THE UNIVERSITY OF THE WEST INDIES
B.Sc. (Engineering)
Department of Electrical and Computer Engineering
ECNG 3020 - SPECIAL PROJECT PROGRESS REPORT
PROJECT TITLE
Solar Photovoltaic Resource Assessment Tool
Adam Khan
808000249
2nd
April, 2012.
ELECTRICAL Project Supervisor: Dr. Sanjay Bahadoorsingh
& COMPUTER Project Type: IV
ENGINEERING
DEPARTMENT
ii
Statement of Academic Honesty
THE UNIVERSITY OF THE WEST INDIES ST. AUGUSTINE, TRINIDAD & TOBAGO,
WEST INDIES FACULTY OF ENGINEERING Department of Electrical & Computer Engineering
B. Sc. in Electrical & Computer Engineering
CHEATING, PLAGIARISM AND COLLUSION DECLARATION FORM
According to The University of the West Indies Undergraduate Regulations (2008/2009), sections
32: “Cheating, Plagiarism and Collusion are serious offences under University Regulations.
(a) Cheating is any attempt to benefit one’s self or another by deceit or fraud.
(b) Plagiarism is the unauthorized and/or unacknowledged use of another person’s
intellectual efforts and creations howsoever recorded, including whether formally published or
in manuscript or in typescript or other printed or electronically presented form and includes
taking passages, ideas or structures from another work or author without proper and
unequivocal attribution of such source(s), using the conventions for attributions or citing used
in this University. Plagiarism is a form of cheating.
(c) For the purposes of these Regulations, ‘collusion’ shall mean the unauthorized
or unlawful collaboration or agreement between two or more students in the preparation,
writing or production of a course assignment and assessment, to the extent that they have
produced the same or substantially the same paper, project, report, as the case may be, as if
it were their separate and individual efforts, in circumstances where they know or had reason
to know that the assignment or a part therefore was not intended to be a group project, but
was rather to be the product of each student’s individual efforts.
Where two or more students have produced the same or substantially the
same assignment for examination and assessment in circumstances that the
assignment was to be the product of each student’s individual efforts, they shall receive
a failing grade in the course.”
I, ………………………………………………………, have read and understood the University’s
Undergraduate Regulations, section 32 on Cheating, Plagiarism and Collusion.
I understand that my submission is subject to the electronic plagiarism checker, Turnitin.
I declare that this assignment is my own work and does not involve cheating, plagiarism or collusion.
Signature:……………………………………………. Date:………………………………
iii
Abstract
The Caribbean as an ideal place to harvest solar energy such as photovoltaic cells. This
report deals with the models at different stages in producing electrical energy from
photovoltaic cells and after justifying appropriate models implement them in a Matlab
software and test them against RETScreen to validate it.
iv
Table of Contents
Chapter 1 Introduction .................................................................................................... 12
1.1 Background ............................................................................................................ 12
1.1.1 PV Configurations .......................................................................................... 12
1.2 Justification ............................................................................................................ 15
1.3 Project Objectives .................................................................................................. 16
1.4 Scope ..................................................................................................................... 16
Chapter 2 Literature Review ........................................................................................... 17
2.1 Available Solar Data .............................................................................................. 18
2.2 Irradiation on a Tilted Surface ............................................................................... 19
2.2.1 Models to Calculate the Total Hourly Irradiation on a Horizontal Surface ... 21
2.2.2 Models to Calculate the Daily Diffuse Irradiation on a Horizontal Surface .. 22
2.2.3 Models to Calculate the Hourly Diffuse Irradiation on a Horizontal Surface 24
2.2.4 Models to Calculate the Irradiation on a Tilted Surface ................................ 25
2.3 PV Performance Models ........................................................................................ 31
2.4 Battery Models ...................................................................................................... 33
2.5 Justification ............................................................................................................ 37
Chapter 3 Methodology ................................................................................................... 39
3.1 Software Model ..................................................................................................... 39
3.2 Software Design .................................................................................................... 39
3.3 Irradiation on a Tilted Surface Module ................................................................. 40
3.3.1 Sunset Hour Angle ......................................................................................... 40
v
3.3.2 Clearness Index .............................................................................................. 42
3.3.3 Total Hourly Irradiation on a Horizontal Surface .......................................... 43
3.3.4 Diffuse Daily Irradiation on a Horizontal Surface ......................................... 45
3.3.5 Hourly Diffuse Irradiation on a Horizontal Surface....................................... 47
3.3.6 Determination of Rb for fixed Arrays ............................................................. 49
3.3.7 RB for a Azimuth Tracking Surface .............................................................. 52
3.3.8 RB for Two Axis Tracking Surface ............................................................... 52
3.3.9 RB for an Axis of Arbitrary Tilt .................................................................... 52
3.3.10 RB for a horizontal axis ............................................................................... 54
3.3.11 Irradiation on Tilted Surface Sub-Function ................................................. 55
3.3.12 Irradiation on Tilted Surface Complete Module .......................................... 55
3.4 Array Module ........................................................................................................ 56
3.5 Battery Module ...................................................................................................... 57
3.6 System Design ....................................................................................................... 57
4 Testing .......................................................................................................................... 61
5 Results .......................................................................................................................... 67
6 Discussion .................................................................................................................... 70
7 Conclusion .................................................................................................................... 71
8 References .................................................................................................................... 72
Appendix A – Progress Report........................................................................................ 74
vi
List of Abbreviations and Symbols
PV - Photovoltaic
TMY-Typical Meteorological Year
ω – Hour Angle
ωs- Sunset Hour Angle
I – Hourly Irradiation Units
H – Daily Irradiation Units
Ī – Monthly Average Hourly Irradiation Units
Ĥ- Monthly Average Daily Irradiation Units
Hd- Daily Diffuse Irradiation
Id-Hourly Diffuse Irradiation
Kt- Daily Clearness Index
tK - Daily Average Clearness Index
kt-Hourly Clearness Index
IT- Hourly Irradiation on a tilted surface
Ib-Hourly Beam Irradiation
ρg – Ground Reflectance
θ – Angle of incidence
vii
θz- Zenith Angle
β – Tilt Angle
HDKR – Hay Davies Klucher Reindl
Id,T – Diffuse irradiation on a tilted surface
Id,T,iso- Isotropic component of diffuse irradiation on a tilted surface
Id,T,cs- Circumsolar component of diffuse irradiation on a tilted surface
Ai – Anisotropy index
Io – Extraterrestrial Hourly Irradiation
F1-Circumsolar Coefficient
F2-Horizon Brightness Coefficients
Ion – Extraterrestrial normal-incident radiation
m- air mass
Tc- Average Module Temperature
Ta-Ambient Temperature
NOCT- Nominal Operating Cell Tempature
sm – optimum tilt
ηp – Array Efficiency
viii
ηr – Array Reference Efficiency
Tr-Reference Temperature
βp-Temperature Coefficient for module efficiency
Cf-Correction factor
δ – Declination
Φ – Latitude
Ho-Daily Extraterrestrial Irradiation
Ĥo- Monthly Average Daily Extraterrestrial Irradiation
Gsc-Solar Constant
γ’ – Axis Azimuth
β’ – Axis Tilt
θ’ – Axis Angle of Incidence
γs- Solar Azimuth
CPRG – Collares Pereira Rabl and Gueymard
ix
List of Figures
Figure 1: Directly Connected System(Messenger & Ventre 2004) ................................ 13
Figure 2: Off Grid with Battery Backup (Lynn 2010) .................................................... 13
Figure 3: Grid Connected Systems(Messenger & Ventre 2004)..................................... 14
Figure 4: Hybrid System(Lynn 2010) ............................................................................. 15
Figure 5: General PV System .......................................................................................... 17
Figure 6: Isoflux Plot....................................................................................................... 18
Figure 7: General Tilted Irradiation Calculation ............................................................. 20
Figure 8: Sky Model from (Duffie and Beckman 2006) ................................................. 26
Figure 9: Components Irradiation on a Tilted Surface Anisotropic Sky (Duffie and
Beckman 2006) ............................................................................................................... 28
Figure 10: Single Diode PV Model (Desoto 2004) ......................................................... 31
Figure 11: Fraction of Load Met Determined by SLR and ALR (NRCan 2005) ........... 36
Figure 12: Iterative Software model................................................................................ 39
Figure 13: Clearness Index Sub Module ......................................................................... 43
Figure 14: Total Hourly Irradiation on a Horizontal Surface Module ............................ 43
Figure 15: CPRG Flow Chart .......................................................................................... 44
Figure 16: Erbs et al Diffuse Daily Irradiation Module .................................................. 45
Figure 17: Erbs et. al Flow Chart .................................................................................... 46
Figure 18: Diffuse Hourly Irradiation ............................................................................. 47
Figure 19: Flow Chart of Liu and Jordan Model ............................................................ 48
Figure 20: RB Fixed Array Module ................................................................................ 50
Figure 21: RB for a Fixed Array Flow Chart .................................................................. 51
x
Figure 22: General Input Output Relation for Tilted Irradiation Calculation ................. 55
Figure 23: Tilted Irradiation Module .............................................................................. 56
Figure 24: Array Module Inputs/Outputs ........................................................................ 56
Figure 25: Solar Resource Assessment Tool Main Screen ............................................. 57
Figure 26: Resource Assessment Screenshot .................................................................. 58
Figure 27: Module Information Screenshot .................................................................... 59
Figure 28: Off Grid/On Grid Screenshot......................................................................... 60
xi
List of Tables
Table 1: Brightness Coefficients for Perez Anisotropic Sky (Duffie and Beckman 2006)
......................................................................................................................................... 30
Table 2: Justification of Models chosen .......................................................................... 37
Table 3: Recommended Average Days for Months and Declination (Duffie and
Beckman 2006) ............................................................................................................... 41
Table 4: Test Data ........................................................................................................... 61
Table 5: Fixed and Isotropic Model ................................................................................ 63
Table 6: Fixed Array and HDKR model ......................................................................... 63
Table 7: Fixed Axis and Perez Model ............................................................................. 64
Table 8: Two Axis Tracking and Isotropic model .......................................................... 64
Table 9: Two axis and HDKR model .............................................................................. 65
Table 10: Two Axis and Perez ........................................................................................ 65
Table 11: Case Study Results Isotropic........................................................................... 68
Table 12: Case Study Results HDKR ............................................................................. 68
Table 13: Case Study Results Perez ................................................................................ 69
12
Chapter 1 Introduction
1.1 Background
The amount of solar energy incident on the earth per day exceeds the requirements for
the entire population of the earth for an entire year (Lynn 2010).
One type of technology that utilizes solar energy is photovoltaic cells. In the Caribbean,
there are potential projects that utilize solar energy and photovoltaic cells such as the
solar powered equipment that are to be installed at the newly established Police
Surveillance Bays along the Uriah Butler and Solomon Hochoy Highways from Caroni
to Golconda in Trinidad and Tobago (Dowlat 2011).
In order to determine if projects are feasible a programme is required to perform
analyses on several factors to determine if a project is feasible. Some of the factors are
the available solar energy at a site, output of a photovoltaic array, shading and a
financial analysis of the entire project.
1.1.1 PV Configurations
Directly Connected
The simplest kind of PV configuration is an off grid, directly connected system where
the PV array supplies the load directly; a diagram of this configuration is given in figure
1 below, where the module is connected to a fan.
13
Figure 1: Directly Connected System(Messenger & Ventre 2004)
Off-Grid with Battery Back-Up
Some systems require a continuous supply of electricity so a battery is used. One of the
configurations is shown in figure 2 below with a charge controller and an inverter so that
the system can supply AC and DC loads.
Figure 2: Off Grid with Battery Backup (Lynn 2010)
14
Grid Connected
A grid connected system is a system which is connected to the electricity power grid by
some means. Three possible configurations are given in figure 3 below.
Figure 3: Grid Connected Systems(Messenger & Ventre 2004)
15
Hybrid
Hybrid systems are systems that are supplied by two different technologies such as a PV
array and a diesel generator or a PV array and a wind turbine. A diagram of a standalone
system supplied by a wind turbine and a PV array is shown figure 4 below.
1.2 Justification
The need for a software tool in the Caribbean to perform feasibility studies on PV
arrays.
Figure 4: Hybrid System(Lynn 2010)
16
1.3 Project Objectives
1. Literature review of models identifying critical factors to produce electrical
energy yields from (historical) solar data set.
2. Assessment of the goodness of fit of the solar data set to PV conversion models.
3. Justifying suitable model(s) and recommended approach(es), develop using
MATLAB a user friendly GUI solar photovoltaic resource assessment tool
(complete with user manual) modeling the production of electrical energy.
4. Determine the annual net average electrical energy production and capacity
factor that would be expected from a particular PV unit at a given site.
5. Validate software using existing available open source data.
6. Appropriate case study.
1.4 Scope
The project deals with the development of a MATLAB based tool to determine the
amount of solar energy available to photovoltaic arrays. Using the energy available at a
particular location and temperature information determine the efficiency of the arrays
and the net energy available from the PV arrays.
17
Chapter 2 Literature Review
In order to quantify the net electrical energy output of a PV array system, models at each
intermediate step need to be looked at and accessed. The general steps involved are
shown in figure 5 below.
As shown in figure 5 above, the first step is the type of solar radiation and climate
information available. Critical information would be the solar irradiation and irradiance
on a titled array. Usually the solar radiation data available are for horizontal surfaces
(Duffie and Beckman 2006) therefore models would be required to determine the solar
radiation a collector would be exposed to.
After determining the type of climate and solar radiation data available that would be
used as inputs to the PV array a model for the array would be required to determine the
energy output of the array.
Then models for components that can be connected to the PV array need to be
determined such as the inverter, battery, charge controller and maximum power point
tracker. The models and available data will be discussed below.
Figure 5: General PV System
18
2.1 Available Solar Data
Different types of solar data are available such as typical mean year data for a
particular location, average daily, monthly or yearly solar insolation, global isoflux
contours, sunshine hours data, solar insolation based on satellite cloud-cover data
and calculations of solar radiation (Bowden).
TMY is hourly solar data that is averaged over a certain number of years. TMY1
data was collected during the period 1948 and 1980(NASA), TMY2 data is averaged
during the time period 1961 to 1990 and TMY3 averaged over 1991 to 2005 (NREL)
. TMY data sets feature information such as the day, hour, irradiation for a particular
hour, air temperature for a particular hour and wind speed. However TMY data is
not suitable for the Caribbean because they do not contain data for Caribbean
countries.
Global isoflux contours are plots that show the variation of solar energy on the globe
as shown below in figure 6.
Figure 6: Isoflux Plot
19
Sometimes sunshine hour and cloud cover data is simpler to obtain than measured
irradiation data and sunshine hours can be used to estimate the solar irradiation
2.2 Irradiation on a Tilted Surface
The most easily accessible solar irradiation data in the Caribbean is monthly average
daily irradiation data on a horizontal surface available on NASA’s website (NASA)
calculated from satellite data. Therefore the irradiation models used to calculate the
irradiation on a titled surface were based on daily irradiation data. Solar irradiation is
made up of two components beam and diffuse. The component that reaches the
surface without being scattered is called the beam component and the component
that reaches the surface after being scattered is called the diffuse component. The
general flow of the calculation is shown in figure 7 below where not all the variables
are highlighted. First the total daily horizontal irradiation data is split up into its
hourly values, occurring in parallel using the daily horizontal irradiation data the
daily diffuse irradiation on a horizontal surface is calculated and from that the hourly
diffuse irradiation on a tilted surface is calculated. Using the total hourly irradiation
and the hourly diffuse irradiation the beam irradiation is calculated. The hourly beam
and diffuse irradiation are used to calculate the irradiation on a titled surface. In this
section, models for the individual blocks in figure 7 will be explored.
20
Figure 7: General Tilted Irradiation Calculation
21
2.2.1 Models to Calculate the Total Hourly Irradiation on a Horizontal Surface
In order to compute the irradiation on a tilted surface the hourly values of the total
irradiation on a horizontal surface must be calculated or measured. Models available to
calculate the hourly irradiation from daily irradiation are:
Collares-Pereira and Rabl as cited by (Alam, Garg and Kaushik 2007)
Liu and Jordan as cited by (Alam, Garg and Kaushik 2007)
Gopinathan and Soler (Alam, Garg and Kaushik 2007)
Jain as cited by (Koussa, Malek, and Haddadi 2009)
Collares-Pereira and Rabl modified by Gueymard as cited by (Ahmad and Tiwari
2008)
Newell Model as cited by (Ahmad and Tiwari 2008)
Baig et. Al Model cited by (Ahmad and Tiwari 2008)
According to (Alam, Garg and Kaushik 2007) the Collares-Pereira and Rabl model is
the universally accepted model. However in a study performed by (Ahmad and Tiwari
2008) the Collares-Pereira and Rabl as modified by Gueymard performs better than the
Collares-Pereira and Rabl model as the study performed by (Alam, Gard and Kaushik
2007) did not consider the Gueymard model.
The Collares-Pereira and Rabl model (Duffie and Beckman 2006) is given as:
22
(2.1)
/tr I H (2.2)
That is the fraction of irradiation allocated to a particular hour.
0.409 0.5016sin( 60)sa (2.3)
And
0.6609 0.4767sin( 60)sb (2.4)
All angles are in degrees and ω is the hour angle. The hour angle is given by:
15*Hour (2.5)
Where Hour is the hours from solar noon, and ωs is the hour angle at sunset or sunrise
assuming they are symmetrical.
For the Collares Pereira and Rabl model as modified by Gueymard (Ahmad and Tiwari
2008) equation 2.1 is multiplied by:
0.5 ( sin cos ) / (sin /180cos )s s s s s sa b (2.6)
2.2.2 Models to Calculate the Daily Diffuse Irradiation on a Horizontal Surface
Models to calculate the daily diffuse irradiation on a horizontal surface are based on
sunshine hours, atmospheric water content and clearness index (Koussa, Malek, and
Haddadi 2009)
Models based on sunshine hours are:
/ 24( cos )cos cos / (sin /180cos )t s s s sr a b
23
Iqbal’s Model (Koussa, Malek, and Haddadi 2009)
Hay’s Model (Koussa, Malek, and Haddadi 2009)
Models based on sunshine hours and atmospheric water content
Hussain’s Model (Koussa, Malek, and Haddadi 2009)
Models based on clearness index
Liu and Jordan Model (Koussa, Malek, and Haddadi 2009)
Page’s Model (Koussa, Malek, and Haddadi 2009)
Collares Pereira and Rabl (Koussa, Malek, and Haddadi 2009)
Iqbal’s Relation(Koussa, Malek, and Haddadi 2009)
Erbs et. al Model (Koussa, Malek, and Haddadi 2009)
Now since the available data does not include sunshine hours only the models based on
clearness index were considered. The clearness index is a ratio of the measured
irradiation to the extraterrestrial irradiation.
The study conducted by (Koussa, Malek, and Haddadi 2009) gave the results of the
models with respect to Algerian climates however the universal applicability of the Erbs
et. Al Model (Duffie and Beckman 2006) was mentioned.
The Erbs et al model (Duffie and Beckman 2006) is:
For sunset hour angle less than or equal to 81.4 degrees and clearness index between 0.3
and 0.8 equation 2.7 is used
24
2 3/ 1.391 3.560 4.189 2.137d T T TH H K K K (2.7)
For sunset hour angle greater than 81.4 degrees and clearness index between 0.3 and 0.8
Equation 2.8 is used
2 3/ 1.311 3.022 4.427 1.821d T T TH H K K K (2.8)
2.2.3 Models to Calculate the Hourly Diffuse Irradiation on a Horizontal
Surface
After calculating the daily diffuse irradiation on a horizontal surface the hourly diffuse
irradiation has to be determined. Models available to determine the hourly diffuse
irradiation on a horizontal surface are:
Model of Jain cited by (Koussa, Malek, and Haddadi 2009)
Liu and Jordan Model cited by (Koussa, Malek, and Haddadi 2009)
According to (Koussa, Malek, and Haddadi 2009) the Liu and Jordan model is superior
to model of Jain.
The Liu and Jordan model is given as:
/ 24cos cos / (sin cos ) /d s s s s d dr I H (2.9)
Where rd is the ratio of the hourly diffuse irradiation to the daily diffuse irradiation.
25
2.2.4 Models to Calculate the Irradiation on a Tilted Surface
Three models to calculate the irradiation on a tilted surface will be considered. An
isotropic model and two anisotropic models.
Isotropic – Liu and Jordan cited by (Duffie and Beckman 2006)
Anisotropic – HDKR cited by (Duffie and Beckman 2006)
– Perez et. al cited by (Duffie and Beckman 2006)
– The Circumsolar model cited (Notton et al. 2006)
– The Bugler Model cited by (Notton et al. 2006)
– The Temps and Coulson model cited by (Notton et al. 2006)
– Ma and Iqbal model cited by (Notton et al. 2006)
– Skartveit and Olseth model cited by (Notton et al. 2006)
– The Gueymard model cited by (Notton et al. 2006)
– The Muneer model cited by (Notton et al. 2006)
The differences with the models is the way they threat with the diffuse components.
Figure 8 below illustrates the components of the diffuse model; it also includes the beam
irradiation.
26
Figure 8: Sky Model from (Duffie and Beckman 2006)
The sky model shown in figure 8 shows irradiation of being made up of the diffuse
isotropic irradiation, circumsolar diffuse and horizon brightening (Duffie and Beckman
2006). The isotropic diffuse irradiation is the radiation received uniformly from the sky
dome (Duffie and Beckman 2006). The circumsolar diffuse is the radiation received due
to the forward scattering of solar radiation and that concentrated in the part of the sky
around the sun (Duffie and Beckman 2006). Horizon brightening is the radiation that is
concentrated around the horizon (Duffie and Beckman 2006). Lastly figure 8 includes
the beam radiation which is the radiation that passes through the sky dome directly
without being scattered.
According to (Duffie and Beckman 2006) the isotropic model tends to underestimate the
solar irradiation on a tilted surface where as the HDKR and Perez et. al gives a better
performance. Skartveit and Olseth, HDKR and Perez et. al models perform the best
according to a study done by (Noorian, Moradi, and Kamali 2008) for south facing
27
surfaces in Kara and the Perez et. al models performs the best for north facing surfaces
also noted is that the Perez et. al model gives the best overall performance. A study done
by (Notton et al. 2006) using data from a French Mediterranean site suggests that the
Perez et. al model, Ma and Iqbal model, Skartveit and Olseth model and previous
versions of the HDKR model gives the best performance. The complexity and the good
performance of the Perez et. al models is noted in a study conducted by (Posadillo and
López Luque 2009) although the model was not tested. The models tested were the
HDRK model, previous version of it and the Liu and Jordan isotropic model. The results
of the study indicated that the HDRK model performed the best among the three as well
as the simple application of it.
Only three models were considered and implemented, the isotropic model because that
is the model that RETScreen uses, the software that is used to test the MATLAB
software and two anisotropic models, that is the HDKR model for its simplicity and
accuracy and the Perez model for its accuracy. The three models are presented in the
remainder of this section.
The Isotropic model as presented by (Duffie and Beckman 2006) is shown below:
(1 cos ) / 2 (1 cos ) / 2T b b d gI I R I I (2.10)
Where cos / cosb zR (2.11)
The total radiation on a tilted surface according to this model consists of three
components the beam component, the diffuse component and the ground albedo
component.
28
Figure 9 below shows the components of radiation incident on a tilted surface. The
HDRK model makes use of this sky model.
Figure 9: Components Irradiation on a Tilted Surface Anisotropic Sky (Duffie and Beckman 2006)
The general diffuse components as presented by (Duffie and Beckman 2006) is shown
below:
, , , , ,d t T d iso T d csI I I (2.12)
Equation 2.12 says that the diffuse irradiation is made up of two components the
isotropic component and the circumsolar component.
The HDKR model (Duffie and Beckman 2006) is shown below:
29
3( ) (1 )(1 cos ) / 2[1 sin ( / 2)]
(1 cos ) / 2
T b d i b d i
g
I I I A R I A f
I
(2.13)
Where /i b oA I I (2.14)
Ai is the anisotropy index which determines the portion of the horizontal diffuse
irradiation which is to be treated as forward scattered (Duffie and Beckman 2006).
And f is a correction factor given by:
/bf I I (2.15)
According to (Duffie and Beckman 2006) the Perez model is based a more detailed
analysis of the three components that make up the diffuse radiation.
The diffuse radiation on a tilted surface calculation as cited by (Duffie and Beckman
2006) is shown below:
, 1 1 2[(1 )(1 cos ) / 2 / sin )]d T dI I F F a b F (2.16)
Where F1 and F2 are circumsolar and horizon brightness coefficients and are given by
(Duffie and Beckman 2006):
1 11 12 13max[0,( ( /180) )]zF f f f (2.17)
2 21 22 23( ( /180) )zF f f f (2.18)
Where f11, f12, f13, f21, f22, f23 are determined from a variable ε which is used to get the
brightness coefficients from a table which is shown below in table 1.
30
6 3,
6 3
( ) 5.535 10
1 5.535 10
d b nz
d
z
I I xI
x
(2.19)
Table 1: Brightness Coefficients for Perez Anisotropic Sky (Duffie and Beckman 2006)
Range of ε f11 f12 f13 f21 f22 f23
1.000-1.065 -0.008 0.588 -0.062 -0.060 0.072 -0.022
1.065-1.230 0.130 0.683 -0.151 -0.019 0.066 -0.029
1.230-1.500 0.330 0.487 -0.221 0.055 -0.064 -0.026
1.500-1.950 0.568 0.187 -0.295 0.109 0.152 0.014
1.950-2.800 0.873 -0.392 0.362 0.226 -0.462 0.001
2.800-4.500 1.132 -1.237 -0.412 0.288 -0.823 0.056
4.500-6.200 1.060 -1.600 -0.359 0.264 -1.127 0.131
6.200-∞ 0.678 -0.327 -0.250 0.156 -1.377 0.251
And the brightness parameter Δ is given by (Duffie and Beckman 2006):
/d onmI I (2.20)
31
2.3 PV Performance Models
Four PV array performance models were considered:
Sandia PV Array Performance Model (Klise and Stein 2009)
5 Parameter Model (Desoto 2004)
4 Parameter Model (Desoto 2004)
Evans and Facinelli as cited by (NRCan 2005)
The Sandia PV Array Performance model requires additional testing of the PV array to
successfully used the model and cannot be used with the datasheet values only.
The 5 Parameter model is based on the single diode model as shown in figure 10 below.
The 4 Parameter model is based on the single diode model as well but the shunt
resistance, Rsh would tend to infinity (Desoto 2004) that is removing it from the circuit.
The 5- parameter model and 4 – parameter model requires the solution of highly non
linear and implicit system of equations.
Figure 10: Single Diode PV Model (Desoto 2004)
32
The Evans and Facinelli model is the simplest to implement and most suitable for
feasibility studies as it only finds the efficiency at the maximum operating point and
only requires information from the manufacturer’s data sheet.
The array’s efficiency based on the Evans and Facinelli model is shown in the following
(NRCan 2005):
The average module temperature, Tc, is calculated first, it is given by:
20
(219 832 )800
c a tNOCT
T T K
(2.21)
If the array’s tilt is not optimal the right hand side of 2.21 is multiplied by a corrector
factor given below (NRCan 2005):
4 21 1.17 10 ( )f mC x s (2.22)
The efficiency is given by:
[1 ( )]p r p c rT T (2.23)
33
2.4 Battery Models
For off-grid applications the need for energy storage is important. Battery models used
for solar applications are:
KiBaM (Klise and Stein 2009)
Riso (Klise and Stein 2009)
RETScreen (NRCan 2005)
The KiBaM and Riso model (Klilse and Stein 2009) requires inputs that the Evans and
Facinelli PV Array does not provide such as voltage and current, they are geared toward
simulation software.
The RETScreen model uses the utilizability concept from (Duffie and Beckman 2006) to
calculate the energy supplied directly to the continuous load and the matched load. After
calculating the energy met directly by the array, the fraction of the load that is supplied
by the battery is found (NRCan 2005)
The mathematics for the RETSCreen model is given below.
Firstly the total DC load is given by:
,dc equ matched continuous batteryD D D D (2.24)
where Dmatched is the load that is supplied by the PV array
Dcontinuous is the load that is constant through the day
Dbattery is that load that is supplied only by the battery
34
The critical absorption level is then calculated:
24
continuouscrit
DP W (2.25)
According to (NRCan 2005) a critical radiation level is the radiation level that must be
exceeded so that the array can produce more energy that can be used by the constant
load and it is given by:
2/
critTc
A
PI W m
S (2.26)
The monthly average critical radiation level is given by (NRCan 2005):
,
Tcc
t n n
IX
r R H (2.27)
The monthly average utilisability is given by (NRCan 2005):
2( )( )n
c cR
a b X cXRe
(2.28)
where
22.943 9.271 4.031T Ta K K (2.29)
24.345 8.853 3.602T Tb K K (2.30)
and 20.170 0.306 2.936T Tc K K (2.31)
35
R is the ratio of the monthly average daily radiation to that on a horizontal plane. It is
given as:
tH
RH
(2.32)
and Rn is the ratio of the irradiation for a particular hour to that on a horizontal surface
for that day.
The energy delivered to the continuous load is given by (NRCan 2005):
(1 )continuous AE E (2.33)
Where EA is the energy from the array
The energy delivered to the matched load is given by (NRCan 2005):
min( , )matched matched A continuousE D E E (2.34)
The energy delivered directly to the load is given by (NRCan 2005):
D continuous matchedE E E (2.35)
and the energy delivered to the battery is the differences between the array energy and
ED
In order to find the amount of energy passing through the battery a number of
simulations were run on WATSUN and the fraction of the load met was determined.
From these simulations it was determined what fraction of the load was met given a
36
particular ALR and SLR and a surface was generated as shown in figure 11 below
(NRCan 2005).
Figure 11: Fraction of Load Met Determined by SLR and ALR (NRCan 2005)
37
2.5 Justification
This section summarizes the justification for the use of each model and data type used.
Table 2: Justification of Models chosen
Model/Data Type
Used
Justification
Solar Data Monthly Average
Daily Total
Irradiation
Availability
Hourly Irradiation on a
Horizontal Plane
Collares Pereira
Rabl and
Gueymard
Accuracy
Daily Diffuse Irradiation on
a Horizontal Plane
Erbs et. al Universal acceptance
Hourly Diffuse Irradiation
on a Horizontal Plane
Liu and Jordan Universal acceptance
Irradiation on a tilted
surface
Isotropic
HDKR
Perez et. al
Isotropic used to test with
RETScreen. HDKR used because
of its accuracy and ease of use.
Perez et. al used because of its
accuracy
38
PV Performance Model Evans and Facinelli Simple and accurate for feasibility
studies
Battery Hybrid Model Some of the RETScreen model is
used the tabulated version of the
SLR and ALR surface is not
available
39
Chapter 3 Methodology
3.1 Software Model
The software model chosen was the iterative model as shown in figure 12.
This model was chosen as the need to go back and refine implementation of code to
achieve an optimal implementation of the chosen solar models. The programming
language chosen was MATLAB.
3.2 Software Design
The requirements of the software led to the decoupling of the system into modules. The
modules were further broken down into its constituent functions in the following
sections. The different modules are:
Figure 12: Iterative Software model
40
Irradiation on a Tilted Surface Module
PV Array Module
On Grid and Off Grid Module
3.3 Irradiation on a Tilted Surface Module
Firstly all the functions that are necessary for the operation of this module will be
discussed first.
3.3.1 Sunset Hour Angle
The sunset hour angle is used to determine the clearness index so its implementation
will be discussed here. The sunset hour angle is the angle the sun is displaced at sunset
or sunrise, it operates on the assumption that they are symmetrical. The formula to
calculate the sunset hour angle stated in (Duffie and Beckman 2006) is shown below:
tan tans (3.1)
The implementation of this function is using the declination for the average day numbers
of each month and the declination at each of these months as stated in (Duffie and
Beckman 2006).The average day of a month is defined as the day in which the average
irradiation for a month is equal to the irradiation for that day (Duffie and Beckman
2006). Table 3 shows the day numbers and the corresponding declination which was
adapter from (Duffie and Beckman 2006). The declination is defined as the angular
position of the sun at solar noon with respect to the equator (Duffie and Beckman 2006).
41
Table 3: Recommended Average Days for Months and Declination (Duffie and Beckman 2006)
Month Day Number Declination
January 17 -20.9
February 47 -13.0
March 75 -2.4
April 105 9.4
May 135 18.8
June 162 23.1
July 198 21.2
August 228 13.5
September 258 2.2
October 288 -9.6
November 318 -18.9
December 344 -23.0
42
3.3.2 Clearness Index
All of the models use clearness index so a function is required to compute the clearness
index. The monthly average clearness index is give by the equation as shown below:
/t oK H H (3.2)
That is the ratio of the monthly average daily horizontal irradiation to the monthly
average daily extraterrestrial irradiation.
The monthly average daily extraterrestrial irradiation is given by the equation shown
below where the average day numbers are used (Duffie and Beckman 2006):
24 3600 360(1 0.033cos )(cos cos sin
365
sin sin )180
sco s
s
x G nH
(3.3)
A pictorial representation of the clearness index sub-module is given below in figure 13
illustrating the inputs and output. Where H is a 1x12 matrix containing the monthly
average daily irradiation for each month, declination is a 1x12 matrix containing the
declination for the average days of each month, n is a 1x12 matrix containing the day
numbers for the average days, w is a 1x24 matrix containing the hour angles at the mid
point of each hour in a day and the output is a 1x12 matrix containing the clearness
index for the average day of each month.
43
Figure 13: Clearness Index Sub Module
3.3.3 Total Hourly Irradiation on a Horizontal Surface
The equation to calculate the total hourly irradiation on a horizontal surface is given by
equation 2.1 as modified by equation 2.6. Figure 14 below shows the inputs and outputs
of the module. H and Hour angle is the same as the previous section and the Sunset
Hour Angle is a 1x24 matrix which gives the hour angles at the mid point of each hour
in a day. The output is a 12x24 matrix where the ith
row represents the month and the jth
column represents the hour and that gives the irradiation for that hour and month.
Figure 14: Total Hourly Irradiation on a Horizontal Surface Module
A flow diagram of the logic of the module is shown in figure 15 below.
44
Figure 15: CPRG Flow Chart
45
3.3.4 Diffuse Daily Irradiation on a Horizontal Surface
The equations to calculate the daily diffuse irradiation on a horizontal surface is given
by equations 2.7 and 2.8, the Erbs et. al equation. Figure 16 below shows the inputs and
outputs of the calculation. The sunset hour angle is the same as before, the clearness
index is a 1x12 matrix representing the average daily clearness index for the average
days of each month as calculated in the previous section and H is the same as before.
The output is a 1x12 matrix containing the diffuse daily irradiation for the average day
of each month.
Figure 16: Erbs et al Diffuse Daily Irradiation Module
A flow chart of the internal working of the module is shown below in figure 16.
46
Figure 17: Erbs et. al Flow Chart
47
3.3.5 Hourly Diffuse Irradiation on a Horizontal Surface
The equation to calculate the diffuse hourly irradiation on a horizontal surface is given
by equation 2.9. Figure 18 below shows the inputs and outputs of the module. Hd is the
diffuse daily irradiation as calculated in the previous section. Hour angle and the Sunset
Hour Angle is the same as section 3.3.3. The output is a 12x24 matrix where the ith
row
represents the month and the jth
column represents the hour and that gives the hourly
diffuse irradiation for that hour and month.
Figure 18: Diffuse Hourly Irradiation
A flow diagram of the logic is shown below in figure 19.Note the output is initialized to
a zero matrix that is why when the if condition is not true the module does nothing.
48
Figure 19: Flow Chart of Liu and Jordan Model
49
3.3.6 Determination of Rb for fixed Arrays
In order to calculate the irradiation on a tilted surface the ratio of the beam radiation on a
tilted surface to that on a horizontal surface must be computed. According to (Duffie and
Beckman 2006) this is calculated as:
cos / cosb zR (3.4)
Where θ is the angle of incidence of the beam radiation on a titled surface and θz the
angle of incidence of the beam radiation on a horizontal surface also known as the zenith
angle.
The general formula for cosθ is given below (Duffie and Beckman 2006):
cos sin sin cos sin cos sin cos cos cos cos cos
cos sin sin cos cos
(3.5)
The formula for cosθz is given below (Duffie and Beckman 2006):
cos cos cos cos sin sinz (3.6)
Figure 20 below identifies the inputs and outputs of the Rb module where the array is
fixed. The declination is as before a 1x12 matrix containing the declination for the
average day of each month, the latitude, the surface azimuth, the surface tilt, the hour
angle a 1x24 matrix as before and the sunset hour angle a 1x12 matrix. The outputs are
12x24 matrices of RB, zenith angle and the angle of incidence.
50
Figure 20: RB Fixed Array Module
Figure 21 below shows the flow chart for calculating RB for a fixed surface. Note the
outputs are initialized as zeros matrices.
51
Figure 21: RB for a Fixed Array Flow Chart
52
3.3.7 RB for a Azimuth Tracking Surface
For an azimuth tracking surface the formula to calculate the angle of incidence is given
by (Duffie and Beckman 2006):
cos cos cos sin sinz z (3.7)
Figures 20 and 21 from the previous section are still applicable here except that the
formula to calculate the angle of incidence, equation 3.7 is used instead and there is no
need to specify the azimuth.
3.3.8 RB for Two Axis Tracking Surface
For two axis tracking the angle of incidence is given by (Duffie and Beckman 2006):
cos 1 (3.8)
Figures 20 and 21 from section 3.3.6 are still applicable here except that the formula to
calculate the angle of incidence, equation 3.8 is used instead and there is no need to
specify the tilt and azimuth.
3.3.9 RB for an Axis of Arbitrary Tilt
In order to calculate RB for this type of array the solar azimuth had to be calculated
because it is used in the calculation of the azimuth of the array, the solar azimuth is
given by the formula (Duffie and Beckman 2006):
1 cos sin sin
( ) | cos ( ) |sin cos
zs
z
sign
(3.9)
The azimuth of the array is calculated from a formula in (Braun and Mitchell 1983):
53
1 2180o (3.10)
where
1 sin sin( ')
' tan [ ]cos 'sin '
z so
(3.11)
1
0 if ( ')( ') 0
1 if otherwise
o s
(3.12)
2
1 if ( ') 0
1 if otherwise
s
(3.13)
The surface slope is given by (Braun and Mitchell 1983):
' ' 180o (3.14)
where
1 tan '' tan [ ]
cos( ')o
(3.15)
o0 if ' 0
'1 otherwise
(3.16)
Then the angle of incidence can be calculated using equation 3.5.
Figures 20 and 21 from section 3.3.6 are still applicable except the equations in this
section are used and the array tilt and azimuth are replaced by the axis tilt and azimuth.
54
3.3.10 RB for a horizontal axis
In order to calculate RB for this type of array the solar azimuth had to be calculated
because it is used in the calculation of the azimuth of the array. The solar azimuth is
calculated using equation 3.9.
The azimuth of the array is calculated from a formula in (Braun and Mitchell 1983):
s
s
' 90 if - ' 0
' 90 if - '<0
(3.17)
The surface slope is given by (Braun and Mitchell 1983):
180o (3.18)
where
1tan (tan cos( ))o z s (3.19)
and
00 if 0
1 otherwise
(3.20)
Then the angle of incidence can be calculated using equation 3.5.
Figures 20 and 21 from section 3.3.6 are still applicable except the equations in this
section are used and the array tilt and azimuth are removed and the axis azimuth is used.
55
3.3.11 Irradiation on Tilted Surface Sub-Function
Three different models were used the isotropic model, HDKR and Perez et. a model.
The equations used are the equations outlined in section 2.
The inputs to all the models were the same; figure 22 below illustrates the inputs and
outputs of the function.
3.3.12 Irradiation on Tilted Surface Complete Module
The complete module for calculating the tilted irradiation on a tilted surface is shown in
figure 23 below. The inputs shown here are the inputs the user will choose. Some of the
inputs in the previous section do not appear here because they are internal to the module.
Figure 22: General Input Output Relation for Tilted Irradiation Calculation
56
Figure 23: Tilted Irradiation Module
3.4 Array Module
The array module is based on equations 2.21 to 2.23; figure 24 below shows the inputs
and outputs required for the array module.
Figure 24: Array Module Inputs/Outputs
57
3.5 Battery Module
The battery module employed is a hybrid model. It uses equations 2.21 to 2.23 to
determine the energy available to the battery from the array. It divides the energy into
hourly average values depending on the amount of hours of sunlight for a particular
month and energy available. Then an hourly balance of the energy available to the
battery taking into account the maximum depth of discharge and capacity of the battery.
Then a balance is done on the demand of the load that needs to be met for that day.
3.6 System Design
Figure 25 below shows a screenshot of the main screen of the MATLAB software.
Figure 25: Solar Resource Assessment Tool Main Screen
58
When ‘Site and Solar’ is clicked another screen pops up to enter the solar and site
information, figure 26 is a screenshot of that screen.
Figure 26: Resource Assessment Screenshot
The Solar irradiance Plot and difference plot plots the irradiation of the different models
and the difference between the models with respect to the isotropic model respectively.
The Module Information button brings up a GUI to input the PV module information. A
screenshot of that screen is shown below in figure 27
59
Figure 27: Module Information Screenshot
The Off Grid/On grid button brings up a screen that gives the energy output of off grid
and on grid systems. A screenshot of that screen is shown in figure 28 below.
60
Figure 28: Off Grid/On Grid Screenshot
61
4 Testing
The software was tested and benchmarked against RETScreen. Blackbox testing was
used because of the ability to get data to verify with that is the data from RETSCreen.
The input data used to test was obtained from RETScreen. The values of irradiance and
temperature are shown in the table 4 below.
Table 4: Test Data
Month Irradiation kWh/m2/day Temperature degrees celcius
January 4.69 26
February 5.28 26
March 5.64 26.6
April 5.69 27.4
May 6.03 27.9
June 5.44 27.5
July 5.89 27.3
August 5.89 27.6
September 5.44 27.7
October 5.44 27.5
November 5.03 26.8
62
December 4.53 26.3
The location is Crown Point, Tobago
Latitude – 11.2 degrees north
The energy demand for each type of load is 7.5kWh both AC and DC aswell.
Battery Capacity of 500Ah and maximum depth of discharge of 90%.
Each Solar radiation model was tested as follows:
Fixed array – 45 degree tilt, 0 degree azimuth
Two Axis Tracking
Module Information :
Reference Efficiency – 13%
Collector Area – 46.2m2
NOCT – 45 degrees celcius
Temperature coefficient – 0.40%
Capacity – 6kW
63
Table 5: Fixed and Isotropic Model
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
1.7417 1.74
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.3
Capacity Factor % 18.31 18.2
Table 6: Fixed Array and HDKR model
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
1.7593 1.74
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.3
Capacity Factor % 18.48 18.2
64
Table 7: Fixed Axis and Perez Model
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
1.7599 1.74
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.3
Capacity Factor % 18.49 18.2
Table 8: Two Axis Tracking and Isotropic model
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
2.534 2.53
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.1
Capacity Factor % 26.27 26.2
65
Table 9: Two axis and HDKR model
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
2.7099 2.53
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.1
Capacity Factor % 28.08 26.2
Table 10: Two Axis and Perez
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
2.78 2.53
Annual Energy Supplied
to Load MWh
7.4734 7.3
% Load Supplied 100 95.1
Capacity Factor % 28.85 26.2
66
The results show that the isotropic model behaves just as the isotropic model in
RETScreen however the battery model used in the solar resource assessment tool yields
better results than RETSCreen. The other two solar models, HDKR and Perez model
produces higher yields of solar energy on a tilted surface as expected. The values are
very close to the values in RETScreen so the software is validated and working.
67
5 Results
The information for the case study is as follows:
Location – Syrian Arab Republic Latitude – 36.3 degrees north
The energy for a battery based load – 8.4kWh
Battery Capacity of 1101Ah and maximum depth of discharge of 80%.
Battery efficiency – 85% Charge Controller Efficiency 95%
Each Solar radiation model was tested as follows:
Fixed array – 45 degree tilt, 0 degree azimuth
Module Information :
Reference Efficiency – 11.4%
Collector Area – 31.5m2
NOCT – 45 degrees celcius
Temperature coefficient – 0.40%
Capacity – 3.6kW
68
Table 11: Case Study Results Isotropic
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
1.937 1.70
Annual Energy Supplied
to Load MWh
2.7594 3.34
% Load Supplied 100 108.9%
Capacity Factor % 23.55 18.3
Table 12: Case Study Results HDKR
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
2.01 1.70
Annual Energy Supplied
to Load MWh
2.7594 3.34
% Load Supplied 100 108.9%
Capacity Factor % 24.55 18.3
69
Table 13: Case Study Results Perez
Solar Resource
Assessment Tool
RETScreen
Annual Tilted Irradiation
MWh
2.06 1.70
Annual Energy Supplied
to Load MWh
7.4734 3.34
% Load Supplied 100 108.9%
Capacity Factor % 25.11 18.3
From the results it can be seen that the RETScreen implementation of the models
underestimate the solar irradiation on a tilted surface however it manages to supply the
load with 108.9% of the required energy.
70
6 Discussion
The report dealt with the models required to determine the net annual energy production
produced by a PV panel and what percent of that energy that can be supplied to a load or
to the grid and to develop a tool geared to be used in the Caribbean.
From the results it can be seen that the energy incident on a collector is underestimated
when using the isotropic model and the other two anisotropic models produce better
results, also the battery model was investigated and the battery model in the solar
resource assessment tool performed better than the one in RETScreen.
71
7 Conclusion
The project had six objectives and the six objectives were met. A Matlab tool was
developed that can determine the net annual electrical energy from a PV unit at a given
site based on minimal amount of information.
The Software was tested, validated and benchmarked against RETScreen and the results
were very close in most cases except for the anistropic models that generally produce
higher irradiance values.
72
8 References
Ahmad, Firoz, and S. A. Husain. 1986. "Computation of monthly average hourly and daily solar radiation incident on a flat tilted surface at Karachi, Pakistan." Solar & Wind Technology no. 3 (4):329-333. doi: 10.1016/0741-983x(86)90014-7.
Alam, S, Sn Garg, and Sc Kaushik. 2007. Computation of Monthly Mean Hourly Global Solar Radiation from Daily Total. Journal of Energy and Environment 6, no. May: 10-17. http://www.buet.ac.bd/ces/shah-alam.doc
Bekker, Bernard, and Trevor Gaunt. 2008. Simulating The Impact of Design-Stage Uncertainties on PV Array Energy Output Estimation. In 16th PSCC.
Glasgow,Scotland Bowden, Christiana Honsberg and Stuart. Available from
http://pvcdrom.pveducation.org/SUNLIGHT/RADDATA.HTM Braun, J. E., and J. C. Mitchell. 1983. "Solar geometry for fixed and tracking surfaces." Solar
Energy no. 31 (5):439-444. doi: 10.1016/0038-092x(83)90046-4. De Soto, W.L. (2004). Improvement and Validation of a Model for Photovoltaic Array
Performance. Master's Thesis, University of Wisconsin-Madison. Dowlat, Rhondor. 2011. "Solar Power for Surveillance Bays." Newsday, August 27th, 2011,
18. Duffie, J.A, and W.A Beckman. 2006. Solar Engineering of Thermal Processes. 3rd Edition ed.
Hoboken, New Jersey: John Wiley & Sons. Farret, F., and M. Simões. 2006. Integration of Alternative Sources of Energy. New Jersey:
John Wiley & Sons. Klise, Geoffrey T, and Joshua S Stein. 2009. Models Used to Assess the Performance of
Photovoltaic Systems. Contract, no. December. http://www.osti.gov/bridge/servlets/purl/974415-t6N0f7/.
Koussa, M., A. Malek, and M. Haddadi. 2009. "Statistical comparison of monthly mean hourly and daily diffuse and global solar irradiation models and a Simulink program development for various Algerian climates." Energy Conversion and Management no. 50 (5):1227-1235. doi: 10.1016/j.enconman.2009.01.035.
Lynn, Paul A. 2010. Electricity from Sunlight: An Introduction to Photovoltaics. United Kingdom: John Wiley & Sons.
Messenger, R.A, and J Ventre. 2004. Photovoltaic Systems Engineering. 2nd Ed. ed. Washington D.C: CRC Press.
NASA. [cited 30-03-12. Available from http://eosweb.larc.nasa.gov/cgi-bin/sse/sse.cgi?#s02. Noorian, Ali Mohammad, Isaac Moradi, and Gholam Ali Kamali. 2008. "Evaluation of 12 models
to estimate hourly diffuse irradiation on inclined surfaces." Renewable Energy no. 33 (6):1406-1412. doi: 10.1016/j.renene.2007.06.027.
Notton, G., C. Cristofari, M. Muselli, P. Poggi, and N. Heraud. 2006. Hourly Solar Irradiations Estimation : From Horizontal Measurements to Inclined Data. Paper read at Environment Identities and Mediterranean Area, 2006. ISEIMA '06. First international Symposium on, 9-12 July 2006.
NRCan. 2005. Clean Energy Project Analysis: RETScreen Engineering & Cases Textbook. Varennes, Québec, Canada: RETScreen International.
NREL. [cited 30-03-12. Available from http://rredc.nrel.gov/solar/old_data/nsrdb/.
73
Posadillo, R., and R. López Luque. 2009. "Evaluation of the performance of three diffuse hourly irradiation models on tilted surfaces according to the utilizability concept." Energy Conversion and Management no. 50 (9):2324-2330. doi: 10.1016/j.enconman.2009.05.014.
Ransome, Steve. 2007. 4EP.1.1 How Well Do PV Modelling Algorithms Really Predict Performance. Milan 22nd European PVSEC
74
Appendix A – Progress Report
Objectives
7. Literature review of models identifying critical factors to produce electrical
energy yields from (historical) solar data set.
8. Assessment of the goodness of fit of the solar data set to PV conversion models.
9. Justifying suitable model(s) and recommended approach(es), develop using
MATLAB a user friendly GUI solar photovoltaic resource assessment tool
(complete with user manual) modeling the production of electrical energy.
10. Determine the annual net average electrical energy production and capacity
factor that would be expected from a particular PV unit at a given site.
11. Validate software using existing available open source data.
12. Appropriate case study.
75
Background and Scope
The amount of solar energy incident on the earth per day exceeds the requirements for
the entire population of the earth for an entire year (Lynn 2010).
One type of technology that utilizes solar energy is photovoltaic cells. In the Caribbean,
there are potential projects that utilize solar energy and photovoltaic cells such as the
solar powered equipment that are to be installed at the newly established Police
Surveillance Bays along the Uriah Butler and Solomon Hochoy Highways from Caroni
to Golconda in Trinidad and Tobago (Dowlat 2011).
In order to determine if the projects are feasible a programme is required to perform
analyses on several factors to determine if a project is feasible. Some of the factors are
the available solar energy at a site, output of a photovoltaic array, shading and a
financial analysis of the entire project.
76
PV Configurations
Directly Connected
The simplest kind of PV configuration is an off grid, directly connected system where
the PV array supplies the load directly; a diagram of this configuration is given below,
where the module is connected to a fan.
Figure 29: Directly Connected System(Messenger & Ventre 2004)
77
Off-Grid with Battery Back-Up
Some systems require a continuous supply of electricity so a battery is used. One of the
configurations is shown below with a charge controller and an inverter so that the
system can supply AC and DC loads.
Grid Connected
A grid connected system is a system which is connected to the electricity power grid by
some means. Three possible configurations are given below.
Figure 30: Off Grid with Battery Backup(Lynn 2010)
78
Figure 31: Grid Connected Systems(Messenger & Ventre 2004)
Hybrid
Hybrid systems are systems that are supplied by two different technologies such as a PV
array and a diesel generator or a PV array and a wind turbine. A diagram of a standalone
system supplied by a wind turbine and a PV array is shown below.
Solutions Proposed and Implemented by Others
Figure 32: Hybrid System(Lynn 2010)
79
The general methodology used by most software is given in the figure below.
What varies among the software are the methods used to quantify the output irradiation
incident on the PV array, the PV algorithm, battery models and all other components
involved.
Currently an algorithm to calculate the titled irradiation incident on a PV array is being
investigated given monthly average daily irradiation.
Two software which are currently being looked at and uses monthly average daily
irradiation are RETScreen and Homer. RETScreen performs its calculations differently
Figure 33: General Procedure for PV Feasibility Studies (Ransome 2007)
80
than Homer, it calculates the titled monthly average daily irradiation incident on a PV
array and performs its calculations based on that (NRCan 2005), whereas Homer
calculates 8760 hourly values for each hour of the year using a more complicated
algorithm by Graham and Hollands(1990) as cited by (Farret & Simões 2006).
(NRCan 2005) compares the results using a particular case study and shows the
difference between the two algorithms shown below
Inspecting the column of incident solar radiation, it can be seen that Homer gives a
monthly average daily irradiation output higher than RETScreen.
A possibility for RETScreen yielding lower results than Homer can be accounted for by
its use of an isotropic model to determine the total irradiation incident on a titled surface
A study conducted by (Bekker & Bernard 2008) suggests replacing RETScreen’s
isotropic model with an anistropic model.
Table 14: Comparison of Homer and RETScreen(NRCan 2005)
81
Details on how the problem is being addressed
Replacing RETScreen’s isotropic model with an anistropic model
Conduct research for an optimal anistropic model
Implement anistropic model
Test complete solar resource evaluation module with measured data
82
Plans for the Completion of the Solution
Complete solar module
Research PV algorithms taking into consideration available data
Research algorithms for components of the system for various configurations
Implement suitable PV algorithm and components algorithms
Implement financial analysis module
Test Completed software with a case study
83
Problems Encountered
No study found evaluating statistical models in the Caribbean
Gantt Chart
Figure 34: Gantt Chart
84
References
Bekker, Bernard, and Trevor Gaunt. 2008. Simulating The Impact of Design-Stage
Uncertainties on PV Array Energy Output Estimation. In 16th PSCC.
Glasgow,Scotland.
Dowlat, Rhondor. 2011. "Solar Power for Surveillance Bays." Newsday, August 27th,
2011, 18.
Duffie, J.A, and W.A Beckman. 2006. Solar Engineering of Thermal Processes. 3rd
Edition ed. Hoboken, New Jersey: John Wiley & Sons.
Farret, F., and M. Simões. 2006. Integration of Alternative Sources of Energy. New
Jersey: John Wiley & Sons.
Lynn, Paul A. 2010. Electricity from Sunlight: An Introduction to Photovoltaics. United
Kingdom: John Wiley & Sons.
Messenger, R.A, and J Ventre. 2004. Photovoltaic Systems Engineering. 2nd Ed. ed.
Washington D.C: CRC Press.
NRCan. 2005. Clean Energy Project Analysis: RETScreen Engineering & Cases
Textbook. Varennes, Québec, Canada: RETScreen International.
Ransome, Steve. 2007. 4EP.1.1 How Well Do PV Modelling Algorithms Really Predict
Performance. Milan 22nd European PVSEC
85