes more than 165 academics, government and industry

sources. The results achieved from chapter 5 are thus provided for in the appendices.

1.11 Conclusion

This introductory chapter of the thesis, presents the research foundation, a theoretical

framework on which the research is based, the research objectives, research questions to

be answered, and the significance of this research. This chapter addresses the need for the

smart power grid system to help in providing energy security assurance, reliable and

available efficient grid systems, optimisation of output efficiency ensuring high quality

standard solar photovoltaic modules. The drive for evolution from traditional power grid

systems to the smart power grid systems in many of the developed countries of the world

and its acceptance globally have been remarkable, increasing a wide range of research

growth and development encouraging corporate and private individual participation into

the new intelligent power grid system. In conclusion, the research has provided the

opportunity to use different simulation and modelling techniques to improve the

optimisation and efficiency of the smart solar photovoltaic module, evaluating the best

performance approach and technique in each of the algorithms employed. The research

outcomes are likely to offer real-life solutions for the future solar energy industry not only

in Australia or Taiwan but also in any part of the world.

The next chapter provides with more detail a review of the current literature and the

research methods employed, crucial to answering the research questions upon which the

study and the results are thus presented and established.


17

Chapter 2 Literature Review

2.1 Introduction

The purpose of this chapter, chapter 2 is to survey literature relevant to the scope of this

research and discuss in brief the existing relevant previous research works. In particular, this

chapter looks at literature relating to smart solar photovoltaic grid systems, sun tracking

optimisation and solar photovoltaic energy policy. It also examines in perspective, reliability

of the smart power grid systems and discuss the theoretical frameworks that provide the basis

for this research. The aim of this chapter is to provide theoretical insights with content

outlined as follows:

Section 2.2: Solar photovoltaic sensor tracking optimisation devices.

Section 2.3: Sun photovoltaic tracking optimisation techniques. In this section, an

overview of literature sources is provided and the modelling and simulations

framework is given attention particularly to focus on the basis of this research.

Section 2.4: Smart solar power grid system. Here, the concept of the smart power

grid system is described, definitional issues and challenges are also highlighted.

Section 2.5: Solar photovoltaic energy policy. The solar photovoltaic energy provides

the regulation policy and support for the smart solar photovoltaic grid system. In this

section, the environmental and global warming challenges are discussed and the

policies for curbing these are addressed.

Section 2.6: Reliability perspective of the smart grid system. In this section, the

frameworks of the grid system and its benefits are outlined and discussed.

Section 2.7: Conclusion.

This literature overview provides the necessary background and context for the research in

modelling and simulation of smart solar photovoltaic grid systems. Furthermore, it has

demonstrated gaps in the literature from which the research questions emerged as itemised in

subsection 1.62.


18

2.2 Solar Photovoltaic Sensor and Tracking Optimisation Devices

Solar photovoltaic module tracking optimisation is one of the alternative renewable energy

sources and its major source the radiated solar energy is unlimited. However, electricity

power generation has faced daunting new challenges in its implementation of abundant and

clean energy supplies for the future. This is underpinned by positive and negative predictions

of the extinction of the fossils fuels by the year 2030 – 2040 [10].

As reported in the Kyoto Protocol, the rate of consumption of the world’s fossil energy has

risen tremendously due to increasing energy demand for consumer satisfaction across all

sectors of the economy (domestic, commercial and industrial uses); hence the negative

impacts on the environment. Similarly, the International Energy Agency has predicted that

about 33% of the global energy demand after 2060 may be produced from solar photovoltaic

energy technologies, reducing greatly the CO2 emissions and other greenhouse gases to a

precise low level [10].

The term ‘solar photovoltaic tracking optimisation’ involves the use of solar sensor tracking

components or devices, microcontroller devices, and sun-tracking mirrors (heliostats),

coupled with tracking servo motor (or d.c motor) to reflect and focus the concentrated solar

irradiance at the perpendicular position throughout the daylight period. These optimisation

components and devices are expressed in terms of their optimal maximum energy efficiency

achievable for electricity generation or thermal processes.

In describing the solar photovoltaic sensor tracking device, the solar sensor device shall be

defined. The dynamic characteristics of the sensors, assessment of the physical sensor

parameters and the solar tracking mechanism devices respectively are highlighted in section

2.2.2. The solar sensor is a device that detects a physical quantity (light) and converts it into a

signal which can be perceived by the controlling unit of the system or a corresponding output

system [11]. The sunlight ray falls on the solar sensor and responds by a feedback signal to

the control mechanism unit (processor). This controls the direction of rotation of the solar

photovoltaic module reception in orthogonal position with the solar irradiance linked

alongside the other system networks, thereby enhancing the efficiency of the solar

photovoltaic module tracking throughout the day.

With the existence and growing body of literature and research on solar photovoltaic tracking

sensors and systems, concerted interest has grown in the last two decades in research


19

employing these solar photovoltaic sensing devices. This will be reviewed in detail in section

2.2.1. Solar photovoltaic sensing devices (sensors) include the light dependent resistors

(LDRs or photoresistors), photo-diode (p-i-n diode) and webcam are under review in this

section. section 2.2.2 examines the comparative assessment parameters on the efficiency of

the sensor devices. It is broadly evaluated with emphasis on the absorption rate, the longevity

of the device, optimal characteristics, wavelength characteristics, climatic conditions

characteristics and response characteristics with respect to the declination angle of the sun to

the solar photovoltaic surface reception. More importantly, improved efficiency experienced

in the overall generated output energy in dynamic solar photovoltaic tracking system has led

to commercialisation and expansion of the solar photovoltaic energy world.

2.2.1 Dynamic Characteristics of Solar Photovoltaic Sensors

Broadly stated, the dynamic characteristic of a solar photovoltaic sensor is time-dependent.

The photovoltaic sensor is fully described by physical characteristics, such as the transfer

function, lifespan, and calibration of the sensor itself. However, its response to light

inducement most times is not always immediate. This generates a dynamic error observed

from the actually specified design function of the sensors. Primarily, sensors are used to

control system processes and its responses are typically described by the input-output

relationship through constant linear differential order equations [12].

In particular, the differential order equation depends on the solar sensor manufacturer's

design model. These models are confined to zero, first and second differential order equations

but higher orders are rarely applicable. The zero differential order sensor model is

characterised by a transfer function that is time independent. This responds instantaneously to

stimuli and no dynamic error occurs in the zero differential order model. A first differential

order solar sensor model equation describes a sensor that has one energy storage component,

𝑎1 and constant coefficient 𝑎0. An input signal s(t), photon light or solar irradiance and the

converted output signal S(t) is given by the differential equation relationship in (1) as [13]:

𝑎1𝑑𝑆(𝑡)

𝑑𝑡 + 𝑎0 𝑆(𝑡) = 𝑠(𝑡) (1)

Figure 4 shows the frequency characteristics and response of the first differential order sensor

model, the frequency response chart specifies how fast a first differential order sensor can

react to a change in the input stimulus. The frequency response is expressed in Hz or rad/s to


20

specify the relative reduction in the output signal at a certain frequency as shown in the chart

and referred to as the cut-off frequency. The chart shows at what frequency the output voltage

(or current) drops, which is at about 30%. A commonly used reduction value (frequency

limit) is - 3dB. The phase shift at specific frequency describes how the output signal lags

behind in representing the stimulus change. The shift is measured in angular degrees/rad for

sensors that process the periodic signal.

Thus, the speed response time chart is another way to relatively determine the response time

of the solar photovoltaic sensor. The photovoltaic sensor only reaches 90% of its steady-state

or maximum level upon exposure to a step stimulus. The time constant measures the

photovoltaic sensor's inertia as shown in Figure 5, which shows the relationship between the

speed response (S) and time constant 𝜏, required for the sensor to reach 90% steady state or

maximum level on exposure to a step stimulus.

Figure 4. Frequency characteristic and response of a first-order sensor [12]

Figure 5. Frequency characteristic with limited upper and lower cut-off frequencies 𝝉𝒖 and 𝝉𝑳are the

corresponding time constants [12]


21

The first differential order system response is given as follows:

𝑆 = 𝑆𝑚(1 − 𝑒𝑡 𝜏⁄ ) (2)

where Sm is the steady-state output, t is the time, and 𝑒 is base of logarithm, substituting t = 𝜏,

in equation (2) above, the steady state response obtained is given thus:

𝑆

𝑆𝑚 = 1 −

1

𝑒 = 0.6321 (3)

It is observed from equation (2) above, that when 𝑡 = 𝜏 (one time constant) the response

reaches about 63% of its steady-state level, similarly when 𝑡 = 2𝜏, the response reaches about

86.5% and also when 𝑡 = 3𝜏, 95% of steady-state level would be reached at infinite time. The

cut-off frequency shows the lowest or highest frequency of stimulus the sensor can process.

This process shows how the sensor reacts slowly or fast to stimuli. The relationship between

cut-off frequency, fc (either 𝝉𝒖 , upper or 𝝉𝑳 , lower) and time constant in a first order sensor is

given by the expression [12, 14-17]:

𝑓𝑐 ≈0.159

𝜏 (4)

The upper and lower cut-off frequency of a device is given by this expression respectively;

𝝉𝑳 = 𝑓𝑜√1+1

4𝑄2 − 1

2𝑄

𝝉𝒖 = 𝑓𝑜√1+1

4𝑄2 + 1

2𝑄

where 𝑓𝑜 is the centre frequency and Q is the Q-factor for the device.

However, the second differential order sensor model equation defines that the model features

two energy storage components, 𝑎2, 𝑎1 and constant coefficient 𝑎0. Thus, the relationship

between the input signal s(t) and output signal S(t) is given by the differential equation:

𝑎2𝑑2𝑆(𝑡)

𝑑𝑡2 + 𝑎1

𝑑𝑆(𝑡)

𝑑𝑡 + 𝑎0 𝑆(𝑡) = 𝑠(𝑡) (5)

Also, the second differential order sensor model responds with a periodic signal and

whenever the periodic signal is precisely momentary, the sensor is said to be damped and

when sustained the sensor oscillates. The sensor is said to be critically damped when its


22

response happens so quickly without an overshoot as shown in Figure 6 of the oscillating

response for the second order differential equation [12, 14-17]. The oscillating response

shows the overdamped, critically damped and underdamped phases of the second order

sensor speed (S) response to time constants (𝜏).

Figure 6. Responses of sensors with different damping characteristics [12]

2.2.2 Assessments of Physical Sensor Parameters

The assessment of the physical sensor parameters in solar photovoltaic tracking optimisation

is important in understanding the relationship between the physical device and rate of

sensitivity, thus determining the effectiveness of the sensor tracking device impact on the

output energy efficiency of the solar photovoltaic module. The advancements made in solar

photovoltaic sensor tracking technology are occurring simultaneously in solar photovoltaic

energy research, requiring a standard benchmark on which the performance and efficiency of

the solar sensors are categorised. These improvements are undertaken to ensure an

appreciable output energy from the huge investments in the solar photovoltaic energy

tracking systems.

The assessment and quality evaluation parameters of the solar photovoltaic sensor device

offer a measurable factor in determining the improved efficiency and output energy generated

in the dynamic solar photovoltaic tracking systems, compared with the static solar

photovoltaic energy system. Based on these measurable factors, the solar sensor

characteristics are closely examined under the following seven parameters. As a result, a

classification summary of the sensor assessment parameters is thus presented in Table 2.


23

Table 2. A Summary of sensor assessment parameters

Assessment Parameters Photoresistor Photodiode Webcam

Absorption rate Partly affected by

casted

shadows

Partly affected by casted

shadows Not affected

Longevity of device 10-15 yrs. Indefinite Life prolonged with

filter shield

Optimal characteristics

Dependent on the

intensity of

light reaching the

device

Dependent on the intensity

of

light reaching the device

High-definition

signal achieved

Wavelength characteristics 400-800 nm, 1-3𝜇m, 3-

100𝜇m 800-3500 nm 400-700 nm

Climatic characteristics

Affected during winter,

rainy

season and extremely

high temperature

Affected during winter,

rainy

season and extremely high

temperature

Adaptable for all

season

Response characteristics 10-90 mS 10% - 90% of the steady

output level 2 mS

Cost relativity Relatively very cheap Relatively very cheap A little higher

2.2.2.1 Absorption Rate

The absorption rate of the solar photovoltaic tracking sensors depends on the physical and

internal composition of the sensor occurring at specific wavelengths. The intensity of

irradiance reaching the sensor device determines the photon generated energy to liberate the

bound electrons migrating into the conduction band, sending an instruction signal to the

tracking control mechanism to either cause clockwise or anti-clockwise rotational movements

of the solar photovoltaic module frame [18].

The rate of absorption of the photo-resistors and p-i-n diodes are greatly affected by partly or

temporal cloudy weather conditions and shadows cast by massive structures over the solar

sensing device during the daylight period. The significance of this effect is enormous,

causing the illumination intensity to become weak and causing the solar tracking mechanism

to have no valuable impact during this period [16]. The webcam absorption has proven to

give a well-defined degree of accuracy compared to the other solar photovoltaic tracking

sensors based on the capability of tracking light sources under variable intensity over its

surface.

2.2.2.2. Longevity of Device

In dynamic solar photovoltaic sensor tracking systems, the life expectancy of solar

photovoltaic tracking sensor devices is of remarkable importance for high precision


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concentration and uninterrupted dynamic solar photovoltaic module tracking systems. This is

due to the fact that huge capital investments are involved in both small and large-scale solar

photovoltaic renewable energy generation. Furthermore, it is important to minimise the risk

of frequent maintenance and replacement of the installed tracking sensors to prevent loss of

tracking.

Over the years, the solar sensor technology industry has been producing cost efficient and

high quality solar photovoltaic tracking sensors. The light dependent resistors (LDRs) have a

life expectancy of 10 - 15 years. The photodiode lasts for an indefinite period of time when

used in accordance to the manufacturer's specification [19]. The webcam optical sensors used

in solar photovoltaic sensor tracking systems are specially designed with a polarised filter

shield to prevent frequent saturation of the charge-coupled device (CCD) when the heat

intensity of the sunlight rays is very high during the daytime, prolonging its life expectancy.

The filter shield creates a real-time pre-binarisation image process for the monitoring system

in tracking the location of the sun [20].

2.2.2.3 Optimal Characteristics

The optimal characteristic of the solar photovoltaic sensor device offers rotational and control

signal stability for the dynamic solar photovoltaic tracking systems to achieve maximum

optimality criterion objectives. This criterion consists of a set of differential equations

describing the variable paths that minimise the control boundary restrictions on the premise

of achieving the best possible results. The optimal characteristics of the sensors are

subdivided into two categories the static and the dynamic characteristics.

The static optimal characteristic of the sensors ensures accuracy, discrimination, precision,

drift, sensitivity, linearity and hysteresis properties while the dynamic optimal characteristics

of the sensors are modelled by a constant-coefficient linear differential equation and are

confined to zero, first and second order variable inputs controlling the movement of the solar

photovoltaic module with the tracking mechanism device ensuring constant orthogonal

positioning relative to the sunlight rays [12, 14-17].

Based on the existing literature, the optimal properties of the LDRs is achieved when there is

a decrease in the resistance value of LDR with a corresponding increase in the incident light

intensity [21]. Photo-diode (p-i-n diode) optimal characteristics occur when the intensity of

light striking the crystal lattice causes the release of holes and electrons drawn away from the


25

wide depletion region by reverse bias producing the needed signal response for the solar

photovoltaic tracking system [22]. Webcam optimal characteristics produce high definition

and resolutions images transferred by means of Hi-speed USB 2.0.

2.2.2.4 Wavelength Characteristics

The wavelength characteristics of the solar photovoltaic sensor devices define the electrical

tracking signal response sent to the tracking control mechanism unit of the solar photovoltaic

tracking system. There are different kinds of solar photovoltaic sensor devices with specific

wavelengths used in solar photovoltaic tracking systems in previous research. Figure 7

shows the solar spectrum energy density that penetrates the atmosphere [23].

This figure describes the sensitivity wavelength range of sensors used in the solar

photovoltaic tracking system. These wavelengths are subdivided into three regions: the

ultraviolet region (300-400 nm), the visible region (400-700 nm), and the near infrared region

(700-2500 nm). Based on this classification, the sunlight rays emission consists of infrared

and ultraviolet rays at the earth’s surface and are filtered by the earth’s atmosphere, bringing

visibility on the earth’s surface. Therefore, sensors built within the specified wavelength

region would best provide an efficient dynamic solar photovoltaic tracking focus compared to

others outside the regions.

The LDRs are made of different chemical combinational elements such as Cadmium (II)

Sulphide and Cadmium (II) Selenide (CdS-CdSe) having wavelengths within the range of

400-850 nm (visible spectrum), Lead (II) Sulphide and Lead (II) Selenide (PbS-PbSe) having

wavelengths within the range of 1-3𝜇m (near IR field) and Indium (III) Antimonide–Indium

(III) Arsenide (InSb-InAs) having wavelengths within the range of 3-1000 𝜇m (middle and

far IR field) [24].

Likewise, the photodiodes are made of single or chemical combination elements having

different wavelengths sensitivity and characteristics. Germanium has a wavelength within the

range of 800-1700nm, Indium gallium arsenide has a wavelength within the range of 800nm-

2600nm, lead (II) Sulphide has a wavelength within the range of ~1000-3500nm and silicon

within the range of 190-1100 nm [22].

The webcam wavelength for visible light rays ranges from about 400-700 nm within the

visible spectrum region [25].


26

Figure 7. Solar intensity wavelength [26]

Figure 7 shows the major solar energy distribution, the ultraviolet (UV) energy distribution

wavelength (300-400 nm), the visible energy distribution (400-700 nm), and near-infrared energy

distribution (700-2500 nm).

2.2.2.5 Climatic Conditions Characteristics

The climatic changes which occur during different seasons in the year have notable effects on

the exposed solar photovoltaic sensor devices used for the dynamic solar photovoltaic

tracking system, reducing its life expectancy. The relative sensitivity of the solar photovoltaic

sensors to the intensity of light is gradually been reduced as a result of the changes in climatic

conditions, leading to the tracking focus errors of the sun by the solar photovoltaic module

resulting to a decrease in the overall output energy generated.

The LDRs and photo-diodes are affected by the change in the weather conditions (cloudy,

rainy, humidity, winter (frost)), but are most suitable during sunny or dry weather conditions.

The webcam has proven to be pretty comfortable with changes experienced during seasonal

periods in the year ensuring a relatively high accuracy in the tracking mechanism processes

of the solar photovoltaic tracking system [27, 28].

2.2.2.6 Response Characteristics

The response characteristics of the sensor devices are relative to the manufacturer design

including a number of factors such as the light level, light history, rise time tr, peak overshoot

Mp, time to peak tp and ambient temperature. The response speed for the LDRs is measured

by the speed at which the photocell responds to change from light-to-darkness and vice versa.

Similarly, the response speed for the photodiode is measured by CR (time constant), carrier

diffusion time, and carrier transit time in the depletion layer [29]. The webcam (CCD) has


27

been experiencing an overall improved performance in design and production ensuring an

enhanced high sensitivity response [30].

The response time and accuracy of the sensor devices used for solar photovoltaic tracking

systems are of high significance. Each of these solar sensor devices has their rise and fall

time. The rise time, tr of LDRs is defined as the time necessary for light conductance of the

photocell to reach 1- 1/ 𝑒 (or about 63%) of its final value. The fall time is defined as the

time necessary for the light conductance of the photocell to decay to 1/ 𝑒 (or about 37%) of

its illuminated state. For a typical LDR such as the CdS, the rise time is 90mS and fall time is

10mS [31].

The rise time of a p-i-n diode is defined as a measure of the response time of a photodiode to

an input stepped light and the required time for the output to change from 10 to 90% of the

steady output level [32]. The response time of the webcam sensor is about two milliseconds

(2 mS) which is quite fast [30].

2.2.2.7 Cost Relativity

Price relativity of the solar photovoltaic sensor device plays a vital role in the choices made

in some of the literature. The major challenge confronting the global solar photovoltaic

industry is the high price market value of solar photovoltaic modules, insufficient

government policy support initiatives and supply chains among manufacturing industries.

The high initial installation cost revealed in some of the literature determines the choice of

solar photovoltaic sensor device employed, thereby defining the results achieved in the past

two decades.

Comparatively, the price of the LDRs and p-i-n diodes are relatively cheap. However,

additional circuit design and construction costs for the integration of the electronic circuits

and power supply are a further cost for consideration. Thus, it implies that, if there are n-

number of solar panels correspondingly, there would be n-number of electronic circuits built

for the solar sensing devices. The webcam has an inbuilt electronic circuit and is easily

adaptable for use without the need of power supply construction.


28

2.3 Solar Photovoltaic Tracking Optimisation Techniques

The solar photovoltaic tracking optimisation techniques improve the output energy efficiency

of the solar photovoltaic system, ensuring that a concentrated amount of sunlight reaches the

solar photovoltaic module throughout the day. The sun tracking optimisation techniques

involve the use of a solar photovoltaic tracker device orientating the solar photovoltaic

module towards the sunlight rays. This technique increases the amount of energy produced as

compared to the fixed solar photovoltaic systems in reviewed literature.

The term “solar photovoltaic tracking optimisation” is often called dynamic solar

photovoltaic tracking system as compared to the traditional fixed solar photovoltaic tracking

system. Over the last decade, there have been recent technological developments and

improvement in research to positively justify the cost investments in the dynamic solar

photovoltaic tracking system. These tracking techniques have been applied to concentrated

photovoltaic (CPV) and concentrated solar thermal (power) (CSP) applications enabling the

optical tracking component to orientate appropriately and ensuring accurate alignment of the

solar photovoltaic surface to harvest the solar energy.

Amidst the concept of solar photovoltaic tracking optimisation, the solar photovoltaic

tracking device is either installed on a floating concrete foundation or on the ground surface.

Some of the solar photovoltaic trackers are permanently mounted on the solar photovoltaic

alloy bracket with the capability to withstand the wind pressure at extreme weather

conditions. The significance and introduction of the solar photovoltaic tracker optimisation

are to ensure a high tracking accuracy to approximately deliver about 90% of the rated output

power of the expected solar photovoltaic module throughout the day.

With the current status in research, the dynamic solar photovoltaic tracking system has been

classified into two major divisions offering a wide range of emerging solar photovoltaic

tracking modes and techniques. The two classifications are closely examined in detail in the

following subsections. Section 2.3.1, dynamic single-axis tracking optimisation definition,

characteristics and types are carefully looked into. In section 2.3.2, the dual-axis tracking

optimisation definition, characteristics, types and benefits over the single axis tracker are

examined.


29

2.3.1 Dynamic Single axis Tracking Optimisation

A dynamic single axis tracking optimisation involves a tracking technique with only one

degree of rotational axis aligned along the north meridian. The path of rotation is azimuthally

from east to west following the path of the sun during the day. The overall objective of the

single axis tracker is to effectively improve the efficiency performance and reliability of solar

photovoltaic module, thereby reducing the cost of electricity utility and the negative

environmental impact of greenhouse gases.

There has been on-going research to ensure higher energy efficiency is collected for the

dynamic solar photovoltaic tracking systems at a comparative cost relative to the fixed solar

photovoltaic tracking system. The performance of the dynamic solar photovoltaic tracking

system has increased research investigation expanding the controller and drive capabilities,

structural design studies leading to increased energy production within the range of 15-35%.

The expanded controller and device capabilities have global positioning system (GPS)

capabilities embedded into the controller for remote access and real-time tracking

information eliminating the possibilities of configuration errors.

With the recent industrial innovations in the dynamic single-axis tracking technology, this

technology eliminates the frequent repairs reducing the impact of any single point failure,

simplifying operations and maintenance (O&M) reducing service and repairs costs. Further

classification and divisions of the dynamic single axis tracking are discussed briefly in the

following subdivisions.

2.3.1.1 Horizontal Single axis Tracker (HSAT)

This is one of the most common single-axis trackers, the conventional axis of rotation is an

east to west horizontal movement with respect to the ground. The tracking technology is

mostly used and proven to be very effective in low-latitude regions. The system simply uses a

set of drives and controllers to achieve automatic tracking for the solar photovoltaic module

ensuring an equal uniform loading without experiencing excessive self-shading. Figure 8

shows a horizontal single-axis tracking architecture with rows of solar photovoltaic module

orientation in a north-south line rotating from east to west [33, 34].


30

Figure 8. Horizontal single axis tracking [35]

2.3.1.2 Vertical Single axis Tracker (VSAT)

A vertical single axis tracker system rotates from east to west with the axis perpendicular to

the ground. The system is more profitable in the northern latitudes between 400 and 450. Due

to the system orientation, the system tends to have a relatively low power density per acre,

spreading units of installed solar photovoltaic module stands to avoid self-shading. Figure 9

shows a vertical single axis tracking architecture with rows of solar photovoltaic module

orientation rotating around a vertical axis facing east mornings and west evenings [36, 37].

Figure 9. A vertical single axis tracking (VSAT) [35]

2.3.1.3 Tilted Single axis Tracker (TSAT)

A tilted single axis tracker seems to be more complex in nature compared to the other single

axis tracker systems and is found to be more efficient in the mid/low latitudes region. The

conventional axis of rotation is from east to west tilted upwards and towards the south (in the

northern hemisphere). Invariably, the tracker is relatively expensive due to the added cost for


31

concrete foundations, is not scalable and requires spreading of units of solar photovoltaic

modules to avoid self-shading. Figure 10 shows a tilted single axis tracking architecture, the

elevation of the axis improves the amount of the total power produced depending on the

latitude at installation site [33, 38].

Figure 10. Tilted single axis tracker [35]

2.3.1.4 Polar Aligned Single axis Tracker

The polar aligned single axis tracker has similar characteristics to the tilted single axis tracker

and is aligned to the polar star. The conventional rotational movement for the solar

photovoltaic modules aligns with the earth’s axis of rotation reducing the aperture to ± 240 in

the north-south direction. The aperture angle is minimal for the polar single axis tracker

installed in the south [39].

2.3.2 Dynamic Dual- axis Solar Tracker

The conventional dynamic solar photovoltaic tracking movement for the dual axis tracker has

two axial degrees of rotation. The primary axis of rotation is at fixed position relative to the

ground and the secondary axis of rotation regarded as the reference position. The dynamic

solar photovoltaic tracking system combines both the azimuth and altitude tracking

mechanisms simultaneously ensuring the solar photovoltaic modules constantly face the sun

at all the times as the earth rotates yielding the best performance in terms of system energy

output and efficiency.


32

In addition, the dual axis tracker achieves optimum solar energy levels due to its tracking

capabilities to follow in east, west, north, south and center directions during the course of the

day. This solar photovoltaic tracking mechanism has increased energy production within the

range of 25-50% compared to the fixed solar energy system. With intensified efforts in

research to improve the dual axis tracking, the tracking system is further classified into two

divisions examined in the following subsections. Figure 11 shows a dual axis tracker

architecture, the DAT rotating around a vertical axis and the vertical elevation drive adjusting

the solar photovoltaic module to the sun’s altitude [28, 40].

Figure 11. Dual axis tracker architecture [35]

2.3.2.1 Tip-Tilt Dual- axis Tracker

The solar photovoltaic tracking mechanism is mounted on the top of a T- or H- rotating

bearing shaped device providing the normal east-west tracking movement and upward

tracking focus movement of solar photovoltaic module frame structures. The tip-tilt dual axis

tracker is typically aligned to the axis of rotation and possibilities of alignment in any

cardinal direction is achievable with advanced developed tracking algorithm. With the

implementation of a tip-tilt dual axis tracker on a solar photovoltaic farm, the unit’s

arrangement should be placed at a fairly low density to avoid self-shading, minimising sun

shading thereby maximising the harvested sun energy [41].

2.3.2.2 Azimuth-Altitude Dual- axis Tracker

The tracking system is typically mounted on the ground with the solar photovoltaic module

mounted on a series of rollers having its weights evenly distributed. The primary (azimuth)


33

axis has its reference to the ground and the secondary (altitude) axis normal to the primary

axis. The rotational movement is quite different from the tip-tilt dual axis tracker system, as

the azimuth-altitude axis tracker rotates using the large roller base ring mounted on the

ground for its horizontal movement [41, 42].

2.3.3 Summary Chart of Solar Photovoltaic Sun Tracking Types

Figure 12 simply represents a brief summary of the different types of solar photovoltaic

tracking systems currently available in the solar photovoltaic energy industry. The two major

classifications as briefly explained in Section 2.3 are the single-axis tracker and the dual-axis

tracker systems. The sub-division of these two major classifications of solar photovoltaic

tracking systems have been addressed in Section 2.3.1 and 2.3.2 respectively.

Figure 12. Summary of types of sun trackers

2.4 Smart Solar Power Grid System

2.4.1 Smart Solar Photovoltaic Power Grid Network

The smart solar photovoltaic power grid network is a modernised and automated form of the

electrical grid system to improve the efficiency, reliability, economics and sustainability of

electrical power generation and distribution of electricity by renewable energy sources of

TYPES OF SUN

TRACKERS

SINGLE-AXIS TRACKER

HORIZONTAL SINGLE-AXIS

TRACKER

(HSAT)

VERTICAL SINGLE-AXIS

TRACKER

(VSAT)

TILT SINGLE-AXIS TRACKER

(TSAT)

POLAR SINGLE-AXIS TRACKER

(PSAT)

DUAL-AXIS TRACKER

TIP-TILT DUAL-AXIS TRACKER

(TTDAT)

AZIMUTH-ALTITUDE DUAL AXIS TRACKER

(AADAT)


34

power generation. This is unlike the traditional power grid system driven by coal, gas, oil

fired and fossil fuels constructed as a centralised, unidirectional systems of electrical power

generation, electricity transmission, electricity distribution and demand driven [43].

The traditional power grid system is strategically sited and a permanent structure erected at

sites close to the source and supply reserves. For instance, hydropower stations are situated

closer to where there is abundance availability of water throughout the year. Another major

factor in the establishment of the traditional grid system is the nearness to the source of fuel

supply, access to rail, road and paths for easy transmission and distribution to its major and

minor consumers [44].

The growing energy demand for industrial and domestic satisfaction has continually

increased hence, the demand for reliable energy supplies from the traditional grid systems

especially at peak periods, and the redundancy of the grid system at lesser peak periods have

resulted in the high tariffs passed onto the electricity consumers. In many situations at peak

periods, the energy demand results in poor power quality resulting in blackouts, power cuts

and brownouts. The high energy demand from the traditional grid system for consumers’

satisfaction has contributed to the emission of greenhouse gases affecting the climate leading

to global warming crisis [45].

The smart solar photovoltaic grid network policy offers rebate options from the government

to private individuals and corporate business organisations willing to upgrade from the

traditionally powered electricity sources to sustainable green energy such as solar

photovoltaic energy installation by improving on the property value cost dramatically by

about 3.5%. The grid system provides a reduction of carbon footprints, saving consumers’

money from monthly or quarterly power utility bills and offering off-grid solutions for rural,

urban communities, agricultural and other industries [46].

2.4.2 Concept of the Smart Solar Photovoltaic Grid Network

The concept of the smart solar photovoltaic grid network has identified energy security and

efficiency as a critical component in its approach in dealing with climate change challenges,

the capacity to achieve substantial energy demand, cost-effective energy solutions and

relatively rapid reductions in greenhouse gas emissions across the sectors of the economy.

This new grid system represents the cutting edge of energy efficient technologies applied in


35

power generation, distribution and finally to the consumers with the intent of securing a low-

carbon future providing a more reliable, with fewer and shorter blackouts [47].

The vision of the grid system comprises application suites and technologies currently at

different levels of technical innovation and developments for cost-effective emissions

reduction, attaining economic maturity, with accrued financial and non-financial benefits.

The grid system provides greater transparency on energy use to various levels of consumers

improving the quality of energy supply. This system offers consumers the advantage to be no

longer passive receivers of bulk power monthly or quarterly utility bills distributed by

existing traditional grid system [48].

The grid system capabilities address the global call by the environmental protection agency

(EPA) to reduce the overall amount of greenhouse gases, including the tons of carbon dioxide

equivalent (CO2-e) produced from traditional electrical power generation, predominantly

altering the climate and affecting the environment. The regulatory bodies are reforming

existing energy policies to increase electricity system reliability, resilience and resource

diversity incorporation over time in order to decarbonise energy production [49].

The dynamic uncertainties and benefits accrued to deployment and implementation of the

smart solar photovoltaic grid system on a large scale, the stakeholders and policy makers

have clearly suggested and identified the concepts, central targets in enhancing the global

acceptance of the new grid system as highlighted [49]:

Efficiency optimisation and prioritising applications and innovations for societal

benefits.

Commercialisation deployment on a large scale to determine the business viabilities.

Synergy collaboration of research institutions and industries.

Public awareness promotion by concerned agencies and full commitment of

government programme and participation.

Instrument and parameter measures to address seemingly difficult technical and

business challenges.

Government declaration and support for private and public adoption of the new grid

system providing attractive incentives and loans.


36

Establish a universal standard smart solar applications and solutions as a cardinal

reference to the global world.

The smart solar photovoltaic grid system is building and leveraging on existing smart

meter trials. The programs on distributed solar renewable generation are on moderate

large scale solar farms for the purpose of measurements and establishing a future grid

database. Smart solar photovoltaic substation grids and feeder monitoring have been

under intensive research investigation for the purpose of fault detection, isolation and

restoration (FDIR) before full commercialization commencement. The FDIR enhances

system reliability saving costs for periodic maintenance costs. This is achieved with the

aid of automation of smart system detection via wireless communication to mobile

devices and PCs for online monitoring. However, pilots tests are been monitored on

integrated volt-var control optimisation (IVVCO) and conservation voltage reduction

(CVR) for dynamic voltage management [50].

Furthermore, the prime concept of the grid system is making a tremendous effort in

ensuring the consortium of the smart solar photovoltaic energy consultants establishes an

agreed universal interoperability protocol among cross vendors design and technology.

This ensures maximum efficiency optimisation of the smart solar photovoltaic grid

system with an open standard application layer protocol and network layer with the

capabilities of solving cyber security challenges creating a seamless interface

communication exchange on the basic fundamental architecture of the grid system.

However, the smart solar photovoltaic grid system promotes energy security, reliability

integration of information and communications technology ensuring almost zero

decarbonisation emission and eco-friendly environment [51, 52].

2.4.3 Challenges and Issues on the Smart Solar Photovoltaic Grid System

The smart solar photovoltaic grid system is one of the renewable energy sources. Smart solar

photovoltaic system has been widely accepted and prominently deployed among other

renewable energy sources as a result of the global renaissance interests in effectively

reducing greenhouse gases emission and decarbonisation of energy pollution from the

existing traditional powered generation. The renewable energy power generation is

undoubtedly confronted by challenges and issues because its source of energy (the fuel

source) cannot be manoeuvred manually either by increasing or decreasing on demand.


37

Hence, the source of energy is not dispatchable unlike the conventional traditional fossil

powered energy systems [53].

In addressing the major challenges and issues of non-controllability of dispatchable energy

sources, has resulted into various solar photovoltaic tracking techniques as discussed in

section 2.3. The use of solar photovoltaic sensor tracking devices has been examined in

section 2.2 to significantly maximise and improve the energy harvested. The introduction of

advanced control techniques is a vital key enabling the deployments of optimised high

performance and steady operation of the grid system to its maximum capacity. However,

controversial proposed future policy reforms stating that renewable energy credits (RECs) for

private homeowners will be permanently withdrawn and will no longer be able to claim tariff

compensation for energy contributed to the national grid is another bane discouraging the

development and promotion of the smart solar photovoltaic grid system [54].

The challenge of establishing a link between the non-dispatchable and penetration smart solar

photovoltaic grid system has necessitated the need for the renewable portfolio standards

(RPS). Several countries in the world have achieved relatively high standards due to

governmental support and policies encouraging the adoption of these smart solar photovoltaic

energy by introducing attractive incentives and subsidies. The renewable portfolio standard

(RPS) mandate has specific targets to be achieved for the pre-configured fraction of energy

capacity produced from installed smart solar photovoltaic grid system over a stated period.

This depends on the following factors: geographical location, provision of a close match to

peak load demands, provision of generation and load balancing services, provision of resilient

power for critical infrastructure, differing transmission and distribution upgrade investments

on existing traditional power grid system, high preferential support for carbon-neutral

generation, optimal efficiency and energy cost saving on tariffs and provision of ancillary

services to the grid [55, 56].

In the meantime, the detrimental impacts of solar photovoltaic grid system involve real and

reactive power imbalances, inverter control loop feedback, incessant exposure of utility

devices to seasonal weather conditions and the compensation of dynamic voltage level

fluctuations requires huge capital investments and civil works for the upgrade of the grid

system to become smart [57]. These challenges affect the optimal performance and efficiency

of the primary smart solar grid concept to safely and reliably distribute steady power through


38

highly monitored and smart controlled wireless network devices on the transmission lines

network [47].

Complexities abound in incorporating cyberinfrastructure across the transmission and

distribution (T&D) infrastructure of smart solar photovoltaic grid networks for continuous

dynamics monitoring and control actions. These challenges have received a degree of

attention from the smart grid cyberinfrastructure networks. Some of the challenges addressed

provides an end to end communication support for data acquisition, data storage, data

management and data integration. In addition, the cyberinfrastructure challenges tackled

includes data mining, data visualisation and computing, information processing services over

the web critical in realising the objective of the grid system. The infrastructure provides a

seasonal database for advanced estimation and forecasting for research studies and potential

improvement of the grid network [58].

Many issues have been addressed in a smart solar photovoltaic grid system with the use of the

Internet of Things (IoT), the aspect of ensuring cyber security due to diversities of

infrastructure components and frameworks. The smart solar photovoltaic grid deploys

possibilities of the remote control operation for power management and distribution. This is a

prime concern against fraudulent theft, abuse and malicious activities over the web.

Cybercrime has been a major global challenge for all sectors of the economy, inadequate law

enforcement and stringent security measures of the grid system will compromise the stability

of the entire grid leading to utility fraud, lack of confidence and trust by smart solar grid users

losing confidential information and credit card details, and manipulation of energy

consumption data by cyber hackers. The unification and enforcement of security mechanisms

at each logical protocol and layer prevent vandalization of the physical infrastructure, data

processing encryption security measures, authentication and application security control

check as a defence against overflow of attacks.

2.5 Green Energy Revolution and Policy

2.5.1 Overview of the State of Evolution

However in the mid-17th and 18th century, the global expectation of the world was the

sudden extinction and scarcity of coal. The major source of energy generation during the

industrial revolution period. The discovery of crude oil in some parts of the world in the 19th

and 20th century delayed the resurgence of a green energy revolution, but a gradual


39

development in research innovations and technologies has been experienced in the last 50

years [59]. The drive behind the green energy revolution has been the global concern of

protecting the climate by replacing the fossil fuels, eliminating the greenhouse gas and CO2-

equivalent emissions ensuring energy security and economic growth [60].

The current global state of the ozone layer and the extreme consequences for continuous

usage of the fossil energies in power generation have led the green energy research

institutions increasing the search for sustainable and justifiable alternatives means of power

generation. This revolution has created renewable energy solutions through decentralisation

of power generation and grid expansions. In addition, it has led energy institutions enacting

global standard regulation and policy reforms for the energy world, providing eco-friendly

energy alternatives as compared to the traditional means of power generation, increasing

intensive research and development for renewable energy sources.

The energy world is gradually shifting it base and switching to available green energy

sources, though a larger percentage of the world energy generation still relies on fossil fuels

and coal as it major means of power generation. The recognition and assessments of the

devastating impacts on climate change, global temperature increase have helped developed

countries to enact laws to support and promote the concept of the green energy revolution.

The global energy demand and consumption are on the rise leading to decentralisation of

green smart-grid networks of renewable energy power generation and distribution [61]. A

green smart grid network concept is as shown in Figure 13. The rapid growth and

implementation of the five (5) major sources of green energy have increased the hope of

energy security, long-term security for investments, the establishment of access to smaller

microgrids by the combination of one or two green energy sources forming a hybrid smart

grid energy system.


40

Figure 13. A green smart grid network concept [62]

The international energies and environmental policies have played significant roles in the

liberalisation of cross-border trade, energy market policy reforms to promote global approval

and expansion creating an enabling environment for its survival. The fast growing renewable

green energy globally is the solar photovoltaic energy, its growth has been accelerated based

on the intensified research in solar photovoltaic optimisation and tracking techniques,

developed maximum power point tracking (MPPT) algorithms ensuring a higher efficiency in

the overall generated energy output.

The radiated energy released from the sun is about 174 PW (petawatts) to the earth, some of

which are reflected and absorbed by the clouds, oceans and land and 3,850,000 exajoules (EJ)

is absorbed by the earth's atmosphere yearly [63, 64]. The solar photovoltaic energy market

has been growing at a rate of over 40% per annum in recent years and has made a significant

contribution to power generation. The United States government invested about 3.4 billion

dollars in 2009 in a solar farm, the largest ever in the world [65]. There are a continuous

growth and improvement on the existing solar photovoltaic (PV) module fabrication

technology, installation modernisation and flexibility in the urban, rural and industrial

environment. Owing to this current revolution in the solar photovoltaic energy world, prices

of the solar photovoltaic modules have reduced to almost half of its cost in last two decades,

giving rise to the production of quality and efficient long lasting solar photovoltaic modules

at a fair healthy competitive market worldwide [66].

However, Figure 14 represents some of the substantial results achieved in the solar

photovoltaic energy world, in countries like China, Japan followed by the United States

which have established its energy base. Other countries such as Germany, Spain, Swiss,

Asian countries, and Australia are having future budgeted plans as well for solar photovoltaic


41

farm investments over large hectares of vast land to connect to the existing grid system for

market supply. Irrespective of the recorded success and research projects in various regions

of the world so far, international bodies are in collaboration to have the best optimum

solution to increase the energy generation base thereby eliminating the negative impacts of

fossil energy [67].

Figure 14. Solar PV Global capacity, shares of top 10 countries, 2012 (Global status report)

2.5.2 Determinants of Green Energy Revolution

The concern for the future development pathway of the green energy revolution has received

credibility, acceptance and is on the rise. The diverse energy mix which includes the

traditionally powered generation with the exciting new renewable energy prospects will

increase the production capacity and satisfy the economy energy demand. The concept and

models of green energy revolution have proven to be relatively competent reducing

environmental degradation of fossil-powered generations, managing global climate change,

achieving more sustainable and eco-friendly renewable power generations.

The economic policy guidelines and frameworks are critical determinants of the green energy

revolution achievements. A thorough implementation, execution of guidelines and

frameworks will foster capitalisation of the strong productive base for both external and

internal factors. However, the external factors involve international systemic structural

institutions such as international renewable agencies (IREAs) and world council for

renewable energy (WCRE) enacting and providing a global policy guidance and support to

improve on the existing regulatory frameworks for both industrialised and developing

countries. These institutions facilitate relevant updated policies, information and data for


42

public access, effective administrative and financing coordination, designs and engineering

update on the latest state-of-the-art technology [68].

The internal factors are measured by performance indicator criterion funding the facilitation

of grants, a structural implementation of energy management policies, cost effectiveness of

energy efficiencies of these renewable energy projects progress is therefore reviewed

annually. Periodic scheduled media advertisements and promotional activities creating

awareness intensifying support for adoption of the smart solar photovoltaic grid system by

the general public is an integral core of strategic management and monitoring targets [69].

The major determining factors for green energy revolution are summarised in Figure 15 and

discussed in the following subsections.

Figure 15. A Green energy revolution determinant

2.5.2.1 Government Policy on Green Energy Revolution

The government policy establishes renewable energy agencies (REAs) to provide support and

implementation of these policies to manage the global climatic change and programmes that

promote renewable energy sources. The constituted agencies set up by the REAs accredits

renewable energy companies with full licence and permission to achieve the renewable

energy targets (RETs) on large, medium and small-scale technologies. This policy critically

prioritises growth and diversification of exports and imports, reorientating and revising of

investment policies to enhance integration and avoiding immobilisation of resources and

inadequacies.


43

The survival and success of a green energy revolution substantially rest on the support of

favourable government policies. The positive influence and contribution of these policies in

the transformation process of the energy sector revolution are massive. It induces mechanism

to advocate for the coalition, promoting the green energy revolution, networking constitution

of technological and business oriented minds, setting up institutional norms and rules

regulating the interaction of the sector, encouraging individual, corporate actors and investors

fusion in ensuring a more self-sustained green energy revolution [70].

2.5.2.2 Revenue Generation Policy on Green Energy Revolution

The green energy revolution is highly capital-intensive, and the energy industry needs an

effective driver for revenue and economic generation policy to sustain the long-term assets

privately-owned and operated by individuals, corporate organisations and government

establishments. The biggest factor driving renewable energy targets (RETs) is ensuring

decarbonisation of electricity generation by significantly promoting renewable energy

business trends, forecasting the economic implication features including investment costs,

energy prices, industrial competitiveness, gross domestic product (GDP) and employment

opportunities.

The relevant government instituted bodies are responsible for identifying market revenue

generation policies to address intensive commercial investments and deployment providing

tenor debts suitable for the renewable infrastructure in large, medium and small-scale

projects. The different renewable energy institutions setup provide consultation,

administrative advice and special investments risk control competence facilitator across all

portfolios for international investors and multinational companies.

The dynamic possibilities of renewable energy efficiency innovation technologies in green

energy have caused government policy makers to strategically invest extensively and support

the commercialisation of patent green technologies for rural, urban and industrial sectors of

the economy. The exportation of the renewable energy products is integral to the sources of

revenue generation for short and long term investments to align with the vision and mission

of the government in advancing the natural greenhouse gases emission reduction objectives

[71].


44

2.5.2.3 Energy Policy on Green Energy Revolution

The global renewable energy targets (RETs) generation policy frameworks emphasize that by

the year 2020, a reasonable percentage, between 20-25%, of electricity generation globally

will emanate from renewable energy sources with the diverse mix of other sources of power

generation from the Kyoto protocol document submitted to the united nations framework

convention on climate control changes. The policy is modelled to measure analytically the

impact of renewable energy targets, renewable portfolio standard scheme contributions in

ensuring a cleaner diverse integration mix of renewable energy sources supporting growth

and development of the energy economic sector.

The advent of renewable energy sources has brought significant transition in energy policies

effectively reducing investors risk in the juvenile energy sector creating new market

opportunities, deploying large, medium and small-scale green energy concepts, offering

energy security guarantee, encouraging eco-friendly energy generation, increasing energy

reassurance and reliability in the implementation of green energy options [72, 73]. Deliberate

commitment on the part of the governments ensures effective management of regulatory,

enforcement and compliance to constituted policies by the participating agencies in achieving

long-term objectives by the year 2050. The government energy policy in Germany is making

significant progress for effective policy implementation of its renewable energy programs

with an increase from 6.3% in the year 2000 to about 30% of its electricity generated from

renewable energy in 2014. The Germany energy policy set goal for the year 2020 is to ensure

that 35% of its electricity generated is from renewable energy sources[74].

2.5.2.4 Environmental Policy on Green Energy Revolution

The objective of the environment protection agency (EPA) through instituted task force

coordinates government agencies on climate change control and global warming related

issues. The EPA ensures effective energy policies on issues of renewable portfolio standards

(RPS) unification is resolved, regulation and guidelines in sustainable energy efficiency

mechanism appropriate in reducing the annual growth rate of greenhouse gases (GHG) and

CO2-equivalent emissions are dealt with by new renewable energy plants with possibilities of

cutting carbon pollution from existing traditional power plants protecting health and the

environment now and for future generation. EPA collaborates with key stakeholders in


45

designing, implementing clean energy policies, cost-effective technologies solution

delivering environmental and economic benefits [75].

The environmental protection agency communicates through various media options giving

warning signals and rapid emergency responses about the current devastating impacts of

climate change either increasing or decreasing the annual expected rainfall. This directly or

indirectly affects agricultural crop yields, the human health and causes changes in forests,

ecosystem and energy supply. The government environmental policy gives reassurance and

support to corporate business organisations committed to investing in green technologies by

setting reasonable minimum green energy tax to encourage environmentally friendly

technologies fostering competitiveness stimulating the market development for energy

efficient technologies and products [76].

2.5.2.5 National Policy on Green Energy Revolution

A national renewable energy action plan (NREAP) policy is established to promote regional

and economic sectoral renewable energy targets (RETs), achievable renewable energy mix,

policy direction path and reform measures to overcoming the peculiar challenges in achieving

successful renewable energy targets. However, the NREAP evaluates the track record and

progress made by other advancing nationals as a relative benchmark to surpass and improve

on their national targets.

Consequently, the NREAP makes a distinct administrative classification of the renewable

energy scheme responsibilities by publishing the national electricity rules and economic

regulation providing policy advice for international business trade, tax incentives initiatives

promoting awareness nationally and strong support for environmental protection in

establishing the growth of green energy [76, 77].

2.5.3 Impacts of Green Renewable Energy

The national renewable energy action plan (NREAP) policy and other various renewable

energy bodies unwinds by evaluating the impacts of renewable energy sources in

substantially minimising the harm, and the intensity of the environmental impacts the fossil

fuel power generations contributed to air and water pollution, damages to public health,

extinction of wildlife and habitat species as a resultant consequence of global warming.

Several studies conducted have shown that by increasing the supply of renewable energy


46

generation network mix, there is a direct knock-on effect in the replacement of carbon-

intensive energy sources significantly reducing global warming emissions by a much more

reasonable percentage [78].

The potential impacts and substantial benefits of green renewable energy significantly

address the current and potential environmental issues, reducing carbon-cutdowns and global

warming emissions and its harmful impacts on our health, environment, and climate. The

transition in the renewable energy sector is gradually experiencing a result-oriented process

owing to the fortification of environment protection agency (EPA) enforcing strict rules and

regulations on carbon pollution from traditional energy power plants contributing one-third of

the world’s energy emissions and accelerating a clean energy economy. Due to uninterrupted

running processes of traditional energy plants, the atmosphere has been overloaded with

carbon dioxide and other global warming emissions steadily trapping heat and increasing

instability experienced in climate [79, 80].

However, electricity generation boosts from renewable energy are gradually replacing

carbon-intensive energy sources due to the negative environmental impacts on climate

change and global warming. Electricity generation from fossil fuels significantly contributes

to air and water borne diseases such as breathing problems, heart attacks, neurological

changes, cancer and premature mortality rates. Power generation from renewable energy

sources from solar, wind and hydroelectric systems are known not to be associated with air

pollution emissions. Especially, the solar and wind energy sources require no water for their

operation, hence water resources are free from pollution for domestic and other water

demands [81, 82].

The advent of green renewable energies has contributed and provided thousands of job

globally to skilled and semi-skilled workers on the full-time and part-time basis. Based on

global renewable energy targets, more jobs will be created in the future improving the gross

domestic product (GDP) of the economy. The jobs created spread across diverse sectors of

the economy industries and capacities such as the manufacturing sector, civil and site

construction sector, including full and part-time workers, project management and

development sector, operation and maintenance departments, transportation and logistics,

financial sector, legal and consulting services sectors either directly or indirectly linked to the

supply chain capabilities of the renewable energy and their economic benefits [83].


47

The renewable energy sources of power generation installation in rural and urban settlements

in large renewable energy schemes (LRES) and small renewable energy schemes (SRES)

have immensely contributed affordable electricity tariffs especially to rural and remote

regions by reducing the financial burden of civil construction and erection of high power

transmission towers and lines. As a result, the cost of renewable energy solutions is

experiencing a decline due to government subsidies and support for eco-friendly electricity

generation. However, the renewable energy sector will further experience future growth as

the market matures and a good percentage of acceptance from the public relieving huge

burdens on electricity tariffs [84].

Renewable energy sources are found to be more reliable and resilient than coal, natural gas,

nuclear and fossil fuel power plants in the face of probable disruption events such as

droughts, earthquakes waves, severe wildfires and extreme storms and weather events. In

conclusion, high dependence on energy sources other than renewable energy runs the risk of

long blackouts until full restoration, maintenance and repairs are carried out. This is not the

state in renewable energy sources operating independently irrespective of extreme weather

conditions. Most often renewable energy sources promote diversification of energy

generation reducing overdependence on imported fuels and toxic carbon emission sources of

power generation [84, 85].

2.5.3.1 Environmental Impacts on Green Renewable Energy

The environmental impacts of green renewable energy are diverse and emphasis on the

positive benefits is due to its strong capacity of curbing and ensuring zero-carbon emissions,

non-toxic gases, liquid pollutions and global warming emissions. In most cases, the

renewable energy sources are found in abundance, are inexhaustible and affordable most

often throughout the year. This makes green renewable energy viable for small and large

scale means of energy production, compared to fossil fuels, natural gas-fired and other toxic

emission sources of energy production.

Based on recent research studies, a comprehensive report presented on the amount of CO2

emissions from green renewable energy generation has shown considerable reductions due to

compliance to renewable energy targets. The solar photovoltaic energy production emission

is found to be with low emission of CO2, the nuclear energy production follows next, whilst

the wind energy is found to be third lowest CO2 emission and hydroelectricity produces the


48

lowest CO2 emissions. The green energy concept has been designed to mitigate the negative

impacts of traditional power plants on local eco-system [86, 87].

2.5.3.2 Market Policy Impacts on Green Renewable Energy

The economic regulatory and financial policy makers in green energy markets may either

increase or impede the expansion and acceptance of green renewable energies. Financial

institutions play an integral role in the economy and energy sector offering some of the

necessary tools to support a smooth transition to sustainable renewable energy schemes by

providing laws, equity, insurance and other financial services to individual and corporate

organisations.

This policy mandates premium rate reimbursement for electricity fed back into the electricity

grid from renewable energy sources of electricity generation. The feed-in tariff is meant to

resolve the market failures and encourage the wider participation of the larger society

providing incentives for adopting the renewable energy [88]. In addition, the policy mandates

electricity suppliers to include a percentage of renewable green energy sources with the

existing traditional power generation fostering an energy mix from electricity suppliers,

thereby increasing the growth of green energy [54].

However, the policy varies from one country to another encouraging existing electricity

suppliers using depletable energy sources to reconsider investing in environmentally friendly

energy sources by introducing heavy tax fines on defaulters. This indirectly decreases the

price of electricity by creating incentives for renewable energy adopters ensuring energy

security, reliability, efficiency reducing the demand on the national grid [89].

2.6 The Prospective Grid: A Smart Grid Network

2.6.1 The Smart Grid Network

The global concern on the current changes experienced through climate change has driven

scientific research and policy makers to promote the growth and expansion of eco-friendly

grid systems known as the smart grid network (SGN). There are other definitions of the term

smart grid network as established in several research works for this new grid network. A

smart grid network is a network consisting of renewable energy sources of power generation

as its bedrock incorporating online automation, remote control access technology and

information and communications technology seamlessly to enhance the grid network. The


49

renewable energy sources of power generation are subdivided into solar energy, wind energy,

wave or ocean energy, geothermal energy and hydrogen and fuel cells energy [78, 90, 91].

The focal intervention point for the SGN policy makers was established on these tripod

targets; assess to up-to-date scientific data and information, evaluating the environmental and

socio-economic implication and formulating policies promoting the concept of the SGN [92].

The existing traditional power generation since inception has depended on fossil fuels,

natural gas and coal-fired power plants [93]. This has significantly contributed to higher

carbon emissions and losses experienced during transmission and distribution of energy

generated before reaching the final consumers [94, 95]. The demand for SGNs is gradually

increasing due to the ageing of most of the existing traditional power grid infrastructures,

desire for quality of service (QoS), energy reliability, growing demand for constant electricity

supply, alarming concern for environmental protection and energy sustainability [96, 97].

An SGN has brought transformation by redefining the old norms of traditional power

generation introducing decentralisation, flexible database management, distribution,

integration and operation of variable renewable energies to form a hybrid SGN, interface

relationship in real-time between the consumers and the grid to adjust the energy use and

costs of electricity consumed [98-101]. The core foundations of the smart grids are built on

network management, intelligent applications, intelligent agents, two-way communication,

smart sensors, distributed remote and automated control [3, 4].

These foundations have enhanced an end-to-end interaction, full integration and installation

of smart sensor technologies into electricity business and services optimising capital assets

and minimising operational and recurrent maintenance costs [102, 103]. An SGN has been on

the rise due to the provisions and support of government policies enacting regulations for the

new grid network to survive. An SGN has been supported in many countries of the world

such as the United States of America, Spain, Japan, China, Australia and Canada and also in

most European countries [104, 105]. Several research works have shown that the smart grid

networks have been widely accepted in some of these countries based on these three factors

[85, 106]:

I. The awareness of the benefits of renewable energy resources for climate change

control, environmental protection and compliance, and energy sustainability.

II. Government incentives for private partnership participation investing in SGN paying

interest in a premium price for energy produced.


50

III. Public patriotism and endorsement of smart grid companies as their supplier of energy

to their respective homes.

Overall, SGNs have brought technological innovations, changing economic and

environmental regulatory policies leading to distributed smart grid networks. This has

contributed to the development of distributed generation technologies, increased and efficient

energy generation, energy market liberalisation and reduction in the overhead cost of

installation of transmission lines.

2.6.2 Conceptual Framework of the Smart Grid Network

The conceptual framework of the smart grid network envisioned is highly dynamic since

inception. The standard and building blocks of the smart grid network have been undergoing

revisions to add new functionalities, unifying layer and protocols, developing a universally

acceptable standard and interoperability smart grid network framework among all

stakeholders. However, the concept of the smart grid network framework has been

established based on these three key factors [107-109]:

Engaging a forum of expertise in various fields of smart grid network to harmonise

the complex nature of the grid network.

Promoting a consensus for smart grid network interoperability standards.

Providing an open source domain for contribution from experts in harmonising and

interfacing the three layers, physical, communications, and information of the smart

grid fields.

The primary objective of establishing a framework for the smart grid network is to ensure a

broad range of technology options, interoperability of the different options of smart grid

systems, ability to maintain the smooth running of the grid system throughout its lifetime.

The possibility of an upgrade enhancement of the existing grid, accommodation of new

innovative energy systems, support for development of scaled pattern systems, establishment

of structural integration, legacy migration system, ensuring strict security protection for the

energy system, allowing flexibility and interoperability within the system, dependable policy

implementation for system operation and affordability of a smart grid equipment in a large

market. The conceptual framework attributes of a smart grid network include [110]:

Self-healing capabilities with resilience from power uncertainties.


51

Real-time participation by consumers’ demand response.

Resilient cybersecurity against malicious attacks.

Guaranteeing reliability and quality constant power supply.

Accommodating and integration of new renewable energy sources and provision for

storage options

Creating an enabling environment for new products, services and markets.

Maximum optimisation and utilisation of assets to it full productivity.

The framework for an SGN as defined by the national institute of standard and technology

(NIST) is subdivided into seven domains and each domain has specific actors and tasks to be

executed [109].

Each domain has an established communication link protocol and application allowing

transfer of data and information across each of the seven domains. Table 3 presents the

domains and actors in the conceptual framework for the SGN model and Figure 16 depicts

the pictorial representation of the conceptual framework for the SGN.

Table 3. Conceptual framework for the smart grid network [24]

Domain Actors Functionality

Customers The end users of electricity. May also generate, store, and manage the

use of energy.

Markets The operators and participants in electricity markets.

Service Providers The organisations providing services to electrical customers and to

utilities

Operations The managers of the movement of electricity

Bulk generation The generators of electricity in bulk quantities. May also store energy

for later distribution.

Transmission The carriers of bulk electricity over long distances. May also store and

generate electricity.

Distribution The distributors of electricity to and from customers. May also store and

generate electricity.


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Figure 16. Conceptual framework for smart grid network [111]

2.6.3. A Smart Grid Network Policy and Implementation Guidelines

The complex nature of an SGN requires guidance in policy implementation for an effective

service delivery at each domain level of the smart grid network for maximum efficiency and

functionality of the grid network. The coherence of vision and commitment by the

international standard ruling organisations such as Institute of Electrical and Electronics

Engineers, IEEE, National Institute of Standards and Technology, NIST, International

Society of Automation, ISA, North American Electric Reliability Corporation Critical

Infrastructure Protection, NERC CIP, National Infrastructure Protection Plan, NIPP and

Electric Power Research Institute, EPRI to develop a global policy framework that includes

unification of protocols and standards for information management, plug and play integration

of different grid cross platforms to achieve interoperability of a SGN. Figure 17 represents

the parameter indicators for the establishment of policy implementation guidelines.

The parameter indicators for the establishment of policy implementation guidelines are

outlined as follows [111]:


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Identification of challenges during policy development and implementation

Governance responsibilities for monitoring, review and upgrade of policy

Risk management in policy implementation

Strategic implementation planning and management milestones

Procurement monitoring and contract management

Managing stakeholder interactions and conflicts

Managing of financial and system resources

Standard communication handshake within the layers of protocols

Monitoring and review of policy before implementation

Figure 17. Parameter indicators for a smart grid network policy and implementation

2.6.4. The Smart Grid Network Challenges

A smart grid network is fast growing with new advancements in technology and innovation

having the potential to provide energy reliability and sustainability curbing carbon emissions.

It is evident that an SGN is key for future energy generation systems. However, in spite of the

Policy development

Governance

Risk management

Planning for implementation

Stakeholder management

Procurement and contract management

Communication

Monitoring and review

Resources


54

smart grid benefits and advantages, there are challenges to be tackled in ensuring the

expected targets and goals are achieved. The challenges of a smart grid network are broadly

classified into four categories as illustrated in Figure 18 [3, 7]:

Regulatory challenges

Commercial challenges

Technology challenges

Political challenges

2.6.5. Benefits of the Smart Grid Network

The concept and benefits of a smart grid network have received a lot of attention with the

flexible combination of renewable energy sources of power generation, integration of smart

sensors devices, intelligent communication networks, automatic protection switching, remote

control monitoring for online real-time structures and assessment of a grid system. The

potentials and design perspective of the smart grid network include [109, 112, 113]:

Improved reliability and power quality.

Ensuring proper coordination of the variety of renewable energy configuration.

Ability to automatically reconfigure interconnected grid network.

Achieving better reliability and asset management.

Ability to relieve optimal power flow constraints.

Ability to establish scalability, broad applications and distinct way to full deployment

for solutions.

Improved outage restoration time.

Increased customer service options.

Private partnership investments to fund smart grid projects.

Peak demand reduction.

Reduction in line losses

Self-healing capabilities

In-built resistant against cyber attacks

Creates competitive energy market competition

Lower environmental pollution impacts

Economic productivity

Energy independence


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Figure 18. Challenges facing a Smart grid network [3, 7]

2.7 Conclusion

A review and discussion of literature examined in the area of smart solar photovoltaic grid

systems include solar photovoltaic sensor tracking devices, solar photovoltaic tracking

optimisation techniques, solar photovoltaic energy policies, reliability perspective of the

smart grid network and the theoretical framework and theories, has been presented in this

chapter. This review and discussion provide the context and background for this doctoral


56

research. In exploring the simulation and modelling of smart solar photovoltaic grid systems,

a thorough investigation and understanding of the existing research is imperative.

The review of these accessible literature sources highlights the gaps in the existing research,

particularly in relation to understanding the positive benefits of renewable energy systems,

the role and advantages the smart solar photovoltaic grid system concept provides ensuring

zero carbon emission policy. Furthermore, the reviewed literature has provided substantial

evidence and potential benefits of these non-depletable energy sources.

The following chapter (chapter 3) describes the simulation and modelling techniques

undertaken to answer the research questions describing the research paradigm that directed

the chosen methods.

Table 4: Summary of the Sub-sections of Literature Chapter Review

Section

Division

Sub-Headings Achieved Target

Section 2.1 Introduction An overview of the literature

chapter.

Section 2.2 Solar Photovoltaic Sensor and Tracking Optimisation

Devices

Dynamic Characteristics of Solar Photovoltaic

Sensors

Assessments of Physical Sensor Parameters

o Absorption Rate

o Longevity of Device

o Optimal Characteristics

o Wavelength Characteristics

o Climatic Condition Characteristics

o Response Characteristics

o Cost Relativity

Assessment of the physical

characteristics of solar

photovoltaic sensors parameters

described.

Section 2.3 Solar Photovoltaic Tracking Optimisation Techniques

Dynamic Single axis Tracking Optimisation

o Horizontal Single Axis Tracker

(HSAT)

o Vertical Single Axis Tracker (VSAT)

o Tilted Single Axis Tracker (TSAT)

o Polar Aligned Single Axis Tracker

(PASAT)

Dynamic Dual- axis Solar Tracker

o Tip-Tilt Dual-axis Tracker

o Azimuth-Altitude Dual-axis Tracker

o Summary Chart of Solar Photovoltaic

Sun Tracking Types

A concise classification of two

solar Photovoltaic Tracking

Optimisation Techniques.

Section 2.4 Smart Solar Power Grid System

Smart Solar Photovoltaic Grid Network

Concept of the Smart Solar Photovoltaic Grid

Network

Challenges and Issues on Solar Smart

Photovoltaic Grid System

Describing the SGN Concept,

Challenges and Issues.


57

Section 2.5 Green Energy Revolution and Policy

Overview of the State of Evolution

Determinants of Green Energy Revolution

o Government Policy on Green Energy

Revolution

o Revenue Generation Policy on Green

Energy Revolution

o Energy Policy on Green Energy

Revolution

o Environmental Policy on Green Energy

Revolution

o National Policy on Green Energy

Revolution

Impacts of Green Renewable Energy

o Environmental Impacts on Green

Renewable Energy

o Market Policy Impacts on Green

Renewable Energy

The major determinants of

Green Energy Revolution and

its impacts are uncovered.

Section 2.6 The Prospective Grid: A Smart Grid Network

The Smart Grid Network

Conceptual Framework of the Smart Grid

Network

A Smart Grid Network Policy and

Implementation Guidelines

The Smart Grid Network Challenges

Benefits of the Smart Grid Network

The components, conceptual

framework, policy and

implementation and benefits of

the SGN are discussed

elaborately.

Section 2.7 Conclusion A brief summary of the

subsections in the literature

chapter was ensured.


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Chapter 3 Modelling and Simulation Techniques for a Solar

Photovoltaic System

3.1 Introduction

This chapter describes the proposed neural network and sparse based algorithm simulation

modelling techniques employed on a smart solar photovoltaic grid system. In particular, the

research methodology is described and justified with cognisance reference to its ability to

answer the research questions. Two classical methods have been chosen for the neural

network and three methods chosen for the sparse based algorithm simulation and modelling

techniques.

These two techniques were chosen for their predictive capabilities on the nonlinear nature of

the solar photovoltaic module for effective validation and implementation in establishing a

tradition in forecasting for this research by comparing techniques on the basis of empirical

results, convergence capability to establish a generalisation and stability iterative pattern.

The neural network technique is exclusively discussed in this chapter, including its

implementation and analyses. This chapter also describes sparse algorithm implementations

on a smart solar photovoltaic grid network to improve the optimisation and output efficiency

of solar photovoltaic modules.

3.2 Static Solar Photovoltaic Modules Modelling and Simulation

Performance

The solar photovoltaic module naturally exhibits nonlinear current-voltage (I-V) and power-

voltage (P-V) characteristics, which has raised the need for modelling its design and

simulation to achieve maximum power point tracking (MPPT) for photovoltaic system

applications. However, due to the nonlinear characteristics nature of the solar photovoltaic

module, extensive research employing different modelling and simulation techniques to

provide reliable and increased output efficiency of the solar photovoltaic module near its

maximum power point based on analytical and numerical techniques to solve this challenge is

crucially important.

Based on recent literature, simulation and modelling techniques have been performed using

various application tools such as Labview, PSpice and Matlab/Simulink to solve the complex

nonlinear characteristics of the solar photovoltaic array based on the standard simplest


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mathematical generalised model equation [114, 115]. The neural network techniques have

been employed in various research fields suitable in handling complex nonlinearities,

uncertainties and variations in the input parameters in a controlled system. Therefore, the

neural network is employed in a comparative modelling and simulation of the static solar

photovoltaic module on a large scale system.

The two neural networks employed in this comparative methodology investigation are the

radial basis function (RBF) and multilayer perceptron (MLP) for the static solar photovoltaic

system. These two networks were chosen because of its simpler network structures, faster

learning algorithm and better approximation capabilities. Both networks use the same training

algorithm which is backpropagation based on the Levenberg-Marquardt minimization method

(the corresponding Matlab function is trainlm).

The static solar photovoltaic system in this research methodology consists of ten thousand

identical photovoltaic cells connected in series, having ten branches of the photovoltaic array

connected in parallel. The results of each of these performance models are empirically based.

However, the versatility and accuracy of these models are presented and discussed based on a

general simplest mathematical model derived equation of a solar photovoltaic module.

The objective of modelling and simulation of the nonlinear characteristics equation of the

solar photovoltaic module is to ensure the solar photovoltaic module performance overcomes

the limitations of environmental factors in a real-life situation. In addition, to effectively

design a reliable solar photovoltaic module capable of withstanding variable factors offering

the possibility of predicting the output efficiency of the photovoltaic module before its final

production and installation. The determination of the solar photovoltaic modules performance

has been a major concern necessitating different modelling and simulation techniques.

Solar photovoltaic modules in the global market are built of crystalline silicon materials with

the presence of impurities affecting their performance. However, modelling and simulation of

the solar photovoltaic module are vital because of the unpredictable nature of the module and

its dependence on the weather and climatic changes resulting in energy variations produced

over time. Sequentially, to efficiently and economically harness the energy from the sun,

assessment and optimisation of the solar photovoltaic module performance is required to

achieve the desired ultimate energy from the solar photovoltaic system.


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3.3 Static Solar Farm Photovoltaic Modules Modelling

The static solar photovoltaic farm module considered in this research methodology is a flat-

plate array of modules. It involves the combination of either series or parallel combinations

of similar photovoltaic modules to form a singular array on a very large scale inclined at a

permanent position to convert the radiated solar energy to useful electrical energy. The

determinant factor of the expected energy output required from the solar farm is the number

and quality of solar photovoltaic modules in the arrangement. An array of static solar

photovoltaic modules is as shown in Figure 19.

Figure 19. Static solar farm photovoltaic module [116]

3.4 Solar Photovoltaic Module Simplest Model and Parameter Definitions

3.4.1 Solar Photovoltaic Module Simplest Model

The ideal solar photovoltaic module is essentially a p-n diode that is capable of converting

the light energy into electrical energy. It is usually represented by the simplest model of an

equivalent solar photovoltaic module circuit as shown in Figure 20 and consists of a

photocurrent generator, a diode, a series resistance and parallel resistance. The current

generator, Iph of the solar photovoltaic module is proportional to the level of radiation, it is

the current generated by the incident light directly proportional to the solar irradiation. In this

simple model of an equivalent circuit of a solar cell, the parallel resistance Rsh, in the

equivalent circuit is high while the series resistance Rs is negligible compared to the open

circuit voltage. The current source Iph depends on the solar radiation, cell temperature and


62

wind speed, 𝑤𝑠 . The general mathematical equation expressing the output current I of a

simplest model of equivalent circuit solar photovoltaic module is given as [117]:

Figure 20. Simplest model of equivalent circuit solar photovoltaic module [116]

𝐼 = 𝐼𝑝ℎ − 𝐼𝑜 [{𝑒𝑞(𝑉+𝐼𝑅𝑠)

𝐴𝐾𝑇 } − 1] − (𝑉 + 𝐼𝑅𝑠)

𝑅𝑠ℎ (6)

3.4.2 Module Parameter Definitions

The definition of the parameters used in the simulation model is as given in table 5.

Table 5. Parameter definitions used in solar photovoltaic model

Definition Parameter Symbol

photocurrent generator 𝐼𝑝ℎ

leakage or reverse saturation current 𝐼𝑜

electron charge q

solar cell voltage V

ideality factor A

Boltzmann constant k

series cell resistance 𝑅𝑆

shunt cell resistance 𝑅𝑠ℎ

Ambient temperature 𝑇𝑎

wind speed 𝑤𝑠 solar irradiation S

𝑰𝒐 at reference temperature at 𝑻𝒓 = 301.18K 𝐼𝑜𝑟

band gap energy 𝐸𝐺

reference temperature 𝑇𝑟

solar cell temperature 𝑇

short circuit current at 𝑻𝒓 𝐼𝑠𝑐𝑟

short circuit current temperature coefficient 𝑘𝑖 open circuit voltage of the photovoltaic module 𝑉𝑂𝐶

maximum power voltage 𝑉𝑚𝑝

maximum power current 𝐼𝑚𝑝

Number of parallel modules 𝑛𝑝

Number of series modules 𝑛𝑠 output power of a solar photovoltaic P


63

The nonlinear and implicit equation is given in equation (6) depends on the insolation, the

cell temperature and the manufacturer’s standard reference values provided.

The efficiency of a PV device depends on the spectral distribution of the solar radiation. The

sun is a light source whose radiation spectrum may be compared to the spectrum of a black

body near 6000 K. The solar radiation is composed of photons of different energies. Photons

with energies lower than the bandgap of the PV cell are useless and generate no voltage or

electric current. The intensity and spectral distribution of the solar radiation depend on the

geographical positioning, time, day of the year, climate conditions, compositions of the

atmosphere, altitude and many other factors [118].

The rate of generation of electric carriers in the PV cell depends on the flux of incident light

and the capacity of absorption depends on the semiconductor energy bandgap on the PV

surface, on the intrinsic concentration of carriers of the semiconductor, on electronic

mobility, on the temperature, and on several other factors.

The temperature of the solar photovoltaic module T varies with solar irradiation, S and wind

speed, 𝑤𝑠 is given as in equation (7) [24]:

𝑇 = 3.12 + 0.25𝑆 + 0.899𝑇𝑎 − 1.3𝑤𝑠 + 273 (7)

where 𝑇𝑎 = ambient temperature

𝑤𝑠 = wind speed

S = solar irradiation

𝐼𝑜 , leakage or reverse saturation current in equation (8) depends on the temperature of the

solar photovoltaic module according to the equation as given in (8) [117]:

𝐼𝑜 = 𝐼𝑜𝑟 (𝑇

𝑇𝑟)3x 𝑒

{𝑞𝐸𝐺𝑘𝐴

(1

𝑇𝑟−1

𝑇)}

(8)

where 𝐼𝑜𝑟 = 𝐼𝑜 reverse saturation current at reference temperature at 𝑇𝑟 = 301.18K

𝐸𝐺 = band gap energy is the band-gap energy of the semiconductor of the PV

𝑇𝑟 = reference temperature

𝑇 = solar cell temperature

𝐼𝑝ℎ, photocurrent generator in equation (6) is a function of the incident solar radiation and

cell temperature and is given as [25]:


64

𝐼𝑝ℎ = {𝐼𝑠𝑐𝑟 + 𝑘𝑖(𝑇 − 𝑇𝑟)}𝑠

100 (9)

where 𝐼𝑠𝑐𝑟 = short circuit current at 𝑇𝑟 and radiation

𝑘𝑖 = short circuit current temperature coefficient

𝑠 = solar radiation

The open circuit voltage, 𝑉𝑂𝐶 corresponds to the voltage drop across the diode (p-n junction),

when it is traversed by the photocurrent 𝐼𝑝ℎ ( namely 𝐼𝑝ℎ = 𝐼𝐿, namely when the generated

current I = 0). It reflects the voltage of the solar photovoltaic module in the night.

𝑉𝑂𝐶, open circuit voltage of the photovoltaic module is given as [119]:

𝑉𝑂𝐶 = 𝐴𝐾𝑇

𝑞 ln (

𝐼𝑝ℎ

𝐼𝑜) = 𝑎𝑉𝑇 ln (

𝐼𝑝ℎ

𝐼𝑜) (10)

The maximum power point is the operating point at which the power dissipated in the

resistive power dissipated in the resistive load is maximum.

The maximum power voltage, 𝑉𝑚𝑝, is given as:

𝑉𝑚𝑝 ≅ 𝑉𝑜𝑐 (1 − ln 𝑐

𝑐) (11)

where the value of c is given as [25]:

𝑐 = 1 + ln 𝐼𝑝ℎ

𝐼𝑑 (126)

where 𝐼𝑑 = shockey-diode current = 𝐼𝑜 [{𝑒𝑞(𝑉+𝐼𝑅𝑠)

𝐴𝐾𝑇 } − 1]

𝐼𝑚𝑝 , maximum power current is given as:

𝐼𝑚𝑝 = 𝐼𝑝ℎ(1 − 𝑐−𝑑) (13)

where 𝑑 = 𝑐

𝑐 + 1 (14)

where c and d are parameters values chosen to determine 𝑉𝑚𝑝 and 𝐼𝑚𝑝 as shown above and

have no units. The above equation (13) is used in determination of the maximum power point

current of the solar photovoltaic module during the simulation and modelling experiments,

which will be shown in the following sections. For a solar photovoltaic array formed by a


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group of solar photovoltaic modules interconnected in parallel ( 𝑛𝑝) and / or series ( 𝑛𝑠)

configuration, is given as [25]:

𝐼(1 + 𝑅𝑆 𝑅𝑠ℎ⁄ ) = 𝑛𝑝𝐼𝑝ℎ − 𝑛𝑝𝐼𝑂[{𝐾𝑂(𝑉 𝑛𝑠⁄ + 𝐼𝑅𝑠)} − 1] − (𝑉 − 𝑛𝑠) 𝑅𝑠ℎ⁄ (15)

Where 𝑛𝑠 = number of solar photovoltaics connected in series

𝑛𝑝 = number of solar photovoltaics connected in parallel

𝑅𝑆 = equivalent series resistance of the array

𝑅𝑠ℎ = equivalent parallel resistance of the array

where 𝐾𝑂 = 𝑞 𝐴𝑘𝑇⁄ . (16)

The output power, P of any solar photovoltaic array is given as [25]:

𝑃 = 𝑛𝑝𝐼𝑝ℎ𝑉 − 𝑛𝑝𝐼𝑂[{𝐾𝑂(𝑉 𝑛𝑠⁄ + 𝐼𝑅𝑠)} − 1]𝑉 − (𝑉 𝑛𝑠⁄ − 𝐼𝑅𝑠)𝑉 𝑅𝑠ℎ⁄ (17)

3.5 Proposed Research Methodology

3.5.1 Neural Network Model

A neural network model is a novel structure used in solving a wide variety of tasks that are

difficult to handle using ordinary rule-based programming, including computer vision, pattern

and speech recognition, pattern identification, classification and control systems. The neural

networks are computational models capable of machine learning of complex systems of

interconnected (elements) neurons and computing values from the input parameters providing

necessary information through the network to solve specific problems [52, 120, 121]. Often

neural network models are closely linked with a particular learning algorithm, rule varying

parameters, connection weights and network structure.

The neural network model employed for our research investigation on solar photovoltaic

systems was subjected to qualitative prediction analysis with respect to the input parameters

to achieve a better optimisation and efficiency extrapolation on the quality of the module

itself under variable temperature and solar irradiance. The basic neural network model

consists of three layers as shown in Figure 21 [122]. The first layer has input neurons called

the input layer; raw information is fed through this layer into the network. The raw data is

sent via synapses to the second layer of neurons called the hidden layer; the activity of each


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hidden layer depends on the activities of the input information and the weights connections

between the inputs and the hidden layer. The hidden layer connects via two or more synapses

to form the third layer of output neurons called the output layer; the outcome of the output

units depends on the hidden units and the weights connections between the hidden and output

layers.

The neural network models are capable of handling more complex systems involving

increased layers of input and output neurons. The synapses store parameters called, “synaptic

weights” connecting the nodes of the neural network and are a determinant of the resulting

output. The changes in the activation values of units and connection weights (synapses)

between the units or layers are governed by the model equation describing the activation and

synaptic dynamic model respectively. The neural network model used in this methodology

study is discussed in Section 3.5.2 and Section 3.5.3 respectively. Figure 21 shows the basic

neural network model.

Figure 21. Basic neural network model

Typically neural networks are defined by these three parameters:

The interconnection pattern between the different layers of neurons.

The learning process for updating the weights of the interconnections.

The activation function that converts a neuron’s weighted input to its output

activation.

The learning process of the patterns and subsequent responses of the neural networks have

been classified into two processes:

I. Associative mapping process involves a systematic learning network process to

produce a particular defined pattern from a pre-defined set of inputs upon the


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introduction of a new pattern on the set of inputs. The mapping network process

stores the relationship among these patterns.

II. Regularity detection process involves a systematic learning process by which units

learn to respond to particular properties of input patterns.

The connecting weights matrix of the neural network contains stored information for the

learning process of the neural network. The learning process networks is categorised into two

major networks:

I. Fixed networks – the connecting weights cannot be altered; i.e dW/dt = 0.

II. Adaptive networks – the connecting weights can be altered; i.e dW/dt ≠ 0.

The learning ability of the neural network is characterised by the algorithm method chosen

for training. These training methods are basically categorised into three divisions [123]:

Unsupervised learning – the learning process is performed by itself without any external

interference. The generated outputs are not fed back into the network to measure against the

predictive performance of input parameters of the model.

Reinforcement learning – the learning process in this neural network architecture in the

hidden layer is randomly arranged and then reshuffled as the network learns its nearness to

the exact solution. This learning differs from the standard supervised learning due to the fact

the correct input/output are not presented nor sub-optimal actions explicitly adjusted.

Back propagation learning (supervised) – the learning process integrates the filtered errors

into the system readjusting the link between the network layers improving the performance of

the network.

For our research investigation on neural network modelling and simulation of a solar

photovoltaic system, the back propagation learning algorithm was employed to compare the

best efficiency of the two chosen methods. This was chosen because of its capabilities to

learn multiple-layer networks and nonlinear transfer functions such as gaussian function,

sigmoid function or any approximate functions.

There are currently various neural network model functions employed in research for

investigating the different solar photovoltaic module parameters. Careful choice of the best

suitable functions to investigate the fundamental physics as stated in section 3.2 associated

with solar photovoltaic module characteristics is thoughtfully chosen and examined for our


68

modelling and simulation experiments in this research are elaborately discussed in the

following sub-sections.

3.5.1.1 Radial Basis Function

Radial basis function (RBF) is a branch of neural network widely used in various fields for

classical mechanics control, potential function approximations, time series prediction,

interpolation techniques, clustering, image and pattern recognition [124-126]. An RBF has

similar characteristics to the feedforward neural networks. The learning and generalisation of

RBF capabilities have been found remarkable and substantially faster; the performance index

attains higher values as compared to other multilayer neural networks. The high-performance

index for the RBF in this research is presented in Table 6 as shown in the summary of

experimental results by seeking the best approximation rather than exact fitting to the training

data for the solar photovoltaic system.

The RBF networks typically have three layers as the basic neural network model as shown in

Figure 21; an input layer, a hidden layer containing the radial basis function, the

transformation process from the input layer to the hidden layer is nonlinear due to the

presence of an activation function similar to the Gaussian density function, and a linear

output function is obtained from the hidden layer connecting link to the output layer as shown

in Figure 22. RBF networks are regarded as universal approximators of a compact subset of

Rn. The approach employed in Figure 22 is to view an RBF network as representing a map of

n-dimensional input space.

Figure 22. Radial basis function architecture [127]

The input parameter, 𝐗(N) can be modeled as a vector of real numbers, R𝑛 given as [128]:

𝐗 ∈ R𝑛 (18)


69

The network parameters are regulated so that the training fits the network model as much as

possible. In radial basis function, all inputs are connected to each hidden neuron. The norm is

taken to be the euclidean distance and the radial basis function is considered as the Gaussian

function expressed in equation (19) [129].

𝜌(‖𝑋 − 𝐶𝑖‖) = 𝑒[−𝛽‖𝑋− 𝐶𝑖‖] (19)

The Gaussian basis functions are local to the center vector in the sense that;

lim‖𝑥‖→∞

𝜌(‖𝑋 − 𝐶𝑖‖) = 0 (20)

where N is the number of neurons in the hidden layer, 𝐶𝑖 is the center vector for neuron i, and

𝑤𝑖 is the weight of neuron i in the linear output neuron. The parameters 𝑤𝑖, 𝐶𝑖 and 𝛽𝑖 are

determined in a manner that best optimises the fit between the output 𝛾 and the data. The

RBF network is used in the function interpolations and approximations where optimisation is

more complex and determination for choice of centres is difficult. The output of the RBF

network is then a scalar function of the input, 𝛾 ∶ Rn→ R given as [128]:

𝛾(X) = ∑ 𝑤𝑖𝜌(‖𝑋 − 𝐶𝑖‖)𝑁𝑖=1 (21)

The parameters of the radial basis function are determined by three significant factors [129]:

Unit centers are determined using clustering algorithms such as k-means;

Widths are determined using the nearest neighbour method; and

Weights in the output layer are determined using the sum squared error to

minimise output outcomes.

RBF networks can be used to interpolate a function h: Rn→ R when the values of that function

are known from a finite number of points: h(𝐶𝑖) = 𝑑𝑖, i = 1,……,N. The known centres points

𝐶𝑖 of the radial basis functions are used in evaluating the values of the basis functions at the

same points 𝑝𝑖𝑗 = (‖𝑋𝑗 − 𝐶𝑖‖), the weights can be solved using the interpolation matrix from

the equation given as [129]:


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[

𝑝11𝑝21

𝑝12𝑝22

⋯ ⋯

⋮ ⋮ ⋱𝑝𝑁1 𝑝𝑁2 ⋯

𝑝1𝑁𝑝2𝑁⋮𝑝𝑁𝑁

] [

𝑤1𝑤2⋮𝑤𝑁

] = [

𝑑1𝑑2⋮𝑑𝑁

] (22)

The interpolation matrix in the above equation is non-singular if the points 𝐶𝑖 are distinct, and

thus the weights 𝑾 can be solved by simple linear algebra given as:

𝑾 = 𝑃−1𝑑 (23)

3.5.1.2 Multilayer Perceptron

Multilayer perceptron is a branch of neural network chosen for this research because of its

analogous characteristics with radial basis function using back-propagation algorithm and its

ability to learn from initial data provided yielding decision function directly via training.

Multilayer perceptron (MLP) is one of the classifications of feedforward neural network

connecting a set of input weights unit arranged in layers completely linked to the hidden

neuron layers, thus generating the appropriate output units. The MLP consists of three or

more layers, the input layer, with one or more hidden layers of non-linearity activation nodes

and an output layer. Most applications in MLP use a supervised learning algorithm called

back-propagation for training the network [130, 131].

The MLP model correctly maps the input to the output using the stored information to

generate the output when the desired output is unknown. The generated output is compared

with the desired output and the error is computed. The computed error is fed back into the

neural network causing an adjustment in the synaptic weights minimising the error with each

iteration until the expected output gets closer to the desired output. The error minimization

process is a function based on traditional gradient descent technique.

A typical MLP feedforward neural network has a similar architecture with the basic neural

network is shown in Figure 21, the input layer and the output layer with one or more hidden

layers having nonlinear activation functions tanh or sigmoid function as shown in Figure 23

[132]. The presence of the hidden layers provides regularisation to address overfitting of the

trained data. The training data set consists of N training patterns, where p is the pattern


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number{(𝑥𝑝, 𝑦𝑝)}. The input vector 𝑥𝑝 and the desired output vector 𝑦𝑝 have dimensions N

and M respectively; where 𝑣𝑝 is the network output vector for the 𝑝𝑡ℎ pattern. These

thresholds are handled by augmenting the input vector with an element 𝑥𝑝(𝑁 + 1) and setting

it equal to one [133].

Figure 23. MLP feed forward neural network [132]

For the MLP networks, the main activation functions currently in use for various applications

[130, 131].

1. Sigmoid activation function

For the jth hidden unit, the net input 𝑛𝑒𝑡𝑝(j) and the output activation 𝑂𝑝(j) for the 𝑝𝑡ℎ

training pattern is given as:

𝑛𝑒𝑡𝑝(𝑗) = ∑ 𝑤(𝑗,𝑖)𝑁+1𝑖=1 𝑥𝑝(𝑖) where 1 ≤ j ≤ 𝑁ℎ

𝑂𝑝(j) = f ( 𝑛𝑒𝑡𝑝(𝑗)) (24)

where 𝑤(𝑗,𝑖) denotes the weight connecting the 𝑖𝑡ℎ input unit to the 𝑗𝑡ℎ hidden unit. The

output sigmoid activation function is given f ( 𝑛𝑒𝑡𝑝(𝑗))

f ( 𝑛𝑒𝑡𝑝(𝑗)) = ( 1 + 𝑒−𝑛𝑒𝑡𝑝(𝑗))−1

(25)

2. Trigonometric activation function

The 𝑘𝑡ℎ output for the 𝑝𝑡ℎ training pattern is 𝑦𝑝𝑘 and is given by:

𝑦𝑝𝑘 =∑ 𝑤𝑖𝑜(𝑘, 𝑖)𝑁+1𝑖=1 𝑥𝑝(𝑖) + ∑ 𝑤ℎ𝑜(𝑘, 𝑗)

𝑁ℎ𝑖=1 𝑂𝑝(j) where 1 ≤ j ≤ 𝑀 (26)


72

where 𝑤𝑖𝑜(𝑘, 𝑖) denotes the output weight connecting the 𝑖𝑡ℎ input unit to the 𝑘𝑡ℎ output

unit and 𝑤ℎ𝑜(𝑘, 𝑗) denotes the output weight connecting the 𝑗𝑡ℎ hidden unit to the 𝑘𝑡ℎ

output unit. The mapping error for the 𝑝𝑡ℎ pattern is given as:

𝐸𝑝 = ∑ (𝑡𝑝𝑘 − 𝑦𝑝𝑘)2𝑀

𝑘=1 (27)

where 𝑡𝑝𝑘 represents the 𝑘𝑡ℎ element of the 𝑝𝑡ℎ desired output vector. In order to train a

neural network in batch mode, the mapping error for the 𝑘𝑡ℎ output unit is given as:

𝐸(𝑘)= 1

𝑁𝑣 ∑ (𝑡𝑝𝑘 − 𝑦𝑝𝑘)

2𝑁𝑣𝑝=1 (28)

The overall performance of the MLP is determined by the mean square error and is given as:

𝐸 = ∑𝐸(𝑘)

𝑀

𝑘=1

= 1

𝑁𝑣∑𝐸𝑝

𝑁𝑣

𝑘=1

(29)

The basic steps in implementing the MLP learning algorithm is as described below:

i. Initialize the network, with all weights set to random numbers between -1 and +1.

ii. Perform the first training process, and obtain the desired output.

iii. Compare the network with the desired output.

iv. Propagate the error backwards.

(a) Correct the output layer of weights using the following formula.

𝑤ℎ𝑘 = 𝑤ℎ𝑘 + (𝜂𝛿𝑘𝑘ℎ) (30)

where 𝑤ℎ𝑘 is the weight connecting hidden units h with output unit k, η is the learning rate,

𝑘ℎ is the output at hidden unit h. 𝛿𝑘 is given by the following.

𝛿𝑘 = 𝑘0(1 − 𝑘0) ( 𝑡0 − 𝑘0) (31)

where 𝑘0 is the output at node 0 of the output layer, and 𝑡0 is the target output for that node.

(b) Correct the input weights using the following formula.

𝑤𝑝𝑘 = 𝑤ℎ𝑘 + (𝜂𝛿𝑘𝑘ℎ) (32)


73

where 𝑤𝑝𝑘 is the weight connecting node I of the input layer with node h of the hidden layer,

𝑘0 is the input at node I of the input layer, η is the learning rate. 𝛿𝑗 is calculated for and is

given by the expression:

𝛿𝑘 = 𝑘0(1- 𝑘0) ∑ (𝛿𝑘𝑘ℎ)𝑜 (33)

v. Determine the error, by taking the difference of the mean of the expected output and

the actual output obtained.

𝐸𝑟𝑟𝑜𝑟𝑑𝑒𝑡 = √∑ (𝑘0− 𝑘𝑘)

2𝑝𝑛=1

𝑝 (34)

where 𝑝 is the number of units in the output layer.

vi. Repeat from (ii) for each pattern in the training set to complete one epoch.

vii. The training set is randomly selected to prevent influence by the arrangement of data.

viii. Repeat from step (ii) for a set number of epochs, or until the error ceases to change.

3.5.1.3 Levenberg-Marquardt Algorithm (LMA)

The radial basis function and multilayer perceptron use back-propagation for training the

network by employing Levenberg-Marquardt algorithm in the Matlab software function

lm.m. The respective equations (18-29) for the radial basis function and multilayer perceptron

are individually integrated into the Levenberg-Marquardt algorithm for comparative analyses

of the solar photovoltaic array under investigation. The Levenberg-Marquardt algorithm

(LMA) is widely used for many nonlinear inverse applications in solving generic curve fitting

problems. The LMA involves an iteration technique locating the minimum multivariate

function expression as the sum of squares of nonlinear real-valued functions. The LMA is an

algorithm combining the steepest descent and gaussian-newton method, when the obtained

solution is far from the expected solution, the algorithm behaves like a steepest descent

method and is said to be quadratically convergent.

Similarly, when the solution is close to the expected solution, it is considered as a gaussian-

newton method using the trust-region technique. This algorithm is also known as the damped

least-squares (DLS) method. The LMA is more robust than the gaussian-newton algorithm


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(GNA) since it finds a steady and convergence solution far off the final minimum using

iterative techniques [134].

The LMA interpolates between the GNA and the method of gradient descent. Like other

numeric minimization algorithms, the LMA employs an iterative procedure. In other to start a

minimisation process, an initial assumption for the parameter vector, 𝜷 , has to be made and

in cases with only one minimum, a uniform assumption is given as :

The parameter vector is given as 𝜷𝒕 = (1, 1, ……1) (35)

In some other cases with multiple minima, the algorithm converges only if the initial

assumption is very close to the final solution. In each iteration step, the parameter

optimisation vector, 𝜷, is replaced by a new estimate, 𝜷 + 𝜹. To determine the 𝜹, the

functions f(𝑥𝑖 , 𝜷 + 𝜹) are approximated by their linearisations [135]:

𝑓(𝑥𝑖 , 𝜷 + 𝜹) ≈ 𝑓(𝑥𝑖 , 𝜷) + 𝐽𝑖𝜹 (36)

where the Jacobian matrix vector, 𝐽𝑖 = 𝜕𝑓(𝑥𝑖 , 𝜷)

𝜕𝜷 (37)

𝐽𝑖 is the gradient of f with respect to 𝜷.

The sum of squares at minimum is given as S(𝜷), the gradient of S with respect to 𝛿 will be

zero. The above first-order approximation of f(𝑥𝑖 , 𝜷 + 𝜹) gives [135]:

𝑆(𝜷 + 𝜹) ≈ ∑(𝑦𝑖 − 𝑓(𝑥𝑖 , 𝜷) − 𝐽𝑖𝜹)2

𝑚

𝑖=1

(38)

Or in vector notation,

𝑆(𝜷 + 𝜹) ≈ ‖𝑦 − 𝑓(𝜷) − 𝐽𝜹‖2 (39)

Taking the derivative with respect to 𝜹 in (39) and setting the result to zero gives;

(𝐉𝐓𝐉) 𝜹 = 𝐉𝐓 [𝑦 − 𝑓(𝜷)] (40)

This becomes a set of linear equations which can be solved for 𝜹.

where J is the Jacobian matrix whose 𝑖𝑡ℎ row equals 𝐽𝑖, and where f and y are the vectors with

𝑖𝑡ℎ component 𝑓(𝑥𝑖 , 𝜷) and 𝑦𝑖 respectively.

Upon introducing the damped LMA into the above equation, the equation then becomes:


75

(𝐉𝐓𝐉 + 𝜆𝐈) 𝜹 = 𝐉𝐓 [𝑦 − 𝑓(𝜷)] (41)

where I is the identity matrix, giving the increment as, 𝜹, and the estimated parameter

vector, 𝜷. The damping factor, 𝜆 is adjusted at each iteration. If the reduction of S is rapid, a

smaller value is used bringing the LMA closer to the GNA, whereas if the iteration gives

insufficient reduction in the residual, 𝜆 can be increased, giving a step closer to the gradient

descent direction.

Therefore, the gradient of S with respect to 𝜹 = -2 (𝐉𝐓 [𝑦 − 𝑓(𝜷)])𝑇 (42)

For larger values of 𝜆, the inverting 𝐉𝐓𝐉 + 𝜆𝐈 is not used at all; the convergence tends toward

the direction of a small gradient. The identity matrix, I is then replaced with the diagonal

matrix consisting of the diagonal elements of 𝐉𝐓𝐉 , the resulting LMA is given as[135]:

(𝐉𝐓𝐉 + 𝜆𝐝𝐢𝐚𝐠(𝐉𝐓𝐉)) 𝜹 = 𝐉𝐓 [𝑦 − 𝑓(𝜷)] (43)

The Levenberg-Marquardt algorithm is chosen to train the radial basis function and

multilayer perceptron because it is considered as one of the fastest method algorithms for

training moderate-sized feedforward networks. The above LMA equation is used to forecast a

more accurate model using statistical parameters as the mean square error (MSE) and the

newrbe performance on the solar photovoltaic array as presented in the following sections.

3.5.1.4 Model Comparison and Performance

A comparative study of two neural network models is under consideration in this research

using Matlab/Simulink program for the simulation process. Each of the models is validated

based on the established current-voltage (I-V) characteristics mathematical model

implemented by iterative analysis comparing the conventional model and simulated results of

the model. The data sets used for this simulation are divided into training, validation and

verification sets for evaluating the model performance.

The training and validation data applied in each of this model, map the entire characteristics

of the simplest model of the equivalent circuit of a static solar photovoltaic system. In this

research, the training data were obtained from a solar photovoltaic manufacturer data manual.

The photovoltaic manufacturer parameters employed in this comparative study for the

simulation experiments are shown in Table 6. The static solar photovoltaic system under

consideration was constructed by connecting ten cell branches in parallel (np = 10). As each


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branch consists of 40 modules branches (250 cells/module), there are 10,000 cells in total

connected in series (ns = 10,000) on a large scale solar farm.

Table 6. Photovoltaic parameters used in the simulation experiments

Parameter symbol Parameter value

electron charge, q 1.602x10-19C

solar cell voltage, V 24 V

ideality factor, A 1.5

Boltzmann constant, k 1.380658x10-23J/K

series cell resistance,𝑹𝑺 5x10-5Ω

shunt cell resistance, 𝑹𝒔𝒉 2.5x102 Ω

Ambient temperature, 𝑻𝒂 200C

wind speed, 𝒘𝒔 1-20m/s

solar irradiation, S 10-1000W/m2

𝑰𝒐 at reference temperature at 𝑻𝒓 = 301.18K,𝑰𝒐𝒓 19.963x10-5A

band gap energy, 𝑬𝑮 (eV) 2.349x10-19 V

reference temperature, 𝑻𝒓 301.18K

short circuit current at 𝑻𝒓, 𝑰𝒔𝒄𝒓 3.3A

short circuit current temperature coefficient, 𝒌𝒊 0.0017

The experiments were performed using a feedforward neural network, referred to as back

propagation network. The training algorithm used for MLP is the Levenberg-Marquardt

algorithm. The input-output data pair is obtained using the conventional method of solving

the non-linear equations of the solar photovoltaic system. The input temperature (T) values

were determined by varying solar irradiation, S and wind speed, ws respectively. The solar

irradiation, S is varied from 10 up to a maximum of 1000 W/m2 in steps of 10 units, while the

range of wind speed, ws varied from 1 to 20 m/s with an increment step size of 2 units. In

overall, a dataset of 1000 input-output pairs was generated for the model.

The MLP neural network training data set is subdivided into training-validation(testing)-

verification sets. The training set is used for the adjustment of weights during training. The

testing or validation sets are used to decide when to stop training. It is observed that the root

mean square value (RMS) of the training set decreases with successive training iterations, as

the RMS value for the test sets reaches a given point it stops to avoid over training. The

verification sets are independent of the neural network training and is considered to be an

unbiased prediction of the neural network performance on the new data.


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The training set consists of 700 randomly selected samples, the validation and verification

sets contain 150 samples each. The same datasets were utilised for the performance tests of

the two models under comparative study. The tests are repeated ten times (10-fold) randomly

varying selected configurations of the train-validate-verification samples for different output

variables. The output variables determined in the tests are open-circuit voltage, Voc,

maximum power point current, Imp, maximum power point voltage, Vmp and maximum power

point power, Pmp.

For the radial basis function network, 850 samples were used for training and 150 samples for

validation processes. The performance metrics for the neural network were measured using

MSE parameter, the output values for the conventional model and the values reverted from

the trained neural network model were compared and results analysed. The best-achieved

results from the experimental setup for the comparative study of MLP and RBF neural

network models are thus presented.

Table 7 shows the computed values of Voc, Imp, Vmp and Pmp MSEs for the developed MLP

and RBF neural network models. The empirical study results indicate that both the multilayer

perceptron and radial basis function neural networks perform equally well for the chosen

configuration and output variables. The table also captures the summary of the experimental

results for open circuit voltage, Voc, maximum power point current Imp, maximum power

point voltage Vmp, maximum power, Pmp variables.

Table 7. The summary of the experimental results

Voc Imp Vmp Pmp

Fold MLP (MSE) RBF (MSE) MLP (MSE) RBF (MSE) MLP (MSE) RBF (MSE) MLP (MSE) RBF (MSE)

1 0.00008715 0.00007119 0.98802080 0.93788551 0.00005132 0.00005123 0.06727343 0.14547358

2 0.00006543 0.00007054 0.97611720 0.96047902 0.00003266 0.00003109 0.07741213 0.07837277

3 0.00010684 0.00011170 0.99141176 1.00134474 0.00002660 0.00002650 0.07144214 0.07049198

4 0.00005524 0.00005038 0.96216595 0.98113911 0.00003421 0.00003555 0.06712235 0.06657531

5 0.00004662 0.00005126 0.85059415 0.82805230 0.00005355 0.00018918 0.07393173 0.07237029

6 0.00006434 0.00006661 0.93029305 0.93308108 0.00003553 0.00003675 0.07556436 0.07556436

7 0.00005848 0.00007076 0.87119129 0.86286992 0.00004806 0.00009308 0.06438292 0.06402745

8 0.00007778 0.00009539 0.84877927 0.86677969 0.00002949 0.00003476 0.07969165 0.07928457

9 0.00007283 0.00007344 0.86715793 0.93678808 0.00005009 0.00004815 0.06370651 0.06171481

10 0.00008102 0.00035611 0.87662342 0.89666237 0.00003478 0.00004074 0.07571086 0.07608310

Mean 0.0000713 0.00010178 0.91623542 0.92050812 0.00003929 0.00005873 0.07162388 0.07899582

The average MSE for the ten validation tests performance were computed for both MLP and

RBF models. For the MLP model, the average computed MSE for Voc, Imp, Vmp and Pmp values

were found to be 0.0000713, 0.91623542, 0.00003929 and 0.07162388 respectively.


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Likewise, for the RBF model, the average computed MSE for Voc, Imp, Vmp and Pmp values

were found to be 0.00010178, 0.92050812, 0.00005873and 0.07899582 respectively.

The MSE value for the static solar farm photovoltaic systems is comparable to those results

from the MLP and RBF neural network model. The graphical results obtained from the

simulation experiments shows that there is not much difference between the output and the

targets data from a statistical perspective. The correlation coefficient obtained from the

validation datasets for the MLP model is 99%. Likewise, the performance correlation

coefficient for the RBF model was found to be 97.89%.

The performance metrics in the figures below depicts the good performance of the simulated

neural network models, hence it can be effectively implemented in real-life design for solar

photovoltaic systems. Figure 24 presents the graphical results showing the performance of the

Pmp variable for train-validation-test samples for the mean square error from the best

validation performance model. Figure 25 depicts the training state for the MLP model, Figure

26 depicts the training fit for the MLP model, Figure 27 depicts the training error histogram

for the MLP model and Figure 28 depicts the regression performance for the MLP model and

fit performance for the MLP model.

Figure 24. Training performance for MLP model

The training performance for the MLP model as shown in Figure 24 has its validation and

test curve very similar. It can be observed that the test curve was quite moderate with the

validation curve, which clears the doubts of overfitting for the training MLP performance

0 5 10 1510

-2

10-1

100

101

102

103

Best Validation Performance is 0.072628 at epoch 9

Me

an

Sq

ua

red

Err

or

(m

se

)

15 Epochs

Train

Validation

Test

Best


79

model. The best point of intersection for the validation and test curve is determined as the

best validation performance for MLP training model, which was found at 0.072628 traced

along the horizontal axis to the vertical axis of the training performance for the MLP model.

Figure 25. Training state for MLP model

Figure 26. Training fit for MLP model

10-5

100

105

gra

die

nt

Gradient = 0.0042866, at epoch 15

10-10

10-5

100

mu

Mu = 1e-07, at epoch 15

0 5 10 150

5

10

val fa

il

15 Epochs

Validation Checks = 6, at epoch 15

300 350 400 450 5000

2

4

6

8

10

12

Function Fit for Output Element 1

Ou

tpu

t a

nd

Ta

rge

t

-1

0

1

Err

or

Input

Training Targets

Training Outputs

Validation Targets

Validation Outputs

Test Targets

Test Outputs

Errors

Fit

Targets - Outputs


80

Figure 27. Training error histogram for MLP model

Figure 28. Training regression performance for MLP model

The four plots in Figure 28 represents the training, validation, testing data and the overall

training regression performance for the solar photovoltaic array. The dashed line in each

0

10

20

30

40

50

60

70

80

90

100

Error Histogram with 20 Bins

Inst

ance

s

Errors = Targets - Outputs

-0.5

733

-0.5

127

-0.4

521

-0.3

915

-0.3

308

-0.2

702

-0.2

096

-0.1

49

-0.0

8838

-0.0

2776

0.03

286

0.09

348

0.15

41

0.21

47

0.27

53

0.33

59

0.39

66

0.45

72

0.51

78

0.57

84

Training

Validation

Test

Zero Error

2 4 6 8 10

2

4

6

8

10

Target

Out

put ~

= 0.

99*T

arge

t + 0

.023

Training: R=0.99719

Data

Fit

Y = T

2 4 6 8 10

2

4

6

8

10

Target

Out

put ~

= 0.

99*T

arge

t + 0

.042

Validation: R=0.99614

Data

Fit

Y = T

2 4 6 8 10

2

4

6

8

10

Target

Out

put ~

= 1*

Targ

et +

0.0

43

Test: R=0.9959

Data

Fit

Y = T

2 4 6 8 10

2

4

6

8

10

Target

Out

put ~

= 0.

99*T

arge

t + 0

.028

All: R=0.99685

Data

Fit

Y = T


81

represents the perfect results – outputs = targets. The solid line represents the best fit linear

regression line between the output and targets. The R-value is an indication of the

relationship between the output and targets. From the MLP training performance for the solar

photovoltaic array, the training, validating and testing indicates a good fit, because the R-

values obtained are close to 1, implying that there exists an exact relationship between the

outputs and targets.

Figure 29 represents the graphical results showing the training phase of Pmp variable for train-

validation-test samples for the RBF model. It is observed from the RBF training window, that

the RBF model shows convergence which indicates that the error goal is reached.

Figure 29. RBF Training Window

3.5.2 Sparse Based Algorithm

The sparse based algorithm utilised in this research is employed to evaluate the comparative

performance of the smart static solar photovoltaic systems. The performance evaluation is

carried out using the regression modelling techniques to predict on a very large scale, the best

suitable model in determining the efficiency and reliability performance for the solar

photovoltaic systems. It is also used in the determination of the maximum power point errors

for the smart static solar photovoltaic systems.

The calibration parameters and coefficients used for the performance evaluation in this

research investigation are the mean square error, (MSE), root mean square error, (RMSE) and

the standard deviation. The regression concept model theory and the three regression models


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considered under this comparative research investigation are briefly introduced and discussed

in the following sub-sections 3.5.2.1, 3.5.2.2, 3.5.2.3 and 3.5.2.4 respectively.

3.5.2.1 Regression Concept and Theory

Regression is one of the most commonly used statistical techniques applied in various

research fields. The regression tool is suitable for analysing, predicting, forecasting,

investigating, hypothesis testing and modelling the relationship between a scalar dependent

variable and an independent variable [136, 137]. The regression analysis tries to fit a model

to one dependent variable based on one or more independent variables. One of the most

common regression models is the simple linear regression model. Simple linear regression is

a statistical method providing a result between two quantitative variables.

The linear regression concept assumes a linear relationship between an independent variable

(predictor) and a dependent variable (response). The linear relationship is represented by a

regression straight line fitting through the set of points in such a way making the sum of the

squared residuals of the model to have the smallest possible error. The best fitting line is

known as the regression line. There are a lot of methods in determining the best-fit line, one

of the methods considered for this research investigation is termed the least square method.

Multi-linear regression exhibits linear characteristics equation with two or more predictor

variables. Non-linear regression depends on multiple independent variables modelled by non-

linear functional combination model parameters.

The characteristics of a good regression model possesses a high regression 𝐑 - value fairly

close to unity [138]. This regression model predicts the best fitting line for the data and

overall summary of the model performance [136]. The plotting of residuals is a tool used in

checking the adequacies of fitted multiple linear regressions based on determined standard

deviation. The data used for analysis covers the entire range of response values for analysis

and prediction.

The simple linear regressions are classified into three groups namely linear, quadratic and

cubic [139];

Linear: 𝒀𝑳 = 𝑎0 + 𝑎1x

Quadratic: 𝒀𝑸 = 𝑎0 + 𝑎1𝑥1 + 𝑎2𝑥2

Cubic: 𝒀𝑪 = 𝑎0 + 𝑎1𝑥1 + 𝑎2𝑥2 + 𝑎3𝑥3

(44)


83

The linear parameters 𝑎0 and 𝑎1 represent the y-intercept and the slope of the equation

respectively.

The multi-linear regression model performs linear and non-linear regressions functions with

two or more independent variables. The multi-linear regression model is classified into two

groups namely, multiple and involving interactions [139];

Multiple: 𝒀𝑴 = 𝑎0 + 𝑎1𝑥1 + 𝑎2𝑥2 + 𝑎3𝑥3

Involving interactions: 𝒀𝑰 = 𝑎0 + 𝑎1𝑥1 + 𝑎2𝑥2 + 𝑎3𝑥1𝑥2 (45)

The non-linear regression model assumes any type of relationship between the dependent

variable and independent variables. The model function uses the least squares approach for

computing the regression. The regression model is classified into two groups namely sine

wave and exponential [139];

Sine Waves: 𝒀𝑺 = 𝑎0 + sin(𝑎1𝑥1)

Exponential: 𝒀𝑬 = 𝑎0 + 𝑒(𝑎1/𝑥1) (46)

3.5.2.2. Regression-type Model

The regression algorithm model considered in the estimation technique of the static solar

photovoltaic module is a sparsely based regression algorithm. The sparsely based algorithm

has established itself among the state of the art algorithm in supervised learning. It learns

classifiers constructed as weighted linear combinations of basis functions. The weights are

estimated in the presence of the training data selected either significantly large or exactly zero

which necessarily removes irrelevant basis functions.

The sparsely based regression algorithm is embedded into our previous Levenberg-Marquardt

algorithm neural network training in subsection 3.5.1.4 [140]. The primary emphasis of the

introduction of the sparsely based algorithm was based on its flexibility and efficiency

performance. The sparsely based algorithm incorporates an iterative linear system solver for

minimising the number of iterations for the model.

Considering a data matrix P and a column vector function k, the optimisation problem is

solved by obtaining a weight of vector w of variables for a sparse based algorithm [141, 142].

𝑚𝑖𝑛‖𝑤‖1, s. t. 𝐏𝒘 = 𝒌 (47)


84

where 1-norm ‖𝑤‖1 is defined as ∑ |𝑤𝑖|𝑀𝑖=1

The optimal solution of equation (47) is denoted by 𝒘𝒐. The absolute value for each entry of

𝒘𝒐 reflects the contribution of its corresponding variable to the regression between the data

matrix P and column vector function k.

where k 𝜖 𝑅𝑁 is a given signal vector and P 𝜖 𝑅𝑁∗𝑀 (N <M) is a basis matrix.

The objective of the sparsely based algorithm is to find a solution w 𝜖 𝑅𝑀 for equation (47).

The assumption for the sparsely based algorithm is set for the non-negatives as [141, 142];

Setting w = u – v , where u = [𝑢1, …… . , 𝑢𝑘0] 𝑇 , v = [𝑣1, …… . , 𝑣𝑘0]

𝑇 𝜖 𝑅𝑀 are non-

negatives

The non-negative expressions can be converted to equivalent linear solvable programming

problems using the Matlab optimisation toolbox [141, 142].

𝑚𝑖𝑛∑(𝑢𝑖 + 𝑣𝑖)

𝑘0

𝑖=1

, s. t. [𝑷, − 𝑷][𝑢𝑇 , 𝑣𝑇]𝑇 = 𝒌, u, v ≥ 0 (48)

The sparse weight identifies the relevant variables or the supposed regression vectors. The

sparsely based algorithm is categorised into two correlations: time series correlated with the

output and time series not significantly correlated with output. There are quite a few

parameter estimators developed in linear regression differing in the simplicity of the

algorithm, robustness in heavy-tailed distributions, theoretical assumptions and close form

solutions to validate asymptotic efficiency and consistency [141, 142].

A brief review of three regression estimation techniques under assessment in this research

investigation employed in the simulation and modelling of the static solar photovoltaic

module using the sparse based algorithm are described in the following sub-sections.

3.5.2.3. Ordinary Least Squares Regression

The ordinary least squares (OLS) is also referred to as linear least squares. This regression

estimator method is applied to analyse both experimental and observational data in the

estimation of unknown parameters in a linear regression model. The OLS minimises the sum

of squared residuals between the observed and predicted responses from the datasets by linear

approximation. Several assumptions occur in OLS to validate predicted and the estimated

model.


85

The residual is determined from the difference between the predicted and the real data; when

a large distortion occurs it is referred to as outliers. These outliers influence the error

variance, the standard deviation and the final estimation to become asymptotically

inconsistent. One of the several assumptions generated is the normality of the residuals along

the parallel line and the other is ensuring the normality of the residuals make the estimation

of significance impaired. In the OLS regression model, it is primarily assumed that there is

zero or negligible errors in the independent variables [143, 144].

Considering a data consisting of n observations [𝑦𝑖, 𝑥𝑖]𝑖=1𝑛 . Each observation includes a scalar

response 𝑦𝑖 and vector p predictors 𝑥𝑖. In a linear regression model the response variable is a

linear function of the regressors:

𝑦𝑖 = 𝑥𝑖𝑇𝛽 + 휀𝑖

where 𝛽 is a px1vector of unknown parameters; 휀𝑖’s are unobserved scalar random variables

which account for discrepancy between the actually observed responses 𝑦𝑖 and the predicted

outcomes 𝑥𝑖𝑇𝛽 and 𝑇 denotes the matrix transpose, so that 𝑥𝑇𝛽 is the dot product between

the vectors x and 𝛽. This model can be written in matrix notation as [143, 144]:

y = X 𝛽 + 휀 (49)

where y and 휀 are nx1 vectors, and X is an n x p matrix of regressors, known as design

matrix.

In the ordinary least squares estimation, an assumption is considered in the determination of

the sum of residuals for the measure of the overall model fit. A b-value is considered for

parameter 𝛽. The quantity 𝑦𝑖 − 𝑥𝑖𝑇𝑏 is called the residual for the i-th observation measuring

the vertical distance between the data point (𝑥𝑖 , 𝑦𝑖), and the hyper plane y = 𝑥𝑖𝑇𝑏 .

The sum squared error is a measure of the overall model fit given by [143, 144]:

𝑺(𝑏) = ∑(𝑦𝑖 − 𝑥𝑖𝑇𝑏)2

n

i=1

= (𝑦 − 𝑿𝑏)𝑇(𝑦 − 𝑿𝑏) (50)

T in the above equation denotes the matrix transpose. The value of 𝑏 minimises this sum

called the OLS estimator for 𝛽. The function possess a global minimum at b = 𝛽 and the

expression for the estimated unknown parameter 𝛽:


86

𝛽 = (𝑿𝑇𝑿)−1𝑿𝑇𝑦 (51)

Or equivalently the explicit expression for the estimated unknown parameter 𝛽 is given by:

𝛽 = (1

n∑xixi

′

n

i=1

)

−1

.1

n ∑xi

n

i=1

yi (52)

The predicted value from the regression is given by the expression:

�̂� = 𝑿�̂� = 𝑨𝑦 (53)

where A =(𝑿𝑇𝑿)−1𝑿𝑇 is the projection matrix. The residual from the regression is given by:

�̂� = 𝑦 − 𝑿�̂� (54)

A simple linear regression model containing two variables, a constant and a scalar

regressor, 𝑿 is given in equation (55). The vector parameters in the model is two-dimensional

and denoted by 𝛽0, 𝛽1 respectively;

𝑌 = 𝛽0𝑿 + 𝛽1 (55)

𝛽1 =(∑ 𝑌𝑖

𝑁𝑖=1 )(∑ 𝑿𝑖

𝑁𝑖=1 ) − (∑ 𝑿𝑖

𝑁𝑖=1 )(∑ 𝑿𝑖𝑌𝑖

𝑁𝑖=1 )

𝑁 ∑ 𝑿2𝑖𝑛𝑖=1 − (∑ 𝑋𝑖

𝑛𝑖=1 )2

(56)

𝛽0 =𝑁∑ 𝑿𝑖𝑌𝑖

𝑁𝑖=1 − (∑ 𝑿𝑖

𝑁𝑖=1 )(∑ 𝑌𝑖

𝑁𝑖=1 )

𝑁∑ 𝑿2𝑖𝑁𝑖=1 − (∑ 𝑿𝑖

𝑁𝑖=1 )2

(57)

The correlation coefficient, r and the standard deviation, S-expressions for the simple linear

regression are given by the following equations respectively:

𝒓 =

𝑁∑ 𝑿𝑖𝑌𝑖𝑁𝑖=1 − (∑ 𝑿𝑖

𝑁𝑖=1 )(∑ 𝑌𝑖

𝑁𝑖=1 )

√[𝑁 ∑ 𝑿2𝑖𝑁𝑖=1 − (∑ 𝑿𝑖

𝑁𝑖=1 )2][𝑁 ∑ 𝑌2𝑖

𝑁𝑖=1 − (∑ 𝑌𝑖

𝑁𝑖=1 )2]

(58)

𝒔 = √∑ 𝑌2𝑖𝑁𝑖=1 − 𝛽1∑ 𝑌𝑖

𝑁𝑖=1 − 𝛽0 ∑ 𝑿𝑖𝑌𝑖

𝑁𝑖=1

𝑁 (59)

The respective equations (49-59) of the ordinary least squares are employed in the simulation

and computational regression experiments in sub-section 3.5.2.6 and the results presented in

Tables 7 and 8 respectively.


87

3.5.2.4. Robust Fit Regression

The robust fit regression is an advanced statistical technique developed to overcome the

influence of outliers. This regression type enhances provision for resistant results in the

presence of outliers in order to achieve the expected stability. The robust fit regression

approach employs a fitting criterion not as vulnerable as the least squares to unusual data.

The robust regression is basically resolved to address these three key challenges:

I. Solving problems with outliers in the y-direction.

II. Solving problems with multivariate outliers in the covariant space (x-space).

III. Solving problems with outliers in both y-direction and the x-space.

The robustness of a data is measured by two criteria, the first is the breakdown point and the

second is the influence curve. The breakdown point of an estimate is the smallest fraction of

the data damped by an arbitrarily large amount causing an arbitrarily large change in the

estimate. The influence curve for a statistical function measures how much an individual

observation changes the value of the estimator. It measures the dependence of the estimator

on the values of each of the points in the sample. The theoretical background for the robust

estimates is described as follows [145]:

Let X = (𝑥𝑖𝑗) denote an n x p matrix, y = (𝑦1, ………𝑦𝑛)𝑇 a given n-vector of responses, and

θ = (𝜃𝑖 …………𝜃𝑝)𝑇 an unknown p-vector of parameters or coefficients whose components

have to be estimated. The matrix X is called a design matrix.

Considering the normal linear model;

𝑦 = 𝑿𝜃 + 𝑒 (60)

where e = (𝑒1……… . 𝑒𝑛)𝑇 is an n-vector of unknown errors. It is assumed that (for given X)

the components 𝑒𝑖 of e are independent and identically distributed according to a distribution

L(./𝜎), where 𝜹 is a scale parameter (usually unknown). Often L(./𝜎) = Ф (.), the standard

normal distribution with density is given as [145] :

𝜙(𝑠) = 1

√2𝜋𝑒(−𝑠2

2⁄ ) (61)


88

The robust distance uses the robust multivariate location and scatter estimates for leverage-

point detection, defined as [145]:

𝑅𝑑(𝑥𝑖) = [(𝑥𝑖 − 𝑇(𝑋))𝑇𝐶(𝑋)−1(𝑋𝑖 − 𝑇(𝑋))]

1/2

(62)

where 𝑇(𝑋) and C(𝑋) are the robust location and scatter matrix for the multivariates. The

leverage points of robust fit is a measure of how far an independent variable deviates from its

mean. High leverage points can have a great amount of effect on the estimate of regression

coefficients. In determining the high leverage points the following assumptions are made

[145]:

Let 𝐶(𝑝) = √𝑥𝑝;1−𝛼2 be the cut − off value (63)

Hence, the leverage variable is defined as:

Leverage = { 0 𝑖𝑓 𝑅𝑑 (𝑥𝑖) ≤ 𝐶(𝑝)

1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (64)

The outliers response for the robust regression residuals 𝑟𝑖 , i =1,……., n is detected based on

the robust estimates 𝜎. Therefore, the variable outlier is defined as;

Outlier = { 0 𝑖𝑓 |𝑟| ≤ 𝑘𝜎1 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(65)

where k denotes the observation which constitutes the outliers

The robust measure of goodness of fit and model selection is defined by the expression as:

𝑅2 = ∑𝜌

(𝑦𝑖−𝜇)

𝑠−∑𝜌

(𝑦𝑖−𝑥𝑖𝑇𝜃)

𝑠

∑𝜌(𝑦𝑖−𝜇)

𝑠

(66)

where 𝜌 is the objective function for the robust estimate, 𝜃 is the high breakdown value

estimate, 𝜇 is the robust location estimator, and s is the robust scale estimator in the full

model. The robust deviance, D is defined as the optimal value of the objective function on the

𝜎2- scale:

𝐷 = 2(𝑠)2∑𝜌(𝑦𝑖 − 𝑥𝑖

𝑇𝜃

𝑠) (67)


89

There are a few known robust estimators such as least mean squares (LMS), least trimmed

squares (LTS), M-estimators, S-estimators and many others. The LMS and LTS have

breakdown points of zero. The introduction of weight functions on the influence curve result

in estimators bounded influence or generalised M-estimators (GM-estimators).

The significance of the weight function is to reduce the impact of a high leverage point

resulting in an increased efficiency of the estimate. The weight function is chosen most

frequently to minimise the asymptotic variance of the estimators. This leads to weights of the

form, for matrix A.

𝑊(𝑥) = ‖Ax‖−1 (68)

Often, the breakdown points for these estimates is better than the M-estimate, but it cannot

exceed 1 ⁄ 𝑝 , where p is the rank of X.

The higher the breakdown point of an estimator, the more robust performance is achieved.

The weighting functions provided in the robust fit Matlab software application gives a

coefficient estimates that is approximately 95% and is statistically regarded as efficient for

the OLS estimates, provided the response has a normal distribution with outliers. This

fundamental principle applies to the overall output efficiency. As the tuning constant

decreases, the weight function increases and vice-versa [146-148].

3.5.2.5. Least Trimmed Squares

The least trimmed squares (LTS) is a robust statistical technique for estimation of unknown

parameters of a linear regression model and provides a robust alternative to classical

regression method based on minimising the sum of squared residuals [149]. The LTS is

considered as one of the most efficient regression estimators. The LTS fits a function to a set

of data and is unduly affected by the presence of outliers. The LTS estimator belongs to the

class of affine-equivariant estimators converging at √𝑛 with the same asymptotic efficiency

under normal conditions.

The LTS has received a lot of attention for its strong consistency, sensitivity analysis,

asymptotic distributions, small-sample corrections, bootstrap and computational methods.

The LTS in non-linear regression model (i = 1,….., n) is defined by [150]:

𝑦𝑖 = (xi,𝜷′) + 휀𝑖 (69)


90

where 𝑦𝑖 represents the dependent variable, (xi,𝜷′) is a regression function, and 𝜷′ ∈ Rp

denotes the underlying parameter value. The vector 𝜷 of the unknown parameters is assumed

to belong to a parametric space S ⊆ Rp. Therefore, the nonlinear least trimmed squares

estimator 𝜷(𝑙𝑡𝑠,ℎ,𝑛) is defined by the expression [150]:

𝜷(𝑙𝑡𝑠,ℎ,𝑛) = argmin∑ 𝑟2(𝑖)(𝜷)h

i=1 (70)

= argmin∑ 𝑟2(𝑖)(𝜷)n

i=1𝐴 = 𝜋𝑟2{𝑟2(𝑖)(𝜷) ≤ 𝑟2ℎ(𝜷)} (71)

where 𝑟2(𝑖)(𝜷) represents the ordered absolute residuals 𝑟2(𝑖)(𝜷)= (y𝑖 − ℎ (𝑥𝑖 , 𝜷))2. The

trimming constant, h must satisfy n/2< ℎ ≤n and determines the breakdown point of the LTS

estimator implies that n→h observations with the largest residuals do not affect the estimator.

The choice of the trimming constant, h vary with the sample size n.

However, the least trimmed squares estimator achieves robustness by trimming away

observations with large residuals. The assumed standard regression model is given as [151]:

𝑦𝑖 = 𝑥𝑖′𝜷 + 휀𝑖 (72)

where y = (𝑦𝑖 …… . 𝑦𝑛)′ be the response and X = (𝑥𝑖𝑗)1≤𝑛,1≤𝑗≤𝑝 the matrix of predictor

variables, where n denotes the number of observations and p the number of variables. The

regression parameter is denoted by 𝜷 = (𝛽1, ………𝛽𝑝)′ and the error terms ε𝑖 have zero

expected value. The penalty parameter, λ is introduced, the least absolute shrinking operator

and selector operator of 𝜷 is given as [150];

𝜷 = 𝑎𝑟𝑔𝑚𝑖𝑛∑ ( yi − 𝑥𝑖′𝛽 )2𝑛

𝑖=1 + n λ∑ |𝛽𝑗|𝑝𝑗=1 (73)

The 𝐿1 penalty allows some coefficients to shrink to zero. The LTS estimator is quite fast to

compute and is one of the most popular robust regression estimator. The vector squared

residuals is denoted by the expression:

𝑟2(𝜷) = ( 𝑟12, …………𝑟𝑛

2) (74)

with 𝑟𝑖2 = ( yi − 𝑥𝑖′𝜷 )

2, i=1,………,n.


91

The LTS estimator, 𝜷𝐿𝑇𝑆 is defined by the expression as [151]:

𝜷𝐿𝑇𝑆 = 𝑎𝑟𝑔𝑚𝑖𝑛 ∑( 𝑟2(𝛽))𝑖:𝑛

ℎ

𝑖=1

, (74)

where ( 𝑟2(𝜷))𝑖:𝑛 ≤………≤ ( 𝑟2(𝜷))𝑛:𝑛 is the order statistic of the squared residuals and h

≤ 𝑛.

A regularised sparse version of the LTS is obtained by adding an 𝐿1 penalty with the penalty

parameter, λ to give the sparse LTS estimator, 𝛽𝑠𝑝𝑎𝑟𝑠𝑒𝐿𝑇𝑆 [151].

𝛽𝑠𝑝𝑎𝑟𝑠𝑒𝐿𝑇𝑆 = 𝑎𝑟𝑔𝑚𝑖𝑛 ∑( 𝑟2(𝜷))𝑖:𝑛

ℎ

𝑖=1

+ ℎ λ ∑|𝜷𝒋|

𝑝

𝑗=1

(75)

The sparse LTS has a high breakdown point resistant to multiple regression outliers and

leverage points. The sparse LTS is efficiently robust compared to the other estimators based

on these following factors [151]:

(i) The prediction performance is much improved through variance reduction relative

to the data size.

(ii) The provision of simultaneous model selection leads to higher interpretability.

(iii) The exclusion of computational probability for traditional robust regression

methods.

It is observed from equation (76) when h = n it yields a lasso solution. The least absolute

deviation (LAD) type of estimator called LAD-lasso, 𝛽𝐿𝐴𝐷−𝑙𝑎𝑠𝑠𝑜 is given as [151]:

𝛽𝐿𝐴𝐷−𝑙𝑎𝑠𝑠𝑜 = 𝑎𝑟𝑔𝑚𝑖𝑛 ∑ | yi − 𝑥𝑖′𝜷|𝑛𝑖=1 + n λ ∑ |𝜷𝑗|

𝑝𝑗=1 (76)

The breakdown point of the sparse LTS estimator is also known as the replacement finite

simple breakdown point, and is given as [151]:

Let 𝒛 = (X, y) (77)

For a regression estimator 𝜷, the breakdown point is defined as [151]

ε∗(𝜷; 𝒛) = min {𝑚

𝑛: �̃�𝑠𝑢𝑝 ‖𝜷(�̃�)‖2 = ∞} (78)


92

where 𝒛 is the computed data obtained from �̃� by replacing m of the original n-data points by

arbitrary values.

For a fixed penalty parameter λ, the objective function is defined as:

Q(H, 𝛽) = ∑( yi − 𝑥𝑖′𝛽 )2

𝑖∈𝐻

+ ℎ𝜆∑|𝛽𝑗|

𝑝

𝑗=1

(79)

The 𝐿1 penalized sum of squares based on the assumption is given as:

H ⊆ (1,……………,n) with |𝐻|=h

𝛽𝐻 = 𝑎𝑟𝑔𝑚𝑖𝑛𝑄 (𝐻, 𝛽𝐻) (80)

Furthermore, to increase the efficiency a reweighting step is introduced which weighs down

the outliers detected by the sparse LTS. The sparse LTS estimator is known to be biased,

therefore, we need to determine the centre of residuals. A natural estimate for the center of

the residuals is given as [151]:

𝜇𝑟𝑎𝑤 = 1

ℎ∑ 𝑟𝑖𝑖∈𝐻𝑜𝑝𝑡 (81)

where 𝑟𝑖 = yi − 𝑥𝑖′𝛽𝑠𝑝𝑎𝑟𝑠𝑒𝐿𝑇𝑆 and 𝐻𝑜𝑝𝑡 is the optimal subset from (81). Therefore, the

residual scale estimate associated to the raw sparse LTS estimator is given by:

𝜎𝑟𝑎𝑤 = 𝑘𝛼√1

ℎ∑ (𝑟𝑐

2)𝑖:𝑛ℎ𝑖=1 (82)

where 𝜎𝑟𝑎𝑤 is a consistent estimate of the standard deviation at the normal model.

The squared central residuals 𝑟𝑖2= ((𝑟1 − 𝜇𝑟𝑎𝑤 )

2,………… (𝑟𝑛 − 𝜇𝑟𝑎𝑤 )2)′, and

𝑘𝛼= (1

𝛼∫ 𝑢2𝛷−1 (

𝛼+1

2)

−𝛷−1(𝛼+1

2)

𝑑Φ(𝑢))

−1 2⁄

(83)

The binary weights are defined by this formulation:

𝑤𝑖 = {1, 𝑖𝑓 |(𝑟𝑖 − 𝜇𝑟𝑎𝑤 )/𝜎𝑟𝑎𝑤| ≤ 𝛷

−1(1 − 𝛿),

0, 𝑖𝑓 |(𝑟𝑖 − 𝜇𝑟𝑎𝑤 )/𝜎𝑟𝑎𝑤| > 𝛷−1(1 − 𝛿),

𝑖 = 1,…… , 𝑛 (84)


93

The reweighted sparse LTS estimator is given by the weighted lasso fit as [151];

𝛽𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 = argmin∑ 𝑤𝑖( yi − 𝑥𝑖′𝛽 )2𝑛

𝑖=1 + 𝑛𝑤 λ∑ |𝛽𝑗|𝑝𝑗=1 (85)

with 𝑛𝑤 = ∑ 𝑤𝑖𝑛𝑖=1 is the sum of the weights.

Considering other weighting schemes, the residual center estimates is given as [151];

𝜇𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 = 1

𝑛𝑤∑ 𝑤𝑖( yi − 𝑥𝑖′𝛽𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 )𝑛𝑖=1 (86)

Therefore, the residual scale estimate of the re-weighted sparse LTS estimator is given as

[151];

𝜎𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 = 𝑘𝛼𝑤√1

𝑛𝑤∑ 𝑤𝑖( yi − 𝑥𝑖′𝛽𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑 − 𝜇𝑟𝑒𝑤𝑒𝑖𝑔ℎ𝑡𝑒𝑑)

2𝑛𝑖=1 (87)

where 𝑘𝛼𝑤is the consistency factor from 𝑘𝛼 with 𝛼𝑤 = 𝑛𝑤/𝑛

The objective of the sparse model estimation is to improve performance prediction using

estimators to determine the root mean squared prediction error (RMSPE). The respective

sampling data without outliers is generated as test data for each simulation experiment. The

RMSPE is given as;

RMSPE (𝛽) = √1

𝑛∑(𝑦𝑖

∗ − 𝑥𝑖∗′𝛽)2

𝑛

𝑖=1

(88)

where 𝑦𝑖∗ and 𝑥𝑖

∗′, i = 1,………,n, denotes the observation of the response and predictor

variables in the test data, respectively.

3.5.2.6. Computational Regression Experiments

The regression model performance is achieved by employing the Levenberg-Marquardt

algorithm in the neural network training in section 3.5.1.4 to solve the nonlinear and implicit

equation of the solar photovoltaic array. The input parameters for the experimental setup

were obtained by varying the solar radiation, S and wind speed, ws, to obtain a new

temperature value, T. The solar radiation, S is increased in steps of 10 units from 10 to

maximum of 1000 W/m2 and the wind speed increased in steps of 2 units from 1 to maximum

of 20 m/s2.


94

A data set of 1000 input-output pairs is generated for the experimental setup. The

experimental data set is subdivided into three categories. The data categories are training,

validation and test data sets. For the experiment, 70% of the total samples randomly were

used for our training set, 15% of the remaining samples were used for validation and test

respectively. A tenfold cross-validation procedure is used for training and testing the solar

photovoltaic array model.

The comparative study performance of the proposed regression estimation algorithm has the

least square loss L1 – norm regularisation and L2 – norm regularisation parameters employed

in solving the non-linear equation of the solar photovoltaic array.

min12‖𝐴𝑋 − 𝑌‖ + 1

2λ1‖𝑋‖2

2 +λ2‖𝑋‖1 (89)

A- Matrix of size m x n

Y - Response vector (of size m x 1)

λ 1- 𝐿1 norm regularization parameter (λ 1 ≥0)

λ 2 - 𝐿2 norm regularization parameter (λ 2= 0)

Output parameters

X - Co-efficient Solution

funVal- Function value during iterations

The maximum number of iterations used during the experiments is 100. The expected

maximum output characteristics for the solar photovoltaic array for the regression models

maximum power current, 𝐼𝑚𝑝 , maximum power voltage, 𝑉𝑚𝑝 and maximum power, 𝑃𝑚𝑝

were obtained respectively.

The performance of the proposed regression estimation techniques on the static solar

photovoltaic array is implemented using the sparse based regression algorithm to compare

three different models. The three regression models under comparison are the ordinary least

squares (OLS), robust fit and least trimmed squares (LTS). The reported performance is

based on two benchmarks; the mean square error (MSE) and root mean squared error

(RMSE). The maximum number of iterations is set at 100 for the experiment while the

dimension for each regression input is 910. The values for temperatures are randomly

obtained from the corresponding solar irradiance, S and wind speed, 𝑤𝑠 given as:

𝑇 = 3.12 + 0.25𝑆 + 0.899𝑇𝑎 − 1.3𝑤𝑠 + 273 (90)


95

The evaluation for the regression method is obtained by a simple linear regression equation

providing corresponding 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 values versus solar irradiance, S respectively. The

dispersion diagram for the OLS 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 versus solar irradiance, S are as shown in

Figure 30, Figure 31 and Figure 32 respectively. The regression standard error estimate

values are 0.96015, 0.0047247, 0.96587 for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 respectively. The standard

estimate value for 𝑉𝑚𝑝 in the linear OLS is not exact due to the presence of unfiltered outliers.

The obtained equation for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 from the OLS regression model is given as:

{

𝑃𝑚𝑝 = −26.9195 + 0.0849𝑆

𝑉𝑚𝑝 = −0.1823 + 0.0015𝑆

𝐼𝑚𝑝 = −37.7989 + 0.1320𝑆 (91)

and the mean square error (MSE) and root mean squared error (RMSE) for 𝑃𝑚𝑝 are 0.9219

and 0.9602 respectively; the MSE and RMSE for 𝑉𝑚𝑝 are 2.232 x 10−5 and 0.0047

respectively; and the MSE and RMSE for 𝐼𝑚𝑝 are 0.9329 and 0.9659 respectively.

The dispersion diagram for the logistic robust fit regression method for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝

versus solar irradiance, S are shown in Figure 33, Figure 34, and Figure 35 respectively. The

regression standard error estimate values are 0.96134, 0.004774, 0.96593 for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and

𝐼𝑚𝑝 respectively. The standard error estimate value for 𝑉𝑚𝑝, in the Logistic robustfit is not

exact due to the presence of unfiltered outliers.

The obtained equations for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 from the logistic robustfit regression model is

given as:

{

𝑃𝑚𝑝 = −26.9941 + 0.0850𝑆

𝑉𝑚𝑝 = −0.01780 + 0.0015𝑆

𝐼𝑚𝑝 = −37.7299 + 0.1318𝑆 (92)

and the MSE and RMSE for 𝑃𝑚𝑝 are 0.9242 and 0.9613 respectively; the MSE and RMSE for

𝑉𝑚𝑝 are 2.2824 x 10−5 and 0.0048 respectively; and MSE and RMSE for 𝐼𝑚𝑝 are 0.9330 and

0.9659 respectively.

The LTS regression standard error estimate values is 0.9871, 0.47638, 0.41815 for 𝑃𝑚𝑝, 𝑉𝑚𝑝

and 𝐼𝑚𝑝 respectively. The standard estimate value for 𝑉𝑚𝑝 in the LTS is not exact due to the

presence of unfiltered outliers.


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The obtained equation for 𝑃𝑚𝑝, 𝑉𝑚𝑝 and 𝐼𝑚𝑝 from the LTS regression model is given as:

{

𝑃𝑚𝑝 = −0.0296 + 0.0849𝑆

𝑉𝑚𝑝 = −0.0002 + 0.0015𝑆

𝐼𝑚𝑝 = −0.0415 + 0.1320𝑆 (93)

and the MSE and RMSE for 𝑃𝑚𝑝 are 0.9756 and 0.9877 respectively; the MSE and RMSE for

𝑉𝑚𝑝 are 0.2286 and 0.4764 respectively; and the MSE and RMSE for 𝐼𝑚𝑝 are 0.1749 and

0.4182 respectively.

The performance evaluation comparison for the standard deviation for the static solar

photovoltaic array for the regression methods results is presented in Table 8. The

experimental results show that the 𝑃𝑚𝑝 standard deviation is relatively comparable. The 𝑉𝑚𝑝

standard deviation is relatively low compared to 𝑃𝑚𝑝 and 𝐼𝑚𝑝 respectively. Likewise, the 𝐼𝑚𝑝

standard deviation results for the OLS and logistic robustfit are better than the LTS obtained

from the experiment.

Table 8. Comparison of standard deviation of the static solar photovoltaic module

Regression

methods 𝑷𝒎𝒑 𝑽𝒎𝒑 𝑰𝒎𝒑

OLS 0.96015 0.0047247 0.96587

Logistic robustfit 0.96134 0.004774 0.96593

LTS 0.9871 0.47638 0.41815

Table 9. Comparison of the MSE and RMSE regression methods of the static solar photovoltaic

module

Benchmark

OLS Logistic Robustfit LTS

𝑃𝑚𝑝 𝑉𝑚𝑝 𝐼𝑚𝑝 𝑃𝑚𝑝 𝑉𝑚𝑝 𝐼𝑚𝑝 𝑃𝑚𝑝 𝑉𝑚𝑝 𝐼𝑚𝑝

MSE 0.9219 2.232e−5 0.9329 0.9242 2.2824e−5 0.9330 0.9756 0.2286 0.1749

RMSE 0.9602 0.0047 0.9659 0.9613 0.0048 0.9659 0.9877 0.4764 0.4182

Table 9. presents the comparison of the MSE and RMSE of the static solar photovoltaic

module results of the regression methods. From the experimental results, the 𝑃𝑚𝑝 , MSE and

RMSE are relatively comparable. The 𝑉𝑚𝑝 standard error estimate is relatively low compared

to 𝑃𝑚𝑝 and 𝐼𝑚𝑝 respectively. Finally, the 𝐼𝑚𝑝 MSE and RMSE results for the OLS and

logistic robustfit are better than the LTS obtained from the experiment. The 𝑉𝑚𝑝


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characteristics have not been reported in related literature due to the fact of the low values

obtained.

Figure 30. Dispersion diagram of 𝑷𝒎𝒑 vs. S

Figure 31. Dispersion diagram of 𝑽𝒎𝒑 vs. S


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Figure 32. Dispersion diagram of 𝑰𝒎𝒑 vs. S

Figure 33. Dispersion diagram of 𝑽𝒎𝒑 vs. S


99

Figure 34. Dispersion diagram of 𝑷𝒎𝒑 vs. S

Figure 35. Dispersion diagram of 𝑰𝒎𝒑 vs. S


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3.6 Conclusion

A broad expository of the two proposed simulation algorithms employed on smart static solar

photovoltaic arrays has been presented in this chapter. It also provides the context and

background of the neural network and sparsed based algorithms, a detailed understanding of

the concept of the comparative measures determining the optimisation efficiency of the solar

photovoltaic module.

This chapter highlights the significance of modelling and simulation algorithms on smart

static solar photovoltaic systems and the achieved results from the proposed algorithms. In

light of these gaps, as outlined in chapter 1, the questions guiding the optimisation modelling

and simulation of the solar photovoltaic module have been answered in this chapter. The

following chapter (chapter 4) describes the analytical and theoretical derivations for dynamic

solar tracking systems and the simulink design implementation for the smart solar

photovoltaic array model.


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Chapter 4 Astronomical and Analytical Derivation for Solar

Photovoltaic Tracking Systems

4.1 Introduction

This chapter describes the astronomy, analytical derivations and simulink modelling

approach for smart solar photovoltaic systems. In particular, the diurnal and seasonal earth’s

revolution is explicitly addressed in this chapter as it affects the solar radiation intensity of

the solar photovoltaic systems. In understanding the dynamism context of the earth’s rotation,

the sun tracker devices compensate by helping to keep the best orientation of the solar

photovoltaic module relative to the sun’s position.

The sun tracking devices improve the efficiency optimisation and the harvested energy by the

solar photovoltaic array. Analyses on minimisation of the misalignment occurrence effect on

the tracking motion device orientation are also presented. Furthermore, the simulink model

design implementation supports the experimental analysis under variable conditions and

credence for the implemented model is quite significant.

4.2 An Astronomy of Dynamic Solar Photovoltaic Tracking System

The historical astronomy study and observations play a vital role in the success achieved so

far in the dynamic smart solar photovoltaic tracking systems. The mathematical expressions,

calculations and algorithms developed have seemingly helped thus far to solve and reduce the

uncertainties in determining the relative sun’s position and precise solar photovoltaic tracking

orientation device. The conventional progress has enabled the scientific solar photovoltaic

research community to have a database server to resolve challenges and inconsistencies

experienced. This has helped in establishing a universal standard algorithm pattern having a

relative solar position with one set of coefficients to calculate the solar incidence angle for an

arbitrary surface orientation valid for a long period.

The earth revolves counterclockwise about the sun in an elliptical orbit observed from a

vantage point above the north pole in a predictable trajectory. The earth completes one

revolution per day around the polar axis and the earth’s orbit is relatively stable over a long

period. The earth’s inclination axis of rotation is tilted at an angle 휀 ≈ 23.450 and the axis

orientation is time dependent. The daily rotation of the earth is defined by its rotation about

the polar axis, and the instant position of the sun is described by the hour angle, 𝜔. The


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geographical latitude (Φ) of a location is the angle determined by the radial line joining the

location to the center of the earth with its projection line to the equatorial plane.

The solar altitude angle (𝛼𝑠) is the vertical angle between the sun’s ray projection on the

horizontal plane and direction of the sun’s rays passing through the point. The solar zenith

angle (𝜃𝑧) is the vertical angle between sun’s rays and a line perpendicular to the horizontal

plane. The solar azimuth angle (𝛾𝑠 𝑜𝑟 𝛽) is the horizontal angle measured from south to the

horizontal projection of the sun’s rays. The celestial coordinates, solar altitude angle (𝛼𝑠) and

the solar azimuth angle (𝛾𝑠/𝛽) are time dependent variables used in determining the specific

location of the sun on the earth’s surface. The general notation of the earth’s surface is vector

based as shown in Figure 36, with its celestial reference coordinates measured from the

north-polar axis. The sun’s vector parameter 𝑆𝑄 (𝛾𝑠, 𝜃𝑧) and solar altitude angle (𝛼𝑠) forms

the integral vector variables describing the sun’s precise position and the intensity of sunlight

rays received by the tracking device of dynamic smart solar photovoltaic system [152-155].

Figure 36. The Solar tracking elevation and azimuth angles [156]

There are several kinds of photosensor trackers design such as the heliostats, photodiodes,

light tracking sensors (Photosensors) and a charged-coupled device (CCD) camera sensors

for the specific purpose of aligning the tracking orientation module surface to the sun’s rays


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and position. The solar photosensors and tracker device compensate for the sun’s diurnal

motion through spectroscopic analyses measuring the direct incident solar irradiation

ensuring orthogonal orientation of the solar photovoltaic module surface, thereby optimising

the efficiency of the collected energy. The optimisation control for the solar photovoltaic

tracking system is significant in achieving correct orthogonal orientation and alignment of the

solar photovoltaic module surface constantly towards the sun throughout the day [157, 158].

The sectional view of the celestial coordinates shown in Figure 36 is represented in three

dimensional x, y, z coordinates respectively showing the sun’s elevation, azimuth angle and

zenith angle. The mathematical expressions are programmed into the solar photovoltaic

tracking database system and are thus defined as follows [159];

Ecliptic longitude of the sun: The ecliptic longitude of the sun, 𝜆 is the angle

between vector 𝑆̅ and the horizontal axis plane. The mathematical expression used in

determining the ecliptic longitude of the sun is given as [159];

𝑠𝑖𝑛 𝜆 = 𝑠𝑖𝑛 [3600 (284+ 𝑛

365.25)] (00 ≤ 𝜆 < 3600) (94)

where n is the number of the day, 𝑆̅ is the Sun’s orthogonal horizontal reference plane

on solar photovoltaic module, such that n = 1 on the 1st of January, this implies the

values of 𝜆 constantly varies and is daily computed for accuracy.

Sun elevation angle: The sun’s elevation angle as shown in Figure 36, 𝛼𝑠 is the

vertical angle between the horizontal plane and the connecting plane to the sun. The

mathematical expression is given as [159];

𝑠𝑖𝑛 𝛼𝑠 = 𝑐𝑜𝑠 𝜔 𝑐𝑜𝑠 𝛿 𝑐𝑜𝑠 𝛷 + 𝑠𝑖𝑛 𝛷 𝑠𝑖𝑛 𝜔 (95)

where Φ is the geographical latitude of the site location, 𝜔 denotes the hour angle

and 𝛿 denotes the declination of the sun.

The Hour angle: The hour angle, 𝜔 is defined as the angular distance the earth

rotates in a particular day. The values for each hour of the day is constantly changing

and at noon day, the hour angle, 𝜔 = 00. The mathematical expression is given as

[159];

𝜔 = 150( hour – 12) (96)


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Declination of the sun: The declination of the sun, 𝛿 is the angle the vector 𝑆̅ makes

with the equatorial plane describing the latitude of the sun. The ecliptic plane and the

equatorial plane intersect on the horizontal axis, the angle between these two planes is

휀 ≈ 23.450. The mathematical expression is given as [159];

𝑠𝑖𝑛 𝛿 = 𝑠𝑖𝑛 𝜆 𝑠𝑖𝑛 𝜖 (97)

The Sun azimuth: The sun’s azimuth angle, (𝛾𝑠 𝑜𝑟 𝛽) is the angle between the vector

𝑆̅ and the sun’s projection in the south direction. The value of the sun’s azimuth

changes every hour and daily. The mathematical expression is given as [160];

𝑠𝑖𝑛 𝛾𝑠 = (𝑠𝑖𝑛 𝜔 𝑐𝑜𝑠𝛿)( 𝑐𝑜𝑠 𝛼)−1 (98)

The mathematical expression used in determining the sun’s azimuth changes, if 𝑠𝑖𝑛 𝛾𝑠 > 1,

is given as;

𝑠𝑖𝑛 𝛾𝑠= (𝑠𝑖𝑛 𝛼 𝑠𝑖𝑛 𝛷 − 𝑠𝑖𝑛𝛿)( 𝑐𝑜𝑠 𝛼 𝑐𝑜𝑠 𝛷)−1 (99)

4.3 Geometric Modelling Equation Derivations for Dynamic Smart Solar

Photovoltaic Systems

In understanding the relationship and developing a generic modelling formulation for

dynamic smart solar photovoltaic systems, this research focuses on how to maximise the

tracking efficiency of the solar irradiation using a concentrated solar photovoltaic module

with two symmetrically disposed mirrors on the left (M1) and (M2) on the right side along the

length of the photovoltaic module.

In the geometrical setup, two critical assumptions are made:

(i) that the two mirrors do not influence the proper functioning of the solar

photovoltaic module and;

(ii) that there are no losses through reflection from radiation that falls on the mirrors

directed to the spectrometer.

The objective of using the symmetrical lateral disposed mirrors is to ensure maximum

optimisation of the dimension of the flat solar photovoltaic module gains maximum direct

radiation, thereby increasing the efficiency of the solar photovoltaic system. Despite the fact


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that there are uncontrollable situations such as strong wind pressure, cloud shadowing of the

sun and many other natural disturbing conditions, these symmetrical mirrors ensure capturing

of sun’s radiation is relatively maximised.

In reality, misalignment occurs in an attempt to focus the direction of the rays of light

resulting in offsets which are added to the calculated positions affecting both the azimuth and

elevation tracking positions and movements. The geometrical setup for the concentrated solar

photovoltaic system using two symmetrical mirrors (M1) and (M2) are as shown in Figure

37.

Figure 37. Geometrical setup of a concentrated solar photovoltaic system using two mirror-

symmetrically disposed on the left (M1) and right (M2) [161]

Three coordinates are considered in the geometric dynamic smart solar photovoltaic systems,

Px(𝛾), Py(𝛽) ,Pz(𝛼) as shown in Figure 38. The resulting matrix 𝑀𝑜𝑓𝑓𝑠𝑒𝑡𝑠 transformation

applying Euler observatory configuration is given as:

𝑀𝑜𝑓𝑓𝑠𝑒𝑡𝑠 = 𝑃𝑥 (𝛾) x 𝑃𝑦 (𝛽) x 𝑃𝑧(𝛼) (100)

𝑀𝑜𝑓𝑓𝑠𝑒𝑡𝑠 = [1 0 00 𝑐𝑜𝑠𝛾 −𝑠𝑖𝑛𝛾0 𝑠𝑖𝑛𝛾 𝑐𝑜𝑠𝛾

] x [𝑐𝑜𝑠𝛽 0 𝑠𝑖𝑛𝛽0 1 0

−𝑠𝑖𝑛𝛽 0 𝑐𝑜𝑠𝛽] x [

𝑐𝑜𝑠𝛼 −𝑠𝑖𝑛𝛼 0𝑠𝑖𝑛𝛼 𝑐𝑜𝑠𝛼 00 0 1

] (101)


106

Figure 38. Euler’s observatory angle compared to altazimuthal coordinate system

Therefore, applying the law of multiplication of matrix to equation (101), the resulting

expression of the expansion yields:

𝑀𝑜𝑓𝑓𝑠𝑒𝑡𝑠 = [𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼 −𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛼 𝑠𝑖𝑛𝛽

𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽 + 𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛼 − 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾 −𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝛽

𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾 − 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾 + 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛽] (102)

The unit vectors ( 𝑥𝑡, 𝑦𝑡, 𝑧𝑡) of the Euler’s observatory offsets in relation to the solar

spherical cartesian coordinates (𝑎𝑧𝑜, 𝑎𝑙𝑡𝑜) in the altazimuthal system is given as [158]:

[

𝑥𝑡𝑦𝑡𝑧𝑡] = Moffsset x [

𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜

𝑠𝑖𝑛𝑎𝑙𝑡𝑜

] (103)

Substituting Moffsets obtained in equation (102) in equation (103), the resulting expression in

equation (104) is obtained:

[

𝑥𝑡𝑦𝑡𝑧𝑡] = [

𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼 −𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛼 𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽 + 𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛼 − 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾 −𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾 − 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽 𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾 + 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛽

] x [

𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜

𝑠𝑖𝑛𝑎𝑙𝑡𝑜

] (104)


107

The unit vectors ( 𝑥𝑡, 𝑦𝑡, 𝑧𝑡) of the Euler’s observatory offsets is obtained by the

multiplication of Moffsets (3x3) matrix and solar spherical cartesian coordinates (1x3) matrix.

The determination of the unit vectors ( 𝑥𝑡 , 𝑦𝑡, 𝑧𝑡) is as shown respectively below:

𝒙𝒕 − 𝒄𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕𝒔 𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏

𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 − 𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜 + 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝛽(𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝑎𝑧𝑜 − 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝑎𝑧𝑜) +𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝛽(cos (𝛼 + 𝑎𝑧𝑜)) +𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝒚𝒕 − 𝒄𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕𝒔 𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏

𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 + 𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 + 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜− 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜 − 𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽(𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝑎𝑧𝑜 − 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝑎𝑧𝑜) + 𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝛾(𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝑎𝑧𝑜 + 𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝑎𝑧𝑜) −

𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽(cos (𝛼 + 𝑎𝑧𝑜)) + 𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝛾 (sin (𝛼 + 𝑎𝑧𝑜)) −𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝒛𝒕 − 𝒄𝒐𝒆𝒇𝒇𝒊𝒄𝒊𝒆𝒏𝒕𝒔 𝒅𝒆𝒕𝒆𝒓𝒎𝒊𝒏𝒂𝒕𝒊𝒐𝒏

𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜 − 𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑐𝑜𝑠𝑎𝑧𝑜+ 𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝛾𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜 +

𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝑎𝑧𝑜+ 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛽 𝑠𝑖𝑛𝑎𝑙𝑡𝑜

−𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝑎𝑙𝑡𝑜(𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝑎𝑧𝑜 − 𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝑎𝑧𝑜) + 𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝛾(𝑠𝑖𝑛𝛼𝑐𝑜𝑠𝑎𝑧𝑜 + 𝑐𝑜𝑠𝛼𝑠𝑖𝑛𝑎𝑧𝑜)

+ 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛽 𝑠𝑖𝑛𝑎𝑙𝑡𝑜

𝑐𝑜𝑠𝑎𝑙𝑡𝑜𝑠𝑖𝑛𝛾(sin (𝛼 + 𝑎𝑧𝑜)) -cos (𝛼 + 𝑎𝑧𝑜) 𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽) 𝑐𝑜𝑠𝑎𝑙𝑡𝑜+ 𝑐𝑜𝑠𝛾𝑐𝑜𝑠𝛽 𝑠𝑖𝑛𝑎𝑙𝑡𝑜

{

𝑥𝑡 = cos(𝛼 + 𝑎𝑧𝑜) 𝑐𝑜𝑠𝛽 𝑐𝑜𝑠𝑎𝑙𝑡𝑜 + 𝑠𝑖𝑛𝛽𝑠𝑖𝑛𝑎𝑙𝑡𝑜𝑦𝑡 = ( cos (𝛼 + 𝑎𝑧𝑜) 𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝛽 + 𝑠𝑖𝑛(𝛼 + 𝑎𝑧𝑜) 𝑐𝑜𝑠𝛾) 𝑐𝑜𝑠𝑎𝑙𝑡𝑜 − 𝑐𝑜𝑠𝛽𝑠𝑖𝑛𝛾𝑠𝑖𝑛𝑎𝑙𝑡𝑜𝑧𝑡 = (𝑠𝑖𝑛(𝛼 + 𝑎𝑧𝑜) 𝑠𝑖𝑛𝛾 − 𝑐𝑜𝑠(𝛼 + 𝑎𝑧𝑜) 𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝛽) 𝑐𝑜𝑠𝑎𝑙𝑡𝑜 + 𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛾𝑠𝑖𝑛𝑎𝑙𝑡𝑜

(105)

These new Cartesian coordinates can then be converted to altitude (altt) and azimuth (αzt)

angles relative to the tracker [158]:

{

𝜌𝑡 = √ 𝑥𝑡2 + 𝑦𝑡

2

𝑎𝑙𝑡𝑡 = 𝑎𝑡𝑎𝑛2(𝑧𝑡 , 𝜌𝑡)

𝑎𝑧𝑡 = 𝑎𝑡𝑎𝑛2(𝑦𝑡 , 𝑥𝑡)

(106)


108

In the above equation, atan2(y,x) is available in many programming languages, stands for the

argument of the complex number x + iy. It is closely related to the arctangent of y/x, but it

indicates unambiguously the quadrant of this angle on the trigonometric circle.

The introduction of the general sun tracking modelling expression above helps in tracking the

sun’s position accurately and provides a cost effective solution regardless of the

misalignment which occurs in the altitude and azimuth configurations setup of the solar

photovoltaic tracking systems. As a result the misalignment optical nonlinear compensation

for the error which occurs during the onsite installation is taken into consideration by

adjusting the values of the orientation angles 𝜑, λ and ζ respectively. The sun tracking

accuracy of the system is highly reliant on the precision of the input parameters of the sun-

tracking algorithm: latitude angle (Φ), hour angle (𝜔) and the declination angle (𝛿) as defined

in section 4.2 is thus introduced in the developed tracking program in the microntroller of the

tracking system.

The Euler’s angles in mathematics are also used to describe the orientation of a frame of

reference typically a coordinate system relative to another. They are typically denoted

𝛼, 𝛽, 𝛾, or 𝜑, 𝜆 and ζ [162]. The orientation angles 𝜑, λ and ζ compensates for the daily sun-

tracking error induced as a result of misalignment of sun tracking axes. The analytical

solutions for the three orientation angles is necessary to compensate for the misalignment

which occurs during the solar photovoltaic system installation on site location and can be

obtained by determining the unit vectors of the sun’s position relative to the successive

transformation matrices coordinates for the orientation angles. Therefore, the unit vector sun

𝑆̅ , relative to the earth position is given as [163];

[𝑆̅] = [𝜑][λ][ζ][𝛷] [𝑆] (107)

[

𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼

] = [1 0 00 𝑐𝑜𝑠𝜑 −𝑠𝑖𝑛𝜑0 𝑠𝑖𝑛𝜑 𝑐𝑜𝑠𝜑

] x [𝑐𝑜𝑠𝜆 −𝑠𝑖𝑛𝜆 0𝑠𝑖𝑛𝜆 𝑐𝑜𝑠𝜆 00 0 1

] x [𝑐𝑜𝑠ζ 0 𝑠𝑖𝑛ζ0 1 0

−𝑠𝑖𝑛ζ 0 𝑐𝑜𝑠ζ]

x [𝑐𝑜𝑠𝛷 0 𝑠𝑖𝑛𝛷0 1 0

−𝑠𝑖𝑛𝛷 0 𝑐𝑜𝑠𝛷] x [

𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿−𝑠𝑖𝑛𝜔𝑐𝑜𝑠𝛿

𝑠𝑖𝑛𝛿]

(108)

The introduced variables 𝛼, 𝛽, 𝜔, 𝛿 and 𝛷 have been defined in section 4.2. Where 𝛼 is the

elevation angle, (𝛾𝑠 𝑜𝑟 𝛽) is azimuth angle, 𝜔 is hour angle, 𝛿 is the declination angle, Φ is

the latitude at which the solar collector is located as well as 𝜑, λ and ζ are the three

orientation angles of two-orthogonal driving axes of the solar photovoltaic collector.


109

In obtaining the result of the multiplication for the transformation matrices, the first three

matrices on the right-hand side are multiplied to give a singular (3 x 3) matrix and the last

two matrices form a singular (1 x 3) matrix. Furthermore, the multiplication of the two

resultant matrices, therefore, gives the expression in equation (110).

[

𝑠𝑖𝑛𝛼𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛼𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼

]= [

𝑐𝑜𝑠𝜆𝑐𝑜𝑠ζ −𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑐𝑜𝑠𝜑+ 𝑠𝑖𝑛𝜑𝑠𝑖𝑛ζ 𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑠𝑖𝑛𝜑+ 𝑠𝑖𝑛ζ𝑐𝑜𝑠𝜑 𝑠𝑖𝑛𝜆 𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜑 −𝑐𝑜𝑠𝜆𝑠𝑖𝑛𝜑

−𝑠𝑖𝑛𝜑𝑠𝑖𝑛ζ 𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑐𝑜𝑠𝜑+ 𝑠𝑖𝑛𝜑𝑐𝑜𝑠ζ 𝑐𝑜𝑠𝜑𝑐𝑜𝑠ζ − 𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑠𝑖𝑛𝜑] x

[𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿

−𝑠𝑖𝑛𝜔𝑐𝑜𝑠𝛿−𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛿𝑐𝑜𝑠𝛷

]

(109)

{

𝑠𝑖𝑛𝛼 = (𝑐𝑜𝑠𝜆𝑐𝑜𝑠ζ)(𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿) + (−𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑐𝑜𝑠𝜑+ 𝑠𝑖𝑛𝜑𝑠𝑖𝑛ζ)(−𝑠𝑖𝑛𝜔𝑐𝑜𝑠𝛿)+(𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑠𝑖𝑛𝜑+ 𝑠𝑖𝑛ζ𝑐𝑜𝑠𝜑)(−𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛿𝑐𝑜𝑠Φ)

𝑠𝑖𝑛𝛽𝑐𝑜𝑠𝛼 = (𝑠𝑖𝑛𝜆)(𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿) + (𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜑)(−𝑠𝑖𝑛𝜔𝑐𝑜𝑠𝛿) +(−𝑐𝑜𝑠𝜆𝑠𝑖𝑛𝜑)(−𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛿𝑐𝑜𝑠Φ)

𝑐𝑜𝑠𝛽𝑐𝑜𝑠𝛼 = (−𝑠𝑖𝑛𝜑𝑠𝑖𝑛ζ)(𝑐𝑜𝑠𝜆𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿) + (𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑐𝑜𝑠𝜑+ 𝑠𝑖𝑛𝜑𝑐𝑜𝑠ζ)(−𝑠𝑖𝑛𝜔𝑐𝑜𝑠𝛿)+(𝑐𝑜𝑠𝜑𝑐𝑜𝑠ζ − 𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑠𝑖𝑛𝜑)(−𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔𝑐𝑜𝑠𝛿 + 𝑠𝑖𝑛𝛿𝑐𝑜𝑠Φ)

(110)

The three linear matrices equation in (110) contain time-dependent variables 𝜔 and 𝛿 with

instantaneous collector sun-tracking angles respectively, which correspondingly produce

three different local times LT1, LT2 and LT3 for a particular day. The three different local

times correspondingly produces three hour angles 𝜔1, 𝜔2 and 𝜔3 and three declination

angles, 𝛿1, 𝛿2and 𝛿3 resulting in three azimuth angles 𝛽1, 𝛽2 and 𝛽3 and three elevation

angles 𝛼1, 𝛼2and 𝛼3 respectively as expressed in three linear equations in a matrix form in

equations (111) - (113).

[

𝑠𝑖𝑛𝛼1𝑠𝑖𝑛𝛼2𝑠𝑖𝑛𝛼3

] = [

𝑐𝑜𝑠𝜆1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆2𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ

]x

[

𝑐𝑜𝑠𝜆𝑐𝑜𝑠ζ−𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑐𝑜𝑠∅ + 𝑠𝑖𝑛∅𝑠𝑖𝑛ζ𝑠𝑖𝑛𝜆𝑐𝑜𝑠ζ𝑠𝑖𝑛∅ + 𝑠𝑖𝑛ζ𝑐𝑜𝑠∅

]

(111)

[

𝑠𝑖𝑛𝛽1𝑐𝑜𝑠𝛼1𝑠𝑖𝑛𝛽2𝑐𝑜𝑠𝛼2𝑠𝑖𝑛𝛽3𝑐𝑜𝑠𝛼3

]=[

𝑐𝑜𝑠𝜆1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆2𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛Φ𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ

] x [𝑠𝑖𝑛𝜆

𝑐𝑜𝑠𝜆𝑐𝑜𝑠∅−𝑐𝑜𝑠𝜆𝑠𝑖𝑛∅

] (112)

[

𝑐𝑜𝑠𝛽1𝑐𝑜𝑠𝛼1𝑐𝑜𝑠𝛽2𝑐𝑜𝑠𝛼2𝑐𝑜𝑠𝛽3𝑐𝑜𝑠𝛼3

]=[

𝑐𝑜𝑠𝜆1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1 + 𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆2𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2 + 𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ 𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3 + 𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ

]x

[

−𝑠𝑖𝑛∅𝑠𝑖𝑛ζ𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑐𝑜𝑠∅+ 𝑠𝑖𝑛∅𝑐𝑜𝑠ζ𝑐𝑜𝑠∅𝑐𝑜𝑠ζ − 𝑠𝑖𝑛𝜆𝑠𝑖𝑛ζ𝑠𝑖𝑛∅

]

(113)


110

The respective angles 𝜑, 𝛷, ζ and 𝜆 are considered as constants with respect to the local

times, therefore, the three arbitary orientation angles 𝜑, 𝜆 and ζ are derived using the third-

order determinants to resolve the three simultaneous equations as expressed in equations

(111) - (113).

The orientation angle, 𝜆 is determined by using the above equation in (112) and its expression

is thus given as:

𝜆 = 𝑠𝑖𝑛−1 {|

𝑠𝑖𝑛𝛽1𝑐𝑜𝑠𝛼1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ

𝑠𝑖𝑛𝛽2𝑐𝑜𝑠𝛼2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2+𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ

𝑠𝑖𝑛𝛽3𝑐𝑜𝑠𝛼3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ |

|

𝑐𝑜𝑠𝜆1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ


𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ |

} (114)

In the same vein, the two arbitrary orientation angles 𝜑 and ζ are derived using the third-

order determinants from equation (112) and (113) respectively:

𝜑 = 𝑠𝑖𝑛−1 {|

𝑐𝑜𝑠Φ1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 𝑠𝑖𝑛𝛽1𝑐𝑜𝑠𝛼1

𝑐𝑜𝑠Φ2𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 𝑐𝑜𝑠𝛽2𝑐𝑜𝑠𝛼2

𝑐𝑜𝑠Φ𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 𝑠𝑖𝑛𝛽3𝑐𝑜𝑠𝛼3 |

|



𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛𝛷𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ |

x 1

−cos𝜆} (115)

ζ= 𝑠𝑖𝑛−1 {|

𝑐𝑜𝑠𝛽1𝑐𝑜𝑠𝛼1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ

𝑐𝑜𝑠𝛽2𝑐𝑜𝑠𝛼2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2+𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ

𝑐𝑜𝑠𝛽3𝑐𝑜𝑠𝛼3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ|

|

𝑐𝑜𝑠𝜆1𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿1 −𝑠𝑖𝑛𝜔1𝑐𝑜𝑠𝛿1 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔1𝑐𝑜𝑠𝛿1+𝑠𝑖𝑛𝛿1𝑐𝑜𝑠Φ

𝑐𝑜𝑠𝜆2𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿2 −𝑠𝑖𝑛𝜔2𝑐𝑜𝑠𝛿2 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔2𝑐𝑜𝑠𝛿2+𝑠𝑖𝑛𝛿2𝑐𝑜𝑠Φ

𝑐𝑜𝑠𝜆3𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛷𝑠𝑖𝑛𝛿3 −𝑠𝑖𝑛𝜔3𝑐𝑜𝑠𝛿3 −𝑠𝑖𝑛Φ𝑐𝑜𝑠𝜔3𝑐𝑜𝑠𝛿3+𝑠𝑖𝑛𝛿3𝑐𝑜𝑠Φ |

x 1

cos𝜆} (116)

The three arbitrary orientation angles are thus computed as seen in equations (114) - (116) by

applying and implementing the input parameters of three measured sun tracking orientation

angles at three different local times (LT) with the other common parameter, latitude Φ,

longitude, 𝜆 and time zone meridan as shown in the equations above. It is observed that for

each set of local times (LT) the sun tracking angles such as the sun elevation angle (𝛼) and

azimuth angle (𝛾𝑠 𝑜𝑟 𝛽), the declination angle (𝛿) and hour angle (𝜔) can be determined

respectively. The advantage of introducing the arbitary orientation angles in the tracking

program is that it helps in simplifying fabrication and installation work for the solar

photovoltaic systems with high tolerance in terms of the tracking axes alignment, saving in

terms of cost, time and effort and avoiding complicated engineering tasks.


111

4.4 Simulink Modelling Approach

The nature of simulation design implementation is fast growing in engineering applications

for smart solar photovoltaic systems. The vast nature is interesting as various approaches are

considered for the ability to simulate continuously variable time-step integration algorithm

and discretized systems. The peculiar characteristics nature of the solar photovoltaic module

has made it necessary for modelling, designing and simulating in ensuring maximum power

point tracking (MPPT) is achieved using the SimPower system tool in the Matlab/Simulink

software package to integrate the photovoltaic component design with other electronic

component designs to establish a high performance model [164, 165].

The Matlab/Simulink developed by Mathworks is a proficient software tool for modelling,

simulating and analysing multi-domain static and dynamic systems. The SimPower system

tool is flexible enough to accommodate different simulation inputs, interfaces and to monitor

various signal levels at any point in the designed model. The software tool allows the design

engineer to perform complex post-processing on simulation results while simulation

processes are running. This tool allows the user the opportunity to independently build

schematics and simulate the built design model visualising the results through connected

simulink scopes and displays provided in the simulink block library [166, 167].

The simulink modelling approach is realised using the generalised photovoltaic user-friendly

masked block module with other Matlab/Simulink block sets in the simulink library for the

design implementation of connecting five thousand solar photovoltaic modules in series and

parallel configuration on a virtual solar farm.

Hence, the focus of this design is to use the simulink model forecast the estimated amount of

energy harvest expected without any physical hardware involvement, overcoming

shortcomings and improving the overall system reliability, ruggedness and dynamic

performance of the pre-site installation. Finally, the performance of the proposed design is

accessed and verified experimentally using the SimPower system tool. This helps the project

designer and site engineer to have a foreknowledge of the expected outcome in a real-life

scenario. This attracts the interest of local and foreign investors on the possibilities and

advantages of the solar renewable energy.


112

4.5 Simulink Implementation for Smart Solar Photovoltaic Systems

This section describes the simulink implementation and design of a solar photovoltaic module

from its general non-mathematical relationship of the current-voltage (I–V) output

characteristics for the developed static smart solar photovoltaic power off-grid system design.

The SimPower system tool is used in the design implementation and simulated results for the

proposed model using Matlab/Simulink software package are thus presented in the following

sub-sections.

4.5.1 Simulink Implementation of a Solar Photovoltaic Module

The simplest model for the solar photovoltaic module based on its physical behaviour as a

diode is employed to determine maximum power point tracking (MPPT) and control

techniques for the current-voltage (I–V) characteristics and power-voltage (P-V)

characteristics performance under variable solar irradiance and cell temperature conditions.

Figure 39. Simplest model of an equivalent circuit solar photovoltaic module [116]

The equivalent circuit-based model of a solar photovoltaic module has been described in the

previous chapter, Chapter 3, and the implementation design consists of a photocurrent, a

diode, a parallel resistor expressing a leakage current, and a series resistor describing the

internal resistance of current flow through the circuit. The simplest equivalent circuit-based

model of a solar photovoltaic is reproduced in Figure 39 from page 62 to make a clear

understanding for the simulink design implementation. The characteristics equation for a

given generalised model of a solar photovoltaic module is given by the mathematical

expression as [117]:

𝐼 = 𝐼𝑝ℎ − 𝐼𝑜 [{𝑒𝑞(𝑉+𝐼𝑅𝑠)

𝐴𝐾𝑇 } − 1] − (𝑉 + 𝐼𝑅𝑠)

𝑅𝑠ℎ (117)


113

The parameters in the above equation have been described in the previous chapter, chapter 3

in section 3.4.1. It is noted that five parameters in the characteristics equation for a

generalised solar photovoltaic module determine the possible outcomes of the physical

behaviour of a particular designed photovoltaic model. These parameters, namely are 𝐼𝑝ℎ , 𝐼𝑜 ,

𝑅𝑠ℎ, 𝑅𝑠 and variable environmental conditions. In the above characteristics equation, the

photovoltaic cell photocurrent, 𝐼𝑝ℎ and the reverse saturation, 𝐼𝑜 of the solar photovoltaic

module mathematical expressions are thus defined.

The photovoltaic cell photocurrent, 𝐼𝑝ℎ depends on solar radiation and temperature. The

mathematical expression for the photovoltaic cell photocurrent, 𝐼𝑝ℎ is given by the

expression as [117];

𝐼𝑝ℎ = [𝐼𝑠𝑐 + 𝑘𝑖 (𝑇 − 298)]𝑠

1000 (118)

The parameters in the above expression, the short-circuit current, 𝐼𝑠𝑐 , cell’s short circuit

current temperature coefficient, 𝑘𝑖 is provided by the photovoltaic manufacturer’s manual.

However, the temperature 𝑇 and solar radiation 𝑠 are constantly varying due to the varied

weather conditions.

The diode reverse saturation current, 𝐼𝑜 varies as a cubic function of temperature and its

mathematical expression is given as [117];

𝐼𝑜 = 𝐼𝑜𝑟 (𝑇

𝑇𝑟)3x 𝑒

{𝑞𝐸𝐺𝑘𝐴

(1

𝑇𝑟−1

𝑇)}

(119)

In a similar manner, the diode reverse saturation current, 𝐼𝑜𝑟 at reference temperature 𝑇𝑟 =

301.18K, the norminal cell temperature, 𝑇𝑟 and the energy band gap of the solar photovoltaic,

𝐸𝐺 are provided for in the manufacturer’s photovoltaic manual.

The simulink block subsystem and the masked simulink block system for the photovoltaic

cell photocurrent, 𝐼𝑝ℎ for varying cell temperature in equation (118), is represented in Figure

40 and Figure 41 respectively. In the same approach, the simulink block subsystem and the

masked simulink block system for the diode reverse saturation current, 𝐼𝑜 for varying cell

temperature in equation (119), is represented in Figure 42 and Figure 43 respectively.


114

Figure 40. PV cell photocurrent, 𝑰𝒑𝒉 Matlab/Simulink subsystem

Figure 41. PV cell photocurrent, 𝑰𝒑𝒉 Matlab/Simulink masked subsystem


115

Figure 42. Diode reverse saturation current, 𝑰𝒐 Matlab/Simulink subsystem

Figure 43. Diode reverse saturation current, 𝑰𝒐 Matlab/Simulink masked subsystem

The simulink masked subsystems model for the photovoltaic cell photocurrent, 𝐼𝑝ℎ and diode

reverse saturation current, 𝐼𝑜 was developed primarily to allow its output nodes to integrate

easily into a generalised simulink subsystem characteristics equation of the solar photovoltaic

module as given in equation (117). The aim of developing the integrated subsystems is to

eliminate the possibilities of errors due to the cumbersome nature of the tracing link lines

between the simulink block elements. The developed simulink model for the simplest

equivalent characteristics equation of a solar photovoltaic model is as shown in Figure 44.

The simulink model output characteristics behaviour exclusively depends on these two major

factors, the variable solar irradiation and temperature conditions.


116

The masked simulink model for the simplest equivalent circuit characteristics equation of a

solar photovoltaic model is as shown in Figure 45. The masked simulink model provides a

less complex structure keeping a record of block sizes, sub-block systems, hidden data in

subsystems, customising its interface by simplifying the physical appearance but with limited

detailed information of the exact simulink block elements. The simulated photovoltaic

module model results obtained using the Sim-Power-system Matlab/Simulink toolbox

predicts the behaviour of any solar photovoltaic module and array under variable climate

conditions and physical parameters is shown in Figure 46.

Figure 44. Simulink Model of the characteristics equation of the solar photovoltaic module

Figure 45. Masked Simulink Model of the characteristics equation of the solar photovoltaic module


117

Figure 46. I-V & P-V characteristics of solar photovoltaic module

The simulink results of characteristics solar photovoltaic generalised model for a cell are as

shown in Figure 46. The nonlinear nature of a PV cell is apparent as the output current and

power of a PV cell depend on the cell’s terminal operation voltage, temperature and solar

insolation. It can be noticed from the figure that as the working temperature increases, the

short-circuit current of the PV cell increases, whereas the maximum power decreases. Also, it

is observed that as the increase in the output current is much less than the decrease in the

voltage, the net power decreases at high temperatures. The maximum power point 𝑃𝑚𝑝 of the

cell is at 1.38 W, the maximum voltage point is at 0.4 V and the maximum current point is

found to be 3.45 A.

4.5.2 Simulink Implementation of a Static Smart Solar Photovoltaic off-

grid model

The objective of using the simulink modelling approach to forecasting the estimated amount

of energy harvested with the design implementation of a static smart solar photovoltaic off-

grid model is fundamental. This section describes the simulink implementation of a static

solar smart photovoltaic off-grid model. The designed model is implemented using the solar

photovoltaic block element and other block elements in the SimPower toolbox to establish an

off-grid model. In the previous section, section 4.5.1, the general simulink model for the

general mathematical expression is developed for a single solar photovoltaic module. The

chosen simulation approach is to establish a valid result for a static solar photovoltaic farm


118

for a five thousand solar photovoltaic array of modules connected in series and parallel

configurations to determine the expected maximum output harvested energy in a real life

scenario under variable environmental conditions. The two major environmental conditions

considered in this design are solar irradiation and temperature; others conditions such as the

wind, humidity etc. are ignored.

However, practical experience and challenges in a real life scenario, a few times do not

correspond in perfect terms with simulated results but the processes and benefits accrued to

site engineers having a foreknowledge and expectation of probable results with direct

relevance to current site practice is an added advantage. The capabilities of simulink

computational processes are steadily gaining recognition in the engineering field due to the

technological breakthroughs achieved over the years. The simulink model representation is a

convenient approach for modelling linear and non-linear block elements using the continuous

power graphic user interface (powergui) as the model simulator to display the steady state

conditions and output characteristics.

In establishing the design model for the simulink implementation for the five thousand solar

photovoltaic modules, a series connection arrangement of ten solar photovoltaic modules is

constructed and a masked subsystem block unit of the array formed is shown in Figure 47 and

Figure 48 respectively. The functional block parameters for the solar photovoltaic module

with the double exponential model is shown in Figure 49 and Figure 50 respectively. The

model consists of a light photocurrent source, two diodes, a series resistance and a parallel

resistance. In the physical characteristics behaviour of the solar photovoltaic cell model, the

shunt resistance, 𝑅𝑠ℎ is inversely related with shunt leakage current to the ground and most

times it is assumed to be infinity (inf) and a small variation in 𝑅𝑠 significantly affects the

output photovoltaic output power. Consequently, ten similar masked subsystem block units of

ten solar photovoltaic modules are connected in series to establish a series connection of a

hundred units of solar photovoltaic modules on a single lane as shown in Figure 51. The

negative PV terminal in Figure 51 has been shortened in words as negative PV term, to allow

the Figure fits into the page.


119

Figure 47. A series connection of ten solar photovoltaic modules

Figure 48. Masked subsystem of the series connection


120

Figure 49. Functional block parameter of a solar PV cell Figure 50. Functional block parameter of a solar PV cell

Figure 51. Masked subsystem block units of a hundred solar photovoltaic modules

The simulink masked unit of a hundred solar photovoltaic modules is thus represented as

shown in Figure 52 with three terminal connections.

Figure 52. Simulink Model of a single block of hundred solar photovoltaic modules


121

The array arrangement for the implementation of five thousand solar photovoltaic modules

involving series-parallel configuration to produce the predictable maximum output power is

shown in Figure 53 on page 122. The equivalent circuit model for the array consists of a

hundred solar photovoltaic series connected modules, Ns, in parallel with fifty similar masked

subsystem block units, Np, connected to establish the total number of modules for the design

implementation. The parallel connection of the fifty-masked subsystem of the series

connection of a hundred solar photovoltaic modules increases the output current value of

entire system design while controlling the generating output voltage.

The series-parallel configuration implemented in this design was chosen because it

significantly increases the output current with a steady output voltage. The solar photovoltaic

array operates efficiently at maximum power point when connected to the inverter system.

The shadowing effect on the series-parallel configuration of the solar photovoltaic array does

not drop in performance in the output energy compared to the ordinary series solar

photovoltaic array configuration. This array configuration is considered to be safer in

operation and efficient in system maintenance.

4.5.3 General Photovoltaic Model Characteristics

The implementation of the simulink general photovoltaic characteristics model is described in

this section. The general block diagram of the photovoltaic array model for simulink GUI

environment is shown in Figure 54. The photovoltaic model consists of simulink block set

models integrated to establish the final design model. As mentioned in the previous section,

the output power generated depends on the configuration arrangement of photovoltaic

modules. The eight model parameter characteristics of the solar photovoltaic cell are chosen

for this design having two diodes in its circuit configuration.


122

Figure 53. A five thousand series-parallel configurations of solar photovoltaic modules


123

Figure 54. Solar photovoltaic array model for GUI environment of Simulink

The eight-parameter model of the solar photovoltaic cell provides an option of varying the

cell configuration parameters such as the diode saturation currents (𝐼𝑆 and 𝐼𝑆2), solar

generated currents, 𝐼𝑝ℎ, irradiance measurements, 𝐼r0, quality factors (diode emission

coefficients) (N and 𝑁2), series resistance, 𝑅𝑆, parallel resistance, 𝑅𝑃, and temperature

dependence parameter variables. During the simulation processes for the simulink model, it is

observed that variation in the quality factors of solar photovoltaic module has significant

effect on the I-V characteristics curve and on the P-V characteristics curve, as well as on the

visual characteristics of the I-scope, P-scope and V-scope as the simulated experiments were

performed for the designed model.

Figure 55 shows the I-V characteristics for the solar photovoltaic model; it is observed that

the solar photovoltaic generated current, 𝐼𝑝ℎ measured was 3.80A and does not exceed the

maximum solar generated current for the solar cell at 4.0A notwithstanding varying the

configuration parameters in the simulink GUI for the design. The I-V characteristics curve

exhibits perfect behaviour at maximum irradiance level of 1000W/m2 with simulation

experiment time preset for 60 seconds.


124

Figure 55. I-V Characteristics behaviour of the solar photovoltaic model

Figure 56 shows the P-V characteristics behaviour for the solar photovoltaic model; the

simulation stop time for the configuration parameters in simulink GUI was preset for 60

seconds. It is observed that the maximum peak power, Pmax from the P-V curve determined is

found to be at 163 Wp at a maximum irradiance level of 1000 W/m2 for a rated peak power

for the solar photovoltaic cell at 170 Wp.

Figure 56. P-V characteristics behaviour of the solar photovoltaic model

A parallel connection configuration of eight similar solar photovoltaic modules was designed

to validate the model design based on the electrical specification for the test solar panel. All

configuration parameters settings in the previous model were kept constant and maximum

irradiance level at 1000 W/m2 was introduced to determine the solar-generated current, Iph


125

and the maximum peak power for the new configuration. Figure 57 depicts the I-V

characteristic performance curve of the I-Scope connected at the output terminal of the

designed model.

The solar-generated current, 𝐼𝑝ℎ correlates with the single photovoltaic module model above

with similar output characteristics. Figure 58 depicts the P-V characteristics performance

curve of the P-Scope connected at the output terminal of the designed model. The maximum

peak power for the parallel configuration, Pmax is found to be 1133 Wp. The parallel

configuration arrangement model validates the behaviour of any photovoltaic module

configuration under variable physical and environmental conditions.

Figure 57. I-V characteristics of the parallel configuration model

Figure 58. P-V characteristics of the parallel configuration model


126

4.5.4 Simulink Implementation of Five thousand Solar Photovoltaic

Modules

Previous sections have described the simulink design models of a single solar photovoltaic

module, the parallel configuration arrangement of solar photovoltaic modules investigating

and validating the performance of the non-linear characteristics behaviour curves of the

photovoltaic modules. The configuration arrangement for the implementation of five

thousand solar photovoltaic modules is described in section 4.5.3 and shown in Figure 53.

The masked subsystem configuration arrangement of Figure 53 is shown in Figure 59.

Figure 59. Masked subsystem for the five thousand solar photovoltaic module

The full simulink model for the five thousand solar photovoltaic modules configuration is

shown in Figure 60.

Figure 60. Full Simulink model for the five thousand solar photovoltaic modules arrangement


127

The simulated graphical output characteristics for the five thousand solar photovoltaic

modules arrangement from graphical scope at an irradiance level of 1000W/m2 for the

current, voltage and power is shown in Figure 61.

Figure 61. Simulation results of the output current, power and voltage against simulation time

The simulated output characteristics at ten different irradiance levels result are thus presented

in Table 10 and the chart representation is as shown in Figure 62 and Figure 63 respectively.

It is observed from the simulated output characteristics of the solar array arrangement that as

the irradiance level increases there is a corresponding increase in the output power level.

Table 10.The simulated output characteristics at ten different irradiance levels

Irradiance Level

(W/m2)

Output

Voltage (V)

Output

Current (A)

Output

Power (W)

100 3640 18.20 66240

200 4347 21.74 94490

300 4994 24.97 124700

400 5618 28.09 157800

500 6246 31.33 195850

600 6834 34.17 233500

700 7433 37.16 276200

800 8028 40.14 322200

900 8620 43.10 371500

1000 9210 46.05 424100


128

Figure 62. Output power, voltage generated with increased irradiance level

Figure 63. Output current generated with increased irradiance level

Figure 62 and 63 respectively depict the output power and output voltage with increased

irradiance level and output current with increased irradiance levels. In Figure 62, OP denotes

the output power and OV denotes the output voltages and OA in Figure 63 denote the output


129

current for the simulink model of the 5000 solar photovoltaic module arrangement. A distinct

look into these figures; gives a clear understanding of the chart, that as the irradiance level is

increased in steps of 100 W/m2 to the maximum irradiance level at 1000 W/m2 for the

Simulink design implementation, there is a corresponding increase in the output current,

voltage and power in the chart represented. The simulink design implementation provides a

vital information for the designer in helping to determine the exact output current, voltage

and power correspondence at any given irradiance under the condition of which the

simulation experiments were performed.

4.6 Conclusion

Analysis and the theoretical basis for the governing equations for dynamic smart solar

photovoltaic tracking systems have been carefully examined in this chapter. In addition, the

determined arbitrary angles are programmed into the solar photovoltaic database system

controller ensuring that constant orthogonal positioning of the sun’s position is achieved

throughout the day. Furthermore, the simulink design and implementation of a single solar

photovoltaic module, the parallel configuration of solar photovoltaic array arrangement and

implementation of simulink design for five thousand solar photovoltaic arrays, are thus

presented in this chapter. The respective results of the modelled experiments performed are

shown in the Figures in this chapter and contributions have been clearly stated.

The following chapter (chapter 5) presents a robust real-time online comparative solar

photovoltaic monitoring of the static and dynamic solar photovoltaic systems. The research

was conducted at the National Kaohsiung University of Applied Sciences, Taiwan, Republic

of China. The results and findings are presented in the same chapter.


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Chapter 5 Robust Real-Time Online Solar Photovoltaic Data

Monitoring Systems

5.1 Introduction

This chapter describes an aspect of this research conducted at the National Kaohsiung

University of Applied Sciences, Taiwan, Republic of China. In this chapter, a thorough

theoretical background and foundation for the design implementation of a robust real-time

online comparative remote solar photovoltaic data monitoring systems via wireless facilities

and services broadcasting instant and exact energy harvested from installed solar photovoltaic

modules is presented.

In addition, this chapter introduces the concept of the Internet of Things (IoT) in establishing

the benefits of remote online real-time solar photovoltaic monitoring and tracking systems

between two classifications of solar photovoltaic tracking systems under investigation in this

research. The uniqueness of the results obtained from the classified tracking systems under

investigation compared with the modelling and simulated experiments as described in chapter

3 of this thesis is strongly emphasized in the concluding chapter of this thesis. This research

investigation offers a real-world experience on which the foundations for future research

investigations on remote solar photovoltaic monitoring systems and applications over its

lifetime can further be established.

5.2 An Overview of Robust Real-Time Remote Solar Photovoltaic

Monitoring and Tracking Systems

A robust real-time online remote solar photovoltaic monitoring and tracking system via cloud

computing devices relaying instant and exact energy harvested from installed solar

photovoltaic modules on-site is under investigation in this research. An intelligent robust

online real-time solar photovoltaic monitoring and tracking system with wireless facilities

and services is one of the recent breakthroughs the solar photovoltaic energy industry has

witnessed in the last decade. The solar photovoltaic energy monitoring system makes use of

information and communications technology (ICT) in addressing the challenges of

uncertainties in the amount of energy generated over a specified period [168-170].

The Internet of Things (IoT) offers advanced connectivity of devices, systems and services

that goes beyond machine to machine communication and covering a variety of protocols,

domains and applications ushering automation in nearly all fields enabling advanced


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applications in smart grid networks [171]. This new concept in smart grid networks and

systems provides automation which has led to expansion, generating large amounts of data

from diverse distributed smart grid networks and systems aggregating quickly, thereby

increasing the need for better index, storage and process such data [172].

The remote monitoring devices for stationary and dynamic hybrid solar photovoltaic tracking

systems is achieved via the internet on mobile phones, tablets, PCs and notebooks through

installed software tracking applications. The introduction of robust adaptive devices has

significantly increased the optimisation, performance and high sun’s concentration on the

hybrid solar photovoltaic tracking modules based on developed solar movement algorithm

models. This research investigates the design of an efficient robust online real-time

comparative data and visual analysis for both stationary and the hybrid solar photovoltaic

tracking and monitoring systems over the lifetime of the installation.

The solar photovoltaic monitoring system consists of two main components: the

programmable logic controller (PLC) box and the data logger connected via the router for

remotely accessing and transfer real-time solar photovoltaic data information generated. A

data acquisition and monitoring system are deployed for this research investigation at the

National Kaohsiung University of Applied Sciences, Taiwan, the Republic of China for

optimal solar photovoltaic energy harvesting to forecast sustainable solar photovoltaic

management policies and validate simulation models. The research outcomes are likely to

offer real-world experience on the future solar photovoltaic energy industry applications not

only in Taiwan but also worldwide.

These robust adaptive devices reduce the extent of energy loss liable to occur due to faulty

devices and parts connected to the solar photovoltaic array providing an expedient, efficient

maintenance and replacement so as to restore to full capacity. The availability and provision

of multi-vendor cloud-based data setup centers globally, various software support

applications developed have brought immense potentials and significant performance in

reducing the response time and cost savings in the solar photovoltaic energy industry [173].

A key component of the solar photovoltaic monitoring system is the provision of cloud

platforms referred to as power management data centers. This provides the ability to enhance

remote visibility, automated integration of energy management and policies, power metering

capabilities, safety and control mechanisms, early fault detection and location resulting in

minimal loss of harvested energy. The cloud platform architecture addresses challenges such


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as interoperability exchanges between different data centers and software applications,

virtualization, scalability, quality of service (QoS) and provision of alternative instant

solutions in the event of mechanism failure [124, 174].

This research investigates the delivery of a virtualisation management and service system,

analysing comparative output energy efficiencies of two solar photovoltaic tracking systems.

This establishes a solar photovoltaic energy harvest database system processing for the

future, comparing the obtained results with developed simulation models, facilitating

prediction and forecasting of power generation on a large scale investment. However, the

solar photovoltaic monitoring system deployed leads to the following outcomes as compared

to other similar systems:

I. Ability to remotely monitor different installed solar photovoltaic modules rating

simultaneously to validate individual hourly energy ratings generated.

II. Availability of an open-ended access to the database for evaluation of the solar

photovoltaic energy system.

III. Ability to predict and forecast based on established database the output energy levels

as a result of variation in climatic and seasonal changes during the year [175-177].

5.3 Robust Real-Time Online Solar Photovoltaic Monitoring

Infrastructure

This section gives an overview, investigation and findings of this research on the practical

implementation of the on-site structural components for a robust real-time online solar

photovoltaic infrastructure design and implementation for a 24-hour telemetry monitoring.

The robust real-time solar photovoltaic monitoring system was aimed at providing an online

continuous monitoring of harvested output energy information with respect to the different

solar photovoltaic modules rating installed at the roof platform of the National Kaohsiung

University of Applied Sciences, Taiwan, R.O.C [178].

The infrastructural design and implementation for the robust real-time solar photovoltaic

monitoring system are subdivided into four different zones. Each zone has solar photovoltaic

modules installed on a pre-determined inclined aluminium alloy brackets. The first zone

comprises of three separate sections of installed solar photovoltaic modules inclined at

permanent 450 position with a pyranometer installed at the top corner of the bracket to

measure solar insolation on the photovoltaic modules. Each of these sections successfully


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accommodates three standard 250Wp solar photovoltaic modules with different photovoltaic

characteristics ratings to compare and determine the output energy harvested.

The second zone consists of a manual incremental adjustable aluminium alloy frame structure

having its horizontal base specially marked for incremental elevation angles from 00, 150, 250,

350, 450, 550 and 750 respectively. This zone has three different standard photovoltaic module

ratings installed to compare and determine the output energy generated from each of the

photovoltaic modules as the elevation angle for the framed structure is either increased or

decreased at different periods during the year.

The third zone is designed to have two manually adjustable aluminium alloy frame structures

having the horizontal base specially marked for incremental elevation angles at 450 and 700

respectively. The framed structure accommodates three standard solar photovoltaic modules

of different power ratings to compare and determine the output energy generated and the best

elevation position to obtain maximum efficiency for the manually static solar photovoltaic

modules.

The fourth zone consists of a two-axis controlled flat surface hybrid solar photovoltaic

tracking stepper motor rotating device having a solar sensor installed at the centre top of the

rectangular aluminium framed structure with a programmable logic controller box attached at

the base of the concrete pole. A robust real-time online solar photovoltaic monitoring

schematic system at the roof building platform is shown in Figure 64 [178].

In this research, the first and the fourth zone arrangements of the schematic figure is under

comparative analysis in determining the advantage and benefits of the solar photovoltaic

tracking systems in terms of the maximum efficiency of the output energy harvested.

The solar photovoltaic monitoring schematic system described on the roof site setup has four

solar photovoltaic modules representing four zones. The Darfon MIG 240 micro-inverter is

installed on the aluminium alloy framed structure at the rear side of each of the zones

consisting three standard solar photovoltaic module ratings [179]. The Darfon MIG 240

micro-inverter device has an inbuilt integral surge protector against induced voltage sparks

preventing damage of the solar photovoltaic monitoring system. The Darfon MIG 240

converts directly the DC power generated from the solar photovoltaic module to

synchronising AC power into the electricity grid network without the need of a high DC

voltage wiring and a central inverter system.


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This device helps in the optimisation performance, easy monitoring for fault detection and

location of solar photovoltaic modules under varying environmental conditions. Furthermore,

it has increased the lifetime and reliability of innovative solar photovoltaic inverting systems

rather than the traditional central inverter system operating in a real-world environment. It is

designed to achieve a peak efficiency of 95.7% for temperatures between -400C (-400F) and

650C (1490F) without degradation in its performance.

Figure 64. A robust real-time online solar monitoring system at roof building platform [178]

The Darfon monitoring system is a combination of two components: Darfon PLC box and

data logger installed along with the Darfon MIG 240 micro-inverter providing a detailed real-

time specific data information of each installed solar photovoltaic modules on-site ensuring

system performance optimisation over its lifetime. The Darfon data logger is connected to the

router or ethernet port connection for routing obtained information from each of the installed

solar photovoltaic modules via the web [179, 180].

The Darfon data logger is connected to the Darfon PLC box via RS485 terminals by the

wiring cables. An alternative improvisation for the solar photovoltaic monitoring system is

deployed by different research groups for easy adaptability and management of harvested

solar photovoltaic energy data information. The Darfon data logger is substituted for by the

arduino data logger essentially for the provision of additional features and functionality [181,

182]. The arduino data logger connects to the Darfon PLC box via the RS232 connecting

terminals.


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The ultrasonic static anemometer device is connected via the RS232, RS485 and SDI-12

communication protocols to the monitoring system for measuring wind speed and direction,

relative humidity and temperature, solar radiation diffusion and barometric pressure. This

device has a heater option preventing the accumulation of snow and ice forming on the

device in cold temperate regions allowing accurate measurements for all environmental

conditions. The GL800 device is a multi-channel data logger colour monitor with an inbuilt

internal flash memory capacity to store data enabling direct capturing of data from the flash

memory through the USB flash drive for off-line data transfer to a PC or a laptop device and

also through ethernet port provision allowing remote data transfer for solar photovoltaic

monitoring [183].

In addition, it is a multi-functional device with full electrical isolation per channel, wide

range of voltages, current and temperature measurements, flexible triggering and sample

interval options, real-time and post recorded calculation capabilities. Figure 65 represents the

schematic solar photovoltaic monitoring wiring system architecture. A standard scheme is

deployed at the roof building platform of a maximum 20 metres distance connecting the T-

cables to each solar photovoltaic module installed for each of the four zones having a

maximum distance of 300 metres of cat5e ethernet cables connecting to the router for remote

data transfer.

Figure 65. A schematic solar photovoltaic monitoring wiring system architecture [179]


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5.4 Solar Photovoltaic Data Monitoring and Acquisition Energy System

The recent growth in internet networks and infrastructure has enhanced the development of

solar photovoltaic energy industry over the last decade in data monitoring and acquisition

systems for on-site, remote data collection and transfer via the internet for evaluating solar

photovoltaic module efficiencies, improving optimisation performance and operational

flexibility, achieving advanced control capabilities, periodic maintenance, fault detection and

location [184].

The solar photovoltaic energy industry transformation is evolving in data monitoring and

acquisition architecture from a client/server architecture employed for distributed measuring

instruments where acquired data is available in the server station and retrieved any time

needed through the internet network by clients as shown in Figure 66 [185]. In an alternative

arrangement as shown in Figure 67, clients access and obtain solar photovoltaic data via

intranet networking from the server station [186].

Figure 66. Client/server internet architecture

Figure 67. Client/server intranet architecture


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The phenomenon of transferring obtained data from the data logger device on-site from the

solar photovoltaic panel through the RS-232 serial interface to a PC or a laptop is been

phased out due to the slow rate of serial data transmission system performance. Several data

monitoring and acquisition systems have been developed with a variety of applications for

monitoring the battery charging status of the solar photovoltaic energy system, solar

photovoltaic powered water pumping machines, solar irradiation and ambient temperatures,

operational parameters of hybrid photovoltaic-diesel plants and comparative output

efficiencies of different photovoltaic ratings and designs [187].

Figure 68 shows a real-time online solar photovoltaic monitoring and acquisition

infrastructure architecture. However, information about the installed solar photovoltaic

systems can be accessed and monitored on mobile devices, tablets, PCs at any moment during

the day.

Figure 68. Real-time solar monitoring and acquisition infrastructure architecture

The data collection for this research on a robust real-time online solar photovoltaic data

monitoring system was carried out at the National Kaohsiung University of Applied Sciences,

Taiwan, Republic of China was achievable through the process of cloud computing. The

NIST definition of cloud computing defines it as a model for enabling universal, convenient,

on-demand network access to a shared pool of configurable computing resources (e.g

networks, storage, applications, and services) that can be rapidly provisioned and released

with minimal management effort or service provider interaction [188].


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The component parts for a robust real-time online solar photovoltaic monitoring system at the

roof building platform has been discussed in detail in section 5.3 and as shown in Figure 64

in this Chapter. The aspect of cloud computing becomes relevant in this research because the

solar photovoltaic data collection and monitoring were achieved over the internet. The

deployment for this research was provided on a private cloud model by the institution.

The four basic fundamental cloud computing service models as shown in Figure 69 are: (i)

Infrastructure as a service (IaaS), (ii) Platform as a service (PaaS), (iii) Software as a service

(SaaS) and (iv) Unified communication as a service (UcaaS) [188, 189].

Figure 69. Basic fundamental cloud computing service model [188]

Each of the cloud computing service model levels is briefly defined as follows:

IaaS – This is a service infrastructure model maintained by the cloud as virtualised hardware

known as computing infrastructure providing virtual multitude server space, network

connections, bandwidths, IP addresses and load balancers distributed across several virtual

data centers.

PaaS – This allows customers to develop a personal software application for flexibility, run

and manage Web applications or rather choose a friendly pre-configured software support

service application developed on the network by periodically upgrading the applications in a

structured, managed and secured database system.

SaaS – This platform is built on international standards protocol for interoperability allowing

customised applications and access to software applications over the internet for a wide range

of needs such as monitoring, planning, forecasting and other related services on mobile apps

devices and PCs without restriction in any part of the world.


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UcaaS – This platform is outsourced to a third-party and co-ordinated by the internet service

providers (ISP) over the network for multi-platform communications such as IP telephony,

video conferencing and unified messaging on mobile devices, tablets and PCs.

The fundamental objective is to employ the provision of cloud computing service models to

achieve the primary purpose of retrieving solar photovoltaic data information and monitoring

remotely via the internet through the IaaS service model. This research basically employs the

IaaS model to achieve its objective. The IaaS service model provides the capability of

processing, storage, networks and other fundamental services.

The Darfon MIG 240 micro-inverter, Data logger and PLC box runs on an arbitrary software

on Java platform adaptable to retrieve solar photovoltaic data information via the internet

from the IaaS service model of each installed solar photovoltaic module. This is made

possible with access to the internet service platform provided by the private cloud model to

the institution. The Darfon data logger provides a user-friendly and flexible GUI for clients

usage on mobile apps devices, tablets and PCs for instant overall assessments of system

performance and retrieving solar photovoltaic data information.

The comparative study of the two solar photovoltaic tracking systems presented in section 5.7

was achieved via cloud computing. The cloud computing process provided access to the

energy data generated by the solar photovoltaic systems through virtualised resources,

parallel processing, security and data service integration with retrievable scalable data

storage. The cloud computing platform has minimised the cost and restriction for automation

and computerisation by individuals and enterprises on a large-scale, thus providing a

reduction in infrastructure maintenance cost, efficient management and friendly user access

of the energy generated data.

5.5 Comparative Solar Photovoltaic Tracking Systems under Investigation

In this section, two of the four zones described in Section 5.3, are evaluated and

comparatively analysed by observing the same physical and environmental conditions. The

two solar photovoltaic tracking systems under investigation are the 450 stationary inclined

solar photovoltaic systems and azimuthal-altitude GST 300-axis solar tracking system. The

output energy efficiencies of the solar energy harvested are compared between the two solar

photovoltaic tracking systems. The azimuthal-altitude dual GST 300-axis is classified as a

dynamic solar photovoltaic energy system whilst the 450 stationary inclined solar


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photovoltaic tracking system is classified as a static (fixed) solar photovoltaic energy system

respectively.

The static (fixed) solar photovoltaic energy system involves the installation of solar

photovoltaic modules at a permanently inclined position over its lifetime. The inclined

installation angle varies depending on the geographic location and best specified sun-rising

position observed throughout the year. The earth rotates relative to the sun’s position,

therefore the inclined installed solar photovoltaic module loses track of the sun’s

concentration and orientation resulting in a drop-off of the maximum expected output energy

performance. The maximum expected output energy performance of the static solar

photovoltaic energy system is directly proportional to the amount of sunlight absorbed.

In addition, the maximum expected output energy performance depends on the solar

irradiance intensity in a clearer air evading the possibility of shading on solar photovoltaic

modules, the size of solar panel area, the solar panel orientation and the tilted installation

angle of the solar photovoltaic module. For any fixed solar photovoltaic energy system, the

global tilt insolation is the best-advised orientation for optimal maximisation of the annual

insolation. The global tilt insolation involves the installation of a solar photovoltaic module at

an angle approximately close to the latitude of the site location [190, 191].

The fixed solar photovoltaic energy system installed at a 450 inclination angle on the roof

platform of the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C for the

comparative research study is shown in Figure 70 [178].

Figure 70. Fixed solar energy system installed at a 450 inclination [178]


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The dynamic solar photovoltaic tracking system involves the movement of solar photovoltaic

modules to constantly be in perpendicular alignment to solar irradiance throughout the day.

The dynamic solar photovoltaic tracking system increases the amount of energy harvested as

compared to the fixed solar photovoltaic tracking system for the same configuration. This

solar photovoltaic tracking system involves the combination of the use of solar sensors and

programmable-logic-controller for its tracking system. The combination of the solar sensor

and the use of programmable-logic-controller tracking system is known as a hybrid dynamic

solar photovoltaic tracking system. This has proven to be very effective and efficient for the

dual-axis solar photovoltaic tracking system [38, 192].

The movement of the dynamic solar photovoltaic tracking system is thus classified into two

categories:

(i) The single axis sun tracking system and

(ii) the dual-axis sun tracking system [193].

The single-axis dynamic solar photovoltaic tracking system implementation involves the

movement of the solar photovoltaic module along one degree of freedom. The dynamic

single-axis solar photovoltaic tracking system implementation is categorised into four

distinctive tracking systems:

(i) the horizontal single axis tracking system (HSAT),

(ii) the vertical single axis tracking system(VSAT),

(iii) the tilt single axis tracking system (TSAT) and

(iv) the polar aligned single axis tracking system (PASAT) [194].

HSAT- In the horizontal single axis tracking system, the axis of rotation is along the

horizontal with respect to the ground, to apparently track the motion of the sun through the

day.

VSAT- In the vertical single axis tracking system, the axis of rotation is along the vertical

with respect to the ground; it apparently tracks the sun by rotating the solar photovoltaic

module from east to west through the day.

TSAT- In the tilt single axis tracking system, the axis of rotation is along the horizontal and

vertical along a fixed plane tracking the sun through the day.


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PASAT- In the polar single axis tracking system, the axis of rotation aligns with the earth’s

axis of rotation, tracking the sun at the site latitude through the day.

Dual-axis solar tracking implementation involves the movement of the solar photovoltaic

module along two degrees of freedom acting on the axis of rotation. The output energy

efficiencies of the dual axis tracking system, as compared to the single axis tracking system,

has proven to be more efficient.

The two common dual-axis solar tracking systems are:

(i) the tip-tilt dual axis tracker (TTDAT) and

(ii) Azimuthal-altitude dual axis tracker (AADAT) [195, 196].

TTDAT- The tip-tilt dual axis tracker – has its primary axis horizontal to the ground and the

secondary axis is typically normal to the primary axis. The axes of rotation are typically

aligned either along a true north meridian or an east-west line of latitude with the possibility

of an advanced tracking algorithm aligning in any cardinal direction.

AADAT- The azimuthal-altitude dual axis tracker – has it primary axis vertical to the ground

and the secondary axis is typically normal to the primary axis.

The azimuthal-altitude dual-axis solar photovoltaic GST 300 tracking system deployed for

the evaluation and comparative data analysis on the roof platform at the National Kaohsiung

University of Applied Sciences, Taiwan, R.O.C is shown in Figure 71[178]. A solar

photovoltaic module as shown in Figure 71 is installed on the aluminium framed structure of

the dual-axis solar photovoltaic tracking system having a Darfon MIG 240 inverter device

mounted at the backside of the photovoltaic module. All electrical wiring connections for

online solar photovoltaic energy data monitoring and comparative analysis with the 450

stationary inclined solar photovoltaic tracking system is being set up for investigation in this

chapter.


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Figure 71. GST 300 tracker deployed at the roof platform [178]

The architectural design for the dual-axis solar tracking frame structure is shown in Figure 72

[178]. The solar photovoltaic sensor is connected to the centre of the top of the aluminium

rectangular frame structure to effectively track the sun’s path and relative position for energy

optimisation increasing the efficiency of harvested solar energy. In addition, the

programmable logic controller junction box is installed at the base of the pole with a pre-

programmed analytical derivation of the sun’s tracking position in the database system to

cause rotational movement of the tracking structure in synchronisation with the solar

photovoltaic sensor at the centre of the top of the aluminium framed structure tracking

system.


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Figure 72. Architectural framework of the GST 300 tracker [178]

The combination of these two tracking components, the solar photovoltaic sensor and the

programmable logic controller, synchronously work to effectively judge the exact present

position of the sun and elevation of the solar framed structure ensuring constant

perpendicular tracking of the sun throughout the day. This improves the overall output energy

harvested as a result of the tracking orientation and movement of the framed structure

throughout the day.

5.6 Data Management and Presentation of a Solar Photovoltaic Tracking

System

Online data management and presentation of solar photovoltaic tracking systems have

significantly brought transformation and evolution in the energy management system helping

to address the need of decentralisation, easy flexible data management of different solar

farms mapping and integration to the grid system. The data management system makes it

easy for fault detection and location since each of the installed solar photovoltaic modules has

an identification label for the optimisation performance of the solar photovoltaic energy grid

system [178].


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In addition, the data management system provides a uniform platform interface for

determining simultaneously the output energy efficiencies of different solar photovoltaic

modules under the same physical and environmental conditions at a glance. The data

management system supports the integration and management of information from a web-

based architectural design and technologies defining each specific photovoltaic module

design with the end user support. The data acquisition, processing, storing and reporting are

transmitted through a dedicated IP address gateway for remote access logging and control on

mobile devices, tablets and PCs.

In particular, the solar photovoltaic data information obtained is time specific based on multi-

threaded functionalities to manage and monitor multiple online requests by remote users of

the output solar photovoltaic characteristics [197]. Remote users and operators have easy

access to database information at the solar farm site via the web through the proprietary

Darfon or any alternative software applications. Remote users and operators have no

permission rights and authority to alter any configuration of the solar photovoltaic model

information in the database system; the administrator has the sole authorization. The GUI

provides the individual input and output solar photovoltaic characteristics measurement for

each of the solar photovoltaic modules connected to the Darfon micro inverter [178].

The GUI provides direct information about the solar insolation parameters available at any

period of the day such as the inverter ID, Eac today, VpvA, IpvA, PpvA, VacA, IacA, PacA and

FacA respectively. The GUI appearance for gaining access to the processed harvested solar

energy database information for each of the installed solar photovoltaic module

characteristics at any remote location is as shown in Figure 73 & Figure 74 respectively.

Figure 73 shows the graphical user interface for the remote Darfon data logger solar solution.


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Figure 73. Graphic User Interface of the remote Darfon

data logger [178]

Figure 74. An overview of the solar modules installed on

roof building [178]

Figure 74 provides the general overview of the installed solar photovoltaic modules at the

roof platform at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C. The

GUI in Figure 74 shows that sixteen out of the seventeen installed solar photovoltaic modules

were online and one of the modules is offline. The offline solar photovoltaic module

configuration characteristics are easily detected through the diagnostic tool provided by the

software application and the actual location of the installed faulty solar photovoltaic module.

Other vital information about the photovoltaic modules can be accessed, monitored for

maintenance and fault rectification.

The solar photovoltaic data monitoring GUI achieves the following objectives:

(i) Data capturing throughout the period of the day.

(ii) Display of numerical data and graphics of the yearly, monthly, daily and hourly

energy statistics.

(iii) Display of the energy statistics generated per minute, total energy produced, total

estimated amount of CO2 emission reduction achieved and the total amount of

money saved by each module per day.

(iv) The processed data is presented online in Excel format for easy analysis and

retrieval.


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The GUI for the comparative evaluation of the two solar photovoltaic tracking systems under

analysis is as shown in Figure 75 & Figure 76 respectively. Figure 75 shows the graphical user

interface for the 450 stationary solar photovoltaic data monitoring system. The interface shows

the overview of the energy produced, today’s energy produced, total energy produced, the

amount of CO2 reduction achieved from a single solar photovoltaic module and the estimated

amount of energy saved. Similarly, Figure 76 shows the graphical user interface for the

azimuthal-altitude dual-axis providing the same information.

At a glance, comprehensive information about the two systems is available for remote users.

Figure 75.GUI for the 450 stationary solar systems[178] Figure 76. GUI for the Azimuthal-altitude dual solar

system[178]

5.7 Presentation of Results and Discussions

This section briefly discusses and presents some of the significant results achieved during the

comparative evaluation of the two solar photovoltaic monitoring systems under consideration

in this research study. The real-time online comparative solar photovoltaic monitoring

systems for the month of July (from 01/07/2014 to 31/07/2014) has been used for evaluation

analysis. The robust real-time online solar photovoltaic data monitoring system is deployed to

monitor the comparative performances between the 450 stationary solar photovoltaic tracking

system and the azimuthal-altitude dual-axis solar photovoltaic tracking system at the National

Kaohsiung University of Applied Sciences, Taiwan, R.O.C [178].


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The overall comparative energy output efficiency of the azimuthal-altitude dual-axis over the

450 stationary solar photovoltaic monitoring system as observed in Figure 75 and Figure 76

respectively is approximately 72% based on the total energy produced, estimated money

saved and the amount of CO2 reduction achieved.

In particular, Figure 77 and Figure 78 respectively shows the daily profile for the mean daily

total energy produced for the month of July 2014. It is observed from these figures that the

daily total energy produced for the azimuthal-altitude dual-axis for the month of July was

found to be 39.93 KWH is relatively higher than the 450 stationary solar photovoltaic

tracking systems which were found to be 21.85KWH subject to variation in solar insolation

level and temperature during each day. In comparing the total amount of energy produced by

the two tracking systems, it was found that the azimuthal-altitude dual-axis tracking systems

was 68.43% efficient considering the overall daily generated energy for the month.

Moreover, it is be observed that energy produced from day 16 to day 21 for the month of July

2014 was almost relatively zero due to the typhoon and bad weather condition during this

period [178].

Similarly, a 24-hourly graphical energy chart generated by the 450 stationary and the

azimuthal-altitude dual-axis solar photovoltaic tracking systems are as shown in Figure 77

and Figure 78 respectively under the same solar insolation, temperature, humidity and wind

direction for the last day of the month in July. A close-by visual observation of the figures

clearly underscores a significant increase in the amount of harvested energy by the dual-axis

solar photovoltaic tracking system as compared with the 450 stationary solar photovoltaic

tracking system from the second to the fifteenth hour with corresponding wattage energy

generated during this last day of the month.


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Figure 77. Daily profile of the mean daily total energy

450 for the stationary solar systems [178]

Figure 78. Daily profile of the mean daily total energy

for the Azimuthal-altitude dual solar system [178]

Another critical aspect of the result of the comparative analysis study is the initial cost

implementation and installation period for the two solar photovoltaic tracking systems under

evaluation. The initial installation setup period and cost implication for the azimuthal-altitude

dual-axis solar photovoltaic energy system is relatively high as compared to the 450 stationary

solar photovoltaic energy system.

Based on the achieved and calculated results for the month of July, the estimated hourly

profile for the 450 stationary solar photovoltaic energy system was found to be 1124W and for

the azimuthal-altitude solar photovoltaic energy system, it was found to be 1515W. The

overall comparative hourly energy efficiency of the azimuthal-altitude dual-axis over the 450

stationary solar photovoltaic energy system is approximately 74.2%. It is evident that over

the installation lifetime as observed in Figure 79 and Figure 80 respectively, the energy

harvested from the dual-axis solar photovoltaic system throughout its lifetime will

significantly outweigh the 450 stationary solar photovoltaic energy system in terms of

estimated amount of money saved hourly irrespective of physical and environmental

conditions.


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Figure 79. Hourly profile of the mean daily total energy

for the 450 stationary solar systems[178]

Figure 80. Hourly profile of the mean daily total energy

for the Azimuthal-altitude solar systems[178]

However, the stationary solar photovoltaic system has an added advantage over the dual-axis

solar photovoltaic system in terms of requiring less periodic maintenance, non-regular

replacement of faulty rotating parts and overall installation cost efficiency as compared to the

latter tracking system. The report generated from the Darfon micro-inverter is presented for

simple analysis, monitored in a tabular form for both the stationary and dual-axis solar

photovoltaic tracking systems respectively. The raw data obtained for the 450 stationary and

the azimuthal-altitude dual solar photovoltaic tracking systems is shown in Table 11 and 12.

In addition, the total amount of energy produced and the overall comparative hourly energy

efficiency by the two tracking systems are given in Table 13 and 14 respectively in Appendix

A.2.

5.8 Conclusion

A robust real-life and real-time online solar photovoltaic data monitoring system framework

has been carefully examined in this chapter to investigate and compare the output energy

harvested by the 450 stationary and the azimuthal-altitude dual-axis solar photovoltaic module

tracking systems. The solar photovoltaic data monitoring and tracking system design

implemented in this chapter involves cloud computing technology, online remote access

monitoring via the web, data storage retrieval and graphic visualisation charts of energy

harvested.


152

The uniqueness and robustness in the design implementation of the Darfon micro-inverter

installed at the back of the solar photovoltaic module for seamless conversion of DC power to

AC power from each solar photovoltaic module removes the need for a separate central

inverter system reducing installation lifetime inefficiency and costs implications.

In addition, this chapter makes a clear distinction from previously proposed research by

contributing to academic knowledge, the newly robust real-time online solar photovoltaic

data monitoring devices to assess performances in determining the maximum energy

harvested from each of the solar photovoltaic modules under varying physical and

environmental conditions over the lifetime of the installation. The results of the newly

proposed online real-time comparative solar photovoltaic data tracking systems for the

energy forecast database is thus presented with detailed figures in this chapter and

appendices.


153

Chapter 6 Conclusion

6.1 Introduction

This research sets out to investigate the modelling and simulation of an efficient smart solar

photovoltaic grid system using the MATLAB/Simulink toolbox by employing two classical

algorithm methods, the neural network and sparse based algorithm simulation techniques to

improve the quality of design and efficiency optimisation of the output energy for solar

photovoltaic modules. The research also critically considers the astronomy and analytical

derivations integrated into the programmable logic controller of the dynamic solar

photovoltaic tracking system in a real-life environment comparing and analysing the benefits

of the two solar photovoltaic tracking systems under investigation in this research.

Through reviewing the relevant literature in relation to solar sensor tracking optimisation

devices, solar photovoltaic tracking optimisation techniques, smart grid systems, solar energy

policy, astronomy and analytical derivation for dynamic smart solar photovoltaic systems, the

context and background for this study of modelling and simulation of dynamic smart solar

photovoltaic grid system was established, the theoretical and practical frameworks were

outlined and specific research questions identified.

In chapter 3, the research methods identified the most proficient technique to solve this

particular research puzzle of modelling and simulation of static smart solar photovoltaic grid

systems in ensuring maximum power point tracking efficiency, optimisation of the design

and improving the efficiency of the output energy were chosen. Two classical modelling and

simulation techniques were adopted in the research methods and have successfully provided

answers to the research questions as set out in sub-section 1.62 in chapter 1 of this thesis.

In chapter 4 of this thesis, analytical and theoretical governing equations for the dynamic

smart solar photovoltaic tracking system was thoroughly examined and the simulink design

for implementing the static smart solar photovoltaic grid system established.

In chapter 5 of this thesis, a robust real-time smart solar photovoltaic data monitoring system

research was conducted at the National Kaohsiung University of Applied Sciences, Taiwan,

the Republic of China comparing the output efficiency of the static and dynamic solar

photovoltaic tracking systems. The chapter also outlines the benefits of remote data access

and monitoring via the internet in retrieving and evaluating the energy output characteristics


154

of the dual-axis solar photovoltaic tracking system over the static solar photovoltaic tracking

system.

This concluding chapter presents a concise deduction integrating all the results achieved in

the previous chapters. Furthermore, significant outcomes in the earlier chapters are discussed

and suggestions made for future research to further contribute to the existing body of

knowledge in understanding the robust real-time online dynamic smart solar photovoltaic

monitoring and tracking systems.

6.2 Impacts and Conceptualisation Benefits of this Research Study

Some of the key concepts and impacts of this research are briefly highlighted and discussed

in context and background of the existing research. The relevance and timeliness of the

research in light of the abundance of solar energy reaching the earth unlike other sources of

power generation which are scarce in some regions of the world. The global awareness of the

impacts and concepts of the solar photovoltaic energy industry has metamorphosized into

many innovative research institutions, creative solar power generation inventions and

contributions in helping to reduce the mammoth emissions of greenhouse gases (carbon

dioxide, chlorofluorocarbons (CFCs), methane, nitrous oxides and ozone) from the

conventional power generation stations contributing to the present crisis of global warming,

climate changes and weather conditions.

The results presented in chapter 5 clearly show the impacts and the benefits of the solar

photovoltaic energy industry, in terms of the total amount of energy produced, estimated

amount of money saved, energy produced from a solar photovoltaic module, inverter status of

the smart solar photovoltaic grid system and the amount of CO2 reduction achieved. The

solar photovoltaic energy policies with government provisional support schemes on rebates

and grants for homes and businesses encourages private participation to reduce carbon

footprints in small and large-scale systems by promoting clean energy generation, thereby

helping owners save a substantial sum on utility bills now and in the future.

The concepts and potentials of using computational modelling in simulating solar

photovoltaic module systems are equally important for improving its overall performance

before actual installation. This facilitates efficient solar photovoltaic module design and

quality improvement by ensuring maximum power point tracking (MPPT) is achieved under


155

any environmental conditions (variable solar irradiance and temperature) due to the peculiar

nonlinear characteristics nature of the solar photovoltaic module. The computational

modelling approach offers remarkable progress in many research fields providing scholars

with a powerful software tool in understanding the characteristic behaviour through cognitive

learning theory with graphical representation and interpretations. Furthermore, the

computational approach helps in analysing built models and making inferences to generic

modelling equations to validate the relationship between structural mathematical equations

underlying the model and research hypotheses.

The energy market is moving from being environmentally green to economically green. The

assessment impacts of small and large-scale photovoltaic systems installed in remote areas

improve the power quality through dispersed renewable generation contributing to

sustainable development of human activities. The ongoing global campaign and support for

environmentally renewable energy sources against conventional power generation options are

obvious because of its negative contribution to air pollution, climate change, water and land

pollution, landscape degradation and harmful radiation emissions. The socio-economic

benefits are massive, providing job opportunities and security for teeming unemployed

citizens and diversification in renewable energy supply encouraging decentralisation of

national grid networks into regional grid networks.

6.3 Significance of Classical Modelling Algorithms on solar photovoltaic

systems

The classical modelling algorithm employs tools from mathematical logic to answer

modelling and theoretical questions arising from algorithmic issues in nonlinear mathematical

structures, modelling data and computations. The classical modelling algorithm in solar

photovoltaic systems provide solutions for complex non-linear mathematical equation models

offering accurate predictions and generalisation under variable input parameters and

conditions.

As has been thoroughly examined in chapter 3, the significance of the two classical

modelling algorithms on the smart static solar photovoltaic module, namely neural network

and sparse based algorithm model in the optimisation improvement and design of high

quality efficient long lasting solar photovoltaic modules, is fundamental for solar


156

photovoltaic manufacturers. The algorithm model ensures a high tolerance level achieving

superlative output consistency and quality checks of the solar photovoltaic modules.

However, classical modelling and simulation explores and estimates the crystal structure and

electrical behaviour of the solar photovoltaic module with respect to changes on

environmental parameters such as temperature and irradiance level. The solar photovoltaic

simulation model uses iterative analysis to evaluate the characteristics model compared with

the conventional model. The datasets for simulation are subdivided into three distinctive

segments namely training, validation and verification sets to assess the performance of the

model. This provides a relatively low-cost way of collecting information for efficiency

optimisation in design due to the complex nature of the solar photovoltaic modules.

6.4 Significance of the Simulink Solar Photovoltaic Design Model

The Mathworks simulink tool is used in various research fields for design processes, image

and pattern recognition, image tracking processes, constructing models for detailed analysis

and code generation, capturing model performances characteristics and integration of

simulink block components versatility in model testing capabilities. This tool enables

flexibility for software application users and engineers working on complex models, control

models, unrealistic applications to design an algorithm process providing a unique solution

by employing advanced methodologies derived from adaptive, nonlinear and robust control

theories to achieve the intended objectives.

The simulink solar photovoltaic model concepts are built on the implementation of open-

system and user-friendly simblock sets in the Matlab toolbox with the flexibility of

modifying the design to accommodate future expansion. The simblock sets are used in power

engineering fields to build the intended design model by assembling different simulink block

component models suitably creating a user-friendly system validating the model with the time

domain solver configuration. The simulink block libraries permit the designer to select and

connect block models of choice from the library parameters and components facilitating

analysis, testing interfaces and nodes, displaying graphical and numerical figures and

variables respectively at connected terminal scopes.

However, the Matlab/Simulink implementation orientates from a perceived process to

address a particular challenge, having a foreknowledge of the intended design objectives,


157

understanding complex requirements and concepts to be transformed into an expected desired

solution. The software tool makes handling complex dynamic analysis in engineering and

non-engineering designs easier with advantages of simulating intended designs with

possibilities of making what is abstract real in its final output presentation. The

Matlab/Simulink software tool is a powerful, versatile and portable tool providing an easy

transition from model-based integration design environment to real-world state-of-the-art

solutions where performance has precedence over price, especially in research fields.

6.5 Benefits of Robust Online Cloud Computing Solar Photovoltaic

Tracking Systems

The emergence of cloud computing technologies in smart solar photovoltaic tracking systems

has made a tremendous impact in the smart solar photovoltaic energy industry through the

use of information and communications technology (ICT) devices for hosting and delivering

energy data information via the web. This platform has been very powerful, reliable and cost-

efficient revealing the current state-of-the-art implementation redefining and making the

renewable energy industry attractive to private, public, foreign and government investors.

Since the inception of cloud computing technologies, many definitions have emerged from

literature; the national institute of standards and technology (NIST) describes it as a model

for enabling ubiquitous, convenient, on-demand network access to a shared pool of

configurable computing resources (e.g. networks, servers, storage, applications, and services)

that can be rapidly provided with minimal management effort and service provider

interaction.

The cloud computing technology is similar to grid computing established on two foundations;

namely information technology (IT) and commercial dexterity. IT is constantly evolving with

fast innovations driven by scientific computational intensive applications in scalable physical

and virtual hardware resources of high-speed processor computers, servers, tablets, mobile

devices, etc. and user-friendly, flexible software resources. The commercial dexterity

perspective of cloud computing challenges the energy industry in providing a cutting-edge

technological cloud solutions functionality and interactive applications responding in real-

time for users globally for rapidly scalable deployment. The stakeholders of commercial

cloud computing offer transaction deals, installation agreements, awarding licensing to


158

private and public organisations, consultation and periodic maintenance services of

technological expansion.

Clouding computing technology architecture has independently revolutionised the smart solar

photovoltaic tracking systems by helping to solve the daunting challenges for up-to-date

access of harvested energy data remotely without a physical presence at the installation site.

The advent of cloud computing technology significantly reduces the complexities of

information technology, recurring maintenance, operational and management services costs.

It has significantly reduced the logistic implication of access to huge energy data centers via

the web backbone and cheap power withdrawing physical computer data infrastructure within

the premises of installation. This technology has been able to ensure the provision and

protection of data security, privacy protection, retrieval of energy data and standardizing the

interfaces between various applications over the seamless web network.

The benefits of cloud computing architecture in robust online comparative solar photovoltaic

tracking and monitoring systems cannot be overemphasized; this has been extensively

discussed in chapter 5 of this research. For instance, in section 5.6, the overview of the

installed solar photovoltaic systems is remotely monitored providing an online and offline

status of any of the solar photovoltaic modules on-site. The GUI for the solar photovoltaic

module, provides data information about each of the installed solar photovoltaic modules,

providing detailed information about the amount of energy produced, the daily energy

produced, total energy produced, CO2 reduction, estimated money saved and graphical

energy chart on a daily, monthly and yearly basis. Hence, this gives any authorised user

access to solar photovoltaic data information via the web, to have an instant situation report

of the status of the solar photovoltaic plant system for fault detection and urgent need for

restoration of the plant system to its full capacity and for regular periodic service

maintenance.

6.6 Evaluation of Simulation Smart Solar Photovoltaic Tracking Systems

Computational modelling of the non-linear solar photovoltaic module characteristics has

received much attention in the recent literature using mathematical equations or numerical

approximations for validation of module characteristics under variable insolation levels,

temperatures and degradation conditions. The Matlab/Simulink software tool is employed to

determine the maximum power point tracking (MPPT) of the solar photovoltaic module for


159

optimal operation, which strongly depends on the matching load and tracker characteristics

resulting in a better overall performance.

The software tool used in modelling possesses the capabilities of being flexible, compatible

and user-friendly with the intent of validating the proof-of-concept for solar photovoltaic

modules prototypes. The computational simulation for the virtual solar photovoltaic module

emulates the expected response in real-life situations, validating the experimental data of

commercial photovoltaic arrays. The results of the simulation experiments performed on the

solar photovoltaic module using the neural network and sparse based algorithm have been

presented in chapter 3 of this thesis.

Furthermore, computational modelling has enhanced advancement in theory and research on

complex behaviours and systems, developing better performance evaluation by using the

software tool to improve the optimal efficiencies in qualitative engineering design attributes,

minimising drawbacks in real-life circumstances to achieve the potential benefits through the

modelling process. This modelling approach significantly facilitates new framework designs

to surpass obsolete proved validated results by improving on the existing underpinning

research areas at low-cost and in a more convenient environment.

Simulation offers abstraction mechanisms for researchers to critically examine models

without mutilating simulators, ratifying abstractions by comparing detailed and abstract

results. Simulator tools can be integrated seamlessly with emulator interface to improve the

expected quality of design in order to achieve desired results. Nonetheless, irrespective of

whatever complex systems are undertaken by the simulator and emulator interface, the

performance results can be dynamically and visually presented in a unique and very clear

way for understanding. The expandability of boundaries of the simulator and emulator

software tool to accommodate new additional functionalities to explore and achieve an

improved and unique design make computational modelling interesting to researchers in

various fields.

6.7 Significance of this Research

Several smart solar photovoltaic simulation and modelling algorithms have been proposed in

the literature. However, all converge towards emphasizing the common graphical charts of

the current-voltage (I-V) and power-voltage (P-V) solar photovoltaic characteristics under

variable insolation levels and temperatures. In the process of answering the research


160

questions as identified in chapter 1 of this thesis, this doctoral research makes a number of

significant contributions, academically and to the commercial solar photovoltaic energy

industry by achieving an accuracy of about 99% with the statistical parameters chosen. The

primary aim of this research was to present a novel cloud computing robust real-time online

comparative monitoring of two solar photovoltaic module tracking systems using simulation

and modelling approach employing the neural network and sparse based regression algorithm

to improve the quality design of photovoltaic modules.

This thesis has presented a cloud computing robust real-time online comparative solar

photovoltaic tracking systems which have been extensively discussed in chapter 5, relating

the innovative research measures of accessing energy data remotely on mobiles, tablets and

PCs at any period of the day. The robust adaptive and tracking devices have substantially

improved on the optimisation, performance and high concentration of harvested energy in

hybrid solar photovoltaic tracking systems. The cloud computing architectural design for the

robust real-time online solar photovoltaic monitoring system is deployed on the roof platform

at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C, which has been

described in chapter 5. The design combination phase is supported by a unique

interconnectivity of robust electronic component devices and tracking system devices.

This research proposed a new simulation and modelling approach based on a comparative

study of two classical neural network methods for the static solar photovoltaic module

(SSPV) under variable input parameters and conditions. The comparative analysis and

performance were based on the general mathematical model equation of the simplest model

of an equivalent circuit solar photovoltaic module. The mean square error (MSE) and

autocorrelation coefficient metrics were employed to measure the output performance and an

accuracy of approximately 99% was achieved with negligible mean square error value

providing precise prediction and generalisation on the quality lifespan of the solar

photovoltaic module in the face of degradation.

Similarly, a sparse based regression algorithm estimation simulation and modelling were

conducted on the static solar photovoltaic module (SSPV) to measure the performance,

efficiency and reliability of the photovoltaic module. The mean square error (MSE), root

mean square error (RMSE) and standard error of estimate metrics were used to measure the

performance of the three regression methods under investigation to evaluate the maximum

power point tracking for current, voltage and power respectively. Statistical based data results


161

of the feasibility and performance studies are reported in chapter 3 evaluating the

performance of these three regression methods.

Alongside the simulation and modelling benefits, this research has proffered transforming

possibilities of information and communications technology (ICT) integration with seamless

remote energy data transmission and accessibility has been established. The solar renewable

research engineers and managers have the opportunity of a first-hand information about the

installed solar photovoltaic array onsite providing interdependent remote access to the

harvested energy data through monitoring on hourly, daily, monthly and yearly basis without

a physical presence at the site location, thereby solving the perennial fundamental challenge

of retrieving accurate harvested energy data. This development framework and innovations in

robust real-time solar photovoltaic modules have increased the validity of energy data

harvested, output efficiency of the system and response feedback performance assessment.

Finally, this research has reviewed the smart solar photovoltaic grid tracking system devices,

solar photovoltaic energy policies, reliability perspective of the theoretical frameworks in

context and background. This doctoral research has made a valuable contribution to both the

academic world in published papers and commercially to the solar photovoltaic energy

industry. The research outcomes have been rationally presented as well in the chapters of this

thesis, some of the results are presented in the appendices. The robust real-time online solar

photovoltaic tracking systems integration with cloud computing technologies was

implemented at the National Kaohsiung University of Applied Sciences, Taiwan, R.O.C,

presenting a new innovation concept and design for the solar energy industry.

6.8 Recommendations for Future Research

While the study has made valuable contributions to both the academic world and the

commercial solar photovoltaic energy industry, it also highlights the need for further research

in a number of areas. Taking into consideration some of the research challenges such as

timeframes, manpower and cost implications of equipment required for this research

implementation, it was a challenge to cover all the scope of the research through a broader

perspective. Additionally, it was not feasible to perform simulation and modelling

experiments with other relevant engineering software applications due to costs and limited

funds allocation for this doctoral research study.


162

Further research work is required to enhance and improve on the novel robust real-time

online cloud computing solar photovoltaic monitoring system deployment on a large scale. In

addition, the introduction of newly robust adaptive tracking devices and designs for

maximum optimisation of the solar photovoltaic tracking system would provide a more

proficient way of accessing harvested energy information via the web overcoming the

outmoded energy data report challenges. Given the importance of this novel discovery of

accessing harvested solar energy data from solar photovoltaic arrays on mobiles, tablets, PCs

and other devices remotely, this study can be extended and applied to other renewable energy

sources of power generation enhancement in small, medium and large-scale deployment.

Other areas for future research extension are in the introduction and application of newly

developed software engineering tools on methodologies to improve the conducted model tests

and quality of the solar photovoltaic module design. Research on the new software

applications needs to be monitored by employing the same simple standard equivalent circuit

with the mathematical equation for a solar photovoltaic module to validate and improve on

the results. The use of this new software will determine how much improvement is

achievable on the quality of the design model for the solar photovoltaic module. This

research has developed an empirical model fit in the simulation and modelling experiments

performed in chapters 3 and 4 respectively, though this needs further improvement to

establish its validity and reliability across a wider range of software application tools.

In conclusion, there is a growing body of knowledge and interest in this new aspect of cloud

computing technology integration with solar photovoltaic energy providing real-time

harvested energy data. This should be encouraged in energy conferences and journal research

institutions to participate in further discovery of new qualitative and innovative design

concepts in this industry. Furthermore, additional simulation and modelling experiments need

to be carried out with the introduction of new engineering software application tools

identifying the demand for a holistic approach to quality improvement and assurance of the

solar photovoltaic module. The solar photovoltaic energy industry is continuously undergoing

review in ensuring the renewable energy targets (RETs) for the industry is achievable. The

RETs welcome collaboration with other sustainable clean energy projects for pioneering

research efforts mainly to fill the gap in solving the global climate control challenges and

greenhouse gases (GHG) emissions contributed by the power generation industry.


163

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Appendix A

Thesis Appendices

A.1 Regression Algorithm Model

The programming algorithm used in implementing the three regression models for the static

solar photovoltaic array to generate the output performance for the tabular and graphical

characteristics shown in Section 3.5.2.6 for the Ordinary Least Squares regression , Logistic

Robustfit regression and Least Trimmed Squares regression is written using the

Matlab/Simulink software package and are giving in Figure 81, Figure 82 and Figure 83

respectively.

clear all

clc

inputs =[ ]; T = [ ];

Io = [ ];

Iph = [ ]; I_init = 2.8;

VT = [ ];

Voc = [ ]; c = [ ];

d = [ ];

Vmp = [ ]; Imp = [ ];

N = [ ];

ki = [ ]; a = [ ];

Ish = [ ]; % constants

Ior = 19.963*10^(-5);

q = 1.602*10^(-19); k = 1.380658*10^(-23);

Tr = 301.18;

A = 1.50; Iscr = 3.3;

Ns = 1000;

Np =10; Eg = 2.349*10^(-19);

Ta = 20;

Rs = 5*10^(-1000); Rsh =2.5*10^(3.8);

V = 12;

last = 1; T(1) = 0 ;

for s = 100:10:1000 for Ws =1:2:20

T(last)= 3.21 + 0.25*s + 0.899*Ta - 1.3*Ws + 273; inputs(last,:) = T(last) ; %[s T(last) Ws];

Io(last) = Ior*(T(last)/Tr)^3*exp(q*Eg/(k*A)*(1/Tr-1/T(last)));

N = Ns + Np; a(last) = (A*k*T(last)*Ns)/q;

ki(last) = 0.0017 ; %(a(last)*q/(A*T(last)*N));

Iph(last) = ( Iscr + (ki(last)*(T(last)-Tr))) * (s/100); c(last) = 1 + log(Iph(last)/Io(last));

d(last) = c(last)/(c(last)+1);

Imp(last) = Iph(last)*(1 - c(last)^(-d(last))); VT(last) = ((k*T(last))/q);

if (last == 1)

%I(last) = Iph(last) - Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh; I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh;


174

else

%I(last) = Iph(last) - Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh;

I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh;

end

Ish(last) = ((V + I(last)*Rs)/Rsh); Voc(last) = A*VT(last)*log(Iph(last)/Ish(last)+1);

Vmp(last) = Voc(last) - VT(last)*log(1+((Voc(last))/VT(last)));

%Vmp(last) = Voc(last)*(1-(log(c(last))/c(last))); Pmp (last) = Imp(last) .* Vmp(last);

last = last + 1 ; end

end

%%

%Regression network

x = inputs'; t=Vmp;%Pmp;%Imp;%Vmp;% Voc;%(2:last)

rho=0.1; % the regularization parameter

% it is a ratio between (0,1), if .rFlag=1

%----------------------- Set optional items sparse least square------------------------

opts=[];

% Starting point

opts.init=2; % starting from a zero point

% termination criterion opts.tFlag=5; % run .maxIter iterations

opts.maxIter=100; % maximum number of iterations

% normalization

opts.nFlag=0; % without normalization

% regularization

opts.rFlag=1; % the input parameter 'rho' is a ratio in (0, 1)

opts.rsL2=0; % the squared two norm term

%----------------------- Run the code LeastR -----------------------

fprintf('\n mFlag=0, lFlag=0 \n'); opts.mFlag=0; % treating it as compositive function

opts.lFlag=0; % Nemirovski's line search

A=inputs;

y=t';

[x1, funVal1, ValueL1]= LeastR(A, y, rho, opts);

systemoutput1=A*x1; %%%%%%%%%%%%%%%%%%%%Ordinary Least Square Regression%%%%%%%%%%%%%

[bls,ab1,ab2,ab3] = regress(y,[ones(length(y),1) A]);

ypred = bls(1)+bls(2)*A; sls =sqrt(sum((y-ypred).^2)/length(y));

abs_error = abs(y-ypred);

mse = mean((y-ypred).^2); %rmse=rms(ypred-y)

RMSE= sqrt(mse);

[max_abs_error, maxpt] = max(abs_error); [r,p] = corrcoef(t);

[i,j] = find(p<0.05); % Find significant correlations.

[i,j] % Display their (row,col) indices rel_error = abs_error./y;

sls = sqrt(sum((y-ypred).^2)/length(y));

figure(1) scatter(A,y,'filled'); grid on; hold on

plot(A,bls(1)+bls(2)*A,'r-','LineWidth',2);

legend('Measured data',['Ordinary least square regression error = ' num2str(sls)])

hold on

%%

Figure 81. Ordinary Least Regression algorithm

clear all clc

inputs =[];

T = []; Io = [];

Iph = [];


175

I_init = 2.8;

VT = [];

Voc = [ ];

c = [];

d = []; Vmp = [];

Imp = [];

N = []; ki = [];

a = [];

Ish = []; % constants

Ior = 19.963*10^(-5);

q = 1.602*10^(-19); k = 1.380658*10^(-23);

Tr = 301.18;

A = 1.50; Iscr = 3.3;

Ns = 1000;

Np =1; Eg = 2.349*10^(-19);

Ta = 20;

Rs = 5*10^(-1000);

Rsh =2.5*10^(3.8);

V = 12;

last = 1; T(1) = 0 ;

for s = 100:10:1000

for Ws =1:2:20

T(last)= 3.21 + 0.25*s + 0.899*Ta - 1.3*Ws + 273;

inputs(last,:) = T(last) ; %[s T(last) Ws];

Io(last) = Ior*(T(last)/Tr)^3*exp(q*Eg/(k*A)*(1/Tr-1/T(last))); N = Ns + Np;

a(last) = (A*k*T(last)*Ns)/q;

ki(last) = 0.0017 ; %(a(last)*q/(A*T(last)*N)); Iph(last) = ( Iscr + (ki(last)*(T(last)-Tr))) * (s/100);

c(last) = 1 + log(Iph(last)/Io(last));

d(last) = c(last)/(c(last)+1); Imp(last) = Iph(last)*(1 - c(last)^(-d(last)));

VT(last) = ((k*T(last))/q);

if (last == 1)

%I(last) = Iph(last) - Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh;

I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh;

else %I(last) = Iph(last) - Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh;

I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh;

end Ish(last) = ((V + I(last)*Rs)/Rsh);

Voc(last) = A*VT(last)*log(Iph(last)/Ish(last)+1);

Vmp(last) = Voc(last) - VT(last)*log(1+((Voc(last))/VT(last))); %Vmp(last) = Voc(last)*(1-(log(c(last))/c(last)));

Pmp (last) = Imp(last) .* Vmp(last);

last = last + 1 ;

end

end %%

%Regression network

x = inputs'; t =

Imp;%Vmp;%Pmp;%Vmp;%Pmp;%Imp;%Pmp;%Vmp;%Pmp;%Imp;%Vmp;%Pmp;%Vmp;%Imp;%Vmp;%Pmp;%Vmp;%Imp;%Voc;%I

mp;%Vmp;%Pmp;%Imp;%Voc;%(2:last)



%----------------------- Set optional items sparse least square------------------------

opts=[];

% Starting point


% termination criterion

opts.tFlag=5; % run .maxIter iterations


176

opts.maxIter=100; % maximum number of iterations

% normalization

opts.nFlag=0; % without normalization

% regularization

opts.rFlag=1; % the input parameter 'rho' is a ratio in (0, 1)



fprintf('\n mFlag=0, lFlag=0 \n'); opts.mFlag=0; % treating it as compositive function

opts.lFlag=0; % Nemirovski's line search

A=inputs; y=t';


systemoutput1=A*x1; %%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%logistic regression%%%%%

[bls,ab1,ab2,ab3] = regress(y,[ones(length(y),1) A]); %ypred = bls(1)+bls(2)*A;

[brob] = robustfit(A,y,'logistic');

ypred = brob(1)+brob(2)*A;

sls =sqrt(sum((y-ypred).^2)/length(y));


mse = mean((y-ypred).^2); %rmse=rms(ypred-y)

RMSE = sqrt(mse); [max_abs_error, maxpt] = max(abs_error);

rel_error = abs_error./y;

srob = sqrt(sum((y-ypred).^2)/length(y)); figure(2)

scatter(A,y,'filled'); grid on; hold on

plot(A,bls(1)+bls(2)*A,'r-','LineWidth',2); legend('Measured data',['logistic Regression error = ' num2str(sls)])

legend()

hold on

Figure 82. Logistic Robustfit regression code

clear all

clc inputs =[];

T = [];

Io = []; Iph = [];

I_init = 2.8;

VT = []; Voc = [ ];

c = [];

d = []; Vmp = [];

Imp = [];

N = []; ki = [];

a = [];

Ish = []; % constants

Ior = 19.963*10^(-5);

q = 1.602*10^(-19); k = 1.380658*10^(-23);

Tr = 301.18;

A = 1.50; Iscr = 3.3;

Ns = 1000;

Np =1; Eg = 2.349*10^(-19);

Ta = 20;

Rs = 5*10^(-1000); Rsh =2.5*10^(3.8);

V = 12;

last = 1; T(1) = 0 ;

for s = 100:10:1000 for Ws =1:2:20


177

T(last)= 3.21 + 0.25*s + 0.899*Ta - 1.3*Ws + 273;

inputs(last,:) = T(last) ; %[s T(last) Ws];

Io(last) = Ior*(T(last)/Tr)^3*exp(q*Eg/(k*A)*(1/Tr-1/T(last)));

N = Ns + Np; a(last) = (A*k*T(last)*Ns)/q;

ki(last) = 0.0017 ; %(a(last)*q/(A*T(last)*N));

Iph(last) = ( Iscr + (ki(last)*(T(last)-Tr))) * (s/100); c(last) = 1 + log(Iph(last)/Io(last));

d(last) = c(last)/(c(last)+1);

Imp(last) = Iph(last)*(1 - c(last)^(-d(last))); VT(last) = ((k*T(last))/q);

if (last == 1)

%I(last) = Iph(last) - Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh; I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I_init*Rs)/(a(last))) - 1) - (V + I_init*Rs)/Rsh;

else

%I(last) = Iph(last) - Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh; I(last) = Np*Iph(last) - Np*Io(last)*(exp((V + I(last-1)*Rs)/(a(last))) - 1) - (V + I(last-1)*Rs)/Rsh;

end

Ish(last) = ((V + I(last)*Rs)/Rsh); Voc(last) = A*VT(last)*log(Iph(last)/Ish(last)+1);

Vmp(last) = Voc(last) - VT(last)*log(1+((Voc(last))/VT(last)));

%Vmp(last) = Voc(last)*(1-(log(c(last))/c(last)));

Pmp (last) = Imp(last) .* Vmp(last);

last = last + 1 ; end

end %%

%inputs=inputs/length(inputs);

%Pmp=Pmp/length(Pmp); clc

%Regression network

x = inputs'; x=x/length(x);

inputs=inputs/length(inputs);

t=Pmp;Vmp;Imp;%Vmp;%Pmp;%Vmp;%Vmp;%Pmp;%Vmp;%Imp;%Vmp;%Pmp;%Vmp;%Imp;%Voc;%(2:last) t=t/length(t);



%----------------------- Set optional items ------------------------

opts=[];

% Starting point


% termination criterion

opts.tFlag=5; % run .maxIter iterations opts.maxIter=100; % maximum number of iterations

% normalization opts.nFlag=0; % without normalization

% regularization opts.rFlag=1; % the input parameter 'rho' is a ratio in (0, 1)



fprintf('\n mFlag=0, lFlag=0 \n');

opts.mFlag=0; % treating it as compositive function opts.lFlag=0; % Nemirovski's line search

A=inputs;

y=t';


systemoutput1=A*x1;

%%%%%%%%%lts REGRESSION %%%%%%%%%%%%%%%%%%%%%%%% gamma=0.8;

result=mlts(A,y,gamma);

output=result; x2=result.dresR;

%%

ypred = A.*result.dresR; smlts1 =sqrt(sum((y-ypred).^2)/length(y));

mse = mean((y-ypred).^2);


178

rmse = sqrt(mse);


rel_error = abs_error./y;

figure(1)

scatter(A,y,'filled'); grid on; hold on plot(A,ypred,'r','LineWidth',2);

legend('Measured data',['MLTS regression error = ' num2str(smlts1)])

hold on %%

Figure 83. Least Trimmed Squares regression code

A.2 Real-time online Solar photovoltaic monitoring data

In this section, the online generated report from the comparative study for both the stationary

and dual-axis solar photovoltaic tracking system are presented in Table x and y respectively.

The obtained data were raw data obtained from the research study conducted at the National

Kaohsiung University of Applied Sciences, Taiwan, R.O.C.

Table 11 and 12 below shows the real-time online remote raw data obtained for the stationary

and dual-axis solar photovoltaic tracking system during one of the days. The GUI chart for

this specific day as been presented in comparison in Section 5.7.

Table 11. Stationary 450 Solar Photovoltaic Obtained Raw data

Time Temperature Eac_Today Vpv Ipv Ppv Vac Iac Pac Fac Eac_Total

31-07-14 2:10 24 0 22.1 0.95 0 218.5 0.065 0 60 172.16

31-07-14 2:11 24 0 24.8 0.95 0 218.7 0.065 0 59.96 172.16

31-07-14 2:12 24 0 26.1 0.76 20 218.6 0.067 14.6 59.96 172.16

31-07-14 2:13 24 0 23.9 0.86 20 218.8 0.069 14.6 59.96 172.16

31-07-14 2:14 24 0 26.6 0.95 0 218.6 0.066 0 59.96 172.16

31-07-14 2:15 24 0 29.3 1 0 218.8 0.065 0 59.99 172.16

31-07-14 2:16 24 0 23.1 0.91 21 218.8 0.07 14.8 60.04 172.16

31-07-14 2:17 24 0 22.8 0.95 21 218.7 0.07 15 59.99 172.16

31-07-14 2:18 24 0 26.2 0.88 22 218.6 0.068 18.7 60.04 172.16

31-07-14 2:19 24 0 22.3 0.95 21 218.5 0.071 15.2 59.98 172.16

31-07-14 2:20 24 0 24.6 0.87 21 218.4 0.072 15 60.02 172.16

31-07-14 2:21 24 0 24.3 0.91 22 218.4 0.082 17.4 59.98 172.16

31-07-14 2:22 24 0 22.4 1 22 218.8 0.083 17.2 60.12 172.16

31-07-14 2:23 24 0 30.3 1.04 0 219.1 0.066 0 60.04 172.16

31-07-14 2:24 24 0 28.3 0.78 22 219 0.078 17 60.04 172.16

31-07-14 2:25 24 0 30.5 1 0 219 0.065 0 60.06 172.16

31-07-14 2:26 24 0 28.3 0.78 22 219 0.08 16.8 60.05 172.16

31-07-14 2:27 24 0 28 0.81 22 219 0.081 18.1 60 172.16

31-07-14 2:28 24 0 27.1 0.81 22 219.2 0.079 18.4 60 172.16

31-07-14 2:29 24 0 26.6 0.84 22 219.1 0.077 18.1 59.94 172.16


179

31-07-14 2:30 24 0 26.6 0.84 22 219.1 0.084 17.7 60.02 172.16

31-07-14 2:31 24 0 26.7 0.84 22 219.1 0.08 18.1 59.98 172.16

31-07-14 2:32 24 0 27.4 0.81 22 218.8 0.082 17.7 59.94 172.16

31-07-14 2:33 24 0 27.6 0.81 22 219 0.082 17.9 60 172.16

31-07-14 2:34 24 0 27.5 0.81 22 218.6 0.081 17.7 59.95 172.16

31-07-14 2:35 24 0 27.7 0.81 22 219.2 0.078 18.1 60.04 172.16

31-07-14 2:36 24 0 28 0.78 22 218.8 0.08 17.2 59.91 172.16

31-07-14 2:37 24 0 28 0.81 22 219 0.083 17 60.04 172.16

31-07-14 2:38 24 0 28.4 0.78 22 217.9 0.08 17.4 60.03 172.16

31-07-14 2:39 24 0 28.2 0.78 22 218.9 0.081 17.9 60.02 172.16

31-07-14 2:40 24 0 28.1 0.75 21 218.9 0.076 16.6 59.95 172.16

31-07-14 2:41 24 0 28.9 0.78 22 218.6 0.077 17.2 59.99 172.16

31-07-14 2:42 24 0 28.9 0.78 22 218.9 0.083 18.1 60.13 172.16

31-07-14 2:43 24 0.01 28.8 0.78 22 218.8 0.079 17 60 172.17

31-07-14 2:44 24 0.01 29 0.75 21 218.6 0.077 16.3 60.01 172.17

31-07-14 2:45 24 0.01 28.9 0.75 22 218.4 0.076 17.4 59.99 172.17

31-07-14 2:46 24 0.01 27.2 0.88 24 218.5 0.098 20.9 60.05 172.17

31-07-14 2:47 24 0.01 26.6 0.96 25 219 0.099 21.6 60.03 172.17

31-07-14 2:48 24 0.01 26.6 1.03 27 218.9 0.11 23.4 60.02 172.17

31-07-14 2:49 24 0.01 27.7 1 27 218.8 0.106 23.6 59.96 172.17

31-07-14 2:50 24 0.01 26.2 1.07 28 219.2 0.105 24.1 60.09 172.17

31-07-14 2:51 24 0.01 25.9 1.12 28 219 0.11 24.2 60 172.17

31-07-14 2:52 24 0.01 27.4 1.03 28 218.8 0.112 23.8 59.95 172.17

31-07-14 2:53 24 0.01 28.1 1.03 29 218.9 0.113 25.3 59.98 172.17

31-07-14 2:54 24 0.01 28.4 1 28 218.9 0.112 24 60.03 172.17

31-07-14 2:55 24 0.01 28.4 0.96 27 218.9 0.111 23.6 59.99 172.17

31-07-14 2:56 24 0.01 28.2 1 28 218.8 0.112 23.8 59.94 172.17

31-07-14 2:57 24 0.01 28.6 1.03 29 218.6 0.107 24.7 60.03 172.17

31-07-14 2:58 24 0.01 29.3 0.93 27 218.9 0.106 23.4 60.06 172.17

31-07-14 2:59 24 0.01 29.6 0.96 28 218.8 0.111 24 60.04 172.17

31-07-14 3:00 24 0.01 30 0.93 28 218.9 0.111 24 60.02 172.17

31-07-14 3:01 24 0.01 30 0.9 27 219 0.112 23.6 60.03 172.17

31-07-14 3:02 24 0.01 29.9 0.96 29 219.1 0.094 24.9 60.13 172.17

31-07-14 3:03 24 0.01 30.3 0.96 29 219 0.118 25.1 60.04 172.17

31-07-14 3:04 24 0.01 30 0.73 22 218.8 0.093 19 60.02 172.17

31-07-14 3:05 24 0.01 30.3 1 30 218.6 0.119 26 59.96 172.17

31-07-14 3:06 24 0.01 30.5 0.96 29 218.6 0.112 25.1 60.06 172.17

31-07-14 3:07 24 0.01 30.6 0.93 28 218.2 0.112 24 59.96 172.17

31-07-14 3:08 24 0.02 30.8 0.9 27 218.6 0.112 22.7 60 172.18

31-07-14 3:09 24 0.02 30.8 0.9 27 218.8 0.105 22.7 60.06 172.18

31-07-14 3:10 24 0.02 31 0.96 29 218.8 0.115 25.1 60.04 172.18

31-07-14 3:11 24 0.02 31.1 0.96 30 219 0.116 26 60.07 172.18

31-07-14 3:12 24 0.02 31.2 0.93 29 218.6 0.1 25.1 59.92 172.18

31-07-14 3:13 24 0.02 31.3 0.96 30 218.7 0.08 26 59.99 172.18

31-07-14 3:14 24 0.02 31.4 0.93 29 218.7 0.086 25.1 60.02 172.18


180

31-07-14 3:15 24 0.02 31.4 0.96 30 218.5 0.079 25.5 60.01 172.18

31-07-14 3:16 24 0.02 31.5 0.93 29 218.5 0.111 25.3 60.02 172.18

31-07-14 3:17 24 0.02 31.5 0.7 22 218.6 0.114 17.2 59.99 172.18

31-07-14 3:18 24 0.02 31.7 0.93 29 218.7 0.111 24.9 60.06 172.18

31-07-14 3:19 24 0.02 31.8 0.9 28 218.7 0.118 24.2 60.06 172.18

31-07-14 3:20 24 0.02 31.6 0.93 29 218.5 0.083 25.3 60.03 172.18

31-07-14 3:21 24 0.02 31.9 0.87 28 218.3 0.102 24.4 60.01 172.18

31-07-14 3:22 24 0.02 27.5 1.22 33 218.5 0.13 28.4 60 172.18

31-07-14 3:23 24 0.02 26.9 1.25 34 218.6 0.135 29.5 60.07 172.18

31-07-14 3:24 24 0.02 27.2 1.25 34 219 0.136 29.7 60.1 172.18

31-07-14 3:25 24 0.02 28 1.32 37 218.9 0.15 33 60.04 172.18

31-07-14 3:26 24 0.02 27.7 1.4 38 218.7 0.152 33.4 59.99 172.18

31-07-14 3:27 24 0.02 27 1.42 37 218.9 0.151 33 60.02 172.18

31-07-14 3:28 24 0.02 27.2 1.4 38 218.9 0.152 33.2 59.97 172.18

31-07-14 3:29 24 0.03 27.2 1.4 38 218.6 0.153 33.2 60.03 172.19

31-07-14 3:30 24 0.03 27.6 1.44 39 218.4 0.156 34 60 172.19

31-07-14 3:31 24 0.03 28 1.37 37 218.6 0.149 32.5 60.09 172.19

31-07-14 3:32 24 0.03 27.4 1.37 37 218.4 0.152 32.9 60 172.19

31-07-14 3:33 24 0.03 27.5 1.4 38 218.9 0.154 33.7 60.11 172.19

31-07-14 3:34 24 0.03 28.1 1.46 41 218.9 0.169 36.7 60.03 172.19

31-07-14 3:35 24 0.03 28.3 1.53 43 219 0.178 38.5 59.95 172.19

31-07-14 3:36 24 0.03 27.4 1.62 44 219.5 0.181 39.2 60.04 172.19

31-07-14 3:37 24 0.03 28.5 1.57 44 219.2 0.178 39 60.02 172.19

31-07-14 3:38 24 0.03 27.5 1.62 44 219.3 0.179 39.6 60.03 172.19

31-07-14 3:39 24 0.03 27.8 1.66 45 219.3 0.187 40.7 60.07 172.19

31-07-14 3:40 24 0.03 28.2 1.57 44 219.1 0.181 39.4 60.04 172.19

31-07-14 3:41 24 0.03 28.2 1.6 45 219.2 0.191 40.9 60.04 172.19

31-07-14 3:42 24 0.03 27.9 1.55 42 219.3 0.172 37.5 60.07 172.19

31-07-14 3:43 24 0.03 27.9 1.42 40 219.1 0.162 35.2 60.03 172.19

31-07-14 3:44 24 0.03 27.7 1.55 42 219.2 0.169 37 59.99 172.19

31-07-14 3:45 24 0.04 27 1.59 43 218.7 0.177 38.6 59.98 172.2

31-07-14 3:46 24 0.04 28.6 1.89 53 219.3 0.22 48 60.08 172.2

31-07-14 3:47 24 0.04 28.2 1.96 55 218.9 0.227 49.6 59.94 172.2

31-07-14 3:48 24 0.04 28.4 2.03 57 219.5 0.236 51.3 60.04 172.2

31-07-14 3:49 24 0.04 28.2 2.03 57 219.3 0.238 51.9 59.96 172.2

31-07-14 3:50 24 0.04 28.5 2.1 59 219.5 0.243 53.1 60 172.2

31-07-14 3:51 24 0.04 27.7 2.14 58 219.5 0.241 52.6 60.05 172.2

31-07-14 3:52 24 0.04 28.6 2.03 57 219.2 0.234 51.3 60.01 172.2

31-07-14 3:53 24 0.04 27.7 2.07 56 219 0.232 50.5 60 172.2

31-07-14 3:54 24 0.04 28 2.03 57 218.9 0.239 52 60 172.2

31-07-14 3:55 24 0.04 27.8 2.07 58 219.3 0.239 52.3 60.08 172.2

31-07-14 3:56 24 0.05 28.1 2.14 60 219.2 0.247 54.3 60.01 172.21

31-07-14 3:57 24 0.05 28.1 2.17 61 219.5 0.254 55.5 60 172.21

31-07-14 3:58 24 0.05 27.7 2.21 62 219.4 0.259 56.8 59.98 172.21

31-07-14 3:59 24 0.05 28.2 2.32 65 219.6 0.272 59.5 60.03 172.21


181

31-07-14 4:00 24 0.05 28.3 2.39 67 219.6 0.28 61.7 60.04 172.21

31-07-14 4:01 24 0.05 28.2 2.35 66 219.2 0.275 60.3 59.96 172.21

31-07-14 4:02 24 0.05 27.9 2.29 62 219.2 0.261 56.9 60.03 172.21

31-07-14 4:03 24 0.05 27.8 2.44 66 219.2 0.274 60.3 59.95 172.21

31-07-14 4:04 24 0.05 28.6 2.39 67 219.2 0.28 61.5 60.09 172.21

31-07-14 4:05 24 0.05 27.9 2.14 58 218.9 0.24 52.7 60.05 172.21

31-07-14 4:06 24 0.06 27.2 2.26 59 218.8 0.249 53.5 59.93 172.22

31-07-14 4:07 24 0.06 28 1.96 55 218.8 0.225 49.6 60.05 172.22

31-07-14 4:08 24 0.06 26.6 1.96 51 218.3 0.209 45.8 59.92 172.22

31-07-14 4:09 24 0.06 27.5 1.74 47 218.1 0.197 42.7 59.99 172.22

31-07-14 4:10 24 0.06 27.5 1.51 41 217.7 0.167 36.3 59.98 172.22

31-07-14 4:11 24 0.06 27.1 1.48 40 217.7 0.16 35 59.97 172.22

31-07-14 4:12 24 0.06 27.3 1.4 38 217.7 0.153 33.3 59.99 172.22

31-07-14 4:13 24 0.06 26.7 1.51 41 217.6 0.165 36.1 59.94 172.22

31-07-14 4:14 24 0.06 28 1.55 42 217.8 0.17 37.2 59.93 172.22

31-07-14 4:15 24 0.06 27.3 1.51 41 217.5 0.169 36.7 60.01 172.22

31-07-14 4:16 24 0.06 27.8 1.85 52 217.3 0.224 47.1 60 172.22

31-07-14 4:17 24 0.06 27.9 1.92 52 216.9 0.215 46.6 60.1 172.22

31-07-14 4:18 24 0.06 28.2 1.78 50 216.8 0.206 44.6 60.05 172.22

31-07-14 4:19 24 0.06 27.7 1.85 50 216.7 0.206 44.6 60.04 172.22

31-07-14 4:20 24 0.07 27.8 1.88 51 217 0.211 45.9 60 172.23

31-07-14 4:21 24 0.07 27.4 2.29 62 217.5 0.262 56.7 60.13 172.23

31-07-14 4:22 24 0.07 28.4 2.5 70 217.4 0.298 64.7 59.99 172.23

31-07-14 4:23 24 0.07 28.5 2.53 71 217 0.301 65.5 60.09 172.23

31-07-14 4:24 24 0.07 26.8 1.88 51 216.6 0.21 45.7 60.02 172.23

31-07-14 4:25 24 0.07 27.9 1.75 49 216.4 0.206 44.3 59.99 172.23

31-07-14 4:26 24 0.07 27.8 2.37 64 216.9 0.269 58.5 60.1 172.23

31-07-14 4:27 24 0.07 28.7 1.82 51 216.1 0.212 45.7 60 172.23

31-07-14 4:28 24 0.07 28.3 1.89 53 216.2 0.221 47.5 60.02 172.23

31-07-14 4:29 24 0.07 27.7 1.96 53 216.2 0.222 47.3 60.1 172.23

31-07-14 4:30 24 0.08 27.8 1.74 47 215.8 0.197 42.5 60.02 172.24

31-07-14 4:31 24 0.08 26.2 1.96 51 216.1 0.211 45.5 60.06 172.24

31-07-14 4:32 24 0.08 27.2 1.81 49 216.1 0.203 43.8 60.04 172.24

31-07-14 4:33 24 0.08 29.3 2 58 216.2 0.241 52.5 59.98 172.24

31-07-14 4:34 24 0.08 27.8 2.37 64 218.6 0.27 58.9 60.02 172.24

31-07-14 4:35 24 0.08 27.9 2.33 63 218.3 0.262 57.4 60.04 172.24

31-07-14 4:36 24 0.08 28.4 2.53 71 218.6 0.296 65.1 60.07 172.24

31-07-14 4:37 24 0.08 28.1 2.6 73 218.8 0.306 66.9 60.04 172.24

31-07-14 4:38 24 0.08 27.8 2.77 75 219 0.316 69.1 60.05 172.24

31-07-14 4:39 24 0.08 28.1 2.71 76 218.6 0.32 69.9 60.07 172.24

31-07-14 4:40 24 0.09 27.9 3.03 85 218.7 0.354 77.6 60.15 172.25

31-07-14 4:41 24 0.09 28.7 2.78 78 218 0.331 71.2 59.96 172.25

31-07-14 4:42 24 0.09 27.7 3.14 85 218.2 0.358 77.8 60.07 172.25

31-07-14 4:43 24 0.09 27.1 2.88 78 217.8 0.321 71.5 60.04 172.25

31-07-14 4:44 24 0.09 27.7 3.07 83 218.2 0.347 75.7 60.02 172.25


182

31-07-14 4:45 24 0.09 28 3.07 86 218.1 0.36 78.5 59.96 172.25

31-07-14 4:46 24 0.09 27.7 3.07 83 218.4 0.35 76.4 60.05 172.25

31-07-14 4:47 24 0.1 28.3 3.07 86 218.2 0.361 78.5 60 172.26

31-07-14 4:48 24 0.1 28.4 3.28 92 218.4 0.383 83.8 60.01 172.26

31-07-14 4:49 24 0.1 28.3 3.42 96 218.7 0.402 87.8 60.09 172.26

31-07-14 4:50 24 0.1 27.4 3.66 99 218.7 0.42 91.7 60.08 172.26

31-07-14 4:51 24 0.1 28.2 3.57 100 218.6 0.427 92.6 60.02 172.26

31-07-14 4:52 24 0.1 28.2 3.6 101 218.2 0.426 93.1 59.96 172.26

31-07-14 4:53 24 0.11 27.6 3.7 100 218.7 0.425 92.9 60.1 172.27

31-07-14 4:54 24 0.11 27.4 3.46 97 218.3 0.408 89 60 172.27

31-07-14 4:55 24 0.11 28.8 2.75 77 217.8 0.33 70.4 59.99 172.27

31-07-14 4:56 24 0.11 28 2 56 217.1 0.233 50.5 59.92 172.27

31-07-14 4:57 24 0.11 27.9 3.7 100 218.1 0.425 92.6 59.95 172.27

31-07-14 4:58 24 0.11 26.8 2.76 72 217.6 0.301 65.7 60 172.27

31-07-14 4:59 24 0.11 27.8 3.74 101 220.6 0.425 93.7 60 172.27

31-07-14 5:00 24 0.12 28 3.82 107 220.7 0.45 98.8 59.99 172.28

31-07-14 5:01 24 0.12 27.7 4 108 220.4 0.452 99.6 59.95 172.28

31-07-14 5:02 24 0.12 27.5 4.03 109 220.4 0.455 100.5 60 172.28

31-07-14 5:03 24 0.12 27.2 4.11 111 220.9 0.46 102.2 60 172.28

31-07-14 5:04 24 0.12 29.1 2.89 84 219.9 0.335 77.1 60 172.28

31-07-14 5:05 24 0.12 27.4 3.53 92 220.3 0.383 83.9 59.96 172.28

31-07-14 5:06 24 0.12 26.7 4.29 116 220.6 0.483 107.4 59.98 172.28

31-07-14 5:07 24 0.13 27.1 4.29 116 220.8 0.485 107.3 60.01 172.29

31-07-14 5:08 24 0.13 27.9 3.96 107 220.5 0.449 99.2 59.97 172.29

31-07-14 5:09 24 0.13 26.8 3.88 105 220.4 0.437 96.9 59.94 172.29

31-07-14 5:10 24 0.13 27.1 2.59 70 219.2 0.296 64.8 59.96 172.29

31-07-14 5:11 24 0.13 27.1 2.18 59 219 0.243 53.2 60.03 172.29

31-07-14 5:12 24 0.13 27.5 2.07 56 218.9 0.233 50.7 59.97 172.29

31-07-14 5:13 24 0.14 25.9 3.12 78 219.4 0.324 71.1 60.08 172.3

31-07-14 5:14 24 0.14 28.3 3.53 99 220 0.415 91.7 60.03 172.3

31-07-14 5:15 24 0.14 27.2 2.48 67 218.9 0.283 61.5 59.94 172.3

31-07-14 5:16 24 0.14 27.8 3.88 105 219.5 0.445 97.2 60.07 172.3

31-07-14 5:17 24 0.14 27.5 3.96 107 219.6 0.45 99.2 59.98 172.3

31-07-14 5:18 24 0.14 27.8 3.89 109 219.7 0.457 100.6 60.03 172.3

31-07-14 5:19 24 0.15 28 3.89 109 219.6 0.458 100.3 59.97 172.31

31-07-14 5:20 24 0.15 28.4 3.64 102 218.8 0.43 93.9 59.94 172.31

31-07-14 5:21 24 0.15 27.4 3.62 98 218.6 0.413 90 59.95 172.31

31-07-14 5:22 24 0.15 28 2.6 73 217.9 0.307 67 59.98 172.31

31-07-14 5:23 24 0.15 27.5 2.25 61 217.6 0.257 56.1 60.06 172.31

31-07-14 5:24 24 0.15 26.7 2.19 57 217.4 0.237 51.5 60.02 172.31

31-07-14 5:25 24 0.15 27.1 1.92 52 217.9 0.215 46.8 60.04 172.31

31-07-14 5:26 24 0.15 27.6 2.03 55 218 0.229 49.6 59.98 172.31

31-07-14 5:27 24 0.16 27.1 2.23 58 217.9 0.241 52.5 59.99 172.32

31-07-14 5:28 24 0.16 27 2.46 64 217.9 0.27 59 60.07 172.32

31-07-14 5:29 24 0.16 27.4 2.57 67 217.7 0.283 61.1 60.05 172.32


183

31-07-14 5:30 24 0.16 28.9 3.6 101 218.3 0.425 93.4 60.04 172.32

31-07-14 5:31 24 0.16 28.1 3.42 96 218.1 0.403 88.1 59.98 172.32

31-07-14 5:32 24 0.16 28.8 3.2 93 218.3 0.398 85.1 60 172.32

31-07-14 5:33 24 0.16 28.8 2.79 81 218 0.343 74.1 60.02 172.32

31-07-14 5:34 24 0.16 27.8 2.37 64 217.7 0.271 58.9 60.07 172.32

31-07-14 5:35 24 0.17 28 2.37 64 217.3 0.272 58.6 59.98 172.33

31-07-14 5:36 24 0.17 27.8 2.03 55 217 0.225 49 60.02 172.33

31-07-14 5:37 24 0.17 26.1 2.73 71 217.5 0.303 65.2 59.99 172.33

31-07-14 5:38 24 0.17 27.6 2.44 66 219.6 0.272 60.6 60 172.33

31-07-14 5:39 24 0.17 26.9 2.34 61 219.3 0.253 55.7 59.97 172.33

31-07-14 5:40 24 0.17 27.9 3.74 101 220.5 0.423 93 60.08 172.33

31-07-14 5:41 24 0.17 29 3.89 109 219.9 0.455 100.7 60.04 172.33

31-07-14 5:42 24 0.18 27.3 3.92 106 220.3 0.445 98.4 60 172.34

31-07-14 5:43 24 0.18 28.5 3.92 110 220.3 0.459 101.7 60.03 172.34

31-07-14 5:44 24 0.18 27.6 4.33 117 220.7 0.487 107.7 60.02 172.34

31-07-14 5:45 24 0.18 28 4.62 125 221.1 0.526 116.9 60.04 172.34

31-07-14 5:46 24 0.18 27.1 4.66 126 220.9 0.528 117.3 59.98 172.34

31-07-14 5:47 24 0.18 26.5 2.07 54 218.9 0.221 48.5 60.04 172.34

31-07-14 5:48 24 0.19 28 3.5 98 220 0.407 89.4 60.02 172.35

31-07-14 5:49 24 0.19 27.7 4.51 122 220.7 0.511 113 60.06 172.35

31-07-14 5:50 24 0.19 25.6 3.85 104 220.3 0.447 96.2 60 172.35

31-07-14 5:51 24 0.19 27 4.44 120 220.5 0.503 110.9 59.96 172.35

31-07-14 5:52 24 0.19 26.7 5.25 142 221.8 0.595 132.7 60.09 172.35

31-07-14 5:53 24 0.19 29.3 2.89 84 219.9 0.329 76.5 60.03 172.35

31-07-14 5:54 24 0.2 26.8 5.57 145 221.3 0.613 135.6 59.99 172.36

31-07-14 5:55 24 0.2 27.6 5.4 146 221 0.612 135.9 60 172.36

31-07-14 5:56 24 0.2 27.4 5.55 150 221 0.633 139.8 59.99 172.36

31-07-14 5:57 24 0.2 26.5 5.73 149 221.1 0.627 138.8 59.98 172.36

31-07-14 5:58 24 0.21 27.2 5.59 151 221.5 0.638 141.3 60.06 172.37

31-07-14 5:59 24 0.21 26.8 5.51 149 221.4 0.627 138.9 60.03 172.37

31-07-14 6:00 24 0.21 27 5.62 152 221.1 0.645 142.2 60.08 172.37

31-07-14 6:01 24 0.21 27.1 5.4 146 221.2 0.615 136.2 59.97 172.37

31-07-14 6:02 24 0.22 27.7 5 135 220.4 0.57 125.9 59.98 172.38

31-07-14 6:03 24 0.22 26.7 5.38 140 220.7 0.595 130.9 60 172.38

31-07-14 6:04 24 0.22 26.9 5.69 148 221.1 0.625 137.9 60 172.38

31-07-14 6:05 24 0.22 26.6 5.85 158 221.4 0.671 147.2 60.07 172.38

31-07-14 6:06 24 0.23 26.5 2.65 69 219 0.293 64.1 60.06 172.39

31-07-14 6:07 24 0.23 26.4 6.46 168 221.3 0.708 156.9 60.03 172.39

31-07-14 6:08 24 0.23 26.2 6.4 160 221 0.683 149.1 60.01 172.39

31-07-14 6:09 24 0.23 26.1 3 75 218.9 0.327 68.9 60.06 172.39

31-07-14 6:10 24 0.23 26.7 6.15 160 221.2 0.674 149.4 60 172.39

31-07-14 6:11 24 0.24 26.4 6.3 164 220.8 0.693 153.3 59.99 172.4

31-07-14 6:12 24 0.24 27 5.88 159 220.6 0.674 148.4 60.11 172.4

31-07-14 6:13 24 0.24 27.7 3.55 96 219 0.4 87.6 60.11 172.4

31-07-14 6:14 24 0.25 26.9 6.34 165 220.7 0.699 154.2 60.13 172.41


184

31-07-14 6:15 24 0.25 27.2 6.3 164 221.2 0.693 153.2 60.1 172.41

31-07-14 6:16 24 0.25 26.7 6.23 162 220.9 0.685 151.3 60.1 172.41

31-07-14 6:17 24 0.25 26.3 3.57 93 219.2 0.383 84.8 60.03 172.41

31-07-14 6:18 24 0.26 26.6 6.19 161 220.9 0.678 149.8 60.07 172.42

31-07-14 6:19 24 0.26 27.2 2.81 76 218.7 0.32 69.7 60.04 172.42

31-07-14 6:20 24 0.26 26.9 6.3 164 221 0.691 152.6 60.06 172.42

31-07-14 6:21 24 0.26 27.1 2.59 70 218.3 0.297 64.8 59.99 172.42

31-07-14 6:22 24 0.26 26.5 6 156 220.8 0.661 145.6 60.09 172.42

31-07-14 6:23 24 0.27 26.3 6.15 160 220.8 0.678 149 59.98 172.43

31-07-14 6:24 24 0.27 26.3 6.03 157 220.8 0.663 146.5 60.03 172.43

31-07-14 6:25 24 0.27 27.2 6.03 163 220.5 0.691 152.3 60.06 172.43

31-07-14 6:26 24 0.28 26.9 6.23 162 220.4 0.686 151.2 60 172.44

31-07-14 6:27 24 0.28 26.8 6.03 157 220.6 0.667 146.9 60.03 172.44

31-07-14 6:28 24 0.28 26.3 6.11 159 220.4 0.67 147.9 60.02 172.44

31-07-14 6:29 24 0.28 27.3 5.81 157 220.3 0.668 146.6 60.03 172.44

31-07-14 6:30 24 0.28 26.7 6.07 158 220.1 0.668 147.4 60.02 172.44

31-07-14 6:31 24 0.29 26.4 6.11 159 220 0.674 148 60.04 172.45

31-07-14 6:32 24 0.29 26.7 5.88 159 219.9 0.678 148.4 60 172.45

31-07-14 6:33 24 0.29 28.6 5.44 147 219.3 0.614 137.3 60.04 172.45

31-07-14 6:34 24 0.29 31.1 3.43 103 219.3 0.459 95 60.11 172.45

31-07-14 6:35 24 0.3 26.5 6.42 167 220.7 0.709 156 59.99 172.46

31-07-14 6:36 24 0.3 25.7 6.53 170 221.2 0.713 158.1 60.02 172.46

31-07-14 6:37 24 0.3 26.6 6.61 172 221.3 0.725 160.2 60 172.46

31-07-14 6:38 24 0.31 26.8 6.33 171 221 0.728 159.9 60.03 172.47

31-07-14 6:39 24 0.31 26.7 6.73 175 221.1 0.738 162.8 60.07 172.47

31-07-14 6:40 24 0.31 26.4 6.76 169 220.9 0.718 157.4 60.04 172.47

31-07-14 6:41 24 0.31 25.8 6.29 170 220.8 0.717 158.3 60.04 172.47

31-07-14 6:42 24 0.32 26.3 3.12 78 218.6 0.326 71 60.05 172.48

31-07-14 6:43 24 0.32 25.5 7.12 178 221.2 0.753 166.3 60.08 172.48

31-07-14 6:44 24 0.32 25.9 2.57 67 218 0.286 62.3 60 172.48

31-07-14 6:45 24 0.32 26.6 2.61 68 218 0.284 62.1 60.02 172.48

31-07-14 6:46 24 0.32 26.4 2.65 69 218.1 0.292 63.8 60.03 172.48

31-07-14 6:47 24 0.32 26.8 2.34 61 217.8 0.255 55.5 60.07 172.48

31-07-14 6:48 24 0.33 26.3 2.34 61 217.7 0.259 56.3 59.99 172.49

31-07-14 6:49 24 0.33 27.6 2.48 67 217.7 0.285 62.2 60.03 172.49

31-07-14 6:50 24 0.33 27 2.44 66 217.8 0.279 60.7 60.01 172.49

31-07-14 6:51 24 0.33 26.7 5.96 161 220.3 0.684 150.6 60.07 172.49

31-07-14 6:52 24 0.33 26.5 6.59 178 220.1 0.747 165.8 59.95 172.49

31-07-14 6:53 24 0.33 28.8 3.28 92 218.4 0.389 84 60.04 172.49

31-07-14 6:54 24 0.34 27.4 2.81 76 217.9 0.32 69.7 60 172.5

31-07-14 6:55 24 0.34 25.9 3.73 97 218.2 0.406 88.5 59.99 172.5

31-07-14 6:56 24 0.34 27.1 2.96 77 218.1 0.328 70.9 60.04 172.5

31-07-14 6:57 24 0.34 27.5 5.78 162 220.2 0.686 150.9 59.99 172.5

31-07-14 6:58 24 0.34 26 2.6 65 217.5 0.273 59.4 59.96 172.5

31-07-14 6:59 24 0.34 26.1 3.11 81 217.9 0.345 73.9 60.02 172.5


185

31-07-14 7:00 24 0.35 27 3.03 82 218.2 0.345 74.9 59.95 172.51

31-07-14 7:01 24 0.35 27.6 6.77 183 220.5 0.772 171 60.02 172.51

31-07-14 7:02 24 0.35 27.3 3.33 90 218 0.382 82.1 59.96 172.51

31-07-14 7:03 24 0.35 26.4 2.88 75 217.5 0.318 69.1 59.97 172.51

31-07-14 7:04 24 0.35 26.8 6.88 179 220 0.754 166.9 60 172.51

31-07-14 7:05 24 0.36 26.9 2.66 72 217.4 0.303 65.6 59.96 172.52

31-07-14 7:06 24 0.36 26.6 2.38 62 217.2 0.263 57.1 59.95 172.52

31-07-14 7:07 24 0.36 26.5 2.34 61 217.2 0.258 55.8 60.02 172.52

31-07-14 7:08 24 0.36 30.8 4.53 136 219 0.534 127 60.04 172.52

31-07-14 7:09 24 0.36 27 3.11 84 217.2 0.354 76.6 60 172.52

31-07-14 7:10 24 0.36 26.5 2.38 62 216.9 0.265 57 60.08 172.52

31-07-14 7:11 24 0.36 27.2 2.55 69 216.9 0.295 64.2 60 172.52

31-07-14 7:12 24 0.36 27.2 2.73 71 217.1 0.3 65.3 60.05 172.52

31-07-14 7:13 24 0.37 27.8 2.92 79 217.2 0.335 72.3 59.99 172.53

31-07-14 7:14 24 0.37 27.3 7.07 184 219.8 0.785 171.5 59.98 172.53

31-07-14 7:15 24 0.37 27.5 3.07 83 217.6 0.353 75.6 60.01 172.53

31-07-14 7:16 24 0.37 28.1 6.03 169 219.7 0.738 157.5 59.96 172.53

31-07-14 7:17 24 0.38 26.6 6.38 166 220.5 0.703 154.8 59.98 172.54

31-07-14 7:18 24 0.38 27.7 6.14 172 220.6 0.733 160.3 59.91 172.54

31-07-14 7:19 24 0.38 27.4 2.7 73 218.1 0.305 66.5 60.02 172.54

31-07-14 7:20 24 0.38 25.6 6.5 169 220.2 0.71 157.8 59.95 172.54

31-07-14 7:21 24 0.38 26.1 6.03 157 219.7 0.652 146.8 59.96 172.54

31-07-14 7:22 24 0.39 29.3 4.46 134 219.3 0.649 125.3 59.98 172.55

31-07-14 7:23 24 0.39 28 6.48 175 220.2 0.74 163.3 59.98 172.55

31-07-14 7:24 24 0.39 27.6 6.53 170 220 0.722 158.9 59.93 172.55

31-07-14 7:25 24 0.39 27.5 7.03 190 220.4 0.798 177.3 59.95 172.55

31-07-14 7:26 24 0.39 25.5 4.85 136 219.3 0.589 126.5 59.99 172.55

31-07-14 7:27 24 0.4 25.4 7.12 178 220.5 0.752 165.8 60.02 172.56

31-07-14 7:28 24 0.4 26.7 6.42 167 220.1 0.709 155.4 59.93 172.56

31-07-14 7:29 24 0.4 26.7 6.5 169 219.9 0.717 157.6 59.97 172.56

31-07-14 7:30 24 0.4 27.1 6.84 178 219.8 0.754 166.1 59.95 172.56

31-07-14 7:31 24 0.41 26 2.23 58 217.2 0.243 52.9 60.06 172.57

31-07-14 7:32 24 0.41 26.9 5.26 137 218.9 0.649 128 59.96 172.57

31-07-14 7:33 24 0.41 26.2 6.88 179 220.1 0.768 169.1 59.98 172.57

31-07-14 7:34 24 0.41 26.3 6.88 179 220.2 0.765 167.2 59.98 172.57

31-07-14 7:35 24 0.42 24.7 4.33 117 218.6 0.438 108.3 59.97 172.58

31-07-14 7:36 24 0.42 27.1 6.77 183 220.2 0.771 170.4 59.96 172.58

31-07-14 7:37 24 0.42 27.4 6.88 179 220.2 0.756 167.3 59.95 172.58

31-07-14 7:38 24 0.42 27.2 6.55 177 220.2 0.753 165.5 60.02 172.58

31-07-14 7:39 24 0.43 27.4 6.62 179 220.2 0.758 166.8 59.96 172.59

31-07-14 7:40 24 0.43 26.4 6.29 170 219.7 0.722 158.4 60 172.59

31-07-14 7:41 24 0.43 26.1 7.11 185 219.9 0.787 172.7 60.04 172.59

31-07-14 7:42 24 0.43 26.9 6.88 179 219.6 0.758 166.8 59.94 172.59

31-07-14 7:43 24 0.44 26.5 7.32 183 219.8 0.778 170.3 59.95 172.6

31-07-14 7:44 24 0.44 26.1 6.8 177 219.6 0.75 164.9 60 172.6


186

31-07-14 7:45 24 0.44 27.3 6.25 169 220 0.719 157.8 60 172.6

31-07-14 7:46 24 0.45 26.7 6.8 177 219.8 0.75 165.4 59.98 172.61

31-07-14 7:47 24 0.45 26.1 6.84 178 219.9 0.756 166.2 59.99 172.61

31-07-14 7:48 24 0.45 24.4 5.11 138 218.5 0.514 128.7 59.96 172.61

31-07-14 7:49 24 0.46 26.4 6.76 169 219.3 0.73 157.9 60.04 172.62

31-07-14 7:50 24 0.46 26 6.81 184 219.6 0.781 171.2 59.99 172.62

31-07-14 7:51 24 0.46 28.2 5.55 161 218.6 0.74 150.4 59.96 172.62

31-07-14 7:52 24 0.46 26.3 7.11 185 219.9 0.781 172.1 59.95 172.62

31-07-14 7:53 24 0.47 34.1 5.96 0 218.4 0.061 0 60.01 172.63

31-07-14 7:54 24 0.47 26.8 6.59 178 219.9 0.761 166.4 59.99 172.63

31-07-14 7:55 24 0.47 26.5 6.53 170 219.9 0.72 158.6 60.02 172.63

31-07-14 7:56 24 0.47 27.3 6.29 170 219.8 0.723 158.4 59.99 172.63

31-07-14 7:57 24 0.48 26.4 2.84 74 217.4 0.311 67.6 59.95 172.64

31-07-14 7:58 24 0.48 25.1 6.61 172 220.1 0.713 160.5 59.94 172.64

31-07-14 7:59 24 0.48 28.8 4.4 119 218.7 0.486 110.3 60 172.64

31-07-14 8:00 24 0.48 26.2 6.65 173 220 0.73 161 60.05 172.64

31-07-14 8:01 24 0.49 27.4 6.57 171 219.7 0.725 159.7 60.02 172.65

31-07-14 8:02 24 0.49 27.1 6.22 168 220 0.719 156.7 59.98 172.65

31-07-14 8:03 24 0.49 26.9 6.42 167 220.1 0.713 156.2 59.95 172.65

31-07-14 8:04 24 0.49 26.5 6.65 173 220.3 0.73 160.9 59.98 172.65

31-07-14 8:05 24 0.5 27.5 4.75 133 219.4 0.584 124.1 59.96 172.66

31-07-14 8:06 24 0.5 27.6 6.59 178 220.9 0.751 167.6 60 172.66

31-07-14 8:07 24 0.5 27.1 6.59 178 221 0.764 167.9 60.04 172.66

31-07-14 8:08 24 0.51 25.6 6.88 179 220.9 0.756 168.6 60.02 172.67

31-07-14 8:09 24 0.51 26.2 6.69 174 220.2 0.735 162.3 60.09 172.67

31-07-14 8:10 24 0.51 27.3 6.48 175 220.1 0.743 163.3 59.98 172.67

31-07-14 8:11 24 0.51 26.9 6.59 178 220.3 0.757 166.1 60.04 172.67

31-07-14 8:12 24 0.51 26.9 6.88 179 220.5 0.757 166.8 59.98 172.67

31-07-14 8:13 24 0.52 26.9 6.77 183 220.9 0.775 170.4 60.07 172.68

31-07-14 8:14 24 0.52 27.4 6.76 176 220.9 0.74 164.3 60.13 172.68

31-07-14 8:15 24 0.52 26.8 6.55 177 221.7 0.753 164.9 60.2 172.68

31-07-14 8:16 24 0.52 27.1 6.66 180 221.6 0.772 169.9 60.11 172.68

31-07-14 8:17 24 0.53 26.8 7.3 190 221.9 0.801 177.2 60.07 172.69

31-07-14 8:18 24 0.53 26.4 3.12 75 218.6 0.325 68.8 59.9 172.69

31-07-14 8:19 24 0.53 26.2 7.15 186 221.7 0.777 173.1 60 172.69

31-07-14 8:20 24 0.54 26.6 7.03 183 222 0.771 171.1 59.99 172.7

31-07-14 8:21 24 0.54 26.4 6.84 178 221.7 0.755 168.1 59.97 172.7

31-07-14 8:22 24 0.54 27 6.88 179 222 0.759 168.7 59.98 172.7

31-07-14 8:23 24 0.55 26.6 6.76 176 221.8 0.742 164.5 59.99 172.71

31-07-14 8:24 24 0.55 26.8 6.55 177 222 0.75 164.7 60.01 172.71

31-07-14 8:25 24 0.55 27.3 3.35 94 219.8 0.443 86.3 59.97 172.71

31-07-14 8:26 24 0.55 33.7 6.46 0 219 0.06 0 60 172.71

31-07-14 8:27 24 0.55 27.7 6.62 179 221.6 0.749 167.3 59.98 172.71

31-07-14 8:28 24 0.55 26.8 7.07 184 221.8 0.772 171.2 59.95 172.71

31-07-14 8:29 24 0.56 26.7 6.84 178 221.7 0.75 166 59.95 172.72


187

31-07-14 8:30 24 0.56 26.5 6.8 177 221.7 0.744 165 59.97 172.72

31-07-14 8:31 24 0.56 26.9 7 182 221.5 0.766 170.1 59.96 172.72

31-07-14 8:32 24 0.57 26.7 6.85 185 221.5 0.783 172.8 59.94 172.73

31-07-14 8:33 24 0.57 27.6 6 162 220.8 0.711 151 59.97 172.73

31-07-14 8:34 24 0.57 28.6 5.3 159 221.2 0.762 148.2 60.06 172.73

31-07-14 8:35 24 0.58 26.7 6.92 180 221.4 0.764 169.3 60 172.74

31-07-14 8:36 24 0.58 30.6 3.7 111 220.2 0.501 102.9 59.95 172.74

31-07-14 8:37 24 0.58 34.3 0.58 20 220 0.059 13.1 59.95 172.74

31-07-14 8:38 24 0.58 26.7 6.44 174 221.9 0.736 162.5 60.03 172.74

31-07-14 8:39 24 0.58 26.7 6.96 174 221.5 0.742 162.3 59.92 172.74

31-07-14 8:40 24 0.59 27.5 6.73 175 221.9 0.734 163.3 60.04 172.75

31-07-14 8:41 24 0.59 26.5 6.62 179 221.9 0.755 166.8 59.96 172.75

31-07-14 8:42 24 0.59 27.3 7.3 190 222.2 0.795 177.6 60.02 172.75

31-07-14 8:43 24 0.6 25.7 7.11 185 221.5 0.774 172.5 59.98 172.76

31-07-14 8:44 24 0.6 25.5 7.2 180 221.5 0.766 169.9 59.95 172.76

31-07-14 8:45 24 0.6 27.1 6.84 178 221.6 0.755 168.2 59.99 172.76

31-07-14 8:46 24 0.6 25.8 7.36 184 222 0.773 171.6 59.95 172.76

31-07-14 8:47 24 0.61 26.4 6.66 180 221.8 0.772 169.5 59.98 172.77

31-07-14 8:48 24 0.61 26.6 3.11 84 219.3 0.352 76.5 59.92 172.77

31-07-14 8:49 24 0.61 26.7 3.16 79 219.2 0.332 72.3 59.97 172.77

31-07-14 8:50 24 0.61 28.2 2.75 77 218.9 0.324 70.2 60.05 172.77

31-07-14 8:51 24 0.62 27.8 3.48 94 219.1 0.39 86.1 59.91 172.78

31-07-14 8:52 24 0.62 26.2 6.96 188 221.4 0.784 174.9 59.99 172.78

31-07-14 8:53 24 0.62 26.8 7.42 193 221.8 0.807 180.2 59.98 172.78

31-07-14 8:54 24 0.62 27.4 3.62 98 219.4 0.405 89.2 59.92 172.78

31-07-14 8:55 24 0.63 27.1 2.85 77 218.7 0.325 70.2 59.98 172.79

31-07-14 8:56 24 0.63 28.4 3.85 104 219.6 0.451 95.7 59.93 172.79

31-07-14 8:57 24 0.63 27.4 3.44 93 219.4 0.401 85.3 60.03 172.79

31-07-14 8:58 24 0.63 30.9 4.09 127 221.1 0.601 118.6 59.98 172.79

31-07-14 8:59 24 0.63 30.7 5.46 164 221.1 0.682 153.3 59.88 172.79

31-07-14 9:00 24 0.63 27.2 7.53 196 222.5 0.827 183 59.99 172.79

31-07-14 9:01 24 0.64 27 6.96 188 221.9 0.79 175.6 60.01 172.8

31-07-14 9:02 24 0.64 26.7 6.88 179 221.8 0.757 168.7 59.98 172.8

31-07-14 9:03 24 0.65 27.8 6.21 174 221.2 0.748 162.4 59.96 172.81

31-07-14 9:04 24 0.65 27.2 7.15 186 221.8 0.782 173 59.99 172.81

31-07-14 9:05 24 0.65 27.2 3.07 83 219.1 0.33 75.6 59.99 172.81

31-07-14 9:06 24 0.65 26.9 7.4 185 221.6 0.788 172.4 59.97 172.81

31-07-14 9:07 24 0.65 26.8 6.66 180 221.5 0.768 170 59.99 172.81

31-07-14 9:08 24 0.66 26.1 6.84 178 221.7 0.745 166 59.98 172.82

31-07-14 9:09 24 0.66 26.8 6.65 173 221.6 0.728 160.9 59.95 172.82

31-07-14 9:10 24 0.66 26.6 6.33 171 221.5 0.722 159.8 60 172.82

31-07-14 9:11 24 0.67 26.7 6.53 170 221.2 0.717 158.5 60.09 172.83

31-07-14 9:12 24 0.67 26.6 6.34 165 220.9 0.695 153.8 60.04 172.83

31-07-14 9:13 24 0.67 27.3 6.22 168 221.1 0.707 156.6 60.07 172.83

31-07-14 9:14 24 0.67 28.8 3.96 111 219 0.485 102.8 59.97 172.83


188

31-07-14 9:15 24 0.67 26.3 6.69 174 220.7 0.736 162.4 59.98 172.83

31-07-14 9:16 24 0.68 34.3 0.58 20 219 0.06 13.1 59.99 172.84

31-07-14 9:17 24 0.68 31.4 3.9 121 220 0.519 112 59.96 172.84

31-07-14 9:18 24 0.68 26.6 4.92 128 219.2 0.546 119.6 59.92 172.84

31-07-14 9:19 24 0.68 26.7 2.26 59 217.1 0.247 53.6 59.95 172.84

31-07-14 9:20 24 0.68 26.7 2.26 59 217.1 0.247 53.6 59.95 172.84

31-07-14 9:21 24 0.69 26.9 6.25 169 220 0.719 157.4 60.01 172.85

31-07-14 9:22 24 0.69 31.1 2.8 87 218.6 0.364 79.8 60.02 172.85

31-07-14 9:23 24 0.69 26.4 6.65 173 220.1 0.736 161.8 59.91 172.85

31-07-14 9:24 24 0.7 27.3 5.66 153 220.1 0.659 143.2 60.02 172.86

31-07-14 9:25 24 0.7 26.2 6.34 165 220.4 0.698 153.9 60 172.86

31-07-14 9:26 24 0.7 25.8 2.46 64 218.1 0.273 59 59.99 172.86

31-07-14 9:27 24 0.7 26.7 6.65 173 220.7 0.728 161.1 59.99 172.86

31-07-14 9:28 24 0.7 28.1 5.75 161 220.1 0.682 150.2 60.01 172.86

31-07-14 9:29 24 0.71 27 2.5 65 217.5 0.275 59.8 59.94 172.87

31-07-14 9:30 24 0.71 29.9 4.27 124 219.6 0.539 116.2 60.04 172.87

31-07-14 9:31 24 0.71 27 6.14 166 220.5 0.706 154.7 60.03 172.87

31-07-14 9:32 24 0.71 25.9 4.64 130 219.9 0.55 121.8 60.02 172.87

31-07-14 9:33 24 0.71 27 6.16 148 219 0.684 138.1 59.98 172.87

31-07-14 9:34 24 0.71 27 6.22 168 220.1 0.713 156.7 60.04 172.87

31-07-14 9:35 24 0.72 26.2 6.88 179 219.8 0.758 167.2 59.95 172.88

31-07-14 9:36 24 0.72 26.7 6.26 163 219.5 0.694 151.6 59.99 172.88

31-07-14 9:37 24 0.72 27.9 5.77 156 219.8 0.671 145.8 59.97 172.88

31-07-14 9:38 24 0.73 25.6 5.41 130 218.9 0.48 121.6 60.06 172.89

31-07-14 9:39 24 0.73 27.3 4.36 109 218.6 0.452 100.5 59.99 172.89

31-07-14 9:40 24 0.73 27.1 6.37 172 220.2 0.72 160.5 60.02 172.89

31-07-14 9:41 24 0.73 27.1 6.07 164 220 0.699 153.1 60 172.89

31-07-14 9:42 24 0.73 27 3.77 102 218.1 0.445 94.4 60 172.89

31-07-14 9:43 24 0.74 27.6 5.15 134 219.3 0.572 124.7 60.06 172.9

31-07-14 9:44 24 0.74 27.3 6.3 164 220.3 0.696 152.6 60 172.9

31-07-14 9:45 24 0.74 27.6 6.22 168 220.2 0.705 156.3 60.02 172.9

31-07-14 9:46 24 0.74 27.1 6.3 164 219.9 0.701 153.1 60 172.9

31-07-14 9:47 24 0.75 26.7 6.22 168 220 0.714 156.8 59.97 172.91

31-07-14 9:48 24 0.75 26.6 6.15 160 220.3 0.675 149.1 60.02 172.91

31-07-14 9:49 24 0.75 27.1 6.19 161 220.3 0.684 150.2 59.96 172.91

31-07-14 9:50 24 0.75 26.4 6.19 161 220.4 0.682 150.3 60.06 172.91

31-07-14 9:51 24 0.76 27 6.15 160 219.8 0.678 149.1 59.95 172.92

31-07-14 9:52 24 0.76 27.1 6 162 219.8 0.686 150.8 60 172.92

31-07-14 9:53 24 0.76 27.3 5.44 147 219.7 0.622 137.3 60.01 172.92

31-07-14 9:54 24 0.76 27.3 6.26 163 219.8 0.691 152.3 60.01 172.92

31-07-14 9:55 24 0.77 26.4 6.34 165 219.3 0.697 154.1 60.08 172.93

31-07-14 9:56 24 0.77 34.1 5.85 0 217.3 0.059 0 60.04 172.93

31-07-14 9:57 24 0.77 26 6.07 164 219.6 0.689 152.8 60.07 172.93

31-07-14 9:58 24 0.77 26.5 6.15 160 219.5 0.68 149.2 60.02 172.93

31-07-14 9:59 24 0.77 26.2 6.11 159 220 0.674 148.5 60.1 172.93


189

31-07-14 10:00 24 0.78 26.4 5.88 153 219.9 0.651 142.7 60.01 172.94

31-07-14 10:01 24 0.78 26.3 5.88 153 219.3 0.649 142.3 60.02 172.94

31-07-14 10:02 24 0.78 27.7 5.16 124 218.6 0.573 114.1 59.99 172.94

31-07-14 10:03 24 0.78 27 5.81 157 219.3 0.669 146.1 59.96 172.94

31-07-14 10:04 24 0.79 26.5 5.76 150 219.2 0.641 140.4 59.95 172.95

31-07-14 10:05 24 0.79 27.6 4.95 119 218.5 0.551 110 60.03 172.95

31-07-14 10:06 24 0.79 27.2 6 156 219.8 0.669 146 59.99 172.95

31-07-14 10:07 24 0.79 26.9 6 156 219.6 0.663 145.8 60.04 172.95

31-07-14 10:08 24 0.8 26.7 5.81 157 219.9 0.667 146.4 60.04 172.96

31-07-14 10:09 24 0.8 26.4 5.8 151 219.2 0.607 140.7 60.04 172.96

31-07-14 10:10 24 0.8 28.4 4.91 118 218.7 0.478 109.2 60.1 172.96

31-07-14 10:11 24 0.8 26.6 4.61 120 218.7 0.444 110.5 60.03 172.96

31-07-14 10:12 24 0.81 25.6 4.66 112 218.7 0.465 103.8 60 172.97

31-07-14 10:13 24 0.81 26.9 2.81 76 217.6 0.325 69.8 59.92 172.97

31-07-14 10:14 24 0.81 27.1 3.03 82 217.8 0.343 75.3 60.02 172.97

31-07-14 10:15 24 0.81 27 2.74 74 217.6 0.311 67.9 59.99 172.97

31-07-14 10:16 24 0.81 28.5 2.64 74 217.4 0.312 67.8 59.97 172.97

31-07-14 10:17 24 0.81 26.8 2.5 65 216.9 0.273 59.4 60.02 172.97

31-07-14 10:18 24 0.82 27.1 4.87 117 218.1 0.502 107.8 60.01 172.98

31-07-14 10:19 24 0.82 29.2 2.31 67 217.2 0.287 61 60.06 172.98

31-07-14 10:20 24 0.82 26.8 5.53 155 219.3 0.662 144.6 59.99 172.98

31-07-14 10:21 24 0.82 33.3 0.6 20 217.5 0.059 12.8 59.99 172.98

31-07-14 10:22 24 0.82 27.5 5.44 147 219.6 0.625 137.4 60 172.98

31-07-14 10:23 24 0.82 27.8 5.32 149 220 0.634 138.8 59.99 172.98

31-07-14 10:24 24 0.83 27.4 3.2 80 218.2 0.355 73.6 60.02 172.99

31-07-14 10:25 24 0.83 26.6 5.55 150 220.1 0.638 139.8 60 172.99

31-07-14 10:26 24 0.83 26 5.41 130 219.5 0.531 120.9 60.04 172.99

31-07-14 10:27 24 0.83 26.3 5.69 148 219.3 0.627 137.8 59.98 172.99

31-07-14 10:28 24 0.84 25.9 3.29 79 217.8 0.328 72.3 59.98 173

31-07-14 10:29 24 0.84 24.9 4.32 108 218.6 0.441 99.9 60.02 173

31-07-14 10:30 24 0.84 27.3 5.44 147 220.1 0.624 137.5 60.03 173

31-07-14 10:31 24 0.84 26.8 2.84 74 218.1 0.307 67.8 59.98 173

31-07-14 10:32 24 0.84 27 5.59 151 219.7 0.632 141.2 59.96 173

31-07-14 10:33 24 0.84 27.4 5.37 145 219.6 0.615 135 59.94 173

31-07-14 10:34 24 0.85 27.9 5.15 134 219 0.57 124.7 60.01 173.01

31-07-14 10:35 24 0.85 26 2.53 66 217.4 0.285 60.6 59.96 173.01

31-07-14 10:36 24 0.85 26.8 2.38 62 217.7 0.26 57 60.02 173.01

31-07-14 10:37 24 0.85 25.5 5.36 134 219.5 0.571 125 60.06 173.01

31-07-14 10:38 24 0.85 26.1 2.57 67 218 0.285 62.5 60.02 173.01

31-07-14 10:39 24 0.85 26.2 2.72 68 217.6 0.291 62 60.07 173.01

31-07-14 10:40 24 0.86 27.2 2.07 56 217 0.238 50.7 60.04 173.02

31-07-14 10:41 24 0.86 26.2 3.11 81 217.7 0.342 73.8 60.09 173.02

31-07-14 10:42 24 0.86 26.8 2.23 58 217.2 0.241 52.2 59.99 173.02

31-07-14 10:43 24 0.86 27.4 3.71 104 218.2 0.438 96 60.02 173.02

31-07-14 10:44 24 0.86 27.9 4.81 130 218.9 0.556 121.7 60 173.02


190

31-07-14 10:45 24 0.86 29.2 4.24 123 218.9 0.526 114 59.98 173.02

31-07-14 10:46 24 0.87 27.5 2.68 67 217.3 0.29 61.3 59.95 173.03

31-07-14 10:47 24 0.87 26.8 4.84 126 219.3 0.535 117.7 60.02 173.03

31-07-14 10:48 24 0.87 25.2 4.8 120 218.5 0.504 111.2 60.02 173.03

31-07-14 10:49 24 0.87 29.5 4.03 117 219 0.48 107.7 60.05 173.03

31-07-14 10:50 24 0.87 27.7 4.46 125 218.9 0.529 115.1 59.96 173.03

31-07-14 10:51 24 0.88 29.6 3.93 114 218.9 0.48 105 60.01 173.04

31-07-14 10:52 24 0.88 27.6 4.59 124 219.4 0.522 114.5 59.97 173.04

31-07-14 10:53 24 0.88 27.5 4.51 122 219.1 0.519 113 60 173.04

31-07-14 10:54 24 0.88 27.2 4.51 122 219.5 0.515 113 59.96 173.04

31-07-14 10:55 24 0.88 27.7 4.32 121 219.7 0.511 111.8 60.01 173.04

31-07-14 10:56 24 0.88 27.3 4.59 124 219.7 0.522 114.4 59.92 173.04

31-07-14 10:57 24 0.89 28.5 4.28 120 219.5 0.501 110.4 60.11 173.05

31-07-14 10:58 24 0.89 27.9 4.28 120 219.2 0.512 110.8 59.98 173.05

31-07-14 10:59 24 0.89 27.5 4.25 115 219.2 0.483 105.8 60.07 173.05

31-07-14 11:00 24 0.89 27.9 4.44 120 218.9 0.506 110.5 59.99 173.05

31-07-14 11:01 24 0.9 27.2 4.51 122 219.2 0.513 112.6 60.07 173.06

31-07-14 11:02 24 0.9 27.3 4.55 123 219.3 0.505 113.8 60.05 173.06

31-07-14 11:03 24 0.9 27.7 4.4 119 219 0.5 109.5 59.96 173.06

31-07-14 11:04 24 0.9 27.5 4.25 115 219.3 0.485 106.5 60.04 173.06

31-07-14 11:05 24 0.9 27.6 4.14 116 219 0.492 107.4 60.02 173.06

31-07-14 11:06 24 0.9 28 4.22 114 219 0.48 105.3 59.98 173.06

31-07-14 11:07 24 0.9 26.6 4.14 112 219.6 0.47 103.6 60.02 173.06

31-07-14 11:08 24 0.91 27.8 4 108 219.8 0.456 100.2 60.1 173.07

31-07-14 11:09 24 0.91 27.7 4 108 219.6 0.453 99.4 60.06 173.07

31-07-14 11:10 24 0.91 29.3 3.03 88 218.7 0.368 80.4 60.01 173.07

31-07-14 11:11 24 0.91 27.4 4.03 109 219 0.458 100.5 59.99 173.07

31-07-14 11:12 24 0.91 27.8 4.07 110 219.2 0.465 101.7 60.02 173.07

31-07-14 11:13 24 0.92 27.6 4.07 110 219.2 0.466 102.1 59.99 173.08

31-07-14 11:14 24 0.92 28.3 3.96 111 219.5 0.463 102.3 60.05 173.08

31-07-14 11:15 24 0.92 27.5 4.07 110 219.7 0.463 101.2 59.99 173.08

31-07-14 11:16 24 0.92 27.6 4.11 111 219.8 0.467 102.6 60.06 173.08

31-07-14 11:17 24 0.92 27.3 4.22 114 219.7 0.479 105 59.98 173.08

31-07-14 11:18 24 0.93 27.6 4.07 110 219.2 0.462 101.2 60 173.09

31-07-14 11:19 24 0.93 27.8 3.92 106 218.7 0.449 97.7 60.01 173.09

31-07-14 11:20 24 0.93 26.7 4 104 218.8 0.443 96 60.01 173.09

31-07-14 11:21 24 0.93 27.9 4 108 219.1 0.457 99.9 59.98 173.09

31-07-14 11:22 24 0.93 25.5 4.2 105 219.2 0.441 96.9 60.02 173.09

31-07-14 11:23 24 0.93 27.5 3.88 105 219.7 0.443 97.5 59.98 173.09

31-07-14 11:24 24 0.94 27.6 3.96 107 219.8 0.451 99.1 60 173.1

31-07-14 11:25 24 0.94 28.4 3.81 103 219.7 0.43 95.3 60.02 173.1

31-07-14 11:26 24 0.94 27.1 3.81 103 219.2 0.436 95.6 60.01 173.1

31-07-14 11:27 24 0.94 27.7 3.81 103 219.3 0.437 95.3 59.95 173.1

31-07-14 11:28 24 0.94 27.7 3.85 104 219.7 0.437 96 59.93 173.1

31-07-14 11:29 24 0.94 27.7 3.77 102 219.7 0.427 94.2 59.98 173.1


191

31-07-14 11:30 24 0.95 29.1 3.03 88 219.4 0.388 80.9 60.02 173.11

31-07-14 11:31 24 0.95 27.6 3.74 101 219.3 0.425 93.8 60.02 173.11

31-07-14 11:32 24 0.95 27.2 3.66 99 219.1 0.419 91.6 60.06 173.11

31-07-14 11:33 24 0.95 27.3 3.59 97 219 0.405 88.9 59.99 173.11

31-07-14 11:34 24 0.95 26.7 3.76 98 218.9 0.405 89.2 59.96 173.11

31-07-14 11:35 24 0.95 27.6 3.62 98 219.2 0.41 89.8 59.97 173.11

31-07-14 11:36 24 0.95 27.3 3.62 98 219.5 0.407 89.2 59.96 173.11

31-07-14 11:37 24 0.96 27.8 3.51 95 219.6 0.397 87.1 60.03 173.12

31-07-14 11:38 24 0.96 26.9 3.37 91 219.4 0.379 83.7 60.02 173.12

31-07-14 11:39 24 0.96 27.7 3.29 89 218.9 0.374 81.8 60.02 173.12

31-07-14 11:40 24 0.96 28.4 3.14 88 219 0.371 80.7 60.04 173.12

31-07-14 11:41 24 0.96 27.6 3.25 88 219.1 0.369 80.4 60.08 173.12

31-07-14 11:42 24 0.96 27.9 3.22 87 219.1 0.361 79.3 59.96 173.12

31-07-14 11:43 24 0.96 27.4 3.14 85 218.9 0.357 77.8 59.98 173.12

31-07-14 11:44 24 0.97 28.1 3.07 86 219.3 0.361 78.9 60.02 173.13

31-07-14 11:45 24 0.97 27.2 3.25 88 219.2 0.366 80.2 60.05 173.13

31-07-14 11:46 24 0.97 28 3.03 85 218.8 0.358 77.9 59.99 173.13

31-07-14 11:47 24 0.97 27.9 3.07 86 219.3 0.36 78.6 60.02 173.13

31-07-14 11:48 24 0.97 27.6 3.25 88 218.8 0.367 80.3 59.97 173.13

31-07-14 11:49 24 0.97 27.4 3.18 86 219.2 0.36 78.9 60.02 173.13

31-07-14 11:50 24 0.97 27.8 3.11 84 218.8 0.352 77 59.95 173.13

31-07-14 11:51 24 0.98 28 3.03 85 219.2 0.358 78 60.02 173.14

31-07-14 11:52 24 0.98 27.8 2.85 80 219.2 0.34 73.6 60.03 173.14

31-07-14 11:53 24 0.98 27.7 3 81 219.1 0.338 74 60.08 173.14

31-07-14 11:54 24 0.98 28 2.82 79 218.9 0.331 72.2 60.01 173.14

31-07-14 11:55 24 0.98 28 2.85 80 219 0.334 73.1 60.02 173.14

31-07-14 11:56 24 0.98 28.2 2.85 80 218.9 0.336 73.5 60 173.14

31-07-14 11:57 24 0.98 28.2 2.85 80 218.7 0.336 73.4 59.99 173.14

31-07-14 11:58 24 0.99 28.5 2.92 82 219.1 0.341 74.9 60.04 173.15

31-07-14 11:59 24 0.99 27.8 2.92 79 219 0.331 72.4 59.99 173.15

31-07-14 12:00 24 0.99 28.8 2.68 78 218.5 0.33 71.2 59.98 173.15

31-07-14 12:01 24 0.99 29 2.65 77 218.3 0.324 70.6 59.97 173.15

31-07-14 12:02 24 0.99 29.1 2.68 78 218.6 0.326 71 60 173.15

31-07-14 12:03 24 0.99 29.2 2.58 75 218.6 0.314 68.4 59.95 173.15

31-07-14 12:04 24 0.99 29.7 2.51 73 218.6 0.301 66.6 60 173.15

31-07-14 12:05 24 0.99 29.4 2.41 70 219.2 0.295 64.6 60 173.15

31-07-14 12:06 24 1 29 2.42 68 218.7 0.291 63.4 60.02 173.16

31-07-14 12:07 24 1 29.7 2.39 67 218.7 0.282 61.2 60.03 173.16

31-07-14 12:08 24 1 29.8 2.24 65 218.9 0.273 59.9 60.02 173.16

31-07-14 12:09 24 1 30 2.16 65 218.9 0.275 59.9 60.03 173.16

31-07-14 12:10 24 1 29.9 2.2 64 218.8 0.27 59 60.02 173.16

31-07-14 12:11 24 1 30 2.1 63 218.9 0.267 57.5 60.09 173.16

31-07-14 12:12 24 1 29.8 2.1 61 218.5 0.254 55.4 60.07 173.16

31-07-14 12:13 24 1 29.7 2 60 218.4 0.252 54.5 60.09 173.16

31-07-14 12:14 24 1 29.8 2.06 60 218.3 0.249 54.1 60.09 173.16


192

31-07-14 12:15 24 1.01 30.2 1.93 58 218.2 0.245 53 60.06 173.17

31-07-14 12:16 24 1.01 30.2 1.93 58 218.4 0.243 52.6 60.06 173.17

31-07-14 12:17 24 1.01 30.1 1.86 56 218.4 0.236 51.1 60.03 173.17

31-07-14 12:18 24 1.01 30.4 1.83 55 218.1 0.227 49 59.95 173.17

31-07-14 12:19 24 1.01 30.3 1.76 53 218.1 0.217 47.3 60.07 173.17

31-07-14 12:20 24 1.01 30.2 1.63 49 217.9 0.201 43.7 60.03 173.17

31-07-14 12:21 24 1.01 29.6 1.62 47 217.6 0.194 42.4 59.99 173.17

31-07-14 12:22 24 1.01 29.6 1.56 47 217.8 0.191 42 60.02 173.17

31-07-14 12:23 24 1.01 30.1 1.58 46 217.8 0.191 41.6 60.02 173.17

31-07-14 12:24 24 1.01 30.4 1.53 46 217.5 0.189 41.3 60.01 173.17

31-07-14 12:25 24 1.01 30.5 1.53 46 217.3 0.188 41.3 60.06 173.17

31-07-14 12:26 24 1.01 26.9 1.25 34 217.3 0.14 30.2 60.03 173.17

31-07-14 12:27 24 1.01 30 1.5 45 218.1 0.187 40.5 59.98 173.17

31-07-14 12:28 24 1.01 30 1.5 45 218 0.19 40.9 60.06 173.17

31-07-14 12:29 24 1.02 30 1.5 45 218 0.187 40.7 59.99 173.18

31-07-14 12:30 24 1.02 29.9 1.55 45 218 0.188 40.9 60 173.18

31-07-14 12:31 24 1.02 29.8 1.55 45 217.8 0.187 40.7 59.95 173.18

31-07-14 12:32 24 1.02 29.6 1.58 46 218.1 0.191 41.4 60 173.18

31-07-14 12:33 24 1.02 29.4 1.58 46 217.8 0.193 41.8 59.98 173.18

31-07-14 12:34 24 1.02 29.2 1.58 46 218 0.192 41.8 60 173.18

31-07-14 12:35 24 1.02 28.6 1.67 47 218.7 0.194 42.4 60.04 173.18

31-07-14 12:36 24 1.02 28.9 1.67 47 218.6 0.197 43 60 173.18

31-07-14 12:37 24 1.02 29.1 1.67 47 218.6 0.195 43 60.03 173.18

31-07-14 12:38 24 1.02 28.4 1.62 47 218.3 0.197 42.7 60.06 173.18

31-07-14 12:39 24 1.02 29 1.62 47 218.2 0.196 42.5 60.02 173.18

31-07-14 12:40 24 1.02 28.9 1.67 47 218.2 0.196 42.7 60.04 173.18

31-07-14 12:41 24 1.02 29.2 1.62 47 218.1 0.196 42.7 60.09 173.18

31-07-14 12:42 24 1.03 28.8 1.67 47 218.2 0.195 42.3 60.11 173.19

31-07-14 12:43 24 1.03 29.1 1.62 47 218.2 0.193 42 60.1 173.19

31-07-14 12:44 24 1.03 28.9 1.58 46 218.6 0.192 41.7 60.06 173.19

31-07-14 12:45 24 1.03 28.9 1.55 45 218.4 0.189 40.6 60.13 173.19

31-07-14 12:46 24 1.03 28.9 1.55 45 218 0.185 40.3 60.15 173.19

31-07-14 12:47 24 1.03 28.2 1.57 44 218.3 0.178 38.8 60.11 173.19

31-07-14 12:48 24 1.03 29 1.57 44 218.5 0.183 39.5 60.13 173.19

31-07-14 12:49 24 1.03 29.1 1.51 44 218.6 0.183 39.9 60.06 173.19

31-07-14 12:50 24 1.03 29.3 1.57 44 218.5 0.183 39.7 60.11 173.19

31-07-14 12:51 24 1.03 28.9 1.57 44 218.4 0.183 39.9 60.05 173.19

31-07-14 12:52 24 1.03 29.3 1.51 44 218.3 0.179 39 60.05 173.19

31-07-14 12:53 24 1.03 28.9 1.57 44 218.1 0.18 39 60.02 173.19

31-07-14 12:54 24 1.03 28.8 1.53 43 217.6 0.177 38.5 60.03 173.19

31-07-14 12:55 24 1.03 28.7 1.53 43 217.6 0.175 38 60.02 173.19

31-07-14 12:56 24 1.03 28.9 1.44 42 217.8 0.173 37.4 60.06 173.19

31-07-14 12:57 24 1.04 28.1 1.5 42 217.9 0.171 37.2 59.95 173.2

31-07-14 12:58 24 1.04 28.2 1.46 41 218.1 0.167 36.6 59.99 173.2

31-07-14 12:59 24 1.04 28.6 1.46 41 217.9 0.165 36.1 60.06 173.2


193

31-07-14 13:00 24 1.04 28.2 1.46 41 217.8 0.166 36.1 59.97 173.2

31-07-14 13:01 24 1.04 27.9 1.42 40 217.6 0.163 35.6 59.94 173.2

31-07-14 13:02 24 1.04 28.5 1.42 40 217.3 0.161 35.2 59.92 173.2

31-07-14 13:03 24 1.04 28.6 1.42 40 217.4 0.16 35 60 173.2

31-07-14 13:04 24 1.04 28.3 1.39 39 216.9 0.157 34 59.93 173.2

31-07-14 13:05 24 1.04 28.2 1.42 40 217.4 0.16 34.9 59.95 173.2

31-07-14 13:06 24 1.04 27.6 1.44 39 217.7 0.158 34.5 59.95 173.2

31-07-14 13:07 24 1.04 27.9 1.4 38 217.7 0.156 33.9 59.98 173.2

31-07-14 13:08 24 1.04 27.5 1.44 39 218 0.156 34 60 173.2

31-07-14 13:09 24 1.04 27.9 1.37 37 217.7 0.151 32.8 59.99 173.2

31-07-14 13:10 24 1.04 28 1.32 37 217.6 0.15 32.6 60.02 173.2

31-07-14 13:11 24 1.04 27.6 1.37 37 217.6 0.148 32.4 60.01 173.2

31-07-14 13:12 24 1.05 27.7 1.33 36 218.2 0.146 31.8 60.02 173.21

31-07-14 13:13 24 1.05 27.8 1.33 36 217.9 0.144 31.6 59.97 173.21

31-07-14 13:14 24 1.05 28.5 1.25 35 218 0.141 31.1 60.08 173.21

31-07-14 13:15 24 1.05 27 1.29 35 218.1 0.144 31.1 59.99 173.21

31-07-14 13:16 24 1.05 27.4 1.29 35 217.9 0.141 30.5 59.96 173.21

31-07-14 13:17 24 1.05 26.8 1.34 35 217.8 0.14 30.5 59.93 173.21

31-07-14 13:18 24 1.05 27 1.29 35 218 0.141 30.7 59.94 173.21

31-07-14 13:19 24 1.05 26.6 1.3 34 218.4 0.137 29.9 60.05 173.21

31-07-14 13:20 24 1.05 26.9 1.3 34 218.6 0.136 29.7 60.02 173.21

31-07-14 13:21 24 1.05 26.8 1.26 33 218.7 0.132 28.6 59.99 173.21

31-07-14 13:22 24 1.05 27.3 1.18 32 218.6 0.128 28.1 59.98 173.21

31-07-14 13:23 24 1.05 27.6 1.18 32 218.5 0.128 28.1 59.96 173.21

31-07-14 13:24 24 1.05 26.9 1.23 32 218.4 0.127 27.7 59.95 173.21

31-07-14 13:25 24 1.05 27.3 1.14 31 218 0.125 27.2 59.96 173.21

31-07-14 13:26 24 1.05 27.2 1.14 31 217.9 0.124 27 59.97 173.21

31-07-14 13:27 24 1.05 27.1 1.14 31 218 0.123 26.8 59.97 173.21

31-07-14 13:28 24 1.05 27 1.11 30 218.1 0.122 26.6 59.94 173.21

31-07-14 13:29 24 1.05 27.2 1.11 30 217.8 0.12 25.9 60 173.21

31-07-14 13:30 24 1.05 26.6 1.15 30 218.2 0.119 25.7 60.02 173.21

31-07-14 13:31 24 1.06 27.1 1.07 29 218.2 0.116 25.3 60 173.22

31-07-14 13:32 24 1.06 26.9 1.11 29 218.1 0.114 24.8 59.99 173.22

31-07-14 13:33 24 1.06 26.7 1.07 28 218 0.112 24.4 59.96 173.22

31-07-14 13:34 24 1.06 26.7 1.07 28 217.9 0.112 24.6 59.98 173.22

31-07-14 13:35 24 1.06 27.4 1.07 29 217.8 0.114 24.8 59.96 173.22

31-07-14 13:36 24 1.06 26.6 1.07 28 218.1 0.111 23.9 59.99 173.22

31-07-14 13:37 24 1.06 27 1.03 27 217.9 0.108 23.5 59.98 173.22

31-07-14 13:38 24 1.06 26.2 1.03 27 218.1 0.106 23.1 59.97 173.22

31-07-14 13:39 24 1.06 27 0.96 26 218.1 0.103 22.6 59.97 173.22

31-07-14 13:40 24 1.06 26 1.04 26 218.4 0.103 22.5 60.1 173.22

31-07-14 13:41 24 1.06 26.5 1 26 218.3 0.102 22.2 59.97 173.22

31-07-14 13:42 24 1.06 26.1 1 26 218.2 0.102 22 59.96 173.22

31-07-14 13:43 24 1.06 26.8 0.96 25 218.1 0.1 21.8 59.94 173.22

31-07-14 13:44 24 1.06 27.3 0.92 25 217.9 0.098 21.8 59.94 173.22


194

31-07-14 13:45 24 1.06 27 0.92 25 218.1 0.098 21.3 59.99 173.22

31-07-14 13:46 24 1.06 26 1 25 217.9 0.097 21.1 59.92 173.22

31-07-14 13:47 24 1.06 26.2 0.96 25 217.8 0.097 21.1 60.01 173.22

31-07-14 13:48 24 1.06 27.6 0.92 25 218.1 0.097 21.1 60 173.22

31-07-14 13:49 24 1.06 25.8 0.96 24 217.6 0.097 20.8 60.03 173.22

31-07-14 13:50 24 1.06 27.2 0.88 24 218 0.095 20.7 60.06 173.22

31-07-14 13:51 24 1.06 26.2 0.92 24 218.1 0.096 20.9 60.06 173.22

31-07-14 13:52 24 1.06 26.2 0.96 25 218.2 0.096 21.1 59.95 173.22

31-07-14 13:53 24 1.06 26.5 0.92 24 218.4 0.095 20.5 59.99 173.22

31-07-14 13:54 24 1.06 26.9 0.92 24 218.8 0.093 20.7 59.99 173.22

31-07-14 13:55 24 1.06 26.2 0.92 24 218.8 0.094 20.5 59.99 173.22

31-07-14 13:56 24 1.06 25.8 0.92 23 219.1 0.091 19.9 60.04 173.22

31-07-14 13:57 24 1.07 26.7 0.88 23 218.8 0.089 19.9 60.03 173.23

31-07-14 13:58 24 1.07 25.9 0.88 22 218.9 0.089 19.4 59.99 173.23

31-07-14 13:59 24 1.07 26.8 0.88 23 218.4 0.088 19.2 59.94 173.23

31-07-14 14:00 24 1.07 26.5 0.88 23 218.4 0.087 18.9 59.98 173.23

31-07-14 14:01 24 1.07 26.4 0.88 23 218.6 0.088 19.2 60.02 173.23

31-07-14 14:02 24 1.07 26.1 0.84 22 218.5 0.086 18.7 60.02 173.23

31-07-14 14:03 24 1.07 26.1 0.84 22 218.4 0.086 19 60.01 173.23

31-07-14 14:04 24 1.07 26.7 0.84 22 218.1 0.086 18.7 60.03 173.23

31-07-14 14:05 24 1.07 26 0.88 22 218.3 0.086 18.7 59.95 173.23

31-07-14 14:06 24 1.07 25.9 0.84 22 218.5 0.085 18.3 60.02 173.23

31-07-14 14:07 24 1.07 25.9 0.88 22 218.7 0.083 18.1 59.95 173.23

31-07-14 14:08 24 1.07 26.4 0.84 22 218.3 0.083 18.1 59.96 173.23

31-07-14 14:09 24 1.07 26.9 0.81 22 218.4 0.082 17.9 60.01 173.23

31-07-14 14:10 24 1.07 26.8 0.84 22 218.3 0.081 17.9 60.03 173.23

31-07-14 14:11 24 1.07 26.4 0.84 22 218 0.081 17.8 59.98 173.23

31-07-14 14:12 24 1.07 29.3 1 29 218.3 0.105 24.9 60.05 173.23

31-07-14 14:13 24 1.07 28.5 0.96 27 218.6 0.107 23.6 59.94 173.23

31-07-14 14:14 24 1.07 28.1 1.03 29 219.1 0.109 24.7 59.99 173.23

31-07-14 14:15 24 1.07 28.1 0.96 27 219 0.109 23.6 59.98 173.23

31-07-14 14:16 24 1.07 26.5 1.07 28 218.7 0.114 24.5 59.97 173.23

31-07-14 14:17 24 1.07 26.6 1.03 27 218.6 0.112 23.6 59.99 173.23

31-07-14 14:18 24 1.07 25.9 1.08 27 218.1 0.107 23.5 60 173.23

31-07-14 14:19 24 1.07 26.2 0.96 25 218.4 0.101 21.6 60.03 173.23

31-07-14 14:20 24 1.07 25.7 1.04 26 218.3 0.097 22 60.01 173.23

31-07-14 14:21 24 1.07 26.4 0.92 24 218.4 0.098 20.5 59.96 173.23

31-07-14 14:22 24 1.07 25.9 0.92 23 218.3 0.091 20 60.05 173.23

31-07-14 14:23 24 1.07 25.5 0.88 22 218.1 0.081 17.6 59.96 173.23

31-07-14 14:24 24 1.07 25.5 0.88 22 218 0.079 17.4 60.06 173.23

31-07-14 14:25 24 1.08 26.8 0.81 22 218.3 0.08 18.1 60 173.24

31-07-14 14:26 24 1.08 26.2 0.84 22 218.1 0.085 17.8 59.99 173.24

31-07-14 14:27 24 1.08 25.6 0.88 22 218.3 0.086 18.5 59.96 173.24

31-07-14 14:28 24 1.08 25.7 0.88 22 217.8 0.084 17.6 59.98 173.24

31-07-14 14:29 24 1.08 25.8 0.88 22 218 0.076 16.5 59.95 173.24


195

31-07-14 14:30 24 1.08 27 0.77 21 218.2 0.069 15 60 173.24

31-07-14 14:31 24 1.08 26.7 0.8 21 218.1 0.068 15 60.02 173.24

31-07-14 14:32 24 1.08 26.5 0.8 21 218.8 0.069 15.3 60.04 173.24

31-07-14 14:33 24 1.08 27.3 0.74 20 218.8 0.068 14.6 60.04 173.24

31-07-14 14:34 24 1.08 26.5 0.8 21 218.5 0.071 15.5 59.98 173.24

31-07-14 14:35 24 1.08 27.3 0.77 21 218.3 0.07 15 59.99 173.24

31-07-14 14:36 24 1.08 26.4 0.8 21 218 0.071 15.2 59.99 173.24

31-07-14 14:37 24 1.08 26.1 0.8 21 217.9 0.067 15.2 59.99 173.24

31-07-14 14:38 24 1.08 26.2 0.8 21 218 0.068 14.3 59.99 173.24

31-07-14 14:39 24 1.08 27.3 0.74 20 218.1 0.066 13.9 60.07 173.24

31-07-14 14:40 24 1.08 26.6 0.76 20 218.2 0.066 13.9 60.09 173.24

31-07-14 14:41 24 1.08 25.9 0.84 21 218.1 0.066 14.3 60.14 173.24

31-07-14 14:42 24 1.08 25.9 0.8 20 218.9 0.065 14 60.13 173.24

31-07-14 14:43 24 1.08 21.5 0.95 20 219 0.066 14 60.1 173.24

31-07-14 14:44 24 1.08 25.2 0.95 0 218.8 0.064 0 60.12 173.24

31-07-14 14:45 24 1.08 25.6 0.8 20 219 0.058 12.9 60.06 173.24

31-07-14 14:46 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:47 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:48 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:49 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:50 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:51 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:52 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

31-07-14 14:53 24 1.08 23.4 1 0 218.2 0.057 0 60.1 173.24

Table 12. Dual-Axis Solar Photovoltaic Obtained Raw data

Time Temperature Eac_Today Vpv Ipv Ppv Vac Iac Pac Fac Eac_Total

31-07-14 2:10 24 0 26.7 0.74 20 218.4 0.067 14.4 60.04 239.57

31-07-14 2:11 24 0 26.3 0.76 20 218.4 0.066 14.6 59.94 239.57

31-07-14 2:12 24 0 26.3 0.8 21 218.3 0.067 14.6 59.96 239.57

31-07-14 2:13 24 0 26.9 0.76 20 218.3 0.067 14.4 59.96 239.57

31-07-14 2:14 24 0 28.2 0.71 20 218 0.068 14.6 60 239.57

31-07-14 2:15 24 0.01 27.9 0.74 20 218.4 0.068 15 59.98 239.58

31-07-14 2:16 24 0.01 27.4 0.77 21 218.4 0.07 15.2 60.02 239.58

31-07-14 2:17 24 0.01 26.2 0.8 21 218.5 0.07 15.2 60.09 239.58

31-07-14 2:18 24 0.01 26.7 0.8 21 218.4 0.072 15.5 60.09 239.58

31-07-14 2:19 24 0.01 27.7 0.77 21 218 0.07 15.6 59.96 239.58

31-07-14 2:20 24 0.01 27.3 0.77 21 218 0.072 15.7 60.04 239.58

31-07-14 2:21 24 0.01 27.4 0.77 21 218.1 0.073 15.9 60.04 239.58

31-07-14 2:22 24 0.01 27.1 0.81 22 218.5 0.074 16.3 60.08 239.58

31-07-14 2:23 24 0.01 27.2 0.77 21 218.4 0.075 16.8 60.04 239.58

31-07-14 2:24 24 0.01 27.4 0.77 21 218.7 0.076 16.6 60.06 239.58


196

31-07-14 2:25 24 0.01 28.3 0.78 22 218.7 0.076 16.6 60.03 239.58

31-07-14 2:26 24 0.01 26.4 0.8 21 218.5 0.076 16.3 60.05 239.58

31-07-14 2:27 24 0.01 26.7 0.8 21 218.5 0.074 16.3 59.97 239.58

31-07-14 2:28 24 0.01 27.7 0.78 22 218.7 0.073 16.1 59.99 239.58

31-07-14 2:29 24 0.01 28.2 0.75 21 218.5 0.072 15.9 59.95 239.58

31-07-14 2:30 24 0.01 27 0.81 22 218.9 0.074 16.1 60.06 239.58

31-07-14 2:31 24 0.01 27.4 0.77 21 218.9 0.072 15.9 60 239.58

31-07-14 2:33 24 0.01 26.9 0.84 22 218.6 0.073 16.1 60 239.58

31-07-14 2:34 24 0.01 28.2 0.78 22 218.1 0.073 16.1 59.91 239.58

31-07-14 2:35 24 0.01 27.9 0.81 22 218.6 0.074 16.1 60.04 239.58

31-07-14 2:36 24 0.01 27.8 0.81 22 218.6 0.075 16.1 59.94 239.58

31-07-14 2:37 24 0.01 28.6 0.75 21 218.8 0.074 16.1 60.02 239.58

31-07-14 2:38 24 0.01 27.8 0.77 21 218.7 0.075 16.1 60.03 239.58

31-07-14 2:39 24 0.01 28 0.75 21 218.7 0.074 16.3 60.03 239.58

31-07-14 2:40 24 0.01 28.2 0.75 21 218.4 0.075 16.5 59.98 239.58

31-07-14 2:41 24 0.01 29.1 0.75 22 218.3 0.074 15.9 59.96 239.58

31-07-14 2:42 24 0.01 27.5 0.81 22 218.6 0.076 16.6 60.13 239.58

31-07-14 2:43 24 0.01 27.7 0.81 22 218.5 0.076 17 59.99 239.58

31-07-14 2:44 24 0.01 27.3 0.81 22 218.1 0.078 17 59.97 239.58

31-07-14 2:45 24 0.01 26.6 0.84 22 217.8 0.078 17.2 59.96 239.58

31-07-14 2:46 24 0.01 27.4 0.81 22 218.3 0.08 17.9 60.05 239.58

31-07-14 2:47 24 0.01 26.2 0.84 22 218.4 0.083 17.9 60.04 239.58

31-07-14 2:48 24 0.01 26.5 0.84 22 218.6 0.083 18.1 59.99 239.58

31-07-14 2:49 24 0.01 27.2 0.84 22 218.5 0.082 18.1 59.99 239.58

31-07-14 2:50 24 0.02 27 0.81 22 218.7 0.086 18.8 60.02 239.59

31-07-14 2:51 24 0.02 27.9 0.81 22 218.6 0.085 18.5 59.98 239.59

31-07-14 2:52 24 0.02 26.7 0.84 22 218.3 0.086 18.7 60 239.59

31-07-14 2:53 24 0.02 26.9 0.84 22 218.2 0.087 18.7 59.91 239.59

31-07-14 2:54 24 0.02 27.9 0.81 22 218.4 0.087 19.2 60.05 239.59

31-07-14 2:55 24 0.02 27.7 0.81 22 218.4 0.088 18.7 60.01 239.59

31-07-14 2:56 24 0.02 27.2 0.81 22 218.2 0.088 19.4 59.95 239.59

31-07-14 2:57 24 0.02 28.6 0.82 23 218.2 0.088 18.9 59.96 239.59

31-07-14 2:58 24 0.02 27.8 0.85 23 218.5 0.089 19.6 60.02 239.59

31-07-14 2:59 24 0.02 26.5 0.92 24 218.1 0.092 20 60.02 239.59

31-07-14 3:00 24 0.02 28.1 0.89 25 218.6 0.1 21.6 60 239.59

31-07-14 3:01 24 0.02 27.2 0.96 25 218.6 0.097 20.9 60.02 239.59

31-07-14 3:02 24 0.02 28.4 1 26 218.6 0.101 22 60.09 239.59

31-07-14 3:03 24 0.02 27.6 0.96 26 218.5 0.103 22.7 60.03 239.59

31-07-14 3:04 24 0.02 27.7 1 27 218.5 0.103 22.7 60.02 239.59

31-07-14 3:05 24 0.02 28.7 0.92 25 218.1 0.099 21.5 60.03 239.59

31-07-14 3:06 24 0.02 26.7 1 26 218.2 0.104 22.7 60.05 239.59

31-07-14 3:07 24 0.02 28.2 0.96 27 217.9 0.106 23.3 59.98 239.59

31-07-14 3:08 24 0.02 26.7 1.07 28 218.1 0.11 23.9 59.96 239.59

31-07-14 3:09 24 0.02 27.9 1.07 29 218.2 0.116 25.3 60.07 239.59

31-07-14 3:10 24 0.02 28.4 1.07 30 218.3 0.12 26.4 59.99 239.59


197

31-07-14 3:11 24 0.02 27.9 1.14 31 218.3 0.123 27 60.02 239.59

31-07-14 3:12 24 0.02 28.9 1.14 32 218.3 0.13 28.3 59.94 239.59

31-07-14 3:13 24 0.02 28.6 1.21 34 218.6 0.136 29.9 60.07 239.59

31-07-14 3:14 24 0.02 29.1 1.17 33 218.3 0.133 29 60 239.59

31-07-14 3:15 24 0.03 28.7 1.21 34 218.3 0.135 29.4 60.02 239.6

31-07-14 3:16 24 0.03 28 1.17 33 218.2 0.131 28.3 60.03 239.6

31-07-14 3:17 24 0.03 28 1.21 34 218.2 0.138 30 60.04 239.6

31-07-14 3:18 24 0.03 28.2 1.25 35 218.3 0.143 31.2 60.03 239.6

31-07-14 3:19 24 0.03 28.5 1.28 36 218.3 0.148 32 60.06 239.6

31-07-14 3:20 24 0.03 30.6 1.17 34 217.8 0.138 30.9 59.99 239.6

31-07-14 3:21 24 0.03 30.4 1.3 39 217.8 0.157 34.2 59.99 239.6

31-07-14 3:22 24 0.03 30.4 1.33 40 218.2 0.16 35.1 59.98 239.6

31-07-14 3:23 24 0.03 30 1.29 40 218.2 0.168 36.2 60.08 239.6

31-07-14 3:24 24 0.03 30.5 1.25 39 218.5 0.171 37.5 60.07 239.6

31-07-14 3:25 24 0.03 31.1 1.48 46 218.5 0.188 41 60.06 239.6

31-07-14 3:26 24 0.03 31 1.51 47 218.4 0.198 43 60.02 239.6

31-07-14 3:27 24 0.03 30.8 1.63 49 218.6 0.201 43.7 60.04 239.6

31-07-14 3:28 24 0.03 30.5 1.51 47 218.5 0.195 42.8 60 239.6

31-07-14 3:29 24 0.03 29.3 1.62 47 218.5 0.184 41.5 60.07 239.6

31-07-14 3:30 24 0.04 30.2 1.53 46 218.3 0.187 41.2 60.02 239.61

31-07-14 3:31 24 0.04 29.8 1.58 46 218.3 0.191 41.9 60.13 239.61

31-07-14 3:32 24 0.04 30.7 1.53 46 218.2 0.189 41.2 60 239.61

31-07-14 3:33 24 0.04 30.3 1.56 47 218.6 0.193 41.2 60.1 239.61

31-07-14 3:34 24 0.04 30.9 1.7 53 218.5 0.217 47.4 60.04 239.61

31-07-14 3:35 24 0.04 31.1 1.83 55 218.6 0.235 50.9 59.96 239.61

31-07-14 3:36 24 0.04 28.8 2.32 65 218.8 0.272 59.5 60.06 239.61

31-07-14 3:37 24 0.04 28.8 2.24 65 219.2 0.276 59.8 60.05 239.61

31-07-14 3:38 24 0.04 28.6 2.28 64 219 0.27 58.6 60 239.61

31-07-14 3:39 24 0.04 29 2.24 65 219.2 0.271 59.1 60.04 239.61

31-07-14 3:40 24 0.04 28.1 2.14 60 218.9 0.25 54.9 60.05 239.61

31-07-14 3:41 24 0.04 28 2 56 218.8 0.24 53.6 60.07 239.61

31-07-14 3:42 24 0.05 28.7 1.85 52 219 0.216 47 60.05 239.62

31-07-14 3:43 24 0.05 28.4 1.75 51 218.7 0.209 45.9 60.03 239.62

31-07-14 3:44 24 0.05 28.4 1.96 55 218.9 0.228 49.9 60.11 239.62

31-07-14 3:45 24 0.05 28.3 2.03 59 218.4 0.242 52.8 59.96 239.62

31-07-14 3:46 24 0.05 30.1 2.46 74 219 0.313 68.1 60.07 239.62

31-07-14 3:47 24 0.05 30.1 2.53 76 218.7 0.315 68.9 60.03 239.62

31-07-14 3:48 24 0.05 31.2 2.06 62 219 0.268 58 60.07 239.62

31-07-14 3:49 24 0.05 30.2 2.12 66 218.9 0.268 59.1 60 239.62

31-07-14 3:50 24 0.05 30.6 2.43 73 219.2 0.303 66.6 60.07 239.62

31-07-14 3:51 24 0.06 29.1 2.82 79 219 0.334 72.6 59.98 239.63

31-07-14 3:52 24 0.06 27.5 2.82 79 219.1 0.334 72.3 60.02 239.63

31-07-14 3:53 24 0.06 28 2.82 79 218.6 0.331 72.5 60.02 239.63

31-07-14 3:54 24 0.06 28.3 2.96 83 218.9 0.349 76.6 59.99 239.63

31-07-14 3:55 24 0.06 26.5 3 84 219 0.346 76.4 60.1 239.63


198

31-07-14 3:56 24 0.06 28.4 3.1 87 218.8 0.363 78.9 60 239.63

31-07-14 3:57 24 0.06 28.6 3.21 90 219.2 0.37 81.5 59.95 239.63

31-07-14 3:58 24 0.06 28.7 3.25 88 219.2 0.371 81.1 60.02 239.63

31-07-14 3:59 24 0.07 28.9 3.32 93 219.6 0.388 84.9 60.04 239.64

31-07-14 4:00 24 0.07 28.7 3.42 96 219.5 0.399 87.8 60.06 239.64

31-07-14 4:01 24 0.07 28.4 3.2 93 219.1 0.393 85.9 59.95 239.64

31-07-14 4:02 24 0.07 27.8 2.96 83 219.1 0.346 75.8 60.08 239.64

31-07-14 4:03 24 0.07 28.6 3.4 92 218.8 0.388 84.8 59.89 239.64

31-07-14 4:04 24 0.07 28.3 3.17 89 219.1 0.368 80.4 60.06 239.64

31-07-14 4:05 24 0.07 28.7 2.78 78 218.9 0.327 71.3 60.04 239.64

31-07-14 4:06 24 0.08 28.2 2.5 70 218.3 0.296 64.8 59.96 239.65

31-07-14 4:07 24 0.08 26.5 2.44 66 218.3 0.273 60 60.04 239.65

31-07-14 4:08 24 0.08 28 2.07 58 218 0.241 52.7 59.94 239.65

31-07-14 4:09 24 0.08 28.2 2 56 217.9 0.232 50.5 60.01 239.65

31-07-14 4:10 24 0.08 28.3 1.75 49 217.7 0.198 43.7 60.02 239.65

31-07-14 4:11 24 0.08 28.4 1.67 47 217.4 0.194 42.1 60.1 239.65

31-07-14 4:12 24 0.08 28.1 1.64 46 217.4 0.192 41.7 60.09 239.65

31-07-14 4:13 24 0.08 28.4 1.88 51 217.2 0.209 45.6 59.93 239.65

31-07-14 4:14 24 0.08 28.2 1.85 52 217.1 0.215 46.6 60.03 239.65

31-07-14 4:15 24 0.08 28.4 1.85 52 217.2 0.214 46.4 60.04 239.65

31-07-14 4:16 24 0.08 28.3 2.39 67 216.8 0.289 63.1 59.99 239.65

31-07-14 4:17 24 0.09 26.8 2.46 64 216.6 0.272 59.1 60.07 239.66

31-07-14 4:18 24 0.09 28.3 2.35 66 216.4 0.277 60.4 60.04 239.66

31-07-14 4:19 24 0.09 27.6 2.4 65 216.6 0.272 59.1 59.98 239.66

31-07-14 4:20 24 0.09 26.9 2.32 65 216.9 0.273 60.7 60.06 239.66

31-07-14 4:21 24 0.09 28.8 3.21 90 217.2 0.38 82.3 60.13 239.66

31-07-14 4:22 24 0.09 28.6 3.46 97 217.1 0.41 88.9 59.96 239.66

31-07-14 4:23 24 0.09 29 3.44 100 216.8 0.428 91.4 60.04 239.66

31-07-14 4:24 24 0.09 29.3 2.2 64 216.1 0.271 57.2 60.03 239.66

31-07-14 4:25 24 0.1 28.5 2.21 62 216 0.262 56.8 60.01 239.67

31-07-14 4:26 24 0.1 29.4 2.93 85 216.3 0.359 77 60.04 239.67

31-07-14 4:27 24 0.1 28.4 2.57 72 215.8 0.301 66 60.06 239.67

31-07-14 4:28 24 0.1 28.6 2.67 75 215.8 0.32 69 60.07 239.67

31-07-14 4:29 24 0.1 28.1 2.57 72 216 0.305 66.1 60.11 239.67

31-07-14 4:30 24 0.1 28.3 2.03 57 215.4 0.243 52.1 60.03 239.67

31-07-14 4:31 24 0.1 28.2 2.14 60 215.7 0.253 54.8 60.11 239.67

31-07-14 4:32 24 0.1 28.9 2.07 58 215.5 0.247 52.9 60.02 239.67

31-07-14 4:33 24 0.1 27.5 2.66 72 215.8 0.311 66.8 60.04 239.67

31-07-14 4:34 24 0.11 28.9 2.96 83 218.1 0.35 76.1 60 239.68

31-07-14 4:35 24 0.11 28.6 3.07 86 218.3 0.361 79.2 60.11 239.68

31-07-14 4:36 24 0.11 28.3 3.25 91 218.3 0.383 83.4 60.03 239.68

31-07-14 4:37 24 0.11 27.5 3.59 97 218.5 0.396 86.9 60.11 239.68

31-07-14 4:38 24 0.11 29.1 3.41 99 218.6 0.419 91.8 60.07 239.68

31-07-14 4:39 24 0.11 29.7 3.27 95 218.5 0.398 87 60.06 239.68

31-07-14 4:40 24 0.12 27.8 4.03 113 218.6 0.471 104.1 60.22 239.69


199

31-07-14 4:41 24 0.12 28.6 3.64 102 217.9 0.436 94.7 60 239.69

31-07-14 4:42 24 0.12 28.8 3.92 110 218.1 0.469 102 60.02 239.69

31-07-14 4:43 24 0.12 26 3.96 103 217.7 0.438 95.5 59.94 239.69

31-07-14 4:44 24 0.12 28.3 4.14 116 218.6 0.489 106.9 60.09 239.69

31-07-14 4:45 24 0.12 29.1 4.25 115 218.2 0.498 109.5 60.01 239.69

31-07-14 4:46 24 0.12 28.2 4.07 114 218.4 0.479 104.6 60.09 239.69

31-07-14 4:47 24 0.13 28.1 4 112 218.3 0.476 103.7 60.07 239.7

31-07-14 4:48 24 0.13 28.2 4.28 120 218.6 0.502 109.7 60.04 239.7

31-07-14 4:49 24 0.13 28 4.5 126 218.8 0.535 117.7 60.06 239.7

31-07-14 4:50 24 0.13 27.9 4.85 131 218.6 0.559 122.4 60.07 239.7

31-07-14 4:51 24 0.14 28.2 4.67 131 218.5 0.562 122.8 60.08 239.71

31-07-14 4:52 24 0.14 28.5 4.85 131 218.1 0.563 122.1 59.97 239.71

31-07-14 4:53 24 0.14 28.4 4.89 137 218.7 0.581 127.5 60.04 239.71

31-07-14 4:54 24 0.14 27.2 4.74 128 218.3 0.542 119.1 60.02 239.71

31-07-14 4:55 24 0.14 27.8 2.48 67 217.1 0.288 62.5 60.08 239.71

31-07-14 4:56 24 0.14 27.5 2.51 68 216.8 0.289 62.6 59.92 239.71

31-07-14 4:57 24 0.15 27.5 5.03 136 218.3 0.577 126.3 59.94 239.72

31-07-14 4:58 24 0.15 27.7 3.65 95 217.3 0.417 87.3 60.02 239.72

31-07-14 4:59 24 0.15 28.5 4.82 135 220.8 0.575 126.7 60.04 239.72

31-07-14 5:00 24 0.15 27.8 5 140 220.6 0.593 131 60.02 239.72

31-07-14 5:01 24 0.15 27.1 5.25 142 220.6 0.595 132.6 59.99 239.72

31-07-14 5:02 24 0.16 27.8 5.48 148 220.7 0.624 137.4 60.02 239.73

31-07-14 5:03 24 0.16 27.5 5.4 146 220.9 0.617 136.3 59.99 239.73

31-07-14 5:04 24 0.16 27.5 4.81 130 220.1 0.564 124.3 60 239.73

31-07-14 5:05 24 0.16 27.4 5.88 159 220.8 0.679 148.8 60.03 239.73

31-07-14 5:06 24 0.17 27.6 5.66 153 220.9 0.644 142.4 60 239.74

31-07-14 5:07 24 0.17 27.5 5.33 144 220.7 0.609 134.6 59.99 239.74

31-07-14 5:08 24 0.17 27.7 5.22 141 220.7 0.596 131.5 60.02 239.74

31-07-14 5:09 24 0.17 27.9 5.07 137 220.5 0.579 127.7 59.99 239.74

31-07-14 5:10 24 0.18 26.1 3.37 91 219.1 0.363 80.1 60.01 239.75

31-07-14 5:11 24 0.18 27.2 2.62 71 218.6 0.3 65.8 60.01 239.75

31-07-14 5:12 24 0.18 30.2 3.4 102 219.2 0.436 95.1 59.98 239.75

31-07-14 5:13 24 0.18 27.9 3.55 96 219.3 0.4 86.8 59.98 239.75

31-07-14 5:14 24 0.18 27.8 4.85 131 220.2 0.553 121.2 60.02 239.75

31-07-14 5:15 24 0.18 28.6 3.17 89 218.5 0.374 81.9 59.96 239.75

31-07-14 5:16 24 0.19 28.9 4.75 133 219.5 0.568 124.8 60.08 239.76

31-07-14 5:17 24 0.19 27.2 4.96 134 219.5 0.561 123.3 59.99 239.76

31-07-14 5:18 24 0.19 27.4 4.89 137 219.5 0.58 127.7 60 239.76

31-07-14 5:19 24 0.19 27.9 5.03 136 219.1 0.579 126.8 59.97 239.76

31-07-14 5:20 24 0.2 28.3 4.67 131 218.9 0.555 121.7 59.93 239.77

31-07-14 5:21 24 0.2 30.2 3.66 110 218.3 0.476 103 59.95 239.77

31-07-14 5:22 24 0.2 26.2 3.25 88 217.5 0.359 79.2 59.98 239.77

31-07-14 5:23 24 0.2 27.5 2.64 74 217.4 0.309 67.6 60 239.77

31-07-14 5:24 24 0.2 27.5 2.48 67 217.1 0.283 61.4 60.04 239.77

31-07-14 5:25 24 0.2 28.3 2.25 63 217.5 0.265 57.4 60.03 239.77


200

31-07-14 5:26 24 0.2 27.1 2.59 70 217.5 0.289 60.7 60.03 239.77

31-07-14 5:27 24 0.21 27.9 2.59 70 217.4 0.298 64.7 59.96 239.78

31-07-14 5:28 24 0.21 28.1 3.96 107 218.2 0.454 99.4 60.04 239.78

31-07-14 5:29 24 0.21 29.2 3.96 115 218.1 0.489 105.9 60.02 239.78

31-07-14 5:30 24 0.21 28.9 4.5 126 218.3 0.54 117.8 60.04 239.78

31-07-14 5:31 24 0.21 28.7 4.46 125 218.3 0.529 115.6 60 239.78

31-07-14 5:32 24 0.21 27.4 4.29 116 218.2 0.489 106.6 60.01 239.78

31-07-14 5:33 24 0.21 28.8 3.96 115 218.1 0.491 107 60 239.78

31-07-14 5:34 24 0.22 27.5 3.03 79 217.4 0.338 72.7 60.09 239.79

31-07-14 5:35 24 0.22 28.8 3.11 84 217.2 0.355 77.3 59.98 239.79

31-07-14 5:36 24 0.22 26.5 2.29 62 216.6 0.262 57.1 60.03 239.79

31-07-14 5:37 24 0.22 28.2 2.8 73 216.7 0.316 68.6 59.99 239.79

31-07-14 5:38 24 0.22 27.6 3.89 109 217.5 0.436 96.6 60.03 239.79

31-07-14 5:39 24 0.22 28.5 2.78 78 219.1 0.324 71.6 59.99 239.79

31-07-14 5:40 24 0.22 27.6 4.53 127 220.4 0.53 118.7 60.1 239.79

31-07-14 5:41 24 0.23 28.6 4.67 131 220.4 0.559 122.9 60.02 239.8

31-07-14 5:42 24 0.23 27.8 4.75 133 220.3 0.568 125 60.04 239.8

31-07-14 5:43 24 0.23 26.7 5.18 140 220.5 0.582 130 60.03 239.8

31-07-14 5:44 24 0.23 27.4 5.33 144 221 0.605 133.8 60.01 239.8

31-07-14 5:45 24 0.24 27.2 5.7 154 220.9 0.654 144.2 60.04 239.81

31-07-14 5:46 24 0.24 27 5.37 145 220.8 0.612 134.9 59.95 239.81

31-07-14 5:47 24 0.24 27.3 2.25 61 218.5 0.255 55.6 60 239.81

31-07-14 5:48 24 0.24 27.5 5.51 149 220.7 0.628 138.5 60.06 239.81

31-07-14 5:49 24 0.24 27.8 5.66 153 220.9 0.643 141.9 60.09 239.81

31-07-14 5:50 24 0.25 28 4.92 133 220.4 0.572 126.5 60.03 239.82

31-07-14 5:51 24 0.25 27.1 3.48 94 219.6 0.388 85.2 59.98 239.82

31-07-14 5:52 24 0.25 27.3 6.66 180 221.6 0.764 169.8 60.05 239.82

31-07-14 5:53 24 0.25 26 6.22 168 221.3 0.634 142.7 60.01 239.82

31-07-14 5:54 24 0.26 26.8 6.53 183 221.2 0.785 174.7 59.99 239.83

31-07-14 5:55 24 0.26 27.6 6.62 179 220.9 0.763 168.3 60.01 239.83

31-07-14 5:56 24 0.26 25.9 7.23 188 221 0.783 173 60.02 239.83

31-07-14 5:57 24 0.27 26.1 6.81 184 220.9 0.768 170.3 59.96 239.84

31-07-14 5:58 24 0.27 26.5 7.23 188 221.4 0.793 175.8 60.03 239.84

31-07-14 5:59 24 0.27 26.9 7.26 189 221 0.798 176.1 60.07 239.84

31-07-14 6:00 24 0.28 26.5 7.26 189 220.9 0.801 177 60.03 239.85

31-07-14 6:01 24 0.28 27.1 6.62 179 221.1 0.763 168.6 60 239.85

31-07-14 6:02 24 0.28 26.5 6.61 172 220.8 0.73 161.1 60.01 239.85

31-07-14 6:03 24 0.28 26.9 6.92 180 220.9 0.769 169.7 60.09 239.85

31-07-14 6:04 24 0.29 26.6 6.88 179 220.9 0.759 167.6 60.03 239.86

31-07-14 6:05 24 0.29 26.6 7.38 192 221.2 0.812 179.1 60.09 239.86

31-07-14 6:06 24 0.29 26.5 7.8 203 221.3 0.859 190 60.03 239.86

31-07-14 6:07 24 0.3 27 7.59 205 221.3 0.865 191.4 60.02 239.87

31-07-14 6:08 24 0.3 30 5.4 162 219.8 0.671 146.8 60.02 239.87

31-07-14 6:09 24 0.3 27.4 7.07 191 220.8 0.807 178.5 60.07 239.87

31-07-14 6:10 24 0.3 25.9 7.65 199 221.1 0.831 184 60.04 239.87


201

31-07-14 6:11 24 0.31 26.5 7.69 200 220.8 0.851 187.1 59.98 239.88

31-07-14 6:12 24 0.31 26.1 7.61 198 220.2 0.843 185.5 60.05 239.88

31-07-14 6:13 24 0.32 26.6 7.38 192 220.1 0.803 176.8 60.07 239.89

31-07-14 6:14 24 0.32 27 7.51 203 220.6 0.865 190.5 60.09 239.89

31-07-14 6:15 24 0.32 26.9 7.88 205 221 0.864 191.3 60.08 239.89

31-07-14 6:16 24 0.33 26.8 7.73 201 220.8 0.849 187.4 60.1 239.9

31-07-14 6:17 24 0.33 27.2 4.76 119 219.4 0.463 102 60.11 239.9

31-07-14 6:18 24 0.33 27.2 6.85 185 220.7 0.791 175 60.05 239.9

31-07-14 6:19 24 0.33 26.1 3.38 88 218.4 0.366 79.8 60.05 239.9

31-07-14 6:20 24 0.33 26.9 7.8 203 220.9 0.854 188.7 60.1 239.9

31-07-14 6:21 24 0.34 26.7 7.23 188 220.4 0.79 174 60.02 239.91

31-07-14 6:22 24 0.34 29.7 5.27 153 220.7 0.644 139.7 60.08 239.91

31-07-14 6:23 24 0.35 27 7.57 197 220.7 0.828 182.7 60.04 239.92

31-07-14 6:24 24 0.35 26.1 7.42 193 220.7 0.82 180.3 60.09 239.92

31-07-14 6:25 24 0.35 26.8 7.61 198 220.4 0.837 185.3 60.07 239.92

31-07-14 6:26 24 0.35 26.3 7.53 196 220.3 0.832 183 60.03 239.92

31-07-14 6:27 24 0.36 26.6 7.42 193 220.5 0.816 180 60.11 239.93

31-07-14 6:28 24 0.36 26.7 7.5 195 220.2 0.824 181.4 60.03 239.93

31-07-14 6:29 24 0.36 26.5 7.5 195 220 0.83 182.6 60.06 239.93

31-07-14 6:30 24 0.37 26.4 7.46 194 219.8 0.826 181 60.06 239.94

31-07-14 6:31 24 0.37 26.4 7.53 196 219.6 0.833 182.7 60 239.94

31-07-14 6:32 24 0.37 26.6 7.73 201 219.7 0.854 187.4 60.08 239.94

31-07-14 6:33 24 0.38 26.1 8.07 210 220 0.891 196.1 60.07 239.95

31-07-14 6:34 24 0.38 27.7 3.33 90 218.2 0.378 82 60.04 239.95

31-07-14 6:35 24 0.38 26.8 7.84 204 220.6 0.865 190.8 59.98 239.95

31-07-14 6:36 24 0.39 25.9 7.88 205 221.4 0.861 191.1 60.06 239.96

31-07-14 6:37 24 0.39 26.1 8.19 213 221.5 0.9 199.3 60.02 239.96

31-07-14 6:38 24 0.39 26.6 8.19 213 220.9 0.899 198.8 60 239.96

31-07-14 6:39 24 0.4 25.9 9.04 226 221.1 0.954 211.1 60.07 239.97

31-07-14 6:40 24 0.4 25.9 8.07 218 220.8 0.923 204.1 59.99 239.97

31-07-14 6:41 24 0.4 25.2 7.38 192 220.1 0.774 171 60.04 239.97

31-07-14 6:42 24 0.41 27.5 3.48 94 218.4 0.391 85.3 60.05 239.98

31-07-14 6:43 24 0.41 26.7 3.57 93 218.4 0.391 84.9 60 239.98

31-07-14 6:44 24 0.41 26.9 3 81 217.8 0.342 74.2 59.99 239.98

31-07-14 6:45 24 0.41 27.2 2.96 80 217.7 0.337 73.1 59.98 239.98

31-07-14 6:46 24 0.41 26 3.69 96 217.8 0.387 85.1 60 239.98

31-07-14 6:47 24 0.42 27.1 2.7 73 217.5 0.308 67.2 60 239.99

31-07-14 6:48 24 0.42 28.3 2.67 75 217.5 0.319 69.1 60.03 239.99

31-07-14 6:49 24 0.42 27.4 3.11 84 217.6 0.354 76.7 60.07 239.99

31-07-14 6:50 24 0.42 28 3.32 93 217.7 0.39 85.3 59.98 239.99

31-07-14 6:51 24 0.42 27.4 7.62 206 220.1 0.871 192.1 60.05 239.99

31-07-14 6:52 24 0.43 27.2 7.85 212 219.8 0.903 199 59.99 240

31-07-14 6:53 24 0.43 28.3 3.66 99 218 0.407 89.8 60.04 240

31-07-14 6:54 24 0.43 27.7 3.53 92 217.7 0.388 84.9 60.03 240

31-07-14 6:55 24 0.43 27.6 4.58 110 217.7 0.427 93.6 59.99 240


202

31-07-14 6:56 24 0.43 27.8 3.29 89 217.8 0.377 82.1 60.01 240

31-07-14 6:57 24 0.43 26.7 6.51 176 219.4 0.817 178.8 60.11 240

31-07-14 6:58 24 0.44 27.6 2.96 80 217.2 0.338 73.4 60 240.01

31-07-14 6:59 24 0.44 26.7 8.59 232 220.6 0.976 215.8 60.01 240.01

31-07-14 7:00 24 0.44 25.6 5.56 139 219 0.477 115.8 59.99 240.01

31-07-14 7:01 24 0.44 25.9 8.76 228 220.3 0.966 212.5 60.03 240.01

31-07-14 7:02 24 0.45 25.9 4.07 110 218 0.47 103.5 59.99 240.02

31-07-14 7:03 24 0.45 26 3.61 94 217.5 0.396 85.9 60.06 240.02

31-07-14 7:04 24 0.45 27.4 8.57 223 220 0.938 207.4 59.97 240.02

31-07-14 7:05 24 0.45 27 3.25 88 217.2 0.368 79.7 59.97 240.02

31-07-14 7:06 24 0.46 27.7 2.62 71 217 0.306 66.1 60.07 240.03

31-07-14 7:07 24 0.46 26.2 3.03 79 217 0.331 72.6 60 240.03

31-07-14 7:08 24 0.46 27 7.62 206 219.4 0.875 191.9 60.11 240.03

31-07-14 7:09 24 0.46 26.7 3.07 80 216.4 0.336 72.7 60 240.03

31-07-14 7:10 24 0.46 27.3 2.74 74 216.8 0.313 67.8 60.07 240.03

31-07-14 7:11 24 0.46 28.3 3.77 102 217.4 0.461 100.6 59.96 240.03

31-07-14 7:12 24 0.47 28.9 3.03 85 216.8 0.358 77.6 59.99 240.04

31-07-14 7:13 24 0.47 27.6 3.85 104 217.2 0.446 97 60 240.04

31-07-14 7:14 24 0.47 27.5 6.53 170 218.3 0.743 160.3 60.04 240.04

31-07-14 7:15 24 0.47 27.2 3.77 102 217.7 0.43 93.6 60 240.04

31-07-14 7:16 24 0.48 26.1 8.23 214 220.3 0.899 199.5 59.99 240.05

31-07-14 7:17 24 0.48 27.2 8.52 213 220.5 0.904 199.5 60.04 240.05

31-07-14 7:18 24 0.48 26.6 8.68 217 220.5 0.913 202.6 59.94 240.05

31-07-14 7:19 24 0.49 27.2 3.03 82 217.4 0.346 75.2 59.98 240.06

31-07-14 7:20 24 0.49 30.9 4.64 144 219.4 0.733 158.9 59.96 240.06

31-07-14 7:21 24 0.49 25.3 7.77 210 220 0.832 189.9 59.98 240.06

31-07-14 7:22 24 0.49 25.8 6.8 177 218.6 0.715 155.9 59.98 240.06

31-07-14 7:23 24 0.5 26.6 8.65 225 220 0.943 207.9 59.95 240.07

31-07-14 7:24 24 0.5 30.8 3.53 99 218.2 0.556 122.2 59.97 240.07

31-07-14 7:25 24 0.5 28.6 6.68 194 220.1 0.856 187 59.93 240.07

31-07-14 7:26 24 0.51 27.2 3.67 103 217.7 0.346 77.7 59.99 240.08

31-07-14 7:27 24 0.51 27.1 5.7 154 219.7 0.773 167.6 60.02 240.08

31-07-14 7:28 24 0.51 26.4 8.15 212 220.1 0.899 197.9 59.94 240.08

31-07-14 7:29 24 0.51 26.1 8.07 210 219.7 0.88 194.4 59.99 240.08

31-07-14 7:30 24 0.52 26.4 8.61 224 219.7 0.956 209 59.97 240.09

31-07-14 7:31 24 0.52 25.9 2.96 74 217 0.313 68.1 60.07 240.09

31-07-14 7:32 24 0.52 29 4.31 125 218.7 0.519 109 60 240.09

31-07-14 7:33 24 0.52 26.3 8.57 223 219.9 0.943 207.4 60 240.09

31-07-14 7:34 24 0.53 25.9 8.8 229 220.2 0.97 213.3 59.99 240.1

31-07-14 7:35 24 0.53 26.2 6.96 188 219.8 0.876 193.8 60.03 240.1

31-07-14 7:36 24 0.53 26.6 8.46 220 220.2 0.934 205.4 59.99 240.1

31-07-14 7:37 24 0.54 26.4 8.42 219 220.1 0.929 204.3 59.98 240.11

31-07-14 7:38 24 0.54 27.3 7.92 214 220 0.91 199.8 60.02 240.11

31-07-14 7:39 24 0.54 26.5 8.68 217 220 0.92 202.8 60.05 240.11

31-07-14 7:40 24 0.55 25.8 8.52 213 219.8 0.904 201 59.97 240.12


203

31-07-14 7:41 24 0.55 30.6 3.93 122 218.3 0.536 113.4 59.98 240.12

31-07-14 7:42 24 0.55 26.2 8.34 217 219.4 0.924 202.5 60.03 240.12

31-07-14 7:43 24 0.56 26.4 7.92 214 219.4 0.938 205.3 59.92 240.13

31-07-14 7:44 24 0.57 25.9 8 208 219.6 0.882 194 60.04 240.14

31-07-14 7:45 24 0.57 26.4 8.19 213 220 0.899 197.8 60.03 240.14

31-07-14 7:46 24 0.57 27.1 6.22 168 219.2 0.733 156.4 59.97 240.14

31-07-14 7:47 24 0.58 26.5 8.3 216 219.5 0.914 201.1 60.07 240.15

31-07-14 7:48 24 0.58 26 8.68 217 219.6 0.927 203.3 60.01 240.15

31-07-14 7:49 24 0.58 25.9 8.56 214 219.5 0.909 199.6 59.96 240.15

31-07-14 7:50 24 0.58 27.6 3.55 96 217.2 0.408 87.9 60.03 240.15

31-07-14 7:51 24 0.59 26.8 7.53 211 219.4 0.947 207.1 60.03 240.16

31-07-14 7:52 24 0.59 26.9 8.4 227 219.1 0.978 212.5 59.99 240.16

31-07-14 7:53 24 0.59 26.4 3.07 80 216.8 0.342 73.7 59.96 240.16

31-07-14 7:54 24 0.59 26.4 8.15 212 219.5 0.898 197.1 60.04 240.16

31-07-14 7:55 24 0.6 25.9 8.19 213 219.8 0.905 199 59.99 240.17

31-07-14 7:56 24 0.6 26.3 7.88 205 219.5 0.877 192.2 59.96 240.17

31-07-14 7:57 24 0.61 26.8 8.4 210 219.7 0.91 197.4 59.99 240.18

31-07-14 7:58 24 0.61 26 8.26 215 220 0.899 198.3 59.97 240.18

31-07-14 7:59 24 0.61 27.6 7.33 198 219.4 0.935 203.6 59.95 240.18

31-07-14 8:00 24 0.61 26.6 8.15 212 219.8 0.901 198.5 60.01 240.18

31-07-14 8:01 24 0.62 26.9 8.48 212 219.6 0.891 196.4 59.99 240.19

31-07-14 8:02 24 0.62 27.5 8.28 207 219.7 0.871 190.3 59.99 240.19

31-07-14 8:03 24 0.63 25.9 8.28 207 219.9 0.876 192.8 60.02 240.2

31-07-14 8:04 24 0.63 26.3 8.07 210 220.1 0.887 195.2 59.98 240.2

31-07-14 8:05 24 0.63 26.1 8.19 213 219.9 0.902 198.3 59.97 240.2

31-07-14 8:06 24 0.64 26.3 8.38 218 220.6 0.921 203.4 59.99 240.21

31-07-14 8:07 24 0.64 30.2 4.46 134 219.8 0.547 120.6 59.98 240.21

31-07-14 8:08 24 0.64 26.2 8.46 220 220.9 0.931 205.3 60.03 240.21

31-07-14 8:09 24 0.65 25.9 8.52 213 220.3 0.901 198.4 60.02 240.22

31-07-14 8:10 24 0.65 26.4 8.34 217 220.3 0.916 201.7 60.03 240.22

31-07-14 8:11 24 0.65 26.9 8.46 220 220.2 0.929 204.5 60 240.22

31-07-14 8:12 24 0.66 26.5 8.65 225 220.2 0.952 209.6 60.03 240.23

31-07-14 8:13 24 0.66 26.4 8.88 231 220.5 0.973 214.2 60.07 240.23

31-07-14 8:14 24 0.66 27.2 8.5 221 220.9 0.925 202.4 60.11 240.23

31-07-14 8:15 24 0.67 26.7 9 225 220.1 0.944 207.7 60.23 240.24

31-07-14 8:16 24 0.67 27.4 8.03 217 221.7 0.911 201.9 60.11 240.24

31-07-14 8:17 24 0.68 29.5 5.37 156 219.7 0.881 173.7 60.07 240.25

31-07-14 8:18 24 0.68 26.6 3.65 95 218.6 0.396 86.7 59.94 240.25

31-07-14 8:19 24 0.68 26.9 8.33 225 221.8 0.95 209 59.97 240.25

31-07-14 8:20 24 0.68 25.9 8.73 227 221.9 0.948 210.4 60.01 240.25

31-07-14 8:21 24 0.69 26.5 8.46 220 222 0.925 205.1 59.97 240.26

31-07-14 8:22 24 0.69 26.3 8.42 219 222 0.922 204.3 60 240.26

31-07-14 8:23 24 0.69 26.4 8.46 220 222.3 0.921 204.6 60.01 240.26

31-07-14 8:24 24 0.7 23.8 9.12 219 221.7 0.816 188.7 59.99 240.27

31-07-14 8:25 24 0.7 27.3 7.85 212 220.9 0.824 180.3 60.02 240.27


204

31-07-14 8:26 24 0.7 29.9 4.3 129 220 0.56 120.3 60.03 240.27

31-07-14 8:27 24 0.71 26.7 8.5 221 221.7 0.935 207.5 60 240.28

31-07-14 8:28 24 0.71 31.9 4.29 133 219.9 0.57 125.7 59.95 240.28

31-07-14 8:29 24 0.71 26.5 8.73 227 221.9 0.951 211.2 59.95 240.28

31-07-14 8:30 24 0.72 25.9 8.3 216 221.9 0.908 201.7 60 240.29

31-07-14 8:31 24 0.72 25.9 9.04 226 221.5 0.955 211.3 59.99 240.29

31-07-14 8:32 24 0.73 27.1 4.11 107 219.5 0.49 102.4 60.01 240.3

31-07-14 8:33 24 0.73 26.3 7.46 194 219.4 0.569 125.4 59.95 240.3

31-07-14 8:34 24 0.73 25.9 5.92 154 220 0.541 117.5 60.09 240.3

31-07-14 8:35 24 0.73 27.7 6.64 186 221.6 0.841 182.2 59.99 240.3

31-07-14 8:36 24 0.74 28.4 4.71 132 220.5 0.573 123.4 60.03 240.31

31-07-14 8:37 24 0.74 27.2 3.44 93 219.3 0.396 86.6 60.01 240.31

31-07-14 8:38 24 0.74 25.9 8.72 218 222 0.916 203.3 60.05 240.31

31-07-14 8:39 24 0.75 26.4 8.3 216 221.4 0.91 202 59.94 240.32

31-07-14 8:40 24 0.75 26.8 7.85 212 221.7 0.909 199.3 60 240.32

31-07-14 8:41 24 0.75 27 8.65 225 222.3 0.941 208.2 59.95 240.32

31-07-14 8:42 24 0.76 29.2 3.37 98 220.5 0.423 89.6 59.94 240.33

31-07-14 8:43 24 0.76 26.3 8.61 224 221.8 0.952 210.2 59.99 240.33

31-07-14 8:44 24 0.77 26.4 8.29 224 221.7 0.886 199.6 59.99 240.34

31-07-14 8:45 24 0.77 26.1 8.92 232 221.9 0.976 216.3 59.98 240.34

31-07-14 8:46 24 0.77 26.1 8.92 232 221.9 0.964 214.3 59.96 240.34

31-07-14 8:47 24 0.78 25.3 8.61 224 221.5 0.864 192 60.04 240.35

31-07-14 8:48 24 0.78 26.7 6.61 172 220.6 0.721 156.9 59.98 240.35

31-07-14 8:49 24 0.78 25.9 9 234 222.1 0.975 218.2 59.97 240.35

31-07-14 8:50 24 0.79 27.2 3.85 104 219.1 0.439 96.4 59.98 240.36

31-07-14 8:51 24 0.79 27.2 3.76 98 218.9 0.461 94 59.88 240.36

31-07-14 8:52 24 0.79 26.9 8.88 231 221.7 0.973 215.7 59.99 240.36

31-07-14 8:53 24 0.79 26.6 8.23 214 221.5 0.949 206.6 59.96 240.36

31-07-14 8:54 24 0.8 27.3 6.92 194 221.3 0.947 202.3 59.98 240.37

31-07-14 8:55 24 0.8 27.6 5.29 143 219 0.472 100.6 59.99 240.37

31-07-14 8:56 24 0.8 27.1 5.24 152 219.2 0.809 170.1 59.91 240.37

31-07-14 8:57 24 0.81 27.1 9.38 244 221.3 1.023 227.2 60.02 240.38

31-07-14 8:58 24 0.81 25.5 8.69 226 221.6 0.872 196.7 59.94 240.38

31-07-14 8:59 24 0.81 28 3.5 98 219 0.417 90.8 59.92 240.38

31-07-14 9:00 24 0.82 26.6 9.03 235 222.6 0.983 218.8 60.02 240.39

31-07-14 9:01 24 0.82 26.3 9.36 234 222.2 0.983 218.5 59.97 240.39

31-07-14 9:02 24 0.82 26.4 8.46 220 222.1 0.939 208 59.96 240.39

31-07-14 9:03 24 0.83 26.2 8.84 230 221.7 0.96 213.2 59.95 240.4

31-07-14 9:04 24 0.83 26.5 8.96 233 221.9 0.981 217.5 59.98 240.4

31-07-14 9:05 24 0.83 26.2 3.76 98 218.7 0.442 96.2 60 240.4

31-07-14 9:06 24 0.84 26.2 9.11 237 221.8 0.993 221.1 60.06 240.41

31-07-14 9:07 24 0.84 27.1 8.69 226 221.4 0.95 210.3 59.99 240.41

31-07-14 9:08 24 0.84 25.9 8.53 222 221.6 0.934 206.9 59.94 240.41

31-07-14 9:09 24 0.85 26.2 8.92 223 221.6 0.94 208 60 240.42

31-07-14 9:10 24 0.85 26.3 8.3 216 221.8 0.91 201.1 60.02 240.42


205

31-07-14 9:11 24 0.85 26.4 8.26 215 221.3 0.905 200.3 60.06 240.42

31-07-14 9:12 24 0.85 27.2 7.74 209 220.8 0.885 193.2 60.04 240.42

31-07-14 9:13 24 0.86 29.3 4.79 139 219.2 0.577 125.2 60.09 240.43

31-07-14 9:14 24 0.86 26.5 8.29 224 220.1 1.007 220.5 59.96 240.43

31-07-14 9:15 24 0.86 26.2 8.73 227 220.7 0.959 211.5 60.02 240.43

31-07-14 9:16 24 0.87 27.1 3.88 105 217.6 0.451 97.9 59.99 240.44

31-07-14 9:17 24 0.87 26.6 8.8 229 220.7 0.971 213.1 59.98 240.44

31-07-14 9:18 24 0.87 26.1 8.8 229 220.3 0.967 213.1 59.96 240.44

31-07-14 9:19 24 0.88 26.4 7.11 192 219.3 0.736 169 60.01 240.45

31-07-14 9:20 24 0.88 26.4 8.26 215 220.1 0.909 200.5 60.02 240.45

31-07-14 9:21 24 0.88 26.6 8.19 213 219.8 0.905 199.1 59.98 240.45

31-07-14 9:22 24 0.89 28.1 7.03 190 220.1 0.813 178 59.95 240.46

31-07-14 9:23 24 0.89 30.7 4.87 151 219.7 0.695 150.2 59.93 240.46

31-07-14 9:24 24 0.89 26.4 8.07 210 220.3 0.889 196.5 60.1 240.46

31-07-14 9:25 24 0.9 26.1 8.11 211 220.6 0.892 196.6 60.05 240.47

31-07-14 9:26 24 0.9 27.3 3.17 89 218.3 0.443 95.1 60.03 240.47

31-07-14 9:27 24 0.9 26.2 8.26 215 220.2 0.932 202.4 59.98 240.47

31-07-14 9:28 24 0.91 26.4 8.29 224 220.2 0.942 208.9 59.99 240.48

31-07-14 9:29 24 0.91 32 4.25 136 219.1 0.606 131.8 60.02 240.48

31-07-14 9:30 24 0.91 26.6 7.25 196 220.7 0.942 207.6 59.98 240.48

31-07-14 9:31 24 0.91 27.7 6.92 194 220.5 0.84 185.4 60 240.48

31-07-14 9:32 24 0.92 30.6 4.56 137 219.1 0.579 127.2 60.04 240.49

31-07-14 9:33 24 0.92 28.7 3.32 93 217.7 0.389 85.5 59.99 240.49

31-07-14 9:34 24 0.92 26.7 8.42 219 220.1 0.927 204.2 60.05 240.49

31-07-14 9:35 24 0.93 26.3 8.84 230 219.8 0.973 214.2 59.95 240.5

31-07-14 9:36 24 0.93 26.6 8.15 212 219.6 0.902 197.7 60.06 240.5

31-07-14 9:37 24 0.93 26.4 8.42 219 219.8 0.931 204.1 59.95 240.5

31-07-14 9:38 24 0.94 26.5 4.23 110 217.7 0.473 101.7 59.99 240.51

31-07-14 9:39 24 0.94 26.6 8.11 219 219.8 0.913 202.3 59.97 240.51

31-07-14 9:40 24 0.94 25.4 8.53 222 219.6 0.905 203 60 240.51

31-07-14 9:41 24 0.94 26 8.34 217 219.9 0.926 203 60.02 240.51

31-07-14 9:42 24 0.95 30.3 5.69 148 218.2 0.596 126.6 60.06 240.52

31-07-14 9:43 24 0.95 26.1 8.23 214 220.3 0.896 199.3 60.04 240.52

31-07-14 9:44 24 0.95 26 8.28 207 220 0.887 194.3 59.98 240.52

31-07-14 9:45 24 0.96 26.6 8.46 220 220 0.933 205.2 60.03 240.53

31-07-14 9:46 24 0.96 26.6 8.38 218 220 0.928 203.9 60.04 240.53

31-07-14 9:47 24 0.96 29.9 5.26 158 219.2 0.786 168.3 60.04 240.53

31-07-14 9:48 24 0.97 26.5 7.92 206 220.1 0.872 191.9 60.08 240.54

31-07-14 9:49 24 0.97 26.3 8.07 210 220 0.891 195.8 60.03 240.54

31-07-14 9:50 24 0.97 26 7.96 207 220.2 0.877 192.6 60.1 240.54

31-07-14 9:51 24 0.97 26.2 7.59 205 220 0.886 194.8 59.99 240.54

31-07-14 9:52 24 0.98 26.6 8.36 209 220.1 0.88 193.9 60.04 240.55

31-07-14 9:53 24 0.98 26.2 8 208 220.1 0.88 193.9 60.02 240.55

31-07-14 9:54 24 0.99 25.9 8.23 214 219.7 0.907 199.4 60.02 240.56

31-07-14 9:55 24 0.99 27 3.66 99 217.6 0.439 94.6 60.11 240.56


206

31-07-14 9:56 24 0.99 29.9 5.3 159 219.5 0.792 173.1 60.06 240.56

31-07-14 9:57 24 0.99 26.3 8.07 210 219.5 0.892 196.1 60.07 240.56

31-07-14 9:58 24 1 25.2 7.84 204 219.1 0.827 188.2 60.04 240.57

31-07-14 9:59 24 1 26.4 7.84 204 220 0.862 189.7 60.07 240.57

31-07-14 10:00 24 1 26.2 7.73 201 219.7 0.853 187.4 60.02 240.57

31-07-14 10:01 24 1.01 25.7 7.84 196 219.1 0.822 181.5 60.06 240.58

31-07-14 10:02 24 1.01 26.7 7.66 207 219.5 0.892 192.9 59.96 240.58

31-07-14 10:03 24 1.01 26.2 7.69 200 219.2 0.848 186.3 59.99 240.58

31-07-14 10:04 24 1.02 26.3 7.65 199 219.1 0.845 184.9 59.91 240.59

31-07-14 10:05 24 1.02 27.1 7.57 197 219 0.842 184 60.07 240.59

31-07-14 10:06 24 1.02 26.5 3.88 101 217.4 0.436 93 59.99 240.59

31-07-14 10:07 24 1.03 25.8 7.96 207 219.7 0.855 192 60 240.6

31-07-14 10:08 24 1.03 25.8 6.22 168 219.1 0.73 162.5 60.06 240.6

31-07-14 10:09 24 1.03 26.1 7.88 205 219.3 0.875 191.3 60.03 240.6

31-07-14 10:10 24 1.04 28.9 5.67 159 218.4 0.694 148.2 60.09 240.61

31-07-14 10:11 24 1.04 26.3 7.61 198 219.6 0.834 182.2 60 240.61

31-07-14 10:12 24 1.04 26.6 3.19 83 217.3 0.355 76.7 60.03 240.61

31-07-14 10:13 24 1.05 26.8 3.65 95 217.3 0.404 87.1 59.94 240.62

31-07-14 10:14 24 1.05 29.4 6.85 192 219.7 0.817 179.9 60.07 240.62

31-07-14 10:15 24 1.05 29 7.71 216 219.2 0.951 207.7 60.06 240.62

31-07-14 10:16 24 1.05 27.6 3.4 92 217 0.393 85.9 59.99 240.62

31-07-14 10:17 24 1.05 27.9 3.03 82 216.7 0.345 75 60.06 240.62

31-07-14 10:18 24 1.06 26.9 3.33 90 217 0.378 81.7 60.02 240.63

31-07-14 10:19 24 1.06 29.9 3.74 116 218 0.414 90.6 60.05 240.63

31-07-14 10:20 24 1.06 27.5 7.46 209 218.8 0.924 202.2 60.02 240.63

31-07-14 10:21 24 1.06 26.8 7.48 202 219.5 0.862 187.6 60.04 240.63

31-07-14 10:22 24 1.07 27.2 7.25 196 219.6 0.841 183.5 59.96 240.64

31-07-14 10:23 24 1.07 27.1 7.55 204 219.7 0.871 190 60.01 240.64

31-07-14 10:24 24 1.07 27 7.88 213 219.8 0.906 198.1 60.02 240.64

31-07-14 10:25 24 1.08 26.4 7.8 203 219.7 0.861 188.8 59.94 240.65

31-07-14 10:26 24 1.08 26.8 7.84 204 219.7 0.87 190.3 60.01 240.65

31-07-14 10:27 24 1.08 27.3 7.46 194 219.3 0.817 179.1 59.97 240.65

31-07-14 10:28 24 1.08 25.7 4 112 218 0.359 84.6 60.02 240.65

31-07-14 10:29 24 1.08 26.9 7.84 204 219.8 0.86 189.9 60.02 240.65

31-07-14 10:30 24 1.09 27.2 7.66 207 220.1 0.874 192.6 60.03 240.66

31-07-14 10:31 24 1.09 27.3 3.73 97 217.9 0.398 88 60.05 240.66

31-07-14 10:32 24 1.09 28.6 4.11 111 218.5 0.525 107.4 60 240.66

31-07-14 10:33 24 1.09 27.2 3.23 84 217.4 0.355 77.3 59.97 240.66

31-07-14 10:34 24 1.1 28.5 6.57 184 219.5 0.801 172 60.08 240.67

31-07-14 10:35 24 1.1 29 4.39 123 218.3 0.555 121.1 59.95 240.67

31-07-14 10:36 24 1.1 27.3 6.85 185 219.8 0.791 173.6 60.04 240.67

31-07-14 10:37 24 1.1 26.8 6.76 176 219.2 0.758 165.8 60.03 240.67

31-07-14 10:38 24 1.11 28.6 3.37 91 217.6 0.38 82.2 60.02 240.68

31-07-14 10:39 24 1.11 30.3 3.51 102 217.5 0.418 92.1 60.03 240.68

31-07-14 10:40 24 1.11 25.7 2.56 64 216.6 0.273 59.1 60.03 240.68


207

31-07-14 10:41 24 1.11 28.6 4.21 118 217.6 0.445 99.7 60.04 240.68

31-07-14 10:42 24 1.11 28 2.42 68 216.8 0.286 62 59.98 240.68

31-07-14 10:43 24 1.11 27.5 3.14 85 217.3 0.37 80.1 60.03 240.68

31-07-14 10:44 24 1.12 27.9 6.59 178 219 0.768 167.8 60.03 240.69

31-07-14 10:45 24 1.12 26.7 2.59 70 216.7 0.299 64.8 59.96 240.69

31-07-14 10:46 24 1.12 29.2 4.37 127 217.8 0.55 121.6 59.91 240.69

31-07-14 10:47 24 1.12 25.9 6.84 178 219.1 0.714 159.4 60 240.69

31-07-14 10:48 24 1.13 26.8 6.76 176 219.2 0.751 163.5 59.98 240.7

31-07-14 10:49 24 1.13 27.5 6.69 174 219.1 0.737 161.9 60.02 240.7

31-07-14 10:50 24 1.13 28.1 6.8 177 219.2 0.741 162.6 59.98 240.7

31-07-14 10:51 24 1.13 27.3 6.22 168 219.2 0.723 158.1 60.04 240.7

31-07-14 10:52 24 1.14 26.5 6.15 160 219.2 0.706 148.8 59.98 240.71

31-07-14 10:53 24 1.14 27.3 6.29 170 219.5 0.722 159 59.99 240.71

31-07-14 10:54 24 1.14 27.3 6.37 172 219.6 0.732 160.7 59.98 240.71

31-07-14 10:55 24 1.15 26.4 6.25 169 220 0.725 159.9 60.07 240.72

31-07-14 10:56 24 1.15 26.9 6.73 175 220 0.745 164.2 59.99 240.72

31-07-14 10:57 24 1.15 27.8 6.29 170 219.7 0.724 158.8 60.03 240.72

31-07-14 10:58 24 1.16 27.3 6.88 172 219.4 0.736 160.8 60.03 240.73

31-07-14 10:59 24 1.16 27.1 6.29 170 219.4 0.714 156.8 60.06 240.73

31-07-14 11:00 24 1.16 26.9 6.25 169 219.1 0.719 157.8 60.02 240.73

31-07-14 11:01 24 1.16 27.2 6.29 170 219.3 0.729 159.7 60.03 240.73

31-07-14 11:02 24 1.17 29.7 5.03 151 219.5 0.675 147.5 60.03 240.74

31-07-14 11:03 24 1.17 26.3 6.18 167 219.4 0.714 156.2 59.99 240.74

31-07-14 11:04 24 1.17 27.2 6.11 165 219.4 0.703 153.9 60.02 240.74

31-07-14 11:05 24 1.17 30.4 4.23 127 218.1 0.556 118.8 59.98 240.74

31-07-14 11:06 24 1.18 26.6 6.23 162 218.9 0.694 151.5 59.91 240.75

31-07-14 11:07 24 1.18 27.1 5.92 160 219.5 0.679 149 60.03 240.75

31-07-14 11:08 24 1.18 27.2 5.81 157 219.9 0.664 146.3 60.07 240.75

31-07-14 11:09 24 1.18 27.9 5.42 152 219.9 0.651 142.8 60.02 240.75

31-07-14 11:10 24 1.19 27.6 5.1 143 219.3 0.619 135.2 60 240.76

31-07-14 11:11 24 1.19 28 5.57 156 219.2 0.665 145.9 60.03 240.76

31-07-14 11:12 24 1.19 27.6 5.92 160 219.5 0.681 149.4 60 240.76

31-07-14 11:13 24 1.19 27 5.92 160 219.4 0.681 149.6 59.98 240.76

31-07-14 11:14 24 1.2 26.4 6.12 153 219.6 0.648 143.2 60.04 240.77

31-07-14 11:15 24 1.2 28 5.78 162 220 0.689 149.5 59.99 240.77

31-07-14 11:16 24 1.2 27.3 6.03 163 219.9 0.692 152.6 60.09 240.77

31-07-14 11:17 24 1.2 27.6 6.07 164 219.7 0.697 153.2 59.96 240.77

31-07-14 11:18 24 1.21 27.5 5.96 161 219.4 0.685 150.7 60.03 240.78

31-07-14 11:19 24 1.21 27.5 5.74 155 219.1 0.663 144.7 59.98 240.78

31-07-14 11:20 24 1.21 27.8 5.77 156 218.8 0.667 145.3 60.03 240.78

31-07-14 11:21 24 1.21 27.6 5.64 158 219.5 0.677 149 59.97 240.78

31-07-14 11:22 24 1.22 27.4 5.85 158 219.6 0.674 147.7 60.03 240.79

31-07-14 11:23 24 1.22 27.3 5.74 155 219.9 0.654 144.1 60.02 240.79

31-07-14 11:24 24 1.22 27.7 5.77 156 219.9 0.665 145.5 60.03 240.79

31-07-14 11:25 24 1.22 26.8 5.8 151 219.9 0.648 140.6 60.02 240.79


208

31-07-14 11:26 24 1.23 28.4 4.62 125 219.1 0.579 123.3 60.03 240.8

31-07-14 11:27 24 1.23 26.4 5.88 153 219.6 0.646 142.5 59.98 240.8

31-07-14 11:28 24 1.23 27.2 5.77 156 219.8 0.661 145.2 59.94 240.8

31-07-14 11:29 24 1.23 27.1 5.55 150 220.1 0.635 139.7 60.08 240.8

31-07-14 11:30 24 1.24 27.5 5.62 152 219.9 0.651 143.1 60.03 240.81

31-07-14 11:31 24 1.24 26.7 5.8 151 219.5 0.646 141.4 60 240.81

31-07-14 11:32 24 1.24 27.8 5.48 148 219.3 0.628 138.5 59.99 240.81

31-07-14 11:33 24 1.24 26.3 5.65 147 219.3 0.62 135.9 59.99 240.81

31-07-14 11:34 24 1.25 27.5 5.44 147 219.1 0.628 137.8 59.94 240.82

31-07-14 11:35 24 1.25 27.6 5.44 147 219.4 0.628 137.1 60.03 240.82

31-07-14 11:36 24 1.25 28.5 4.79 139 219.6 0.596 128.9 59.99 240.82

31-07-14 11:37 24 1.25 29.3 4.88 132 219.5 0.562 123.1 60.03 240.82

31-07-14 11:38 24 1.26 27.5 5.18 140 219.6 0.596 130.6 60.05 240.83

31-07-14 11:39 24 1.26 27.9 5.07 137 219.1 0.585 128.1 60.01 240.83

31-07-14 11:40 24 1.26 27.6 4.96 134 219.1 0.575 125.9 60.06 240.83

31-07-14 11:41 24 1.26 27.3 5.03 136 219.2 0.578 126.2 60.01 240.83

31-07-14 11:42 24 1.27 26.8 4.82 135 219.1 0.57 125.9 59.95 240.84

31-07-14 11:43 24 1.27 28.4 4.71 132 219.1 0.558 122.6 60.06 240.84

31-07-14 11:44 24 1.27 27.9 4.96 134 219.4 0.569 124.8 60.01 240.84

31-07-14 11:45 24 1.27 27.7 4.82 135 219.3 0.578 127 60.04 240.84

31-07-14 11:46 24 1.27 28.9 2.75 80 217.6 0.323 70 59.98 240.84

31-07-14 11:47 24 1.28 27.3 5 135 219.4 0.574 125.9 60.02 240.85

31-07-14 11:48 24 1.28 26.9 5.18 140 219.2 0.586 128.4 59.97 240.85

31-07-14 11:49 24 1.28 27.8 5.03 136 219.2 0.58 126.9 59.99 240.85

31-07-14 11:50 24 1.28 27.8 4.96 134 218.8 0.571 125.1 59.99 240.85

31-07-14 11:51 24 1.29 28.5 4.82 135 219.2 0.574 125.7 60.03 240.86

31-07-14 11:52 24 1.29 27.6 4.77 129 219 0.553 120.8 60.01 240.86

31-07-14 11:53 24 1.29 27.9 4.81 130 219.3 0.553 121.2 60.09 240.86

31-07-14 11:54 24 1.29 27.7 4.66 126 219.1 0.538 117.9 59.96 240.86

31-07-14 11:55 24 1.29 25.7 4.85 131 219.2 0.542 120.8 60.03 240.86

31-07-14 11:56 24 1.3 28.9 4.6 129 218.9 0.546 120 60 240.87

31-07-14 11:57 24 1.3 26.8 4.88 132 218.9 0.561 123.4 60.04 240.87

31-07-14 11:58 24 1.3 28 5 135 219.2 0.576 126.4 60.1 240.87

31-07-14 11:59 24 1.3 28.5 4.71 132 218.9 0.564 123.4 59.99 240.87

31-07-14 12:00 24 1.3 27.9 4.92 133 218.6 0.566 123.8 60.03 240.87

31-07-14 12:01 24 1.31 28.5 4.67 131 218.4 0.56 121.8 60 240.88

31-07-14 12:02 24 1.31 27.8 4.75 133 218.5 0.571 123.2 60.07 240.88

31-07-14 12:03 24 1.31 27.7 4.6 129 218.8 0.559 121.4 59.99 240.88

31-07-14 12:04 24 1.31 27.2 4.77 129 218.6 0.553 120.6 60.04 240.88

31-07-14 12:05 24 1.32 28.2 4.57 128 219.3 0.544 120 60.06 240.89

31-07-14 12:06 24 1.32 27.5 4.77 129 219 0.546 119.7 60.06 240.89

31-07-14 12:07 24 1.32 26.5 4.5 126 218.8 0.536 119.1 60.01 240.89

31-07-14 12:08 24 1.32 27.8 4.62 125 218.8 0.528 116 60.09 240.89

31-07-14 12:09 24 1.33 28.1 4.46 125 218.9 0.531 116.6 60.11 240.9

31-07-14 12:10 24 1.33 27.9 4.42 124 219.1 0.53 115.6 60.1 240.9


209

31-07-14 12:11 24 1.33 27.2 4.62 125 218.9 0.526 115 60.07 240.9

31-07-14 12:12 24 1.33 27.7 4.4 119 218.7 0.501 109.6 60.05 240.9

31-07-14 12:13 24 1.33 28 4.33 117 218.4 0.498 108.5 60.04 240.9

31-07-14 12:14 24 1.33 27.3 4.25 119 218.8 0.505 110 60.11 240.9

31-07-14 12:15 24 1.34 26.6 4.44 120 218.8 0.5 109.8 60.1 240.91

31-07-14 12:16 24 1.34 27 4.48 121 218.8 0.495 111.4 60.02 240.91

31-07-14 12:17 24 1.34 28.2 4.21 118 218.8 0.498 109 60.04 240.91

31-07-14 12:18 24 1.34 27.9 4.29 116 218.3 0.495 107.8 59.97 240.91

31-07-14 12:19 24 1.35 27.8 3.77 102 218 0.434 94.3 60.06 240.92

31-07-14 12:20 24 1.35 27.9 3.66 99 217.7 0.419 91.2 60.01 240.92

31-07-14 12:21 24 1.35 28.3 3.42 96 217.5 0.406 88.5 60.03 240.92

31-07-14 12:22 24 1.35 28.3 3.55 96 217.4 0.4 87.8 60.01 240.92

31-07-14 12:23 24 1.35 27.9 3.55 96 217.8 0.411 87.9 60.03 240.92

31-07-14 12:24 24 1.35 28.1 3.5 98 217.8 0.412 89.7 60.06 240.92

31-07-14 12:25 24 1.35 28 3.46 97 217.4 0.411 88.9 59.99 240.92

31-07-14 12:26 24 1.35 27.9 3.4 92 217.9 0.387 84.3 60.04 240.92

31-07-14 12:27 24 1.36 28.6 3.32 93 218.1 0.389 84.8 60 240.93

31-07-14 12:28 24 1.36 27.9 3.4 92 217.9 0.385 84.3 60 240.93

31-07-14 12:29 24 1.36 28.3 3.21 90 217.9 0.379 82.5 60.04 240.93

31-07-14 12:30 24 1.36 28.7 3.28 92 217.9 0.385 84 59.99 240.93

31-07-14 12:31 24 1.36 28.6 3.14 88 217.6 0.37 80.7 60.03 240.93

31-07-14 12:32 24 1.36 28.9 3.42 89 217.8 0.367 81.9 60.05 240.93

31-07-14 12:33 24 1.37 28.3 3.21 90 217.8 0.38 82.9 60 240.94

31-07-14 12:34 24 1.37 28.6 3.21 90 217.9 0.382 82.8 60.02 240.94

31-07-14 12:35 24 1.37 27.9 3.33 90 218.8 0.379 82.6 60.03 240.94

31-07-14 12:36 24 1.37 28.6 3.25 91 218.7 0.384 83.5 59.99 240.94

31-07-14 12:37 24 1.37 28.5 3.21 90 218.6 0.38 82.6 60.02 240.94

31-07-14 12:38 24 1.37 28.2 3.25 91 218.2 0.383 83.5 60.04 240.94

31-07-14 12:39 24 1.37 28 3.37 91 218 0.38 83.2 60.03 240.94

31-07-14 12:40 24 1.38 27.9 3.37 91 218.1 0.384 83.7 60.03 240.95

31-07-14 12:41 24 1.38 28.1 3.32 93 217.9 0.4 85.4 60.05 240.95

31-07-14 12:42 24 1.38 28.7 3.32 93 218.2 0.388 84.8 60.06 240.95

31-07-14 12:43 24 1.38 28.9 3.28 92 218.5 0.385 83.6 60.11 240.95

31-07-14 12:44 24 1.38 28.5 3.4 92 218.5 0.387 84.5 60.07 240.95

31-07-14 12:45 24 1.38 27.9 3.37 91 218.3 0.386 84 60.07 240.95

31-07-14 12:46 24 1.38 28.8 3.14 88 217.6 0.375 81.8 60.07 240.95

31-07-14 12:47 24 1.39 28.1 3.14 88 217.8 0.375 80.4 60.1 240.96

31-07-14 12:48 24 1.39 28.5 3.17 89 218.5 0.374 81.6 60.07 240.96

31-07-14 12:49 24 1.39 27.9 3 84 218.3 0.347 77 60.1 240.96

31-07-14 12:50 24 1.39 28.3 2.07 58 217.8 0.249 52.5 60.11 240.96

31-07-14 12:51 24 1.39 28.2 3.17 89 218.3 0.369 80.7 60.03 240.96

31-07-14 12:52 24 1.39 27.5 3.18 86 218.3 0.365 78.3 60.07 240.96

31-07-14 12:53 24 1.4 28.3 3.1 87 217.9 0.367 80.1 59.99 240.97

31-07-14 12:54 24 1.4 29.2 2.93 85 217.7 0.359 78.1 60.03 240.97

31-07-14 12:55 24 1.4 28.5 2.92 82 217.5 0.352 76.3 59.98 240.97


210

31-07-14 12:56 24 1.4 28.6 2.96 83 217.6 0.351 76.5 60.02 240.97

31-07-14 12:57 24 1.4 28.1 2.96 83 217.5 0.352 76.3 59.98 240.97

31-07-14 12:58 24 1.4 28.2 2.96 80 217.9 0.335 72.5 60.05 240.97

31-07-14 12:59 24 1.4 27.6 2.85 80 217.8 0.33 71.4 60.07 240.97

31-07-14 13:00 24 1.4 28.3 2.82 79 217.8 0.333 72.4 59.97 240.97

31-07-14 13:01 24 1.4 27.6 2.82 79 217.4 0.331 72.6 59.93 240.97

31-07-14 13:02 24 1.41 26.1 2.8 73 217.1 0.31 67.1 59.92 240.98

31-07-14 13:03 24 1.41 27.6 2.85 77 217.1 0.323 70.5 60.03 240.98

31-07-14 13:04 24 1.41 28.6 2.66 72 217.1 0.313 67.4 59.93 240.98

31-07-14 13:05 24 1.41 27.2 2.71 76 217.3 0.321 70.1 59.98 240.98

31-07-14 13:06 24 1.41 28.7 2.64 74 217.6 0.312 67.8 59.98 240.98

31-07-14 13:07 24 1.41 28.8 2.53 71 217.5 0.304 66.3 59.97 240.98

31-07-14 13:08 24 1.41 28.2 2.57 72 217.4 0.305 66.3 59.96 240.98

31-07-14 13:09 24 1.41 28.5 2.42 68 217.5 0.29 62.6 60.03 240.98

31-07-14 13:10 24 1.42 28.8 2.5 70 217.4 0.297 64.5 59.99 240.99

31-07-14 13:11 24 1.42 28.3 2.5 70 217.5 0.297 64.3 60.06 240.99

31-07-14 13:12 24 1.42 28.1 2.55 69 218.1 0.292 63.4 60.04 240.99

31-07-14 13:13 24 1.42 28 2.42 68 218 0.291 63.4 60 240.99

31-07-14 13:14 24 1.42 28.2 2.51 68 218.1 0.291 63.2 60.03 240.99

31-07-14 13:15 24 1.42 29.1 2.42 68 218 0.287 62.1 59.92 240.99

31-07-14 13:16 24 1.42 27.9 2.48 67 217.9 0.287 62.5 59.96 240.99

31-07-14 13:17 24 1.42 28.8 2.39 67 218.1 0.285 62.3 59.96 240.99

31-07-14 13:18 24 1.42 27.8 2.51 68 218 0.288 62.5 59.96 240.99

31-07-14 13:19 24 1.43 27.5 2.44 66 218.5 0.277 60.4 60.05 241

31-07-14 13:20 24 1.43 28.3 2.25 63 218.2 0.267 58 59.9 241

31-07-14 13:21 24 1.43 28.5 2.25 63 218.8 0.265 57.9 60.03 241

31-07-14 13:22 24 1.43 27.3 2.29 62 218.6 0.256 56.1 59.94 241

31-07-14 13:23 24 1.43 28.8 2.25 63 218.3 0.262 57 60.02 241

31-07-14 13:24 24 1.43 27.5 2.29 62 218.5 0.26 56.8 59.94 241

31-07-14 13:25 24 1.43 28.5 2.17 61 218.1 0.253 55.3 59.95 241

31-07-14 13:26 24 1.43 28.8 2.07 58 218 0.244 53.1 59.98 241

31-07-14 13:27 24 1.43 28.9 2 56 217.7 0.233 50.7 59.99 241

31-07-14 13:28 24 1.44 28.9 1.96 55 217.7 0.231 50.3 59.96 241.01

31-07-14 13:29 24 1.44 28.4 1.85 52 217.7 0.214 46.5 60.01 241.01

31-07-14 13:30 24 1.44 28.6 1.57 44 218 0.18 39 60.03 241.01

31-07-14 13:31 24 1.44 28.2 1.46 41 217.9 0.167 36.1 60 241.01

31-07-14 13:32 24 1.44 28.3 1.39 39 217.5 0.156 33.9 60.02 241.01

31-07-14 13:33 24 1.44 27.7 1.35 38 217.3 0.155 33.2 59.94 241.01

31-07-14 13:34 24 1.44 28.3 1.32 37 217.6 0.15 32.8 59.99 241.01

31-07-14 13:35 24 1.44 28 1.35 38 217.6 0.154 33.7 59.98 241.01

31-07-14 13:36 24 1.44 27.6 1.33 36 217.5 0.148 32.3 60 241.01

31-07-14 13:37 24 1.44 27.6 1.25 35 217.6 0.145 31.7 60.02 241.01

31-07-14 13:38 24 1.44 27.7 1.29 35 217.6 0.142 30.8 60.01 241.01

31-07-14 13:39 24 1.44 27.8 1.29 35 217.9 0.14 30.5 60.06 241.01

31-07-14 13:40 24 1.44 26 1.3 34 218.1 0.135 29.2 60.04 241.01


211

31-07-14 13:41 24 1.44 27.3 1.25 34 218 0.137 29.8 60.01 241.01

31-07-14 13:42 24 1.44 27.9 1.22 33 217.6 0.135 29.3 59.97 241.01

31-07-14 13:43 24 1.44 26.9 1.26 33 217.7 0.13 28.5 59.98 241.01

31-07-14 13:44 24 1.45 26.6 1.22 33 217.8 0.131 28.9 60.07 241.02

31-07-14 13:45 24 1.45 27.4 1.22 33 217.7 0.132 28.5 60.03 241.02

31-07-14 13:46 24 1.45 28.4 1.14 32 217.5 0.13 28 59.95 241.02

31-07-14 13:47 24 1.45 28 1.22 33 217.5 0.129 28 60.03 241.02

31-07-14 13:48 24 1.45 27.6 1.18 32 217.4 0.129 28.2 59.92 241.02

31-07-14 13:49 24 1.45 26.4 1.19 31 217.3 0.127 27.3 60.03 241.02

31-07-14 13:50 24 1.45 27.5 1.14 32 217.4 0.128 27.6 60.06 241.02

31-07-14 13:51 24 1.45 26.1 1.23 32 217.8 0.122 27.2 60.02 241.02

31-07-14 13:52 24 1.45 27.5 1.14 32 218 0.128 27.6 59.94 241.02

31-07-14 13:53 24 1.45 27.3 1.14 31 218.1 0.124 27.4 59.95 241.02

31-07-14 13:54 24 1.45 27.9 1.14 31 218.4 0.124 26.8 60.08 241.02

31-07-14 13:55 24 1.45 28.9 1.07 30 218.6 0.121 26.2 59.99 241.02

31-07-14 13:56 24 1.45 27.4 1.11 30 218.6 0.118 25.5 60.02 241.02

31-07-14 13:57 24 1.45 27.4 1.07 29 218.4 0.116 25.1 59.92 241.02

31-07-14 13:58 24 1.45 27.7 1.07 29 218.4 0.114 24.8 60 241.02

31-07-14 13:59 24 1.45 27.8 1.03 28 218.5 0.112 24.2 60.05 241.02

31-07-14 14:00 24 1.45 28.4 1 28 218.2 0.11 24 59.94 241.02

31-07-14 14:01 24 1.45 28.9 0.96 27 218.4 0.106 23.3 59.95 241.02

31-07-14 14:02 24 1.45 27 1.03 28 218.3 0.11 24 60 241.02

31-07-14 14:03 24 1.45 28.5 0.96 27 218.4 0.107 23.5 60.02 241.02

31-07-14 14:04 24 1.45 27.7 1 27 218.1 0.105 22.8 59.98 241.02

31-07-14 14:05 24 1.45 27.4 1 27 218 0.106 23.3 59.98 241.02

31-07-14 14:06 24 1.46 27.5 1 27 218.5 0.104 22.9 60 241.03

31-07-14 14:07 24 1.46 27.7 0.92 26 218.4 0.105 22.7 59.95 241.03

31-07-14 14:08 24 1.46 26.1 1 26 218.5 0.101 22.2 60 241.03

31-07-14 14:09 24 1.46 26.5 0.96 25 218.5 0.101 22 60.06 241.03

31-07-14 14:10 24 1.46 27.8 0.92 25 217.9 0.099 21.7 60.03 241.03

31-07-14 14:11 24 1.46 28.4 0.89 25 217.9 0.099 21.3 59.94 241.03

31-07-14 14:12 24 1.46 28 0.89 25 218.2 0.096 20.9 60.02 241.03

31-07-14 14:13 24 1.46 27.9 0.88 24 218.3 0.095 20.5 60.01 241.03

31-07-14 14:14 24 1.46 27.4 0.88 24 218.8 0.094 20.3 60.01 241.03

31-07-14 14:15 24 1.46 26.5 0.88 23 218.9 0.092 20.1 59.99 241.03

31-07-14 14:16 24 1.46 26.5 0.88 23 218.3 0.091 19.6 59.95 241.03

31-07-14 14:17 24 1.46 26.6 0.88 23 217.9 0.088 19.1 59.96 241.03

31-07-14 14:18 24 1.46 26.4 0.88 23 218 0.088 19.1 59.98 241.03

31-07-14 14:19 24 1.46 26.6 0.84 22 218 0.083 18.3 60.06 241.03

31-07-14 14:20 24 1.46 27.3 0.81 22 218 0.083 18.3 59.94 241.03

31-07-14 14:21 24 1.46 26.3 0.84 22 217.9 0.083 18 60.02 241.03

31-07-14 14:22 24 1.46 27.4 0.81 22 218.1 0.081 17.6 59.98 241.03

31-07-14 14:23 24 1.46 26.8 0.84 22 217.9 0.078 17.2 59.99 241.03

31-07-14 14:24 24 1.46 27.3 0.77 21 217.9 0.076 16.5 60.09 241.03

31-07-14 14:25 24 1.46 26.3 0.8 21 218 0.077 16.7 60 241.03


212

31-07-14 14:26 24 1.46 26.9 0.8 21 217.9 0.076 16.7 60.03 241.03

31-07-14 14:27 24 1.46 26.6 0.84 22 218.3 0.076 16.5 59.95 241.03

31-07-14 14:28 24 1.46 26.4 0.8 21 217.7 0.076 16.7 60.05 241.03

31-07-14 14:29 24 1.46 26.9 0.8 21 217.8 0.072 15.8 59.99 241.03

31-07-14 14:30 24 1.46 27.9 0.75 21 217.8 0.071 15.4 59.96 241.03

31-07-14 14:31 24 1.46 27 0.77 21 217.8 0.073 15.6 60.02 241.03

31-07-14 14:32 24 1.46 27.1 0.77 21 218.4 0.071 15.7 60.03 241.03

31-07-14 14:33 24 1.46 27.9 0.77 21 218.4 0.07 15.5 59.99 241.03

31-07-14 14:34 24 1.46 28.1 0.75 21 218.2 0.071 15.7 59.95 241.03

31-07-14 14:35 24 1.46 28.3 0.75 21 217.9 0.072 15.4 59.98 241.03

31-07-14 14:36 24 1.46 28 0.77 21 217.6 0.071 15.2 59.95 241.03

31-07-14 14:37 24 1.47 26.7 0.8 21 217.5 0.07 15.4 59.99 241.04

31-07-14 14:38 24 1.47 28 0.75 21 217.5 0.069 14.7 60.04 241.04

31-07-14 14:39 24 1.47 27 0.8 21 217.9 0.069 14.8 60.05 241.04

31-07-14 14:40 24 1.47 28.1 0.75 21 217.6 0.066 14.5 60.09 241.04

31-07-14 14:41 24 1.47 26.7 0.8 21 217.7 0.067 14.5 60.15 241.04

31-07-14 14:42 24 1.47 26.5 0.8 21 218.4 0.068 14.8 60.1 241.04

31-07-14 14:43 24 1.47 26.1 0.8 21 218.5 0.068 14.6 60.05 241.04

31-07-14 14:44 24 1.47 26.6 0.8 21 218.6 0.066 14.8 60.11 241.04

31-07-14 14:45 24 1.47 28.5 0.71 20 218.6 0.06 13.1 60.1 241.04

31-07-14 14:46 24 1.47 26.4 0.8 21 218.3 0.068 15 60.05 241.04

31-07-14 14:47 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:48 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:49 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:50 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:51 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:52 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:53 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:54 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:55 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:56 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 14:57 24 1.47 25.8 0.76 20 218.3 0.061 13.5 60.1 241.04

31-07-14 18:16 0 0 0 0 0 0 0 0 0 241.04


213

Table 12: Comparative Total Energy Generated For a Month

Total Energy Generated For a Month

DAY Azimuthal-altitude

(KWh)

45 Stationary

(KWh)

1 1.80 1.10

2 1.80 1.00

3 1.90 1.10

4 1.30 0.75

5 1.40 0.80

6 1.45 0.90

7 0.30 0.20

8 1.45 0.90

9 1.45 0.95

10 1.5 1.00

11 1.75 1.10

12 2.00 1.15

13 1.98 1.15

14 1.90 1.10

15 1.45 1.00

16 0.10 0.10

17 0.10 0.10

18 0.10 0.10

19 0.10 0.10

20 0.10 0.10

21 0.10 0.10

22 0.50 0.40

23 0.25 0.20

24 0.80 0.70

25 1.00 0.70

26 1.30 1.00

27 1.05 1.00

28 1.25 0.80

29 0.10 1.00

30 0.15 0.15

31 1.50 1.10

31.93 21.85


214

Table 13: Comparative Hourly Energy Efficiency

Hourly Energy Efficiency

Hour Azimuthal-altitude(KWh) 45 Stationary(KWh)

1 0 0

2 0 0

3 22 22

4 88 60

5 132 95

6 176 140

7 118 76

8 198 160

9 220 185

10 185 145

11 154 110

12 130 74

13 70 38

14 22 19

15 0 0

16 0 0

17 0 0

18 0 0

19 0 0

20 0 0

21 0 0

22 0 0

23 0 0

24 0 0

1515 1124

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