Environmental Impact on Residential Load Modelingeprints.kfupm.edu.sa/10554/1/10554.pdf · 2011-04-06 · Environmental Impact on Residential Load Modeling Khaled Hamed Al-Ghamdi

Environmental Impact on Residential Load Modeling

Khaled Hamed Al-Ghamdi

Electrical Engineering

May 2003

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KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS

DHAHRAN, SAUDI ARABIA

DEANSHIP OF GRADUATE STUDIES

This thesis, written by

KHALED HAMED ABDULLAH AL-GHAMDI

under the direction of his Thesis advisor, and approved by his Thesis Committee, has been

presented to and accepted by Dean of Graduate Studies, in partial fulfillment of the

requirements for the degree of

MASTER OF SCIENCE IN ELECTRICAL ENGINEERING

Thesis Committee:

________________________________ Dr.Chokri Belhaj Ahmed (Chairman) _________________________________ Dr.Rached Ben-Mansour (Co-Chairman) _________________________________ Dr.Ibrahim M. El-Amin (Member)

_______________________________ _________________________________ Dr.Jamil M. Bakhashwain Dr.Ibrahim O. Habiballah (Member) Department Chairman

_________________________________ Dr.Essam Z. Abdel-Aziz (Member)

_______________________________ Dr.Osama A. Jannadi Dean of Graduate Studies

Date: ______________________

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بسم اهللا الرحمن الرحيم

أهــــــداء

جنات أسأل اهللا ان يرحمه ويجمعني به في-إلي والدي العزيز .الخلد

أسأل اهللا ان ُيحسن خاتمتها ويرزقها -ةوإلي والدتي العزيز .االعلـى الفردوس

التي كانت عوناً لي بـعد اهللا، وكانت -ةوإلي زوجتي الغالي . السراِء والضراء معي في

أسأل اهللا أن يجـعلهم - تركي وروانأوالديوإلي قرة عيني . صالحين أبـناًء

. تيوإلي من اُحب أخواني و أخوا

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Acknowledgement

Acknowledgment is due to King Fahd University of Petroleum and Minerals for providing

support for this work.

I wish to express my deep appreciation to Dr.Chokri Belhaj Ahmed, who served as my

major advisor, for his guidance and invaluable suggestions through the course of this

work. I also wish to thank the other members of my Thesis Committee Dr.Rached Ben-

Mansour, Dr.Ibrahim El-Amin, Dr.Ibrahim Habiballah and Dr.Essam Abdel-Aziz for their

cooperation, encouragement and help. Thanks are also due to Electrical Engineering

Department Chairman, Dr.Jamil Bakhashwain and other faculty members for their interest

and support.

Thanks are also due to the Saudi Electricity Company-Eastern Region Branch and all its

staff members who provided me with the information needed for this work.

Special thanks are due to my parents who took care of me and instilled in me the self-

dependence, to my wife who was very patient in encouraging me to complete this work,

and to all family members for their support.

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Contents

Acknowledgement iv

List of Tables viii

List of Figures x

Abstract (English) xv

Abstract (Arabic) xvi

1. INTRODUCTION 1 2. LITERATURE REVIEW 5 3. LOAD MODELING CONCEPTS AND APPROACH 10

3.1 Basic Load Modeling Concepts…………………………………….. 10 3.2 Load Model Theory…………………………………………………. 16 3.3 Load Model Derivation……………………………………………... 17 3.4 Load Model Parameter Estimation………………………………….. 26

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4. PROBLEM DEFINITION AND OBJECTIVE 28

4.1 Problem Definition………………………………………………….. 28 4.2 Objective……………………………………………………………. 43

5. LOAD MODEL RESULTS AND DISCUSSION 44 5.1 Parameter Estimation Method………………………………………. 44 5.2 EPRI Load Model Example………………………………………… 45 5.3 Load Modeling Structure Selection…………………………………. 50 5.4 Data For Load Modeling……………………………………………. 53

5.4.1 Basic Approaches to Obtain Data…………………………... 53

5.4.2 Data Selected……………………………………………….. 55

5.5 Load Model Development Steps……………………………………. 56 5.6 Formulated Load Model…………………………………………….. 58

5.6.1 Residential Load Model for June………………………….... 58 5.6.2 Residential Load Model for July ………………………….... 61 5.6.3 Residential Load Model for August……………………….... 61 5.6.4 Residential Load Model for September...………………....... 66

5.7 Statistical Error Analysis …………………………………………… 69

5.8 Forecasting Hourly Residential Load Demand..……………………. 82

5.8.1 Utility Current Approach…………………………………… 82 5.8.2 Weather Related Approach…………………………………. 83

5.9 Test Load Model With New Substation ……………………………. 87

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6. CONCLUSIONS AND RECOMMENDATIONS 96

6.1 Conclusions…………………………………………………………. 96 6.2 Recommendations…………………………………………………... 98

APPENDICES 99

A Load Modeling Structure Selection…………………………………. 100 B Data For Load Modeling……………………………………………. 112

B.1 Original Raw Data …………………………………………… 113 B.2 Data For Load Modeling……………………………………… 124

C Error Bars Plots……………………………………………………... 140

BIBLIOGRAPHY 197 Vita 200

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List of Tables

3.1 Comparison Among Load Parameters of Various Kinds of Typical System Load…………………………………………………….….. 23

4.1 Load Data of AGRABIA Substation 1st August 2000……………………… 29 4.2 Load Data of AGRABIA Substation 1st February 2000……………………. 32 5.1 Load Data of The Heat Pump……………………………………………….. 48 5.2 Data of Matrix X for EPRI Example………………………………………... 49 5.3 Load Model Structures for Active Power Demand…………………………. 51 5.4 Load Model Structures for Reactive Power Demand……………………….. 52 5.5 Formulated Residential Load Model for June at 2 am ……………………... 59 5.6 Formulated Residential Load Model for June at 2 pm ……………………... 60 5.7 Formulated Residential Load Model for July at 2 am ……………………... 62 5.8 Formulated Residential Load Model for July at 2 pm ……………………... 63 5.9 Formulated Residential Load Model for August at 2 am …………………... 64 5.10 Formulated Residential Load Model for August at 2 pm ………………….. 65 5.11 Formulated Residential Load Model for September at 2 am ………………. 67 5.12 Formulated Residential Load Model for September at 2 pm ………………. 68 5.13 Statistical Error analysis for June Models ………………………………….. 70 5.14 Statistical Error analysis for July Models…………………………………... 71

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5.15 Statistical Error analysis for August Models………………………………... 72 5.16 Statistical Error analysis for September Models……………………………. 73 A.1 Load Model Structure A (1999 August at 2 pm)…………………………… 101 A.2 Load Model Structure B (1999 August at 2 pm)…………………………… 102 A.3 Load Model Structure C (1999 August at 2 pm)…………………………… 103 A.4 Load Model Structure D (1999 August at 2 pm)…………………………… 104 A.5 Load Model Structure E (1999 August at 2 pm)…………………………… 105 A.6 Load Model Structure F (1999 August at 2 pm)…………………………… 106 A.7 Load Model Structure G (1999 August at 2 pm)…………………………… 107 A.8 Load Model Structure H (1999 August at 2 pm)…………………………… 108 A.9 Load Model Structure I (1999 August at 2 pm)…………………………… 109 A.10 Load Model Structure J (1999 August at 2 pm)…………………………… 110 A.11 Load Model Structure K (1999 August at 2 pm)…………………………… 111 B.1 Load Model Data for June 2 am…………………………………………….. 124 B.2 Load Model Data for June 2 pm…………………………………………….. 126 B.3 Load Model Data for July 2 am…………………………………………….. 128 B.4 Load Model Data for July 2 pm…………………………………………….. 130 B.5 Load Model Data for August 2 am………………………………………….. 132 B.6 Load Model Data for August 2 pm………………………………...……….. 134 B.7 Load Model Data for September 2 am……………..……………………….. 136 B.8 Load Model Data for September 2 pm……………………………..……….. 138

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List of Figures

2.1 Power System Configuration……………………………………………….. 12 2.2 Terminology for Component-Based Load Modeling………………………. 13 3.1 EMTP (Electromagnetic Transient Program) Voltage and Frequency-

Dependent Static Loads……………………………………………………... 25 4.1 Active Power, Temperature and Humidity Vs. Hour at 1st August 2000…… 30 4.2 Reactive Power, Temperature and Humidity Vs. Hour at 1st August 2000.... 31 4.3 Active Power, Temperature and Humidity Vs. Hour at 1st February 2000…. 33 4.4 Reactive Power, Temperature and Humidity Vs. Hour at 1st February 2000 34 4.5 Power verses Temperature Summer 2001 at 2 am………………………….. 37 4.6 Power verses Temperature Summer 2001 at 10 am………………………... 38 4.7 Power verses Temperature Summer 2001 at 2 pm………………………….. 39 4.8 Power verses Temperature Summer 2001 at 11 pm………………………… 40 4.9 Power verses Temperature Winter 2001 at 2 am………….………………... 41 4.10 Power verses Temperature Winter 2001 at 2 pm…………………………… 42 5.1 Space Heating Heat Pump Characteristics ……………….………………... 46 5.2 Residential Load Model Development Steps ….…….……………….......... 57 5.3 Error Bar for the Active Power Model for 1998 August at 2 pm.…………. 74 5.4 Error Bar for the Active Power Model for 1999 August at 2 pm.…………. 75

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5.5 Error Bar for the Active Power Model for 2000 August at 2 pm.…………. 76 5.6 Error Bar for the Active Power Model for 2001 August at 2 pm.…………. 77 5.7 Error Bar for the Reactive Power Model for 1998 August at 2 pm.……….. 78 5.8 Error Bar for the Reactive Power Model for 1999 August at 2 pm.……….. 79 5.9 Error Bar for the Reactive Power Model for 2000 August at 2 pm.……….. 80 5.10 Error Bar for the Reactive Power Model for 2001 August at 2 pm.……….. 81 5.11 Actual and Forecasted Active Power of Agrabia Substation for 2002

August at 2 pm…………………………………………………………….. 85

5.12 Actual and Forecasted Reactive Power of Agrabia Substation for 2002

August at 2 pm…………………………………………………………….. 86

5.13 Actual and Simulated Active Power of Bayonia Substation for 2001 June

at 2 am……………………………………………………………………... 88

5.14 Actual and Simulated Reactive Power of Bayonia Substation for 2001

June at 2 am……………………………………………………………….. 89

5.15 Actual and Simulated Active Power of Bayonia Substation for 2001

August at 2 pm…………………………………………………………….. 90

5.16 Actual and Simulated Reactive Power of Bayonia Substation for 2001

August at 2 pm…………………………………………………………….. 91

5.17 Error Bar for the Active Power of Bayonia for 2001 June at 2 am………… 92 5.18 Error Bar for the Reactive Power of Bayonia for 2001 June at 2 am……… 93 5.19 Error Bar for the Active Power of Bayonia for 2001 August at 2 pm……... 94 5.20 Error Bar for the Reactive Power of Bayonia for 2001 August at 2 pm…… 95 C.1 Error Bar for the Active Power Model for 1998 June at 2 am……………... 141 C.2 Error Bar for the Reactive Power Model for 1998 June at 2 am…………… 142 C.3 Error Bar for the Active Power Model for 1998 June at 2 pm……………... 143 C.4 Error Bar for the Reactive Power Model for 1998 June at 2 pm…………… 144

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C.5 Error Bar for the Active Power Model for 1999 June at 2 am……………... 145 C.6 Error Bar for the Reactive Power Model for 1999 June at 2 am…………… 146 C.7 Error Bar for the Active Power Model for 1999 June at 2 pm……………... 147 C.8 Error Bar for the Reactive Power Model for 1999 June at 2 pm…………… 148 C.9 Error Bar for the Active Power Model for 2000 June at 2 am……………... 149 C.10 Error Bar for the Reactive Power Model for 2000 June at 2 am…………. 150 C.11 Error Bar for the Active Power Model for 2000 June at 2 pm……………. 151 C.12 Error Bar for the Reactive Power Model for 2000 June at 2 pm…………. 152 C.13 Error Bar for the Active Power Model for 2001 June at 2 am….………... 153 C.14 Error Bar for the Reactive Power Model for 2001 June at 2 am…………. 154 C.15 Error Bar for the Active Power Model for 2001 June at 2 pm……………. 155 C.16 Error Bar for the Reactive Power Model for 2001 June at 2 pm…………. 156 C.17 Error Bar for the Active Power Model for 1998 July at 2 am…………... 157 C.18 Error Bar for the Reactive Power Model for 1998 July at 2 am………… 158 C.19 Error Bar for the Active Power Model for 1998 July at 2 pm…………….. 159 C.20 Error Bar for the Reactive Power Model for 1998 July at 2 pm………… 160 C.21 Error Bar for the Active Power Model for 1999 July at 2 am…………... 161 C.22 Error Bar for the Reactive Power Model for 1999 July at 2 am………… 162 C.23 Error Bar for the Active Power Model for 1999 July at 2 pm…………... 163 C.24 Error Bar for the Reactive Power Model for 1999 July at 2 pm………… 164 C.25 Error Bar for the Active Power Model for 2000 July at 2 am…………... 165 C.26 Error Bar for the Reactive Power Model for 2000 July at 2 am…………. 166 C.27 Error Bar for the Active Power Model for 2000 July at 2 pm……………. 167

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C.28 Error Bar for the Reactive Power Model for 2000 July at 2 pm…………. 168 C.29 Error Bar for the Active Power Model for 2001 July at 2 am….………... 169 C.30 Error Bar for the Reactive Power Model for 2001 July at 2 am…………. 170 C.31 Error Bar for the Active Power Model for 2001 July at 2 pm……………. 171 C.32 Error Bar for the Reactive Power Model for 2001 July at 2 pm…………. 172 C.33 Error Bar for the Active Power Model for 1998 August at 2 am…………. 173 C.34 Error Bar for the Reactive Power Model for 1998 August at 2 am………. 174 C.35 Error Bar for the Active Power Model for 1999 August at 2 am…………. 175 C.36 Error Bar for the Reactive Power Model for 1999 August at 2 am………. 176 C.37 Error Bar for the Active Power Model for 2000 August at 2 am…………. 177 C.38 Error Bar for the Reactive Power Model for 2000 August at 2 am………. 178 C.39 Error Bar for the Active Power Model for 2001 August at 2 am….……… 179 C.40 Error Bar for the Reactive Power Model for 2001 August at 2 am………. 180 C.41 Error Bar for the Active Power Model for 1998 September at 2 am……… 181 C.42 Error Bar for the Reactive Power Model for 1998 September at 2 am…… 182 C.43 Error Bar for the Active Power Model for 1998 September at 2 pm……... 183 C.44 Error Bar for the Reactive Power Model for 1998 September at 2 pm…… 184 C.45 Error Bar for the Active Power Model for 1999 September at 2 am……… 185 C.46 Error Bar for the Reactive Power Model for 1999 September at 2 am…… 186 C.47 Error Bar for the Active Power Model for 1999 September at 2 pm…….. 187 C.48 Error Bar for the Reactive Power Model for 1999 September at 2 pm…… 188 C.49 Error Bar for the Active Power Model for 2000 September at 2 am……… 189 C.50 Error Bar for the Reactive Power Model for 2000 September at 2 am…… 190 C.51 Error Bar for the Active Power Model for 2000 September at 2 pm…….. 191

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C.52 Error Bar for the Reactive Power Model for 2000 September at 2 pm…… 192 C.53 Error Bar for the Active Power Model for 2001 September at 2 am….….. 193 C.54 Error Bar for the Reactive Power Model for 2001 September at 2 am…… 194 C.55 Error Bar for the Active Power Model for 2001 September at 2 pm…….. 195 C.56 Error Bar for the Reactive Power Model for 2001 September at 2 pm…… 196

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Abstract Name : Khaled Hamed Abdullah Al-Ghamdi

Title : Environmental Impact on Residential Load Modeling

Major Field : Electrical Engineering

Date of Degree : May 2003

Residential loads in Gulf area are highly affected by environmental conditions. The drastically changeable weather conditions in particular ambient temperature and relative humidity influence the residential air-conditioning demand. This thesis presents the derived mathematical form of power system loads that reflect the environmental conditions namely temperature and relative humidity. Large amount of measured data for several years (year 1998 to year 2002) have been collected. These data concern a highly hot and humid area at the eastern province in Saudi Arabia. Typical data for residential load models has been selected. The data have been selected to reflect the impact of temperature and relative humidity at steady voltage and at constant frequency. Throughout the analysis, observations and investigations of the data the sensitivity of power demand to temperature and relative humidity has shown the natural expected behavior. The derived mathematical models have shown a non-linear relation of the power demand with temperature as well with relative humidity and a coupling between temperature and humidity. These formulated Load models have been tested and validated.

MASTER OF SCIENCE DEGREE King Fahd University of Petroleum and Minerals

Dhahran, Saudi Arabia May 2003

xvi

خالصة الرسالة

الـغـامديعبدا هللاخـالد حـامد : اسم الطالب

الجوية على استهالك الطاقة السكنيةاألحوالتأثير : عنوان الرسالة

ةكهر بائيهندسة : التخصص

هـ١٤٢٤ األولربيع : تاريخ الشهادة

ومن هذه األحوال التغيير العنيف . المحيطة بهاتتأثر األحمال الكهربائية السكنية في منطقة الخليج باألحوال البيئية الطقس وخصوصاً درجة الحرارة ودرجة الرطوبة النسبية، حيث تأثر على استهالك الطاقة الكهربائية أحوالفي

.للمكيفات المنزلية

دامها في عملية تحليل واختبار أنظمة الطاقة هذة الرسالة تعرض عملية تمثيل األحمال الكهربائية التي يتم استخهذة . ٢٠٠٢ الي سنة ١٩٩٨ المعلومات من سنة القياسات ولقد تم جمع عدد هائل من. الكهربائية ودراستها

إن. المعلومات تعود الي منطقة في شرق المملكة العربية السعودية حيث تتصف بالحرارة والرطوبة العاليةستخدمة في هذا البحث تم جمعها وترتيبها بحيث تُبين تأثير األحوال الجوية على استهالك المعلومات والبيانات الم

. الطاقة الكهربائية السكنية دون وجود أي تغيير في الجهد والتردد

وقد بينت التحاليل والمالحظات أن حساسية العالقة بين درجة الحرارة ودرجة الرطوبة النسبية واستهالك الطاقة .ية، هي عالقة طبيعية، كما كان متوقعالكهربائ

أن العالقة بين درجة الحرارة ودرجة أوضحت النماذج الحسابية المشتقة الستهالك الطاقة الكهربائية السكنية إن

وقد تم اختبار هذة النماذج الحسابية، وذلك . معقدة رياضيةالرطوبة النسبية واستهالك الطاقة الكهربائية، هي عالقة . الناتجة من النموذج الحسابياالفتراضيةمقارنة األحمال األصلية مع األحمال عن طريق

درجة الماجسـتير في العلوم جامعـة المـلك فهـد للبـترول والمعـادن

الظهران ، المملكة العربية السعودية هـ١٤٢٤ ألولربيع ا: التاريخ

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Chapter 1

INTRODUCTION The system loads have normally been represented by constant values of active and

reactive power for power flow purposes. This is adequate for most studies, but the

response of system loads to voltage variation and environmental factors are useful in some

types of analysis.

Load modeling is important for different power system studies such as steady state,

transient stability, voltage stability and small-signal stability damping studies.

Steady state studies

Most power programs, currently in use, do not have provisions for representing the

voltage sensitivity of the load, since all loads are represented as constant MVA. This is

appropriate for baseline planning studies and for the evaluation of steady-state conditions

following contingencies, when voltage regulating devices will have returned the voltage

to near its normal value. For studies of voltages and flows immediately after

contingencies, a representation of the load’s voltage sensitivity is necessary. [1]

1

2

Transient stability studies

Transient stability studies provide information on the capability of a power system to

remain in synchronism following major disturbances, such as system faults and equipment

outages. The dynamic response of system voltages, machine angles, and power flows are

computed by numerical integration of the differential equations of the system. Loads are

usually represented by static models that are sensitive to voltage and frequency changes,

but without differential equations. Dynamic induction motor models are usually available

and have been used in the past primarily for representing large industrial or power plant

auxiliary motors. [1]

Voltage stability studies

Voltage stability is influenced by nonlinear time-variant controls (e.g. generator excitation

limiters, under-load tap-changing transformers) and load characteristics (e.g. motors),

which change with both voltage level and time. The proper representation of load is

important for system stability studies. [2]

Small-signal stability studies

Inter-area modes of oscillation, involving a number of generators widely distributed over

the power system, often results in significant variations in voltage and local frequency. In

such cases, the load voltage and frequency characteristics may have a significant effect on

the damping of the oscillations. Many studies showed that using a constant impedance

load representation in small-signal analysis tend to overestimate the damping. [3]

3

Many studies have shown that load representation can have a significant impact on results

analysis. Therefore, efforts directed at improving load modeling are of major importance.

The accurate modeling of loads continues to be a difficult task due to following factors:

• The large number of diverse load components.

• The ownership and location of load devices in customer facilities not directly

accessible to the electric utility.

• Changing load composition with time of day, week and seasons.

• The lack of precise information on the composition of the load.

• The lack of accurate system tests for identifying load models. [3,4]

Electric utility analysis and their management require evidence of the benefits of

improved load representation in order to justify the effort and expense of collecting and

processing load data and, perhaps, modifying computer program load models. The

benefits of improved load representation fall into the following categories:

A. If present load representation produces overly-pessimistic results:

1. In planning studies, the benefits of improved modeling will be in deferring or

avoiding the expense of system modifications and equipment additions.

2. In operating studies, the benefits will be in increasing power transfer limits,

with resulting economic benefits.

4

B. If present load representation produces overly-optimistic results:

1. In planning studies, the benefit of improved modeling will be in avoiding

system inadequacies that may result in costly operating limitations.

2. In operating studies, the benefit may be in preventing system emergencies

resulting from overly-optimistic operating limits.

In addition, failure to represent loads in sufficient detail may produce results that miss

significant phenomena. [3]

The residential load in Saudi Arabia is mostly affected by the weather conditions

especially in summer where the temperature and the relative humidity are varying [5, 6].

Therefore, this work was initiated to provide more realistic residential load models where

the variation of active and reactive power represented as a function of the temperature and

relative humidity, in terms of the associated model parameter estimation.

This thesis is divided into six chapters as follows

• Introduction is given in chapter 1.

• Literature review is given in chapter 2.

• Load modeling concepts and approach are presented in chapter 3.

• Problem definition and objective are discussed in chapter 4.

• Chapter five presents the load modeling results and discussion.

• Conclusions and recommendations are given in chapter 6.

5

Chapter 2

LITERATURE REVIEW Aggregate load modeling is a traditional field in power system planning; however,

modeling of residential appliance loads for use in direct load control has been a concern

for only the last decade.

Because of the high cost of the installation of new generation capacity, and the high price

of oil, several utilities have attempted to use the existing generation capacity more

efficiently by applying sophisticated direct load control strategies, rather than building

new capacity. Much research is taking place in order to develop high accuracy load

models to be used by the utilities for this purpose.

In 1984, EPRI contracted with General Electric [7], under project RP849-7, “Load

Modeling for Power Flow and Transient Stability Computer Studies,” to develop

production-grade computer programs and documentation that would provide an easy way

for electric utility engineers to prepare better load models for power flow and transient

stability studies. This has been accomplished by the development of the Load Model

Synthesis (LOADSYN) computer program package, which permits the user to develop

5

6

load models for his system with a minimum amount of data on the system loads, simply

the mix of various classes, e.g., residential, commercial, industrial. Default data, which

can be easily modified by user, is provided for the composition of each class and for the

characteristics of the load components. A Load Modeling Reference Manual was written

to assist utility engineers in gathering data and applying the software.

IEEE Task Force on load representation for dynamic performance [3] summarized the

state of the art of representation of power system loads for dynamic performance analysis

purposes. It includes definition of terminology, discussion of the importance of load

modeling, important considerations for different types of analyses. Typical load model

data and methods for acquiring data are reviewed.

Dias and Hawary [8] considered the problem of estimating the parameters of static power

system load models intended for use in load flow studies that incorporate the variation of

active and reactive power with busbar voltages. A number of load model forms are

considered, where the parameters estimation task involves the iterative solution of

nonlinear equations. The use of Newton method to obtain the parameters provided is

considered to be unsatisfactory in many instances. Alternative iterative techniques such as

the BFGS (Broyden, Fletcher, Goldfarb and Shanno) and modified BFGS methods are

explored, and computational experience using actual field data is reported in the paper.

The work reported in the paper suggests that the modified BFGS method offers more

reliable performance than the other three methods under many conditions, including

severe data noise. It is also shown that the optimal parameter set may not be unique in

certain cases, and that the initial guesses of the unknown parameters is instrumental in the

7

computational performance of the methods. Further evaluation of the results reveals that

complicated models need not necessarily be used to obtain satisfactory results.

Coker and Kgasoane [4] presented a brief overview of load model implementation in

computer simulation packages and the derivation of load models for the ESKOM

interconnected power system using a component based methodology. Also, they

compared the load models using voltage stability analysis and time domain techniques.

They conclude that application of an overly conservative load model may lead to incorrect

analysis of future loading impacts on the system. This may lead to over-investment in the

transmission system. Also, static load models can adequately represent load dynamic in

time domain simulation studies for voltage disturbances.

Hajagos and Danai [2] described laboratory measurements and derived models of modern

loads subjected to large voltage changes and their effect on voltage stability studies. Low-

voltage, long-time models of such loads as modern air conditioners, discharge lighting,

and devices containing electronic regulated power supplies were developed. One means

used by utilities to avert voltage collapse has been system voltage reduction. The

characteristics of modern loads and controls reduce the effectiveness of this voltage

reduction. The results indicate the importance using accurate load models, especially for

large industrial loads where the load composition can be identified.

Baghzouz and Quist [9] presented some field data illustrating the response of several

types of load to small voltage deviations. Model parameters were derived from these

measurements for each load type using curve-fitting techniques for both of its static and

8

dynamic components. The results of modeling indicate that the pure residential and

combined residential/commercial load have a static component, followed by a significant

dynamic component with an unexpectedly large time constant. However, these load

responses are not entirely due to the staged voltage disturbance, but also to the

uncontrollable high voltage and natural load variations that took place during the test

period. Correlation of multiple measurements is necessary to minimize the effect of these

fluctuations.

Ohyama, Watanabe, Nishimura and Tsuuta [10] presented the voltage dependence of

composite loads in power systems. Based upon continuous field measurements by

automatic monitoring devices, dynamic responses of typical system loads to sudden

voltage changes have been obtained. The residential, commercial and industrial loads

show a remarkable difference in their responses to both small voltage changes and voltage

drops due to faults. The load parameters for active power vary daily and annually. The

variations are influenced by the working rate of motor loads such as air-conditioners and

refrigerators. The parameters for reactive power are affected by the VAR compensation,

but no substantial correlation to season was found.

In reference [11] a broad-based bibliography on load modeling papers complements the

IEEE Task Force paper analyzing and organizing standardized load models. Papers listed

are categorized based on the applications of the load models discussed. A set of tables

supplements the paper categories by illustrating load models presented in multiple papers

and generalized models from which other models are derived. The tables also list

experimental results reported in the papers to verify the load models.

9

Finally, in reference [12] a composite multiregression-decomposition model is developed

to predict the monthly peak demand of a typical fast growing utility faced with high

annual growth, namely the Saudi Electric Company-Central Region Branch of Kingdom

of Saudi Arabia (SCE-CRB). The authors highlighted that Riyadh system peak demand is

dominated by the residential demand that is mainly used for air conditioning and is

therefore highly influenced by ambient temperatures. The developed model has the

advantage of simulations and cyclic effects, such as Ramadan, Eid and Hajj effects, etc.

10

Chapter 3

LOAD MODELING CONCEPTS AND

APPROACH 3.1 Basic Load Modeling Concepts

This section provides basic definitions and concepts related to load modeling.

LOAD- the term “load” can have several meanings in power system engineering,

including:

a. A device connected to a power system that consumes power.

b. The total power (active and/or reactive) consumed by all devices connected to

a power system.

c. A portion of the system that is not explicitly represented in a system model,

but rather is treated as if it was a single power-consuming device connected to

a bus in the system model.

d. The power output of a generator or generating plant.

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11

Where the meaning is not clear from the context, the term, “load device’, “system load”,

“bus load”, and “generator or plant load”, respectively, may be used to clarify the intent.

Definition “c” is the one that is of main concern in the present Thesis.

As illustrated in Figure 2.1, “load” in this context includes, not only the connected load

devices, but some or all of the following:

Substation Step-down transformer

Subtransmission feeders

Primary distribution feeders

Secondary distribution feeders

Shunt capacitors

Voltage regulators

Customer wiring, transformers and capacitors

In describing the composition of load, the following terms, illustrated in Figure 2.2, are

recommended:

LOAD COMPONENT – a load component is the aggregate equivalent of all devices of a

specific or similar type, e.g., water heater, room air conditioner, fluorescent lighting.

LOAD CLASS – A load class is a category of load, such as, residential, commercial, or

industrial. For load modeling purposes, it is useful to group loads into several classes,

where each class has similar load composition and load characteristics.

12

Figure 2.1: Power System Configuration

SystemFeeders

Substation Transformer

Bus A

13

Figure 2.2: Terminology for Component-Based Load Modeling

Commercial

Residential

Bus Load

LoadMix

Class Composition

Industrial

P

Q

Resistive Heat

Room Air Cond.

Lighting

Water Heater

Load Classes

Load Components

14

RESIDENTIAL LOAD – It is defined as individual residences, individual flats,

individual apartments in multiple family residences, and religious institutions receiving

separately metered service.

COMMERCIAL LOAD – It is defined as institutions involved in trade.

INDUSTRIAL LOAD – It is defined as any enterprise engaged in extractive, fabricating,

or processing activities, which yield raw or unfinished materials, or which transform such

materials into another product.

LOAD COMPOSITION – It is the fractional composition of the load by load

components. This term may be applied to the bus load or to a specific load class.

LOAD CLASS MIX – It is the fractional composition of the bus load by load classes.

LOAD CHARACTERISTIC – A set of parameters, such as power factor, variation of P

and V, etc., that characterize the behavior of a specific load. This term may be applied to a

specific load device, a load component, a load class, or the total bus load.

The following terminology is commonly used in describing different types of load

models:

15

LOAD MODEL – A load model is a mathematical representation of the relationship

between a bus voltage (magnitude and frequency), weather factor and the power (active

and reactive) or current flowing into the bus load.

STATIC LOAD MODEL – A model that expresses the active and reactive powers at any

instant of time as functions of the voltage magnitude and frequency at the same time.

Static load models are used both for essentially static load components, e.g., resistive and

lighting load, and as an approximation for dynamic load components, e.g., motor-drive

loads.

DYNAMIC LOAD MODEL – A model that expresses the active and reactive powers at

any instant of time as functions of the voltage magnitude and frequency at past instants of

time and, usually, including the present instant. Difference or differential equations can be

used to represent such models.

CONSTANT IMPEDANCE LOAD MODEL – A static load model where the power

varies directly with the square of the voltage magnitude. It may also be called a constant

admittance load model.

CONSTANT CURRENT LOAD MODEL – A static load model where the power

varies directly with the voltage magnitude.

CONSTANT POWER LOAD MODEL – A static load model where the power does not

vary with changes in voltage magnitude. It may also be called constant MVA load model.

16

Because constant MVA devices, such as motors and electronic devices do not maintain

this characteristic below some voltage (typically 80 to 90%), many load models provide

for changing constant MVA (and other static models) to constant impedance or tripping

the load below a specified voltage. [1, 3, 7]

In the coming sections a brief overview of load model theory, load model derivation and

load model parameter estimation will be presented.

3.2 Load Model Theory

Two main approaches to load model development have been considered by the electric

utility industry:

“Measurement-based models” and “Component-based models.”

The measurement-based approach involves placing monitors at various load substations to

determine the sensitivity of load active and reactive power to voltage, frequency and

weather variations to be used directly or to identify parameters for more detailed load

models [1, 7].

The purpose of the component-based approach is to develop load models by aggregating

models of the individual components forming the load. Individual components

characteristics have been determined by theoretical and laboratory analysis and have been

17

extensively reported in literature. This approach is shown schematically in Figure 2.2 in

section 2 [4].

3.3 Load Model Derivation

The load at a bus in a power flow study can be represented as a function of voltage in a

number of ways.

• Polynomial Load Model

A static load model that represents the power relationship to voltage magnitude as a

polynomial equation, usually in the following form:

+

+

= 32

2

1 aVVa

VVaPP

ooo [3.1]

+

+

= 65

2

4 aVVa

VVaQQ

ooo [3.2]

The parameters of this model are the coefficients (a1 to a6) and the power factor of the

load. This model is sometimes referred to as the “ZIP” model, since it consists of the sum

of constant impedance (Z), constant current (I), and constant power (P) terms. If this, or

other, models are used for representing a specific load device, and Po and Qo should be the

power consumed at rated voltage Vo. However, when using these models for representing

18

a bus load, Vo, Po, and Qo are normally taken as the values at the initial system operating

condition for the study. [3]

• Exponential Load Model

A static load model that represents the power relationship to voltage as an exponential

equation, usually in the following form:

np

ooA V

VPP

=

[3.3]

np

ooA V

VQQ

=

[3.4]

Where

PA, QA = Actual real and reactive load powers

Po, Qo = Nominal real and reactive load powers

Vo = Nominal voltage at which Po, Qo are calculated

V = Actual voltage

np = Real power voltage exponent

nq = Reactive power voltage exponent

The parameters (np and nq) determine which load model is used to represent the load

power viz.

19

np = nq = 2

This is commonly called the constant impedance load model (Z) where the load power

varies directly with the square of the voltage magnitude. It may also be called a constant

admittance model. At below nominal voltages, this type of load will draw less current.

The opposite applies at above nominal voltages. Constant current loads will have a

tendency to decrease (or reduce) voltage oscillations on a system.

np = nq = 1

This is commonly called the constant current load model (I) where the load power varies

directly with the voltage magnitude. It has been accepted that, in the absence of data,

composite loads can be approximated using a constant current load model.

np = nq = 0

This is commonly called the constant power load model (P) where the load power does

not vary with changes in the voltage magnitude. It may also be called a constant MVA

model. This type of load draws higher current under low voltage conditions to maintain

constant power. It is thus very onerous on the system. [4]

• Frequency-Dependent Load Model

A static load model that includes frequency dependence. This is usually represented by

multiplying either a polynomial or exponential load model by a factor of the following

form:

20

( )[ ]of ffa −+1 [3.5]

where f is the frequency of the bus voltage, fo is the rated frequency, and af is the

frequency sensitivity parameter of the model. [3]

Examples of Load Models of Previous Forms

Example of ZIP Model

In reference [2], ZIP load models derived from measurements.

+

+

= P

oP

oPototal P

VVI

VVZPP ***

2

[3.6]

+

+

= q

oq

oqototal P

VVI

VVZQQ ***

2

[3.7]

where Z, I and P are constant impedance, constant current and constant power fractions

respectively.

The ZIP model is appropriate for both steady-state and dynamic studies for voltages above

the minimum voltage (Vmin).

21

Example of Exponential Load Model

In reference [13], the following load model is employed.

pnVKP *= [3.8]

qnno VKKQ *+= [3.9]

∆

∆

=

o

op

VV

PP

n [3.10]

∆

∆

=

o

oq

VV

QQ

n [3.11]

where

np = voltage slope of active power.

nq = voltage slope of reactive power.

Ko = initial power value.

Kn = voltage-dependent gain.

22

Table 3.1 shows the comparison of the load parameters among three types of system loads

already mentioned. When the parameters nq was calculated, the absolute of Ko was

assumed to be equal to the apparent power. For the industrial load, the value of parameter

np is approximately zero, indicating that this load is predominantly occupied by induction

motors. The parameter np of the residential/commercial load is close to 2.0. this is because

the load contains predominantly constant impedance load elements. The parameter np of

the building load is 1.5, showing that various kind of load element are included in this

load [10].

These values of parameters correspond to the features of the three types of load, which

were seen in the comparison of power responses.

From this result, it is obvious that the characteristics of the system load are closely

associated with its load composition. The values of parameters, therefore, vary according

to the variation in working rate of the load elements. For example, an increase in the

power consumed by air-conditioners may lower the load parameter of the total composite

load.

23

Table 3.1: Comparison Among Load Parameters Of Various Kinds Of Typical

System Load

Kind of load np nq Season

Industrial 0.2 0.6 September night & day

Residential/ Commercial 1.9 1.6 January & April

Night

Building 1.5 1.5 January night

24

Example of Voltage and Frequency-Dependent Loads

Voltage and frequency-dependent loads such as televisions and fluorescent lighting are

simulated by passive elements and a current source (figure 3.1), which is adjusted to

satisfy the following formulas:

( )

−+

=

o

op

N

oo f

ffK

VVPP

p

1 [3.12]

( )

−+

=

o

oq

N

oo f

ffK

VVQQ

q

1 [3.13]

In reference [11], there is many load models summarized from many different cases in

previous work done in this field.

25

Figure 3.1: EMTP (Electromagnetic Transient Program) Voltage and Frequency-

Dependent Static Loads

Vo,Po,Qo

V & f Measurement

Is = f (V,f) R=Vo2/Po X=Vo

2/Qo

P , Q

26

3.4 Load Model Parameter Estimation

Parameter estimation techniques are used for evaluating the required model parameters.

Many iterative computational methods are considered in load model parameters

estimation:

(i). Newton Method

(ii). Modified Newton method

(iii). Broyden, Fletcher, Goldfarb and Shanno (BFGS) method

(iv). Modified BFGS method

The first method, or Newton method, is well known in the power systems engineering

area. The second method is a modification of the Newton method such that after each

iteration the updated values of the coefficients are discarded, and new values for the

coefficients are calculated using the current exponents so as to obtain a minimum sum of

the squares of the error (SSE). The third method is an extension to the Newton method

devised by Broyden, Fletcher, Goldfarb and Shanno and it is commonly referred to as the

BFGS method. The BFGS method is recommended in cases where the standard Newton

method fails to converge. This method employs a line search that steers the iterations in

the required direction and often converges even if the regular Newton method fails.

Fourth method is the same as third method (BFGS method) with similar modification as

in second method (Modified Newton method). [8]

27

Genetic algorithms (GA) methods also used in load modeling or parameter estimation.

GA is search algorithms for finding the optimum solutions of maximization problems. GA

simulates the natural selection mechanism of biological systems such as reproduction,

crossover and mutation. The main features of GA are a coding of the parameter set in the

problem, a multi-point search algorithm, no necessity of the information about the

derivative of objective function, and the probabilistic transition rules. These features

contribute to a genetic algorithm’s robustness and increase the likelihood of finding the

global optimal solution. [13]

Also, load parameters are derived from existing data using curve-fitting techniques for

both of static and dynamic components. Based on many graphs for developing models

describing load responses to weather variations is a load-weather correlation curves; i.e., a

plot of real and reactive powers as functions of weather. Least squared error curve fitting

is one of the methods used parameter estimation. [9]

28

Chapter 4

PROBLEM DEFINITION AND

OBJECTIVE In the coming sections and overview of problem definition and objective will be

presented.

4.1 Problem Definition

Of all the other factors that give rise to system peak demand, weather is the main factor,

which dictates the peak load significantly. If other contributing factors to peak load are

neglected the system demand will move in harmony with ambient temperatures and

humidity, and the peak demand will occur during the period of high temperatures and/or

high humidity.

Tables 4.1 and 4.2 show sample of load research data brought from utility. Figures 4.1

and 4.3 show the plots of active power, temperature and humidity versus time (hour).

Where as figures 4.2 and 4.4 show the plots of reactive power, temperature and humidity

versus time (hour)

28

29

Table 4.1: Load Data of AGRABIA Substation 1st August 2000

Hour Frequency Temperature Humidity Agrabia Substation Power Current

HZ C % kV MW MVAR Factor A 1 60 32.8 57 14.2 40 17 0.92 1773 2 60 31.7 77 14.2 39 17 0.92 1736 3 60 30.6 84 14.2 37 16 0.92 1645 4 60 31.1 76 14.2 36 16 0.91 1607 5 60 30.0 82 14.1 35 15 0.92 1556 6 60 32.2 69 14.1 33 15 0.91 1481 7 60 33.9 54 14.1 34 15 0.91 1518 8 60 36.1 29 14.1 37 17 0.91 1664 9 60 38.3 22 14.1 41 19 0.91 1846

10 60 41.1 14 14.2 43 19 0.91 1918 11 60 43.9 8 14.2 44 20 0.91 1972 12 60 44.4 8 14.2 43 19 0.91 1918 13 60 43.9 18 14.2 44 19 0.92 1956 14 60 44.4 11 14.2 44 19 0.92 1956 15 60 42.8 19 14.2 44 18 0.93 1940 16 60 43.3 15 14.2 44 19 0.92 1956 17 60 40.6 25 14.2 46 21 0.91 2063 18 60 39.4 27 14.2 46 21 0.91 2063 19 60 36.7 53 14.1 49 23 0.91 2220 20 60 36.7 45 14.2 47 23 0.90 2130 21 60 35.0 63 14.2 46 22 0.90 2076 22 60 33.3 72 14.2 44 21 0.90 1985 23 60 33.3 73 14.2 43 20 0.91 1931 24 60 33.9 62 14.1 42 18 0.92 1868

30

Figure 4.1: Active Power, Temperature and Humidity Vs. Hour at 1st August 2000

0

20

40

60

80

100

1 4 7 10 13 16 19 22

Hour

Act

ive

Pow

er T

empe

ratu

re &

Hum

idity

Temperature (C)Humidity (%)Power (MW)

31

Figure 4.2: Reactive Power, Temperature and Humidity Vs. Hour at 1st August 2000

0

20

40

60

80

100

1 4 7 10 13 16 19 22

Hour

Rea

ctiv

e Po

wer

Tem

pera

ture

& H

umid

ity

Temeprature (C)Humidity (%)Power (MVAR)

32

Table 4.2: Load Data of AGRABIA Substation 1st February 2000

Hour Frequency Temperature Humidity Agrabia Substation Power Current

HZ C % kV MW MVAR

Factor A 1 60 8.9 79 14.1 12 5 0.92 534 2 60 8.3 80 14.1 10 5 0.89 459 3 60 6.7 82 14.1 10 4 0.93 442 4 60 7.2 78 14.1 10 4 0.93 442 5 60 7.8 74 14.1 10 4 0.93 442 6 60 8.9 65 14.1 13 5 0.93 572 7 60 10.0 60 14.1 15 5 0.95 649 8 60 11.1 55 14.1 15 6 0.93 662 9 60 13.9 51 14.1 16 7 0.92 714

10 60 15.6 46 14.0 17 8 0.90 773 11 60 18.3 43 14.0 18 8 0.91 811 12 60 19.4 30 14.1 16 7 0.92 717 13 60 19.4 37 14.0 16 7 0.92 719 14 60 19.4 33 14.1 16 6 0.94 701 15 60 18.9 46 14.1 15 6 0.93 662 16 60 17.2 52 14.1 18 8 0.91 808 17 60 16.7 60 14.1 21 10 0.90 954 18 60 16.1 62 14.0 24 12 0.89 1103 19 60 16.1 64 14.1 22 11 0.89 1004 20 60 15.6 66 14.0 23 11 0.90 1049 21 60 15.0 68 14.1 22 11 0.89 1011 22 60 14.4 69 14.2 21 10 0.90 949 23 60 13.9 70 14.1 18 8 0.91 808 24 60 12.8 72 14.1 14 6 0.92 625

33

Figure 4.3: Active Power, Temperature and Humidity Vs. Hour at 1st February 2000

0

20

40

60

80

100

1 4 7 10 13 16 19 22

Hour

Act

ive

Pow

erTe

mpe

ratu

re &

Hum

idity

Temperature (C)Humidity (%)Power (MW)

34

Figure 4.4: Reactive Power, Temperature and Humidity Vs. Hour at 1st February

2000

0

20

40

60

80

100

1 4 7 10 13 16 19 22

Hour

Rea

ctiv

e Po

we

Tem

pera

ture

& H

umid

i t

Temperature (C)Humidity (%)Power (MVAR)

35

As can be seen from figure 4.1 (summer example), the power consumption is following

the temperature rises. Figure 4.1 also shows that temperature effect is more dominant than

the relative humidity effect.

As shown in figure 4.3 (winter example) the power consumption is reduced during the

winter almost by the half. Moreover, it can be seen that the humidity effect is not

significant.

Figures 4.2 and 4.4, which are for the reactive power consumption, confirm that the

reactive power consumption also effected by weather condition. The reactive power

consumed in summer is almost double the one consumed in winter. This high increase is

due to the air conditioning load.

Figures 4.5 to 4.8 show the plots of active power versus temperature where the change in

relative humidity is limited with small interval for summer period. These figures illustrate

four different cases of environmental impact on residential load consumption.

First case is shown in figure 4.5 where the temperature is low and the relative humidity is

high. So, the power consumption is low. Figure 4.6 shows the second case where the

temperature is moderate and the relative humidity is low. In this case the power demand

start to increase due to the increase in the temperature. The maximum temperature is

occurring in the third case where the relative humidity is low. It can be seen from figure

4.7 that the power consumption is reaching their maximum value compared to the other

36

cases. In the last case, average power consumption is shown in figure 4.8 due to moderate

temperature and varying relative humidity.

Figures 4.9 and 4.10 show the plots of active power versus temperature where the change

in relative humidity is limited with small interval for winter period. These figures

represent two different cases.

In the first case, the temperature is low and the relative humidity is high. However, in the

second case both the temperature and the relative humidity are low. In both cases the

power consumptions can be assumed constant.

On an hourly basis, the large dependence of the load demand on temperature is quit

apparent as shown in the previous figures. However, preliminary analyses indicate that the

relative humidity is not a major determinant of the maximum demand requirements of

residential customers. Also, this is the conclusion approached by utility engineers [5, 6].

Hourly load profiles also show that maximum demand increases in summer because of the

dominant air conditioning load.

In summary, the summer figures reveal that the residential loads are relatively more

sensitive to the change in temperature than the change in the relative humidity. However,

the temperature variations during the winter have minor effect on the power requirements.

This is because the power requirement for heating purposes during the winter season is

not significant.

37

Figure 4.5: Power versus Temperature Summer 2001 at 2 am

38

Figure 4.6: Power versus Temperature Summer 2001 at 10 am

39

Figure 4.7: Power versus Temperature Summer 2001 at 2 pm

40

Figure 4.8: Power versus Temperature Summer 2001 at 11 pm

41

Figure 4.9: Power versus Temperature Winter 2001 at 2 am

42

Figure 4.10: Power versus Temperature Winter 2001 at 2 pm

43

4.2 Objective

In the previous section a detailed discussion about the power demand relation with

temperature and relative humidity was presented. This relation cannot be shown by a

simpler straight-line model, since the plots show a non-linear relation between power

demand, temperature and relative humidity.

The aim of this work is to find forms of power system static load models representing the

variation of active and reactive power with the temperature and relative humidity, in term

of the associated model parameter estimation.

The load model selected for parameter estimation in this research is the polynomial load

model (Equation 3.1 and 3.2) where the active and reactive power is function of

temperature and relative humidity. Also, equations 4.1 and 4.2 show a brief formulation of

this relation.

( )HTFP ,= [4.1]

( )HTFQ ,= [4.2]

In the next chapter, the active and reactive power models results and discussion will be

presented in more details.

44

Chapter 5

LOAD MODEL RESULTS AND

DISCUSSION

This chapter gives a detail discussion about the process, procedure, formulation and

testing of load modeling derivation.

5.1 Parameter Estimation Method

One of the most important problems in technical computing is the solution of

simultaneous linear equations [14]. In matrix notation, this problem can be stated as

Ax=B. Similar considerations apply to sets of nonlinear equations with more than one

unknown. MATLAB solves such equations without computing the inverse of the matrix.

Identification of the coefficient of the function often leads to the formulation of an over-

determined system of simultaneous nonlinear equations for experimental data and field

measurement data.

44

45

Over-determined systems of simultaneous nonlinear equations Ax=B obtained with A as

non-square matrix, x is the coefficients vector and B is the field data points. Therefore

solves for unknown coefficients by performing a least squares solution is achieved using a

QR factorization technique which allows the minimization of ||Ax-B||. [15]

Multiple regression solves for unknown coefficients by performing a least squares fit.

Construct and solve the set of simultaneous equations by forming the regression matrix

and solving for the coefficients using the backslash operator. The coming section

illustrates the multiple regression method with an example.

5.2 EPRI Load Model Example

The following example is taken from EPRI report [7]. EPRI derived the model for this

example using their program LOADSYN (Load Model Synthesis program package),

which was developed to convert load composition and load characteristic data into

parameters required for the power flow and transient stability programs.

This example is for a heat pump, which consists of a resistance heater and a single-phase

central air conditioner. These devices have characteristics as shown in figure 5.1, which

were taken from EPRI report. Table 5.1 shows the data for voltage (V), frequency (f),

active power (P), reactive power (Q) and power (KVA) of this heat pump.

An assumed model structure is given in equations 5.1 and 5.2, where VR, fR are equal to

one.

46

(a) Resistance Heater

(b) Single-Phase Central Air Conditioner

Figure 5.1: Space Heating Heat Pump Characteristics

47

( ) ( ) ( ) ( ) ( )( )RRRRRR ffVVcffbVVaVVaVVaaP −−+−+−+−+−+= 113

32

210 [5.1]

( ) ( ) ( ) ( ) ( )( )RRRRRR ffVVcffbVVaVVaVVaaQ −−+−+−+−+−+= 113

32

210 [5.2]

This model structure is used because it is the same model structure used by EPRI. Also, to

compare the model will be derived with the model derived by EPRI.

As explained in section 5.1 solves for unknown coefficients a0, a1, a2, a3, b1, and c1 by

performing a least squares technique (QR factorization technique). Construct and solve

the set of simultaneous equations by forming the matrix X and solving for the coefficients.

V = V – VR

F = f - fR

X = [ones(size(V)) V V2 V3 F V*F]

Table 5.2 shows the complete data of matrix X. Therefore, the complete models are:

FVFVVVP 0886.28690.07778.85994.11942.09640.0 32 −+−++= [5.3]

FVFVVVQ 1200.96240.03111.67695.65380.02340.0 32 −−−++= [5.4]

The model, thus obtained, is same as the model obtained by EPRI. So, the load model

parameters estimated without any error by using different approach than the EPRI used.

48

Table 5.1: Load Data of The Heat Pump

V f P Q KVA

1.15 1.00 0.9995 0.4457 1.0944 1.10 1.00 0.9907 0.3492 1.0504 1.05 1.00 0.9766 0.2770 1.0151 1.00 1.00 0.9640 0.2340 0.9920 0.95 1.00 0.9594 0.2248 0.9854 0.90 1.00 0.9694 0.2542 1.0022 0.85 1.00 1.0005 0.3269 1.0526 1.15 1.05 1.0273 0.3461 1.0840 1.10 1.05 1.0237 0.2724 1.0593 1.05 1.05 1.0148 0.2230 1.0390 1.00 1.05 1.0075 0.2028 1.0277 0.95 1.05 1.0081 0.2164 1.0311 0.90 1.05 1.0233 0.2686 1.0580 0.85 1.05 1.0596 0.3641 1.1204 1.15 0.95 0.9717 0.5453 1.1142 1.10 0.95 0.9577 0.4260 1.0482 1.05 0.95 0.9384 0.3310 0.9951 1.00 0.95 0.9206 0.2652 0.9580 0.95 0.95 0.9107 0.2291 0.9391 0.90 0.95 0.9155 0.2398 0.9464 0.85 0.95 0.9414 0.2897 0.9850

49

Table 5.2: Data of Matrix X for EPRI Example

Ones V V2 V3 F V*F

1.0000 0.1500 0.0225 0.0034 0.0000 0.0000 1.0000 0.1000 0.0100 0.0010 0.0000 0.0000 1.0000 0.0500 0.0025 0.0001 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 -0.0500 0.0025 -0.0001 0.0000 0.0000 1.0000 -0.1000 0.0100 -0.0010 0.0000 0.0000 1.0000 -0.1500 0.0225 -0.0034 0.0000 0.0000 1.0000 0.1500 0.0225 0.0034 0.0500 0.0075 1.0000 0.1000 0.0100 0.0010 0.0500 0.0050 1.0000 0.0500 0.0025 0.0001 0.0500 0.0025 1.0000 0.0000 0.0000 0.0000 0.0500 0.0000 1.0000 -0.0500 0.0025 -0.0001 0.0500 -0.0025 1.0000 -0.1000 0.0100 -0.0010 0.0500 -0.0050 1.0000 -0.1500 0.0225 -0.0034 0.0500 -0.0075 1.0000 0.1500 0.0225 0.0034 -0.0500 -0.0075 1.0000 0.1000 0.0100 0.0010 -0.0500 -0.0050 1.0000 0.0500 0.0025 0.0001 -0.0500 -0.0025 1.0000 0.0000 0.0000 0.0000 -0.0500 0.0000 1.0000 -0.0500 0.0025 -0.0001 -0.0500 0.0025 1.0000 -0.1000 0.0100 -0.0010 -0.0500 0.0050 1.0000 -0.1500 0.0225 -0.0034 -0.0500 0.0075

50

5.3 Load Modeling Structure Selection

As mentioned in chapter four the power demand is more affected by the temperature

change. Also, it was mentioned that the relation between power demand, temperature and

relative humidity couldn’t be shown by a simpler straight-line model, since the plots show

a non-linear relations. So, selecting appropriate load model structure for active and

reactive power demand can be started from these points.

Tables 5.3 and 5.4 show different types of active and reactive power demand load model

structures. Also, appendix-A gives more detailed information about these models.

Models G in both tables 5.3 and 5.4 were selected based on the following:

• Model G gives the minimum RMS (Root Mean Square) value.

• Adding higher order terms did not reduce the RMS value.

• From a practical implementation point of view, it is clearly preferable to adopt

models of low order to reduce the computational burden in the parameter

estimation task.

51

Table 5.3: Load Model Structures for Active Power Demand

Model Name Model Structure

RMS

Value

A 2210 TaTaaP ∗+∗+= 0.026

B 33

2210 TaTaTaaP ∗+∗+∗+= 0.027

C 44

33

2210 TaTaTaTaaP ∗+∗+∗+∗+= 0.085

D HbTaTaaP ∗+∗+∗+= 12

210 0.023

E 221

2210 HbHbTaTaaP ∗+∗+∗+∗+= 0.022

F 33

221

2210 HbHbHbTaTaaP ∗+∗+∗+∗+∗+= 0.022

G THcHbHbTaTaaP ∗∗+∗+∗+∗+∗+= 12

212

210 0.021

H HTcTHcHbHbTaTaaP ∗∗+∗∗+∗+∗+∗+∗+= 221

221

2210 0.021

I 221

221

2210 HTcTHcHbHbTaTaaP ∗∗+∗∗+∗+∗+∗+∗+= 0.021

J 2221

221

2210 HTcTHcHbHbTaTaaP ∗∗+∗∗+∗+∗+∗+∗+= 0.021

K 221

221

2210 HTcHbHbTaTaaP ∗∗+∗+∗+∗+∗+= 0.021

52

Table 5.4: Load Model Structures for Reactive Power Demand

Model Name Model Structure

RMS

Value

A 2210 TaTaaQ ∗+∗+= 0.043

B 33

2210 TaTaTaaQ ∗+∗+∗+= 0.044

C 44

33

2210 TaTaTaTaaQ ∗+∗+∗+∗+= 1.109

D HbTaTaaQ ∗+∗+∗+= 12

210 0.042

E 221

2210 HbHbTaTaaQ ∗+∗+∗+∗+= 0.037

F 33

221

2210 HbHbHbTaTaaQ ∗+∗+∗+∗+∗+= 0.036

G THcHbHbTaTaaQ ∗∗+∗+∗+∗+∗+= 12

212

210 0.036

H HTcTHcHbHbTaTaaQ ∗∗+∗∗+∗+∗+∗+∗+= 221

221

2210 0.035

I 221

221

2210 HTcTHcHbHbTaTaaQ ∗∗+∗∗+∗+∗+∗+∗+= 0.036

J 2221

221

2210 HTcTHcHbHbTaTaaQ ∗∗+∗∗+∗+∗+∗+∗+= 0.036

K 221

221

2210 HTcHbHbTaTaaQ ∗∗+∗+∗+∗+∗+= 0.036

53

5.4 Data For Load Modeling

One of the major important parts of this research is the data collection and manipulation.

This section discusses the data for load models, including both measurement-based and

component-based methods of obtaining data. Selected data is also discussed.

5.4.1 Basic Approaches to Obtain Data

As discussed briefly in chapter three, there are two basic approaches to obtain data for

load modeling measurement-based data and component-based data. The measurement-

based approach is to directly measure the voltage, frequency and weather conditions

sensitivity of active and reactive power at represented substations and feeders. The

component-based approach is to build up a composite load model from knowledge of the

mix of load classes and served by a substation, the composition of each class and typical

characteristics of each load component. [3]

• Measurement-Based Approach

Data for load modeling can be obtained by installing measurement and data acquisition

devices at points where bus load are to be represented. These devices must measure

voltage, frequency, and weather and the corresponding variation in active and reactive

power demand.

Several utilities have been developing systems to gather such data. Electricity utility in

eastern branch in Saudi Arabia uses a computerized database containing hourly data about

system generation, loads and weather [5].

54

Measurement-based techniques have the obvious advantage of obtaining data directly

from the actual system. However, there are several disadvantages, including:

Application of data gathered for load models at one substation may not only be

possible for other substations if the loads are very similar.

Determination of characteristics over a wide range of voltage and frequency may

be impractical.

Accounting for variation of load characteristics due to daily, seasonal, weather,

and end-use changes requires on-going measurements under these varying

conditions.

• Component-Based Approach

The purpose of the component-based approach is to develop load models by aggregating

models of individual components forming the load. Component characteristics, e.g., for

air conditioners, fluorescent lights, etc., can be determined by theoretical analysis and

laboratory measurements and, once determined, used by all utilities. Much of this data has

been determined and documented by EPRI project [7], although it needs to be updated for

new and redesigned load devices.

The composition-based approach to load modeling has the advantage of not requiring

field measurements and of being adaptable to different systems and conditions. Its main

disadvantage is in requiring the gathering of load class mix, and perhaps load composition

data, which are not normally used by power system analysis.

55

5.4.2 Data Selected

The residential load models reported in this research are based on available field data

which consists of five years, each of which has data points listing the temperature,

humidity, active power and reactive power versus time, for the load on a residential

substation in the Saudi Electricity Company in Eastern Region Branch (SEC-ERB).

The data is available in computerized files containing hourly data about generation,

voltage, frequency, load and weather.

For this research, the hourly demand data for the years 1998, 1999, 2000 and 2001 were

used for formulated residential load models. However, the year 2002 hourly demand data

was used for testing and validation of the formulated residential load models. The

literature [12] reveals that for such kinds of seasonal study of time series, historical data

for 5-6 years is sufficient.

As mentioned in chapter four the effect of weather in residential load is in summer period

where the temperature and relative humidity reach their maximum values. June, July,

August and September are the summer months where the variation in temperature and

relative humidity effect the power demand consumption.

In order to represent the effect of the weather condition on the residential load and

excluding any other load contributing variables, only the weekdays (Saturday, Sunday,

Monday, Tuesday and Wednesday) were included. Also, depending on the characteristics

56

and contribution of the non-temperature dependent load, hours 2 am and 2 pm were

selected. Appendix B gives a detail description of the original raw data and the selected

Agrabia substation data used to derive the residential load models.

These data has been selected to reflect the impact of temperature and relative humidity

and exclude the impact of the load variation.

5.5 Load Model Development Steps

The flow chart of the steps developed to formulate the residential load models based on

the environmental factor is shown in figure 5.2.

Initially the raw data collected from utility will be classified based on the type of the load

(industrial, residential or commercial). Then a typical data will be selected.

The typical data will be selected for the summer period including the hot and the humid

months of the year (June, July, August and September) and the hours (2 am and 2 pm)

where the temperature and humidity are varying.

The data is normalized with respect to nominal values Po, Ho, To and Qo. Then the data

will be converted from ASCII format to MATLAB data file format. Finally, the

residential load models will be derived by applying the QR factorization method in the

MATLAB program.

57

Figure 5.2: Residential Load Model Development Steps

Utility Raw Data

Classification of Load data

Industrial Load Residential Load Commercial Load

Summer Period

June

2 14

July August September

Typical Data (T, H, P &Q)

Normalization (To, Ho, Po & Qo)

Residential Load Model

Convert ASCII data to Matlab data Format

Least Square (QR Factorization Method)

2 14 2 14 2 14

58

5.6 Formulated Load Model

This section present the formulated residential load models for June, July, August and

September. The models represented by equations 5.5 and 5.6 below, which were selected

previously, are applied to historical load data for the year 1998-2001 using the parameter

estimation method explained in the section 5. After doing some preliminary analysis of

the data the power (P and Q) and weather factor (T and H) normalized with respect to

nominal values Po, Qo, To and Ho.

+

+

+

+

+=

ooooooo HH

TTa

HHa

HHa

TTa

TTaa

PP

5

2

43

2

210 [5.5]

+

+

+

+

+=

ooooooo HH

TTb

HHb

HHb

TTb

TTbb

QQ

5

2

43

2

210 [5.6]

5.6.1 Residential Load Model for June

Simulations have been performed to derive the required residential load models. Tables

5.5 and 5.6 present the coefficients of the active and reactive residential load models for

June 2 am and 2 pm respectively.

Generally, the magnitude of the active and reactive load model coefficients for June 2 pm

are higher than those for June 2 am. This is due to the impact of the high temperature

degree in 2 pm.

59

Table 5.5: Formulated Residential Load Model for June at 2 am

(a) Active Power Models

Year a0 a1 a2 a3 a4 a5 Interval T (C0) H (%)

1998 4.40 -10.20 6.20 0.41 -0.11 -0.22 [28-36] [21-78]

1999 -2.10 5.70 -2.80 0.95 -0.11 -0.86 [29-38] [8-78]

2000 -1.40 4.70 -2.40 2.40 -0.26 -2.80 [27-35] [11-71]

2001 -0.22 1.40 -0.30 0.50 -0.04 -0.55 [25-35] [15-89]

(b) Reactive Power Models

Year b0 b1 b2 b3 b4 b5 Interval T (C0) H (%)

1998 6.00 -14.50 9.80 0.54 -0.12 -0.34 [28-36] [21-78]

1999 -3.50 8.70 -4.40 1.20 -0.13 -1.10 [29-38] [8-78]

2000 -0.21 2.10 -1.10 1.50 -0.10 -2.00 [27-35] [11-71]

2001 0.30 -0.10 0.76 0.60 -0.07 -0.67 [25-35] [15-89]

60

Table 5.6: Formulated Residential Load Model for June at 2 pm



1998 -5.30 9.70 -3.70 7.50 -1.80 -6.30 [38-45] [6-28]

1999 13.70 -24.30 11.40 -3.60 -3.20 5.30 [38-46] [6-25]

2000 -1.70 6.30 -3.40 -6.10 4.20 4.00 [37-45] [5-20]

2001 -7.60 16.70 -8.20 0.51 -0.30 -0.13 [37-42] [6-25]



1998 -21.70 39.60 -17.40 13.60 -3.10 -11.40 [38-45] [6-28]

1999 6.00 -11.70 6.30 5.60 -5.50 -2.50 [38-46] [6-25]

2000 -5.30 12.30 -6.00 -1.70 2.80 0.33 [37-45] [5-20]

2001 -7.70 16.70 -8.20 0.51 -0.30 -0.13 [37-42] [6-25]

61

However, the effect of the humidity is different. When the magnitude of the humidity

coefficients are high (2 pm models), the range of the humidity values are low (5 to 30

percent). Where as the magnitude of the humidity coefficients are low (2 am models), the

range of the humidity values are high (8 to 89 percent).

5.6.2 Residential Load Model for July

Tables 5.7 and 5.8 give the magnitude of the coefficients of the active and reactive

residential load models for July 2 am and 2 pm respectively.

The correlation between the magnitude of the active and reactive load model coefficients

for July models are different than for June models. The general trend of the magnitude of

the active and reactive load model coefficients for July 2 am are similar to those for July 2

pm. The temperature is reaching their maximum value in the summer period, it is 52

degree. Also, the humidity range in July is relatively higher than June.

It was noticed that the humidity coefficients (a3 & a4) for the active and reactive load

model for July are smaller compared to the other model coefficients. So, this gives

indication that the power demand influenced more by the temperature variation.

5.6.3 Residential Load Model for August

The magnitude of the coefficients of the active and reactive residential load models for

August 2 am and 2 pm are given in tables 5.9 and 5.10 respectively.

62

Table 5.7: Formulated Residential Load Model for July at 2 am



1998 -2.30 6.30 -3.30 0.13 -0.01 -0.05 [31-36] [11-87]

1999 34.0 -77.90 45.70 -3.60 0.12 4.20 [29-36] [10-85]

2000 -1.90 5.10 -2.30 1.10 0.10 -1.0 [25-38] [13-94]

2001 -8.90 23.10 -13.60 0.70 -0.14 -1.20 [29-36] [12-83]



1998 -34.0 78.50 -44.20 4.10 -0.15 -4.50 [31-36] [11-87]

1999 47.10 -108.7 63.90 -4.20 0.12 4.8 [29-36] [10-85]

2000 -1.50 4.00 -1.60 1.20 -0.14 -1.00 [25-38] [13-94]

2001 -1.00 3.80 -1.90 0.90 -0.03 -1.10 [29-36] [12-83]

63

Table 5.8: Formulated Residential Load Model for July at 2 pm



1998 4.80 -8.70 4.60 2.00 -0.17 -1.70 [39-46] [7-50]

1999 -3.50 7.80 -3.40 3.80 -0.10 -3.80 [38-45] [7-57]

2000 0.96 -0.50 0.41 1.40 -0.20 -1.10 [41-52] [4-30]

2001 12.50 -20.80 9.30 -4.30 0.41 3.80 [37-46] [7-41]



1998 5.50 -10.10 5.30 2.10 -0.08 -1.80 [39-46] [7-50]

1999 -11.00 22.40 -10.40 4.80 -0.14 -4.70 [38-45] [7-57]

2000 0.45 0.30 0.04 1.10 -0.17 -0.80 [41-52] [4-30]

2001 17.30 -29.80 13.50 -4.40 0.73 3.50 [37-46] [7-41]

64

Table 5.9: Formulated Residential Load Model for August at 2 am



1998 -0.57 3.10 -1.90 0.48 -0.09 -0.31 [32-37] [20-88]

1999 -0.42 5.00 -3.80 -0.80 0.24 0.23 [27-36] [18-93]

2000 -17.10 37.0 -18.80 3.50 -0.10 -3.90 [32-36] [41-88]

2001 1.6 -3.90 3.00 0.67 -0.12 -0.36 [27-36] [35-96]



1998 2.08 -1.90 0.26 -0.34 -0.05 0.57 [32-37] [20-88]

1999 -1.40 8.00 -5.70 -1.00 0.35 0.20 [27-36] [18-93]

2000 -39.0 84.90 -4.50 6.70 -0.28 -7.20 [32-36] [41-88]

2001 -0.42 0.77 0.17 1.00 -0.18 -0.58 [27-36] [35-96]

65

Table 5.10: Formulated Residential Load Model for August at 2 pm



1998 12.70 -19.60 8.20 -3.50 0.44 2.70 [38-47] [11-48]

1999 3.10 -3.70 1.60 -1.60 0.12 1.50 [38-46] [7-57]

2000 -2.10 4.90 -1.90 2.10 -0.36 -1.60 [39-47] [8-47]

2001 17.40 -29.20 12.90 -6.40 0.53 5.80 [39-44] [9-48]



1998 8.90 -12.40 4.90 -3.50 0.60 2.50 [38-47] [11-48]

1999 14.70 -24.70 11.00 -3.90 0.08 3.90 [38-46] [7-57]

2000 -0.35 1.40 -0.27 2.60 -0.42 -2.00 [39-47] [8-47]

2001 16.10 -29.60 14.20 -1.80 -0.12 2.05 [39-44] [9-48]

66

The temperatures during the August are varying from 27 to 37 degree at 2 am, while

during the 2 pm the variations are from 38 to 47 degree. However, the relative humidity is

reaching their maximum value during August at 2 am.

Also, it was noticed that the humidity coefficients (a3 & a4) for the active and reactive

load model for July are smaller compared to the other model coefficients. So, this gives

indication that the power demand influenced more by the temperature variation.

5.6.4 Residential Load Model for September

Tables 5.11 and 5.12 give the magnitude of the coefficients of the active and reactive

residential load models for September 2 am and 2 pm respectively.

The correlation between the magnitude of the active and reactive load model coefficients

for July models are similar to that for June models.

Generally, the magnitude of the active and reactive load model coefficients for September

2 pm are relatively higher than those for September 2 am. The temperatures are varying

from 24 to 36 degree at 2 am, whereas the variations at 2 pm are from 34 to 44 degree.

The temperature starts decreasing during September. However, the relative humidity is

also start decreasing in September varying from 20 to 88 percent at 2 am and varying

from 9 to 47 percent at 2 pm.

Also, it was noticed that the humidity coefficient a4 for the active and reactive load model

for July are smaller compared to the other model coefficients.

67

Table 5.11: Formulated Residential Load Model for September at 2 am



1998 6.40 -13.80 8.60 -1.20 0.20 1.00 [28-33] [35-88]

1999 5.20 -12.4 8.10 -0.81 -0.07 1.50 [26-33] [35-88]

2000 13.10 -32.40 21.20 -1.60 0.07 2.10 [26-32] [21-86]

2001 5.20 -10.30 5.90 -1.70 0.18 1.80 [24-36] [20-88]



1998 11.80 -27.20 16.80 -1.50 0.22 1.40 [28-33] [35-88]

1999 9.60 -22.60 14.10 -1.95 0.06 2.60 [26-33] [35-88]

2000 12.0 -29.80 19.50 -1.40 0.04 1.80 [26-32] [21-86]

2001 -3.60 8.90 -4.40 1.15 0.01 -1.40 [24-36] [20-88]

68

Table 5.12: Formulated Residential Load Model for September at 2 pm



1998 20.40 -35.40 16.10 -7.30 1.0 6.40 [38-43] [12-47]

1999 3.90 -9.30 5.70 1.20 -1.40 0.85 [36-44] [11-44]

2000 23.30 -43.20 20.70 -8.20 0.77 7.90 [36-41] [9-44]

2001 13.70 -23.70 10.80 -6.70 0.67 6.30 [34-44] [9-48]



1998 37.5 -67.80 31.40 -10.20 0.94 9.25 [38-43] [12-47]

1999 1.08 -3.30 2.60 1.70 -1.20 0.05 [36-44] [11-44]

2000 33.20 -62.10 29.60 -13.70 1.20 13.40 [36-41] [9-44]

2001 15.10 -25.70 11.50 -5.70 0.43 5.30 [34-44] [9-48]

69

5.7 Statistical Error Analysis

This section gives a statistical error analysis for the formulated residential load models for

June, July, August and September.

The statistical error analysis of the formulated residential load models involves two

aspects:

One is based on the calculation of the Mean absolute error (MAE), Standard

deviation errors (SDE) and variance value (VAR) for the active and reactive

power models.

The other aspect is based on plotting the error bars along the active and reactive

power.

Tables 5.13 to 5.16 give statistical error values for the four years models presented in the

previous section.

However, figures 5.3 to 5.10 show samples of the error bar plots for the active and

reactive power models for the month of August of the four year models at 2 pm. The rest

of the error bar plots for the active and reactive power models for the other months are

shown in the appendix C.

70

Table 5.13: Statistical Error analysis for June Models

(a) Time: 2 am

Statistical Error 1998 1999 2000 2001

P 0.0303 0.0369 0.0199 0.0212 MAE

Q 0.0356 0.0307 0.0243 0.0212

P 0.0371 0.0508 0.0310 0.0277 SDE

Q 0.0530 0.0390 0.0356 0.0306

P 0.0014 0.0026 0.0010 0.0008 VAR

Q 0.0028 0.0015 0.0013 0.0009

(b) Time: 2 pm


P 0.0378 0.0385 0.0236 0.0183 MAE

Q 0.0544 0.0378 0.0258 0.0180

P 0.0527 0.0493 0.0337 0.0261 SDE

Q 0.0657 0.0502 0.0395 0.0229

P 0.0028 0.0024 0.0011 0.0007 VAR

Q 0.0043 0.0025 0.0016 0.0005

71

Table 5.14: Statistical Error analysis for July Models

(a) Time: 2 am


P 0.0174 0.0611 0.0103 0.0223 MAE

Q 0.0252 0.0781 0.0165 0.0306

P 0.0217 0.0788 0.0122 0.0273 SDE

Q 0.0336 0.1035 0.0204 0.0411

P 0.0005 0.0062 0.0002 0.0008 VAR

Q 0.0011 0.0107 0.0004 0.0017

(b) Time: 2 pm


P 0.0269 0.0269 0.0176 0.0197 MAE

Q 0.0203 0.0393 0.0221 0.0260

P 0.0372 0.0374 0.0216 0.0245 SDE

Q 0.0298 0.0496 0.0264 0.0309

P 0.0014 0.0014 0.0005 0.0006 VAR

Q 0.0009 0.0025 0.0007 0.0010

72

Table 5.15: Statistical Error analysis for August Models

(a) Time: 2 am


P 0.0655 0.0853 0.0212 0.0119 MAE

Q 0.0306 0.1160 0.0244 0.0230

P 0.0542 0.0995 0.0266 0.0157 SDE

Q 0.0385 0.1358 0.0308 0.0284

P 0.0029 0.0099 0.0007 0.0003 VAR

Q 0.0015 0.0184 0.0010 0.0008

(b) Time: 2 pm


P 0.0206 0.0215 0.0168 0.0126 MAE

Q 0.0361 0.0362 0.0260 0.0175

P 0.0254 0.0282 0.0207 0.0185 SDE

Q 0.0441 0.0449 0.0309 0.0254

P 0.0006 0.0008 0.0004 0.0003 VAR

Q 0.0019 0.0020 0.0010 0.0007

73

Table 5.16: Statistical Error analysis for September Models

(a) Time: 2 am


P 0.0213 0.0288 0.0190 0.0390 MAE

Q 0.0259 0.0388 0.0255 0.0459

P 0.0272 0.0411 0.0226 0.0526 SDE

Q 0.0310 0.0565 0.0309 0.0669

P 0.0007 0.0017 0.0005 0.0028 VAR

Q 0.0010 0.0032 0.0010 0.0045

(b) Time: 2 pm


P 0.0334 0.0359 0.0237 0.0214 MAE

Q 0.0364 0.0357 0.0251 0.0394

P 0.0433 0.0450 0.0287 0.0284 SDE

Q 0.0480 0.0417 0.0286 0.0498

P 0.0019 0.0020 0.0008 0.0008 VAR

Q 0.0023 0.0017 0.0008 0.0025

74

Figure 5.3: Error Bar for the Active Power Model for 1998 August at 2 pm

75


76


77


78

Figure 5.7: Error Bar for the Reactive Power Model for 1998 August at 2 pm

79


80


81


82

5.8 Forecasting Hourly Residential Load Demand

Electricity demand forecasts used in power system planning should be as accurate as

possible. The forecast is one of the major input parameters in developing future

generation, transmission and distribution facilities. Furthermore, it is also used to forecast

the utility's cash flow requirements, and thereby determine the prices of electricity. Any

substantial deviation in the forecast will result in either overbuilding of supply facilities,

or curtailment of demand.

This section discusses the current and the proposed approach for future residential load

forecasting.

5.8.1 Utility Current Approach

In developing the electricity demand forecast for the power system of the SEC-ERB, the

customer demand is segregated into various categories to reflect the mixture of

geographic grouping and large customer classes.

The SEC-ERB prepares a demand forecast each year to assess the additional capacity

requirements for generation, transmission and distribution facilities, and also to develop

the operation and investment plans. The present methodology places main emphasis on

the peak demand of the system. To develop the system peak demand forecast, a hybrid

analytical/judgmental approach is used to derive the maximum demand of each category

of customers. The customer classification is primarily by way of operating areas mainly

consisting of residential and commercial loads, while the oil industry and other large

83

industries are treated separately. The informations on demand growth in operating areas

are gathered from in-house data, while for oil and large industries are obtained through

power demand surveys. The system peak demand is then calculated by applying

coincidence factors to each customer group. [5, 6]

5.8.2 Weather Related Approach

Electricity demand estimates are the cornerstone of electricity operation and planning.

Without an adequate knowledge of the past and present electricity consumption patterns

and the likely future development, electricity operation and planning would be impossible.

In addition, load forecasting helps the utility to determine the system's spinning reserve, to

assess the fuel requirements, and to plan their unit maintenance scheduling. [6]

Residential load represent a high percentage of the total electric demand in the eastern

province of Saudi Arabia. Also, the residential load is highly influenced by weather

factors. Therefore, the residential load demand can be forecasted using the derived load

models. So, the power consumption can be forecasted using equation 5.7, whereas the

power can be calculated by using the previous year residential load model and the growth

rate of the current year.

NNNelN RateGrowthPPP )(1)1(mod ∗+= −− [5.7]

Where N is the current year need to be forecasted.

84

Let us illustrate this approach by forecasting the Agrabia substation load for year 2002

August at 2 pm.

The value of N is 2002 and the growth rate is 5.0 (source is utility). So, equation 5.7

becomes as follows:

20022001)2001(mod2002 )( RateGrowthPPP el ∗+= [5.8]

Figures 5.11 and 5.12 show the plots of the actual and forecasted values of active and

reactive power of August 2002 at 2pm for Agrabia substation.

The active and reactive power obtained from simulated results had shown the same shape

and trend of the actual one, but some differences are visible in their values.

Thus, the conclusion is that the derived load models can be used as another source to

forecast the residential load and to check the load value forecasted by the

analytical/judgmental approach which is used to derive the maximum demand.

Also, the approach presented in this thesis can be used for operational purpose where the

hourly and daily load forecasts are needed for many operational studies such as units

commitment and schedule outages of the equipment.

85

0

10

20

30

40

50

1 3 5 7 9 11 13 15 17 19

Day

Act

ive

Pow

er (

MW

)

Actual

Forecasted

Figure 5.11: Actual and Forecasted Active Power of Agrabia Substation for 2002

August at 2 pm

86

0

5

10

15

20

25

1 3 5 7 9 11 13 15 17 19

Day

Rea

ctiv

e P

ower

(M

VA

R)

Actual

Forecasted

Figure 5.12: Actual and Forecasted Reactive Power of Agrabia Substation for 2002

August at 2 pm

87

5.9 Test Load Model With New Substation

The formulated models can be used to forecast the load of any substation. This can easily

be done because of the normalized load models. So, the load can be forecasted by

identifying the normalized parameters of the new substation.

Let us illustrate this for another substation in the same area of Agrabia substation.

Bayonia substation is one of the grid stations in this area feeding residential load.

Therefore, using 2001 model load to predict the load for Bayonia substation for June 2 am

and August 2 pm respectively.

Figures 5.13 to 5.16 show the actual and predicted active and reactive power of Bayonia

substation for 2001models. The predicted power curves show same pattern and trend of

the actual ones. Also, the predicted active power are in a good agreement with actual

active power, where the reactive power have some significant differences in their values.

This is quite apparent in the error bar plots.

The error bar plots for the active and reactive power models for Bayonia substation are

shown in figures 5.17, 5.18, 5.19 and 5.20. The error bar plots for the active power

models are showing a reasonable error pattern. However, as mentioned in the previous

paragraph the reactive power results show big error range. This is due to the nature of the

reactive power where it is affected by the reactive compensation in the system.

88

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17 19 21

Day

Act

ive

Pow

er (

MW

)

Actual

Simulated

Figure 5.13: Actual and Simulated Active Power of Bayonia Substation for 2001

June at 2 am

89

0

5

10

15

20

25

1 3 5 7 9 11 13 15 17 19 21

Day

Rea

ctiv

e P

ower

(M

VA

R)

Actual

Simulated

Figure 5.14: Actual and Simulated Reactive Power of Bayonia Substation for 2001

June at 2 am

90

0

10

20

30

40

50

60

1 3 5 7 9 11 13 15 17

Day

Act

ive

Pow

er (

MW

)

Actual

Simulated

Figure 5.15: Actual and Simulated Active Power of Bayonia Substation for 2001

August at 2 pm

91

0

5

10

15

20

25

1 3 5 7 9 11 13 15 17

Day

Rea

ctve

Pow

er (

MV

AR

)

Actual

Simulated

Figure 5.16: Actual and Simulated Reactive Power of Bayonia Substation for 2001

August at 2 pm

92

Figure 5.17: Error Bar for the Active Power of Bayonia for 2001 June at 2 am

93

Figure 5.18: Error Bar for the Reactive Power of Bayonia for 2001 June at 2 am

94

Figure 5.19: Error Bar for the Active Power of Bayonia for 2001 August at 2 pm

95

Figure 5.20: Error Bar for the Reactive Power of Bayonia for 2001 August at 2 pm

96

Chapter 6

CONCLUSIONS AND

RECOMMENDATIONS This chapter presents a summary of the work performed in this thesis. Also, it gives some

recommendations for future work.

6.1 Conclusions

In this thesis the load representation for static performance analysis was presented and

discussed.

Specific conclusions resulting from this work are as follows:

Year’s 1998 to 2002 measured data for highly hot and humid area at the eastern

province in Saudi Arabia data have been collected. Typical data for residential

load models has been selected from these data to reflect the impact of temperature

and relative humidity at steady voltage and at constant frequency.

96

97

The analysis, observations and investigations show four different modes of

weather conditions in summer period affect the power demand. These modes are

as follows:

- Mode1: High temperature with a moderate humidity will result in an

increasing power demand.

- Mode 2: Steady temperature with an increasing humidity will result in an

increasing power demand, but not sharp like mode one.

- Mode 3: High temperature with an increasing humidity will result in an

increasing power demand, but at up to a certain value where the humidity

moderate the temperature.

- Mode 4: Both of the temperature and the humidity are increasing. This will

result in a sharp increase in the power demand.

The parameters (coefficients) of the formulated residential load models were

identified by using the least squares fit technique in the MATLAB program.

The derived load models indicate that the relation of the temperature and the

relative humidity with load demand is a complex relation. It is a nonlinear relation.

Also, for different time of the day and the year there is a different behavior of the

load with respect to weather.

The load demand could be extracted on an hourly basis for residential load for

operational purposes.

98

The obtained fitting was tested and compared the measured load. They were in

good agreement. The analysis of the derived relations has shown behavior of the

load demand real and reactive as function of temperature and relative humidity.

6.2 Recommendations

There are a number of recommendations where further work can be done:

Since the collected data is measured at the bus feeding a diversified residential and

service load, a measured data taken, as input to a residence would reflect better

behavior.

Also, as extension to this work, it is good to repeat the same deriving load model

procedure done in this thesis to the Saudi Arabia Central Region where the system

peak demand is dominated by the residential demand that is mainly used for air

conditioning and is highly influenced by temperatures alone.

In the Gulf area air condition load represents high percentage of the residential

load in summer. So, determination of the dynamic behavior of air conditioner

using the component-based technique will give more accurate representation of the

residential load. Reference [16] describes techniques to derive the load models for

many home-heating appliances from field measurement.

99

APPENDICES

100

Appendix A

LOAD MODELING STRUCTURE

SELECTION

101

Table A.1: Load Model Structure A (1999 August at 2 pm)

Actual Predicted T H P Q P RMS Q RMS

(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.984 0.016 1.011 0.039

1.028 0.320 0.909 0.900 0.980 0.071 1.006 0.106

0.986 0.700 1.000 1.050 0.992 0.008 1.017 0.033

0.972 0.640 0.909 0.950 0.996 0.087 1.019 0.069

0.986 0.660 1.000 1.050 0.992 0.008 1.017 0.033

1.083 0.440 0.932 0.950 0.963 0.031 0.975 0.025

1.097 0.160 0.932 0.950 0.959 0.027 0.965 0.015

1.083 0.300 0.955 0.950 0.963 0.009 0.975 0.025

1.139 0.140 0.955 0.900 0.945 0.010 0.927 0.027

1.069 0.360 0.955 0.950 0.968 0.013 0.984 0.034

1.125 0.180 0.909 0.900 0.949 0.040 0.940 0.040

1.028 0.620 0.932 0.900 0.980 0.048 1.006 0.106

0.958 1.100 1.023 1.000 0.999 0.023 1.019 0.019

0.958 1.140 1.023 1.000 0.999 0.023 1.019 0.019

1.042 0.500 0.955 0.950 0.976 0.021 1.000 0.050

1.069 0.440 1.000 1.000 0.968 0.032 0.984 0.016

1.000 0.940 1.000 1.000 0.988 0.012 1.014 0.014

0.986 0.920 1.000 1.050 0.992 0.008 1.017 0.033

1.111 0.440 1.000 1.050 0.954 0.046 0.953 0.097

0.958 1.020 1.000 1.050 0.999 0.001 1.019 0.031

0.972 0.840 1.000 1.050 0.996 0.004 1.019 0.031

1.056 0.580 1.000 1.050 0.972 0.028 0.993 0.057

1.083 0.480 1.000 1.050 0.963 0.037 0.975 0.075

RMS value 0.026 0.043

22343.01883.00341.1 TTP ∗−∗+=

28835.25354.56376.1 TTQ ∗−∗+=

102

Table A.2: Load Model Structure B (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.969 0.031 0.991 0.059

1.028 0.320 0.909 0.900 0.966 0.057 0.989 0.089

0.986 0.700 1.000 1.050 0.981 0.019 1.003 0.047

0.972 0.640 0.909 0.950 0.992 0.083 1.014 0.064

0.986 0.660 1.000 1.050 0.981 0.019 1.003 0.047

1.083 0.440 0.932 0.950 0.964 0.032 0.978 0.028

1.097 0.160 0.932 0.950 0.961 0.030 0.970 0.020

1.083 0.300 0.955 0.950 0.964 0.009 0.978 0.028

1.139 0.140 0.955 0.900 0.940 0.015 0.916 0.016

1.069 0.360 0.955 0.950 0.965 0.010 0.983 0.033

1.125 0.180 0.909 0.900 0.950 0.041 0.940 0.040

1.028 0.620 0.932 0.900 0.966 0.035 0.989 0.089

0.958 1.100 1.023 1.000 1.008 0.015 1.031 0.031

0.958 1.140 1.023 1.000 1.008 0.015 1.031 0.031

1.042 0.500 0.955 0.950 0.965 0.011 0.987 0.037

1.069 0.440 1.000 1.000 0.965 0.035 0.983 0.017

1.000 0.940 1.000 1.000 0.974 0.026 0.996 0.004

0.986 0.920 1.000 1.050 0.981 0.019 1.003 0.047

1.111 0.440 1.000 1.050 0.957 0.043 0.958 0.092

0.958 1.020 1.000 1.050 1.008 0.008 1.031 0.019

0.972 0.840 1.000 1.050 0.992 0.008 1.014 0.036

1.056 0.580 1.000 1.050 0.965 0.035 0.986 0.064

1.083 0.480 1.000 1.050 0.964 0.036 0.978 0.072

RMS value 0.027 0.044

32 6295.434371.1362209.1447871.51 TTTP ∗−∗+∗−=

32 7240.640199.2022815.2109816.73 TTTQ ∗−∗+∗−=

103

Table A.3: Load Model Structure C (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.901 0.099 2.029 0.979

1.028 0.320 0.909 0.900 0.900 0.009 2.060 1.160

0.986 0.700 1.000 1.050 0.902 0.098 1.972 0.922

0.972 0.640 0.909 0.950 0.910 0.001 1.939 0.989

0.986 0.660 1.000 1.050 0.902 0.098 1.972 0.922

1.083 0.440 0.932 0.950 0.865 0.066 2.236 1.286

1.097 0.160 0.932 0.950 0.851 0.081 2.282 1.332

1.083 0.300 0.955 0.950 0.865 0.089 2.236 1.286

1.139 0.140 0.955 0.900 0.840 0.114 2.352 1.452

1.069 0.360 0.955 0.950 0.879 0.075 2.187 1.237

1.125 0.180 0.909 0.900 0.834 0.075 2.348 1.448

1.028 0.620 0.932 0.900 0.900 0.032 2.060 1.160

0.958 1.100 1.023 1.000 0.930 0.093 1.897 0.897

0.958 1.140 1.023 1.000 0.930 0.093 1.897 0.897

1.042 0.500 0.955 0.950 0.897 0.057 2.098 1.148

1.069 0.440 1.000 1.000 0.879 0.121 2.187 1.187

1.000 0.940 1.000 1.000 0.900 0.100 2.000 1.000

0.986 0.920 1.000 1.050 0.902 0.098 1.972 0.922

1.111 0.440 1.000 1.050 0.839 0.161 2.322 1.272

0.958 1.020 1.000 1.050 0.930 0.070 1.897 0.847

0.972 0.840 1.000 1.050 0.910 0.090 1.939 0.889

1.056 0.580 1.000 1.050 0.890 0.110 2.140 1.090

1.083 0.480 1.000 1.050 0.865 0.135 2.236 1.186

RMS value 0.085 1.109

432 11794945776554121413 TTTTP ∗+∗−∗∗−=

432 155864691005869431794 TTTTQ ∗−∗+∗−∗+−=

104

Table A.4: Load Model Structure D (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.942 0.058 0.972 0.078

1.028 0.320 0.909 0.900 0.948 0.039 0.977 0.077

0.986 0.700 1.000 1.050 0.980 0.020 1.006 0.044

0.972 0.640 0.909 0.950 0.962 0.053 0.988 0.038

0.986 0.660 1.000 1.050 0.974 0.026 1.001 0.049

1.083 0.440 0.932 0.950 0.978 0.046 0.988 0.038

1.097 0.160 0.932 0.950 0.939 0.007 0.947 0.003

1.083 0.300 0.955 0.950 0.958 0.004 0.971 0.021

1.139 0.140 0.955 0.900 0.931 0.024 0.914 0.014

1.069 0.360 0.955 0.950 0.965 0.011 0.982 0.032

1.125 0.180 0.909 0.900 0.939 0.030 0.931 0.031

1.028 0.620 0.932 0.900 0.990 0.058 1.015 0.115

0.958 1.100 1.023 1.000 1.016 0.007 1.034 0.034

0.958 1.140 1.023 1.000 1.021 0.002 1.039 0.039

1.042 0.500 0.955 0.950 0.978 0.024 1.002 0.052

1.069 0.440 1.000 1.000 0.976 0.024 0.992 0.008

1.000 0.940 1.000 1.000 1.022 0.022 1.045 0.045

0.986 0.920 1.000 1.050 1.010 0.010 1.034 0.016

1.111 0.440 1.000 1.050 0.978 0.022 0.974 0.076

0.958 1.020 1.000 1.050 1.004 0.004 1.023 0.027

0.972 0.840 1.000 1.050 0.990 0.010 1.013 0.037

1.056 0.580 1.000 1.050 0.993 0.007 1.012 0.038

1.083 0.480 1.000 1.050 0.983 0.017 0.993 0.057

RMS value 0.023 0.042

HTTP ∗+∗−∗+−= 1400.09443.24490.66147.2 2

HTTQ ∗+∗−∗+−= 1266.03338.51960.119366.4 2

105

Table A.5: Load Model Structure E (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.940 0.060 0.955 0.095

1.028 0.320 0.909 0.900 0.946 0.037 0.957 0.057

0.986 0.700 1.000 1.050 0.982 0.018 1.027 0.023

0.972 0.640 0.909 0.950 0.965 0.056 1.021 0.071

0.986 0.660 1.000 1.050 0.976 0.024 1.023 0.027

1.083 0.440 0.932 0.950 0.979 0.047 0.997 0.047

1.097 0.160 0.932 0.950 0.936 0.004 0.912 0.038

1.083 0.300 0.955 0.950 0.957 0.003 0.959 0.009

1.139 0.140 0.955 0.900 0.931 0.024 0.915 0.015

1.069 0.360 0.955 0.950 0.964 0.010 0.974 0.024

1.125 0.180 0.909 0.900 0.939 0.030 0.927 0.027

1.028 0.620 0.932 0.900 0.991 0.059 1.021 0.121

0.958 1.100 1.023 1.000 1.014 0.009 1.013 0.013

0.958 1.140 1.023 1.000 1.018 0.005 1.006 0.006

1.042 0.500 0.955 0.950 0.978 0.024 1.003 0.053

1.069 0.440 1.000 1.000 0.977 0.023 0.995 0.005

1.000 0.940 1.000 1.000 1.020 0.020 1.030 0.030

0.986 0.920 1.000 1.050 1.010 0.010 1.031 0.019

1.111 0.440 1.000 1.050 0.980 0.020 1.004 0.046

0.958 1.020 1.000 1.050 1.004 0.004 1.023 0.027

0.972 0.840 1.000 1.050 0.992 0.008 1.033 0.017

1.056 0.580 1.000 1.050 0.994 0.006 1.019 0.031

1.083 0.480 1.000 1.050 0.985 0.015 1.006 0.044

RMS value 0.022 0.037

22 0228.01734.03702.22568.50056.2 HHTTP ∗−∗+∗−∗+−=

22 2930.04914.09342.08195.17125.1 HHTTQ ∗−∗+∗+∗−=

106

Table A.6: Load Model Structure F (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.941 0.059 0.954 0.096

1.028 0.320 0.909 0.900 0.947 0.038 0.955 0.055

0.986 0.700 1.000 1.050 0.981 0.019 1.028 0.022

0.972 0.640 0.909 0.950 0.965 0.056 1.020 0.070

0.986 0.660 1.000 1.050 0.976 0.024 1.024 0.026

1.083 0.440 0.932 0.950 0.980 0.048 0.996 0.046

1.097 0.160 0.932 0.950 0.934 0.002 0.915 0.035

1.083 0.300 0.955 0.950 0.958 0.003 0.958 0.008

1.139 0.140 0.955 0.900 0.930 0.025 0.917 0.017

1.069 0.360 0.955 0.950 0.965 0.011 0.973 0.023

1.125 0.180 0.909 0.900 0.938 0.029 0.928 0.028

1.028 0.620 0.932 0.900 0.990 0.058 1.023 0.123

0.958 1.100 1.023 1.000 1.015 0.008 1.011 0.011

0.958 1.140 1.023 1.000 1.020 0.002 1.002 0.002

1.042 0.500 0.955 0.950 0.979 0.024 1.003 0.053

1.069 0.440 1.000 1.000 0.977 0.023 0.993 0.007

1.000 0.940 1.000 1.000 1.018 0.018 1.035 0.035

0.986 0.920 1.000 1.050 1.008 0.008 1.035 0.015

1.111 0.440 1.000 1.050 0.982 0.018 1.001 0.049

0.958 1.020 1.000 1.050 1.004 0.004 1.024 0.026

0.972 0.840 1.000 1.050 0.990 0.010 1.035 0.015

1.056 0.580 1.000 1.050 0.994 0.006 1.020 0.030

1.083 0.480 1.000 1.050 0.985 0.015 1.005 0.045

RMS value 0.022 0.036

322 0546.01333.02318.01274.27458.47458.1 HHHTTP ∗+∗−∗∗−∗+−=

322 1054.00873.03786.04652.08324.02107.1 HHHTTQ ∗−∗−∗+∗+∗−=

107

Table A.7: Load Model Structure G (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.951 0.049 0.981 0.069

1.028 0.320 0.909 0.900 0.951 0.042 0.968 0.068

0.986 0.700 1.000 1.050 0.978 0.022 1.019 0.031

0.972 0.640 0.909 0.950 0.967 0.058 1.027 0.077

0.986 0.660 1.000 1.050 0.974 0.026 1.018 0.032

1.083 0.440 0.932 0.950 0.979 0.047 0.998 0.048

1.097 0.160 0.932 0.950 0.932 0.000 0.902 0.048

1.083 0.300 0.955 0.950 0.953 0.001 0.949 0.001

1.139 0.140 0.955 0.900 0.930 0.025 0.913 0.013

1.069 0.360 0.955 0.950 0.960 0.006 0.964 0.014

1.125 0.180 0.909 0.900 0.937 0.028 0.922 0.022

1.028 0.620 0.932 0.900 0.987 0.056 1.013 0.113

0.958 1.100 1.023 1.000 1.014 0.009 1.014 0.014

0.958 1.140 1.023 1.000 1.021 0.002 1.013 0.013

1.042 0.500 0.955 0.950 0.975 0.020 0.993 0.043

1.069 0.440 1.000 1.000 0.974 0.026 0.988 0.012

1.000 0.940 1.000 1.000 1.025 0.025 1.041 0.041

0.986 0.920 1.000 1.050 1.009 0.009 1.028 0.022

1.111 0.440 1.000 1.050 0.991 0.009 1.030 0.020

0.958 1.020 1.000 1.050 1.002 0.002 1.016 0.034

0.972 0.840 1.000 1.050 0.987 0.013 1.022 0.028

1.056 0.580 1.000 1.050 0.994 0.006 1.019 0.031

1.083 0.480 1.000 1.050 0.987 0.013 1.012 0.038

RMS value 0.021 0.036

THHHTTP ∗∗+∗+∗−∗+∗−= 5355.11198.05685.15882.17372.30987.3 22

THHHTTQ ∗∗+∗+∗−∗+∗−= 9102.30805.09445.30143.117230.247107.14 22

108

Table A.8: Load Model Structure H (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.951 0.049 0.981 0.069

1.028 0.320 0.909 0.900 0.951 0.041 0.969 0.069

0.986 0.700 1.000 1.050 0.979 0.021 1.017 0.033

0.972 0.640 0.909 0.950 0.967 0.058 1.027 0.077

0.986 0.660 1.000 1.050 0.974 0.026 1.016 0.034

1.083 0.440 0.932 0.950 0.978 0.047 1.002 0.052

1.097 0.160 0.932 0.950 0.932 0.000 0.903 0.047

1.083 0.300 0.955 0.950 0.953 0.002 0.953 0.003

1.139 0.140 0.955 0.900 0.931 0.023 0.905 0.005

1.069 0.360 0.955 0.950 0.960 0.005 0.968 0.018

1.125 0.180 0.909 0.900 0.937 0.028 0.919 0.019

1.028 0.620 0.932 0.900 0.988 0.056 1.009 0.109

0.958 1.100 1.023 1.000 1.013 0.009 1.018 0.018

0.958 1.140 1.023 1.000 1.020 0.002 1.017 0.017

1.042 0.500 0.955 0.950 0.975 0.020 0.993 0.043

1.069 0.440 1.000 1.000 0.974 0.026 0.991 0.009

1.000 0.940 1.000 1.000 1.026 0.026 1.028 0.028

0.986 0.920 1.000 1.050 1.010 0.010 1.021 0.029

1.111 0.440 1.000 1.050 0.990 0.010 1.036 0.014

0.958 1.020 1.000 1.050 1.001 0.001 1.022 0.028

0.972 0.840 1.000 1.050 0.987 0.013 1.022 0.028

1.056 0.580 1.000 1.050 0.994 0.006 1.018 0.032

1.083 0.480 1.000 1.050 0.987 0.013 1.016 0.034

RMS value 0.021 0.035

HTTHHHTTP ∗∗−∗∗+∗+∗−∗+∗−= 222 036.1719.3127.0723.2054.2729.4626.3

HTTHHHTTQ ∗∗+∗∗−∗+∗+∗+∗−= 222 118.7085.11029.0981.3811.7911.17088.11

109

Table A.9: Load Model Structure I (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.951 0.049 0.981 0.069

1.028 0.320 0.909 0.900 0.951 0.042 0.968 0.068

0.986 0.700 1.000 1.050 0.978 0.022 1.018 0.032

0.972 0.640 0.909 0.950 0.967 0.058 1.027 0.077

0.986 0.660 1.000 1.050 0.974 0.026 1.018 0.032

1.083 0.440 0.932 0.950 0.980 0.048 0.999 0.049

1.097 0.160 0.932 0.950 0.931 0.001 0.901 0.049

1.083 0.300 0.955 0.950 0.954 0.000 0.950 0.000

1.139 0.140 0.955 0.900 0.929 0.026 0.911 0.011

1.069 0.360 0.955 0.950 0.961 0.007 0.965 0.015

1.125 0.180 0.909 0.900 0.937 0.027 0.921 0.021

1.028 0.620 0.932 0.900 0.987 0.055 1.012 0.112

0.958 1.100 1.023 1.000 1.015 0.008 1.015 0.015

0.958 1.140 1.023 1.000 1.022 0.001 1.015 0.015

1.042 0.500 0.955 0.950 0.975 0.020 0.994 0.044

1.069 0.440 1.000 1.000 0.975 0.025 0.989 0.011

1.000 0.940 1.000 1.000 1.022 0.022 1.037 0.037

0.986 0.920 1.000 1.050 1.008 0.008 1.026 0.024

1.111 0.440 1.000 1.050 0.992 0.008 1.031 0.019

0.958 1.020 1.000 1.050 1.002 0.002 1.017 0.033

0.972 0.840 1.000 1.050 0.987 0.013 1.022 0.028

1.056 0.580 1.000 1.050 0.994 0.006 1.019 0.031

1.083 0.480 1.000 1.050 0.988 0.012 1.013 0.037

RMS value 0.021 0.036

222 280.0710.1386.0731.1500.1567.3014.3 HTTHHHTTP ∗∗−∗∗+∗+∗−∗+∗−=

222 353.0130.4416.0149.4903.10509.24604.14 HTTHHHTTQ ∗∗−∗∗+∗+∗−∗+∗−=

110

Table A.10: Load Model Structure J (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.951 0.049 0.981 0.069

1.028 0.320 0.909 0.900 0.951 0.042 0.968 0.068

0.986 0.700 1.000 1.050 0.978 0.022 1.019 0.031

0.972 0.640 0.909 0.950 0.967 0.058 1.027 0.077

0.986 0.660 1.000 1.050 0.974 0.026 1.018 0.032

1.083 0.440 0.932 0.950 0.980 0.048 0.999 0.049

1.097 0.160 0.932 0.950 0.931 0.001 0.901 0.049

1.083 0.300 0.955 0.950 0.954 0.000 0.950 0.000

1.139 0.140 0.955 0.900 0.929 0.026 0.912 0.012

1.069 0.360 0.955 0.950 0.961 0.007 0.965 0.015

1.125 0.180 0.909 0.900 0.937 0.028 0.921 0.021

1.028 0.620 0.932 0.900 0.987 0.055 1.012 0.112

0.958 1.100 1.023 1.000 1.015 0.008 1.015 0.015

0.958 1.140 1.023 1.000 1.022 0.001 1.014 0.014

1.042 0.500 0.955 0.950 0.975 0.020 0.994 0.044

1.069 0.440 1.000 1.000 0.975 0.025 0.989 0.011

1.000 0.940 1.000 1.000 1.022 0.022 1.038 0.038

0.986 0.920 1.000 1.050 1.008 0.008 1.027 0.023

1.111 0.440 1.000 1.050 0.992 0.008 1.031 0.019

0.958 1.020 1.000 1.050 1.002 0.002 1.017 0.033

0.972 0.840 1.000 1.050 0.987 0.013 1.022 0.028

1.056 0.580 1.000 1.050 0.994 0.006 1.019 0.031

1.083 0.480 1.000 1.050 0.988 0.012 1.013 0.037

RMS value 0.021 0.036

2222 1485.0731.12553.0751.1528.1629.3047.3 HTTHHHTTP ∗∗−∗∗+∗+∗−∗+∗−=

2222 148.0106.4216.0128.4954.10614.24659.14 HTTHHHTTQ ∗∗−∗∗+∗+∗−∗+∗−=

111

Table A.11: Load Model Structure K (1999 August at 2 pm)


(p.u) (p.u) (p.u) (p.u) (p.u) (p.u)

1.014 0.320 1.000 1.050 0.942 0.058 0.961 0.089

1.028 0.320 0.909 0.900 0.947 0.038 0.958 0.058

0.986 0.700 1.000 1.050 0.982 0.018 1.027 0.023

0.972 0.640 0.909 0.950 0.965 0.056 1.023 0.073

0.986 0.660 1.000 1.050 0.976 0.024 1.023 0.027

1.083 0.440 0.932 0.950 0.978 0.046 0.994 0.044

1.097 0.160 0.932 0.950 0.936 0.004 0.913 0.037

1.083 0.300 0.955 0.950 0.956 0.001 0.953 0.003

1.139 0.140 0.955 0.900 0.932 0.022 0.920 0.020

1.069 0.360 0.955 0.950 0.963 0.008 0.968 0.018

1.125 0.180 0.909 0.900 0.939 0.030 0.927 0.027

1.028 0.620 0.932 0.900 0.991 0.059 1.021 0.121

0.958 1.100 1.023 1.000 1.012 0.010 1.009 0.009

0.958 1.140 1.023 1.000 1.017 0.005 1.003 0.003

1.042 0.500 0.955 0.950 0.977 0.023 1.000 0.050

1.069 0.440 1.000 1.000 0.975 0.025 0.990 0.010

1.000 0.940 1.000 1.000 1.024 0.024 1.044 0.044

0.986 0.920 1.000 1.050 1.012 0.012 1.036 0.014

1.111 0.440 1.000 1.050 0.981 0.019 1.006 0.044

0.958 1.020 1.000 1.050 1.003 0.003 1.018 0.032

0.972 0.840 1.000 1.050 0.991 0.009 1.031 0.019

1.056 0.580 1.000 1.050 0.994 0.006 1.021 0.029

1.083 0.480 1.000 1.050 0.984 0.016 1.005 0.045

RMS value 0.022 0.036

2222 179.0167.0126.0689.1743.3159.1 HTHHTTP ∗∗+∗−∗+∗−∗+−=

2222 628.0786.0327.0322.3126.7680.4 HTHHTTQ ∗∗+∗−∗+∗+∗−=

112

Appendix B

DATA FOR LOAD MODELING

113

B.1 Original Raw Data

The mathematical models reported in this thesis are based on available measured data

which is a computerized database containing hourly data about generation, voltage,

frequency, load and weather for SEC-ERB utility in eastern province of Saudi Arabia.

These data are available from 1st January 1998 up to 31st December 2002.

The database files consist of three different files (CP, MS and M2). Each of these files

contains different kind of information for 24-hour a day. The contents of these files are as

follows:

CP - Substations Loads (MW & MVAR)

MS - Temperature

M2

- System Frequency

- Substation Voltage

- Relative Humidity

However, the data selected for residential load modeling derivation were extracted from

these files. So a program was made in excel sheet using Macro to extract the load

modeling data from the original raw data files.

The visual basic language was used to write the Macro program. Below are the program

written to extract the load data used in this thesis.

114

Macro Program Sub ' ' M0206 Macro ' Macro recorded 31/10/01 by MICROSOFT ' ' Range("A1").Select ActiveCell.FormulaR1C1 = "HOUR" Range("B1").Select ActiveCell.FormulaR1C1 = "FREQUENCY" Range("B2").Select ActiveCell.FormulaR1C1 = "HZ" Range("B3").Select Columns("B:B").EntireColumn.AutoFit Range("C1").Select ActiveCell.FormulaR1C1 = "TEMPERATURE" Range("C2").Select ActiveCell.FormulaR1C1 = "F" Range("C3").Select Columns("C:C").EntireColumn.AutoFit Range("D1").Select ActiveCell.FormulaR1C1 = "HUMIDITY" Range("D2").Select ActiveCell.FormulaR1C1 = "%" Range("D3").Select Columns("D:D").EntireColumn.AutoFit Range("E2").Select ActiveCell.FormulaR1C1 = "kV" Range("F2").Select ActiveCell.FormulaR1C1 = "MW" Range("G2").Select ActiveCell.FormulaR1C1 = "MVAR" Range("E1:G1").Select With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Selection.Merge ActiveCell.FormulaR1C1 = "AGRABIA SUBSTATION" Range("A1:G2").Select Selection.Font.Bold = True Columns("A:G").Select With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0

115

.ShrinkToFit = False .ReadingOrder = xlContext End With ' Enter the number of days Ndays = InputBox( _ prompt:="Please enter the # of Days 31,30,29,28.") ' LOOP 2002/06 For i = 1 To Ndays c = 3 + 24 * (i - 1) ' Cells(c, "A").Select ActiveCell.FormulaR1C1 = "1" Cells(c, "A").Select Selection.DataSeries Rowcol:=xlColumns, Type:=xlLinear, Date:=xlDay, _ Step:=1, Stop:=24, Trend:=False ' '====== Directory================== ChDir "D:\E\DATA\2002\06" '================================== If i = 1 Then M2day = "M2020601.DBF" ElseIf i = 2 Then M2day = "M2020602.DBF" ElseIf i = 3 Then M2day = "M2020603.DBF" ElseIf i = 4 Then M2day = "M2020604.DBF" ElseIf i = 5 Then M2day = "M2020605.DBF" ElseIf i = 6 Then M2day = "M2020606.DBF" ElseIf i = 7 Then M2day = "M2020607.DBF" ElseIf i = 8 Then M2day = "M2020608.DBF" ElseIf i = 9 Then M2day = "M2020609.DBF" ElseIf i = 10 Then M2day = "M2020610.DBF" ElseIf i = 11 Then M2day = "M2020611.DBF" ElseIf i = 12 Then M2day = "M2020612.DBF" ElseIf i = 13 Then M2day = "M2020613.DBF" ElseIf i = 14 Then M2day = "M2020614.DBF" ElseIf i = 15 Then M2day = "M2020615.DBF"

116

ElseIf i = 16 Then M2day = "M2020616.DBF" ElseIf i = 17 Then M2day = "M2020617.DBF" ElseIf i = 18 Then M2day = "M2020618.DBF" ElseIf i = 19 Then M2day = "M2020619.DBF" ElseIf i = 20 Then M2day = "M2020620.DBF" ElseIf i = 21 Then M2day = "M2020621.DBF" ElseIf i = 22 Then M2day = "M2020622.DBF" ElseIf i = 23 Then M2day = "M2020623.DBF" ElseIf i = 24 Then M2day = "M2020624.DBF" ElseIf i = 25 Then M2day = "M2020625.DBF" ElseIf i = 26 Then M2day = "M2020626.DBF" ElseIf i = 27 Then M2day = "M2020627.DBF" ElseIf i = 28 Then M2day = "M2020628.DBF" ElseIf i = 29 Then M2day = "M2020629.DBF" ElseIf i = 30 Then M2day = "M2020630.DBF" ElseIf i = 31 Then M2day = "M2020631.DBF" End If Workbooks.Open FileName:=M2day ActiveWindow.LargeScroll ToRight:=2 Cells.Find(What:="HZ", After:=ActiveCell, LookIn:=xlFormulas, LookAt:= _ xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, MatchCase:=False).Activate ActiveWindow.ScrollColumn = 1 Range("A301:X301").Select Selection.Copy Windows("M0206").Activate Cells(c, "B").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Range("C11").Select Windows(M2day).Activate ActiveWindow.ScrollRow = 1 Range("I292").Select Application.CutCopyMode = False Cells.FindNext(After:=ActiveCell).Activate ActiveWindow.ScrollColumn = 1 Range("A1897:X1897").Select Selection.Copy Windows("M0206").Activate

117

Cells(c, "D").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Windows(M2day).Activate Range("D1889").Select Application.CutCopyMode = False Cells.Find(What:="AGRB-3-BUS1", After:=ActiveCell, LookIn:=xlFormulas, _ LookAt:=xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, _ MatchCase:=False).Activate Range("AB1721:AC1724").Select Range("AC1721").Activate ActiveWindow.ScrollColumn = 1 ActiveWindow.ScrollColumn = 19 Range("Y1710").Select ActiveWindow.ScrollColumn = 1 Range("A1710:X1710").Select Selection.Copy Windows("M0206").Activate Cells(c, "E").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Windows(M2day).Activate Application.CutCopyMode = False Range("D1705").Select ActiveWindow.Close ' CP File If i = 1 Then CPday = "CP020601.DBF" ElseIf i = 2 Then CPday = "CP020602.DBF" ElseIf i = 3 Then CPday = "CP020603.DBF" ElseIf i = 4 Then CPday = "CP020604.DBF" ElseIf i = 5 Then CPday = "CP020605.DBF" ElseIf i = 6 Then CPday = "CP020606.DBF" ElseIf i = 7 Then CPday = "CP020607.DBF" ElseIf i = 8 Then CPday = "CP020608.DBF" ElseIf i = 9 Then CPday = "CP020609.DBF" ElseIf i = 10 Then CPday = "CP020610.DBF" ElseIf i = 11 Then CPday = "CP020611.DBF" ElseIf i = 12 Then CPday = "CP020612.DBF" ElseIf i = 13 Then

118

CPday = "CP020613.DBF" ElseIf i = 14 Then CPday = "CP020614.DBF" ElseIf i = 15 Then CPday = "CP020615.DBF" ElseIf i = 16 Then CPday = "CP020616.DBF" ElseIf i = 17 Then CPday = "CP020617.DBF" ElseIf i = 18 Then CPday = "CP020618.DBF" ElseIf i = 19 Then CPday = "CP020619.DBF" ElseIf i = 20 Then CPday = "CP020620.DBF" ElseIf i = 21 Then CPday = "CP020621.DBF" ElseIf i = 22 Then CPday = "CP020622.DBF" ElseIf i = 23 Then CPday = "CP020623.DBF" ElseIf i = 24 Then CPday = "CP020624.DBF" ElseIf i = 25 Then CPday = "CP020625.DBF" ElseIf i = 26 Then CPday = "CP020626.DBF" ElseIf i = 27 Then CPday = "CP020627.DBF" ElseIf i = 28 Then CPday = "CP020628.DBF" ElseIf i = 29 Then CPday = "CP020629.DBF" ElseIf i = 30 Then CPday = "CP020630.DBF" ElseIf i = 31 Then CPday = "CP020631.DBF" End If Workbooks.Open FileName:=CPday Cells.Find(What:="AGRABIA STATION", After:=ActiveCell, LookIn:=xlFormulas _ , LookAt:=xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, _ MatchCase:=False).Activate ActiveWindow.SmallScroll ToRight:=-19 Range("A134:X134").Select Selection.Copy Windows("M0206").Activate Cells(c, "F").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Windows(CPday).Activate ActiveWindow.SmallScroll ToRight:=17 ActiveWindow.LargeScroll ToRight:=-2 Range("A135:X135").Select

119

Application.CutCopyMode = False Selection.Copy Windows("M0206").Activate Cells(c, "G").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Range("H11").Select Windows(CPday).Activate ActiveWindow.Close ' Ms File If i = 1 Then Msday = "Ms020601.DBF" ElseIf i = 2 Then Msday = "Ms020602.DBF" ElseIf i = 3 Then Msday = "Ms020603.DBF" ElseIf i = 4 Then Msday = "Ms020604.DBF" ElseIf i = 5 Then Msday = "Ms020605.DBF" ElseIf i = 6 Then Msday = "Ms020606.DBF" ElseIf i = 7 Then Msday = "Ms020607.DBF" ElseIf i = 8 Then Msday = "Ms020608.DBF" ElseIf i = 9 Then Msday = "Ms020609.DBF" ElseIf i = 10 Then Msday = "Ms020610.DBF" ElseIf i = 11 Then Msday = "Ms020611.DBF" ElseIf i = 12 Then Msday = "Ms020612.DBF" ElseIf i = 13 Then Msday = "Ms020613.DBF" ElseIf i = 14 Then Msday = "Ms020614.DBF" ElseIf i = 15 Then Msday = "Ms020615.DBF" ElseIf i = 16 Then Msday = "Ms020616.DBF" ElseIf i = 17 Then Msday = "Ms020617.DBF" ElseIf i = 18 Then Msday = "Ms020618.DBF" ElseIf i = 19 Then Msday = "Ms020619.DBF" ElseIf i = 20 Then Msday = "Ms020620.DBF" ElseIf i = 21 Then Msday = "Ms020621.DBF" ElseIf i = 22 Then Msday = "Ms020622.DBF"

120

ElseIf i = 23 Then Msday = "Ms020623.DBF" ElseIf i = 24 Then Msday = "Ms020624.DBF" ElseIf i = 25 Then Msday = "Ms020625.DBF" ElseIf i = 26 Then Msday = "Ms020626.DBF" ElseIf i = 27 Then Msday = "Ms020627.DBF" ElseIf i = 28 Then Msday = "Ms020628.DBF" ElseIf i = 29 Then Msday = "Ms020629.DBF" ElseIf i = 30 Then Msday = "Ms020630.DBF" ElseIf i = 31 Then Msday = "Ms020631.DBF" End If Workbooks.Open FileName:=Msday Cells.Find(What:="DAMTEMP_CT", After:=ActiveCell, LookIn:=xlFormulas, _ LookAt:=xlPart, SearchOrder:=xlByRows, SearchDirection:=xlNext, _ MatchCase:=False).Activate ActiveWindow.ScrollColumn = 1 Range("A602:X602").Select Selection.Copy Windows("M0206").Activate Cells(c, "C").Select Selection.PasteSpecial Paste:=xlAll, Operation:=xlNone, SkipBlanks:=False _ , Transpose:=True Windows(Msday).Activate ActiveWindow.Close Next i ' MODIFICATION ' Columns("A:G").Select With Selection .HorizontalAlignment = xlGeneral .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext End With With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext End With

121

Columns("D:D").Select Selection.Insert Shift:=xlToRight Range("C1:D1").Select With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Selection.Merge Range("D2").Select ActiveCell.FormulaR1C1 = "C" Range("D3").Select ActiveCell.FormulaR1C1 = "=(RC[-1]-32)*5/9" Range("D3").Select Selection.Copy ' T = 3 + 24 * Ndays - 1 Range(Cells(4, "D"), Cells(T, "D")).Select ' Range("D4:D746").Select ActiveSheet.Paste Application.CutCopyMode = False Range("I10").Select ActiveWindow.SmallScroll Down:=13 ActiveWindow.ScrollRow = 1 ' MODIFICATION # 2 Range("I1").Select ActiveCell.FormulaR1C1 = "T" Range("I1").Select ActiveCell.FormulaR1C1 = "THETA" Range("I1").Select Selection.Font.Bold = True With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Range("I3").Select ActiveCell.FormulaR1C1 = "=ATAN(RC[-1]/RC[-2])" Range("I3").Select Selection.Copy ' Range("I4:I746").Select Range(Cells(4, "I"), Cells(T, "I")).Select ActiveSheet.Paste ' CONDITION IF DIVID BY ZERO

122

For i = 3 To T If Cells(i, "H") = 0 Then Cells(i, "I") = 0 End If Next i Range("J20").Select Application.CutCopyMode = False ActiveWindow.SmallScroll Down:=1 ActiveWindow.ScrollRow = 725 ActiveWindow.ScrollRow = 1 Range("J1").Select ActiveCell.FormulaR1C1 = "P.F" Range("J1").Select Selection.Font.Bold = True With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Range("J3").Select ActiveCell.FormulaR1C1 = "=COS(RC[-1])" Range("J3").Select Selection.Copy ' Range("J4:J746").Select Range(Cells(4, "J"), Cells(T, "J")).Select ActiveSheet.Paste For i = 3 To T If Cells(i, "J") = 1 Then Cells(i, "J") = 0 End If Next i Range("L4").Select ActiveWindow.ScrollRow = 725 ActiveWindow.ScrollRow = 1 Application.CutCopyMode = False Range("K1").Select ActiveCell.FormulaR1C1 = "CURRENT" Range("K2").Select ActiveCell.FormulaR1C1 = "A" Range("K1:K2").Select Selection.Font.Bold = True Columns("K:K").ColumnWidth = 8.57

123

Columns("K:K").EntireColumn.AutoFit Range("K3").Select ActiveCell.FormulaR1C1 = "=(RC[-4]/(1.73205*RC[-5]*RC[-1]))*1000" Range("K3").Select Selection.Copy ' Range("K4:K746").Select Range(Cells(4, "K"), Cells(T, "K")).Select ActiveSheet.Paste For i = 3 To T If Cells(i, "F") = 0 Then Cells(i, "K") = 0 End If If Cells(i, "H") = 0 Then Cells(i, "K") = 0 End If Next i Range("L19").Select ActiveWindow.SmallScroll Down:=0 Columns("I:K").Select Application.CutCopyMode = False Selection.NumberFormat = "0.0000" Columns("K:K").Select Selection.NumberFormat = "0.0" Columns("I:K").Select With Selection .HorizontalAlignment = xlGeneral .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With With Selection .HorizontalAlignment = xlCenter .VerticalAlignment = xlBottom .WrapText = False .Orientation = 0 .ShrinkToFit = False .ReadingOrder = xlContext .MergeCells = False End With Range("K11").Select Columns("I:I").Select Selection.EntireColumn.Hidden = True End Sub

124

B.2 Data For Load Modeling

Table B.1: Load Model Data for June 2 am

Temperature Humidity Active Power Reactive Power (C0) (%) MW MVAR

1998 30.56 31.00 30.00 14.00 31.67 35.00 32.00 14.00 32.78 51.00 37.00 16.00 33.89 28.00 32.00 15.00 35.00 33.00 38.00 19.00 34.44 40.00 34.00 16.00 35.00 29.00 35.00 17.00 35.56 28.00 39.00 17.00 30.00 29.00 32.00 14.00 32.22 21.00 32.00 14.00 31.67 43.00 32.00 14.00 31.11 64.00 34.00 16.00 30.00 78.00 31.00 13.00 30.56 69.00 31.00 14.00 31.11 54.00 31.00 13.00 27.78 25.00 31.00 14.00 31.11 58.00 33.00 14.00 33.89 52.00 34.00 15.00 32.78 27.00 30.00 13.00 32.78 33.00 34.00 15.00 32.78 52.00 32.00 14.00 35.00 35.00 33.00 14.00

1999 30.00 74.00 38.00 16.00 29.44 56.00 38.00 16.00 38.33 17.00 39.00 16.00 31.67 42.00 43.00 18.00 33.33 34.00 43.00 18.00 32.22 21.00 38.00 16.00 37.78 8.00 40.00 17.00 35.00 18.00 42.00 17.00 35.56 57.00 40.00 17.00 31.67 39.00 38.00 16.00 34.44 36.00 37.00 16.00 35.56 25.00 37.00 16.00 32.78 22.00 35.00 15.00 32.22 21.00 36.00 15.00 31.67 28.00 36.00 15.00 32.22 25.00 36.00 15.00 32.78 20.00 36.00 15.00 31.67 60.00 38.00 16.00 36.67 10.00 37.00 16.00 32.78 32.00 38.00 16.00 31.67 47.00 34.00 15.00

125

Continuation of Table B.1: Load Model Data for June 2 am

Temperature Humidity Active Power Reactive Power

(C0) (%) MW MVAR 2000

32.22 14.00 31.00 13.00 32.22 42.00 31.00 13.00 33.33 20.00 32.00 13.00 33.33 26.00 32.00 13.00 31.67 35.00 34.00 14.00 33.33 21.00 36.00 15.00 31.67 25.00 34.00 14.00 31.11 14.00 35.00 15.00 30.56 25.00 35.00 15.00 27.22 71.00 35.00 15.00 30.56 32.00 34.00 14.00 32.78 14.00 35.00 15.00 32.78 17.00 37.00 16.00 32.22 18.00 36.00 15.00 35.00 11.00 35.00 15.00 32.22 18.00 35.00 15.00 31.67 17.00 35.00 15.00 31.67 14.00 35.00 15.00 30.56 15.00 35.00 15.00

2001 28.89 19.00 31.00 13.00 28.33 20.00 30.00 13.00 25.00 89.00 31.00 13.00 26.11 89.00 33.00 14.00 28.89 45.00 34.00 14.00 32.78 42.00 32.00 13.00 30.56 31.00 32.00 14.00 31.11 15.00 34.00 14.00 30.00 25.00 33.00 14.00 30.00 18.00 32.00 13.00 31.11 34.00 31.00 13.00 28.89 56.00 33.00 14.00 31.11 24.00 34.00 14.00 33.89 20.00 36.00 15.00 32.22 25.00 34.00 15.00 29.44 55.00 35.00 15.00 35.00 31.00 37.00 16.00 33.33 18.00 35.00 15.00 30.56 22.00 34.00 14.00 32.78 18.00 34.00 15.00 35.00 35.00 37.00 16.00

126

Table B.2: Load Model Data for June 2 pm


(C0) (%) MW MVAR 1998

39.44 12.00 39.00 16.00 38.33 20.00 39.00 18.00 40.56 15.00 43.00 21.00 42.22 14.00 42.00 20.00 42.78 10.00 44.00 21.00 41.67 15.00 34.00 16.00 44.44 7.00 43.00 17.00 43.33 6.00 35.00 17.00 40.56 14.00 42.00 20.00 43.33 7.00 42.00 20.00 42.78 10.00 42.00 20.00 39.44 28.00 38.00 17.00 38.89 23.00 38.00 17.00 40.56 25.00 38.00 17.00 42.22 22.00 38.00 17.00 45.00 13.00 40.00 18.00 42.78 19.00 37.00 17.00 42.78 16.00 40.00 17.00 40.56 22.00 39.00 17.00 41.11 20.00 39.00 18.00 41.11 16.00 39.00 18.00 41.67 9.00 38.00 18.00

1999 45.56 6.00 47.00 21.00 44.44 11.00 48.00 21.00 41.11 18.00 49.00 21.00 40.00 17.00 47.00 21.00 38.89 17.00 47.00 21.00 42.78 7.00 46.00 20.00 43.33 14.00 48.00 21.00 44.44 8.00 50.00 23.00 43.33 12.00 49.00 22.00 40.00 11.00 45.00 20.00 41.67 7.00 44.00 19.00 42.22 8.00 45.00 20.00 41.67 18.00 46.00 20.00 41.67 11.00 44.00 20.00 41.67 11.00 41.00 18.00 41.11 13.00 43.00 19.00 41.11 8.00 44.00 19.00 37.78 25.00 34.00 15.00 37.78 21.00 43.00 19.00

127

Continuation of Table B.2: Load Model Data for June 2 pm


(C0) (%) MW MVAR 2000

42.78 7.00 37.00 15.00 45.00 7.00 37.00 15.00 38.33 14.00 35.00 15.00 36.67 18.00 37.00 16.00 38.33 14.00 37.00 16.00 40.00 13.00 39.00 17.00 40.00 11.00 40.00 17.00 39.44 8.00 41.00 17.00 44.44 7.00 40.00 17.00 41.11 16.00 40.00 17.00 43.33 6.00 40.00 17.00 45.00 5.00 42.00 18.00 40.56 12.00 42.00 18.00 38.89 18.00 40.00 17.00 39.44 8.00 40.00 17.00 40.00 9.00 40.00 17.00 41.67 8.00 40.00 17.00 41.11 8.00 40.00 17.00 41.11 7.00 40.00 17.00

2001 40.56 6.00 37.00 16.00 36.67 21.00 37.00 16.00 42.22 8.00 36.00 16.00 42.22 14.00 39.00 17.00 40.00 8.00 38.00 16.00 36.67 15.00 37.00 16.00 37.22 14.00 37.00 16.00 38.89 8.00 36.00 16.00 39.44 15.00 36.00 16.00 37.22 19.00 37.00 16.00 40.56 18.00 39.00 17.00 41.11 17.00 40.00 17.00 40.00 10.00 39.00 17.00 38.33 13.00 39.00 17.00 39.44 12.00 39.00 17.00 38.89 25.00 41.00 18.00 38.33 15.00 39.00 17.00 38.89 15.00 39.00 17.00 40.00 11.00 40.00 17.00 41.11 8.00 39.00 17.00 40.56 12.00 41.00 18.00

128

Table B.3: Load Model Data for July 2 am


(C0) (%) MW MVAR 1998

33.33 17.00 32.00 13.00 35.00 19.00 32.00 14.00 33.89 16.00 31.00 14.00 33.33 38.00 32.00 14.00 33.33 17.00 32.00 14.00 34.44 25.00 34.00 16.00 33.89 13.00 30.00 13.00 36.11 17.00 32.00 13.00 35.00 11.00 30.00 14.00 32.78 28.00 30.00 14.00 32.22 29.00 29.00 11.00 31.67 47.00 30.00 13.00 35.00 23.00 31.00 13.00 32.22 29.00 31.00 12.00 30.56 77.00 32.00 14.00 33.33 87.00 34.00 14.00 34.44 58.00 33.00 14.00 33.89 79.00 34.00 14.00 35.00 59.00 35.00 14.00 35.56 31.00 33.00 14.00 34.44 70.00 35.00 14.00

1999 31.67 18.00 35.00 15.00 31.67 20.00 35.00 15.00 33.89 40.00 35.00 15.00 33.89 18.00 37.00 16.00 33.89 38.00 37.00 16.00 32.22 80.00 38.00 16.00 32.78 37.00 35.00 15.00 33.89 29.00 36.00 15.00 33.89 22.00 37.00 16.00 36.11 16.00 44.00 21.00 34.44 28.00 36.00 15.00 31.67 23.00 44.00 21.00 32.22 19.00 44.00 21.00 32.78 15.00 30.00 13.00 32.78 29.00 32.00 14.00 33.89 42.00 33.00 14.00 31.11 85.00 32.00 13.00

129

Continuation of Table B.3: Load Model Data for July 2 am


(C0) (%) MW MVAR 2000

35.00 14.00 37.00 15.00 26.67 94.00 39.00 16.00 27.22 89.00 39.00 17.00 29.44 69.00 38.00 16.00 25.00 87.00 37.00 16.00 34.44 57.00 39.00 16.00 37.22 14.00 39.00 16.00 34.44 26.00 39.00 16.00 33.33 35.00 39.00 16.00 37.78 44.00 40.00 17.00 34.44 40.00 40.00 17.00 37.22 14.00 39.00 16.00 33.33 30.00 38.00 16.00 34.44 64.00 39.00 16.00 33.33 66.00 39.00 17.00 31.67 84.00 39.00 16.00 33.89 72.00 39.00 17.00 31.67 76.00 38.00 16.00 32.22 68.00 38.00 16.00 32.78 61.00 39.00 17.00

2001 32.78 15.00 35.00 15.00 31.67 17.00 34.00 15.00 33.89 12.00 38.00 16.00 32.78 24.00 36.00 16.00 32.78 18.00 35.00 15.00 34.44 15.00 36.00 15.00 32.78 25.00 36.00 16.00 31.67 19.00 35.00 15.00 34.44 26.00 31.00 14.00 29.44 74.00 32.00 15.00 32.78 24.00 32.00 15.00 36.11 14.00 33.00 15.00 32.22 63.00 33.00 15.00 32.22 61.00 33.00 15.00 36.11 15.00 34.00 16.00 36.11 13.00 36.00 17.00 35.00 20.00 33.00 13.00 31.67 75.00 35.00 16.00 31.67 83.00 34.00 14.00 32.22 74.00 34.00 14.00 32.22 74.00 34.00 14.00 31.67 80.00 34.00 14.00

130

Table B.4: Load Model Data for July 2 pm


(C0) (%) MW MVAR 1998

43.89 10.00 40.00 18.00 43.33 9.00 39.00 16.00 44.44 10.00 40.00 17.00 43.89 7.00 39.00 17.00 42.78 7.00 34.00 16.00 39.44 18.00 39.00 16.00 42.22 8.00 37.00 16.00 39.44 15.00 36.00 16.00 41.11 10.00 37.00 16.00 39.44 17.00 36.00 16.00 42.78 10.00 37.00 16.00 43.33 11.00 38.00 17.00 43.33 21.00 34.00 15.00 42.78 11.00 39.00 16.00 40.00 50.00 40.00 18.00 40.56 38.00 42.00 18.00 45.56 14.00 41.00 18.00 45.00 23.00 41.00 18.00 41.11 35.00 41.00 18.00 39.44 47.00 41.00 18.00 44.44 39.00 40.00 17.00

1999 40.00 12.00 43.00 19.00 41.67 8.00 43.00 19.00 38.33 33.00 44.00 19.00 40.56 27.00 45.00 20.00 43.89 7.00 44.00 20.00 45.00 7.00 46.00 20.00 44.44 11.00 43.00 19.00 38.33 57.00 47.00 21.00 40.56 19.00 44.00 20.00 40.56 18.00 44.00 20.00 42.78 12.00 44.00 20.00 40.00 25.00 44.00 21.00 40.56 9.00 44.00 21.00 41.67 12.00 44.00 21.00 42.22 9.00 44.00 21.00 42.78 9.00 39.00 18.00 44.44 14.00 40.00 18.00 43.33 16.00 39.00 17.00 38.89 26.00 44.00 21.00

131

Continuation of Table B.4: Load Model Data for July 2 pm


(C0) (%) MW MVAR 2000

45.56 20.00 43.00 18.00 45.00 29.00 44.00 19.00 44.44 19.00 43.00 18.00 45.56 10.00 41.00 18.00 42.78 10.00 41.00 17.00 46.67 10.00 43.00 18.00 44.44 10.00 42.00 18.00 51.67 4.00 45.00 19.00 42.78 15.00 44.00 19.00 41.67 18.00 45.00 19.00 41.11 25.00 43.00 18.00 43.89 16.00 43.00 18.00 43.89 13.00 44.00 19.00 41.67 30.00 45.00 19.00 45.56 8.00 44.00 18.00 46.11 11.00 44.00 19.00 43.89 18.00 44.00 19.00 41.67 17.00 43.00 18.00 43.33 20.00 43.00 18.00

2001 41.67 7.00 40.00 17.00 40.00 12.00 39.00 17.00 41.11 9.00 41.00 18.00 41.11 9.00 40.00 18.00 40.56 16.00 40.00 18.00 40.56 14.00 40.00 17.00 40.00 12.00 41.00 18.00 39.44 16.00 39.00 18.00 37.22 38.00 38.00 17.00 42.22 11.00 36.00 17.00 41.67 15.00 37.00 17.00 43.89 8.00 37.00 17.00 39.44 41.00 38.00 17.00 43.89 12.00 40.00 18.00 45.56 7.00 40.00 19.00 43.33 13.00 39.00 17.00 42.78 12.00 39.00 16.00 42.22 16.00 38.00 16.00 42.78 16.00 40.00 16.00 43.89 12.00 38.00 16.00 43.33 14.00 39.00 16.00 43.33 24.00 39.00 16.00

132

Table B.5: Load Model Data for August 2 am

Temperature Humidity Active Power Reactive Power (C0) (%) MW MVAR

1998 37.22 60.00 32.00 14.00 35.00 20.00 31.00 13.00 36.67 23.00 32.00 13.00 32.78 84.00 32.00 14.00 31.67 88.00 34.00 16.00 35.56 69.00 33.00 14.00 34.44 78.00 34.00 15.00 35.56 60.00 34.00 15.00 33.89 70.00 32.00 14.00 32.78 83.00 33.00 15.00 35.56 81.00 33.00 15.00 33.89 75.00 34.00 15.00 34.44 74.00 34.00 15.00 33.33 84.00 34.00 16.00 33.89 68.00 34.00 16.00 32.22 39.00 35.00 16.00 31.67 80.00 36.00 15.00 33.33 70.00 35.00 15.00 33.89 72.00 37.00 16.00 32.78 80.00 37.00 17.00 33.33 86.00 37.00 16.00 32.78 79.00 38.00 17.00 31.67 47.00 31.00 13.00

1999 33.33 18.00 44.00 21.00 32.22 73.00 44.00 21.00 31.67 70.00 44.00 21.00 33.33 47.00 32.00 14.00 30.00 86.00 44.00 21.00 35.00 27.00 40.00 19.00 36.11 33.00 33.00 14.00 34.44 28.00 35.00 15.00 27.78 93.00 34.00 15.00 33.33 32.00 42.00 19.00 31.67 73.00 33.00 14.00 31.67 76.00 34.00 15.00 31.11 85.00 36.00 16.00 32.22 51.00 33.00 14.00 32.78 52.00 34.00 14.00 31.67 85.00 35.00 16.00 33.89 68.00 35.00 15.00 30.00 87.00 35.00 15.00 30.00 84.00 44.00 21.00 30.00 77.00 44.00 21.00 27.22 90.00 44.00 21.00 32.22 73.00 36.00 16.00

133

Continuation of Table B.5: Load Model Data for August 2 am


(C0) (%) MW MVAR 2000

31.67 77.00 39.00 17.00 31.67 72.00 39.00 16.00 35.00 57.00 37.00 16.00 35.00 67.00 39.00 16.00 31.67 82.00 38.00 16.00 33.33 75.00 38.00 16.00 32.22 70.00 38.00 16.00 32.78 72.00 38.00 16.00 33.33 80.00 39.00 16.00 33.33 44.00 39.00 16.00 33.89 75.00 39.00 16.00 33.33 41.00 37.00 16.00 32.22 67.00 38.00 16.00 32.78 64.00 38.00 17.00 33.33 74.00 40.00 17.00 32.22 88.00 40.00 17.00 32.22 76.00 40.00 17.00 33.33 75.00 41.00 18.00 33.33 73.00 41.00 18.00 33.89 69.00 41.00 18.00 33.89 44.00 40.00 17.00 35.56 51.00 42.00 17.00

2001 32.78 79.00 34.00 13.00 35.56 35.00 33.00 13.00 33.89 59.00 34.00 14.00 33.89 68.00 34.00 14.00 33.89 64.00 34.00 15.00 35.00 61.00 34.00 15.00 33.33 87.00 35.00 15.00 35.00 54.00 35.00 15.00 32.22 79.00 34.00 15.00 32.78 72.00 34.00 15.00 30.00 86.00 33.00 15.00 31.67 75.00 32.00 14.00 26.67 96.00 33.00 14.00 32.78 87.00 32.00 14.00 27.78 85.00 33.00 14.00 32.22 52.00 31.00 14.00 31.67 92.00 33.00 14.00 27.78 80.00 33.00 14.00 28.33 83.00 34.00 15.00 28.89 79.00 33.00 14.00

134

Table B.6: Load Model Data for August 2 pm


(C0) (%) MW MVAR 1998

43.89 26.00 39.00 17.00 46.67 13.00 40.00 17.00 43.33 29.00 39.00 18.00 43.33 34.00 41.00 18.00 41.67 47.00 41.00 19.00 44.44 25.00 41.00 19.00 45.56 14.00 41.00 19.00 45.56 11.00 42.00 20.00 43.89 20.00 40.00 18.00 45.00 11.00 41.00 18.00 42.78 36.00 39.00 17.00 44.44 22.00 42.00 19.00 42.22 36.00 40.00 18.00 41.11 46.00 43.00 20.00 40.56 29.00 41.00 18.00 39.44 39.00 43.00 19.00 38.33 46.00 44.00 20.00 38.89 48.00 42.00 18.00 38.33 43.00 44.00 20.00 40.00 34.00 45.00 20.00

1999 40.56 16.00 44.00 21.00 41.11 16.00 40.00 18.00 39.44 35.00 44.00 21.00 38.89 32.00 40.00 19.00 39.44 33.00 44.00 21.00 43.33 22.00 41.00 19.00 43.89 8.00 41.00 19.00 43.33 15.00 42.00 19.00 45.56 7.00 42.00 18.00 42.78 18.00 42.00 19.00 45.00 9.00 40.00 18.00 41.11 31.00 41.00 18.00 38.33 55.00 45.00 20.00 38.33 57.00 45.00 20.00 41.67 25.00 42.00 19.00 42.78 22.00 44.00 20.00 40.00 47.00 44.00 20.00 39.44 46.00 44.00 21.00 44.44 22.00 44.00 21.00 38.33 51.00 44.00 21.00 38.89 42.00 44.00 21.00 42.22 29.00 44.00 21.00 43.33 24.00 44.00 21.00

135

Continuation of Table B.6: Load Model Data for August 2 pm


(C0) (%) MW MVAR 2000

44.44 11.00 44.00 19.00 45.56 12.00 44.00 19.00 47.22 8.00 45.00 19.00 45.00 30.00 45.00 19.00 40.56 38.00 45.00 19.00 41.67 30.00 45.00 19.00 43.89 13.00 44.00 18.00 40.56 40.00 45.00 19.00 41.11 47.00 46.00 19.00 43.33 33.00 45.00 18.00 42.78 16.00 44.00 18.00 42.22 21.00 44.00 18.00 43.89 15.00 44.00 18.00 43.89 8.00 44.00 19.00 42.78 27.00 46.00 19.00 43.33 20.00 45.00 19.00 41.11 26.00 46.00 20.00 42.78 23.00 47.00 20.00 42.78 25.00 47.00 20.00 41.67 26.00 46.00 20.00 41.11 28.00 48.00 20.00 38.89 22.00 44.00 19.00

2001 42.22 31.00 41.00 17.00 42.78 23.00 39.00 16.00 40.00 47.00 41.00 17.00 41.11 37.00 40.00 17.00 41.67 31.00 39.00 17.00 41.11 32.00 39.00 17.00 41.67 36.00 42.00 19.00 42.22 32.00 38.00 17.00 40.56 32.00 38.00 17.00 43.89 20.00 39.00 18.00 43.89 9.00 37.00 16.00 38.89 48.00 38.00 17.00 40.00 24.00 38.00 16.00 41.67 23.00 38.00 16.00 40.56 34.00 38.00 17.00 42.78 21.00 38.00 17.00 38.89 40.00 39.00 17.00 41.11 29.00 38.00 17.00

136

Table B.7: Load Model Data for September 2 am


(C0) (%) MW MVAR 1998

32.22 86.00 38.00 17.00 32.22 77.00 37.00 16.00 31.11 64.00 33.00 14.00 32.78 70.00 34.00 15.00 31.67 80.00 35.00 15.00 31.11 35.00 32.00 14.00 31.11 77.00 31.00 14.00 31.67 77.00 34.00 15.00 33.33 67.00 35.00 16.00 32.78 85.00 36.00 16.00 32.22 52.00 32.00 13.00 28.89 55.50 30.00 13.00 30.56 73.00 30.00 13.00 29.44 75.00 31.00 13.00 31.11 61.00 30.00 13.00 31.67 45.00 30.00 13.00 28.89 85.00 34.00 15.00 28.33 88.00 33.00 15.00 29.44 73.00 33.00 15.00 28.33 82.00 32.00 15.00 28.89 88.00 33.00 14.00

1999 32.78 60.00 36.00 16.00 32.78 66.00 44.00 21.00 32.22 70.00 36.00 16.00 30.56 83.00 32.00 14.00 31.67 55.00 33.00 14.00 28.89 81.00 33.00 15.00 33.33 39.00 33.00 15.00 29.44 49.00 30.00 13.00 29.44 50.00 30.00 13.00 30.00 58.00 31.00 13.00 30.00 35.00 28.00 12.00 27.22 64.00 28.00 12.00 28.33 77.00 29.00 13.00 27.22 40.00 27.00 13.00 27.22 67.00 26.00 11.00 26.11 85.00 28.00 12.00 29.44 73.00 32.00 14.00 27.78 82.00 29.00 13.00

137

Continuation of Table B.7: Load Model Data for September 2 am


(C0) (%) MW MVAR 2000

31.67 43.00 36.00 16.00 32.22 22.00 34.00 15.00 28.89 27.00 32.00 14.00 27.22 53.00 32.00 14.00 27.78 64.00 32.00 14.00 29.44 39.00 31.00 14.00 31.67 22.00 31.00 13.00 30.56 24.00 32.00 14.00 30.56 21.00 30.00 13.00 27.22 72.00 32.00 13.00 28.33 30.00 30.00 13.00 27.22 86.00 33.00 15.00 28.33 56.00 31.00 14.00 28.89 41.00 30.00 13.00 26.11 86.00 33.00 14.00 28.89 76.00 32.00 14.00 27.78 76.00 30.00 13.00 28.33 75.00 31.00 14.00 26.11 76.00 31.00 14.00 28.89 68.00 30.00 13.00 29.44 76.00 33.00 14.00

2001 36.11 24.00 33.00 15.00 36.11 40.00 37.00 15.00 32.78 20.00 31.00 14.00 23.89 88.00 31.00 14.00 32.78 28.00 31.00 14.00 33.89 49.00 33.00 14.00 29.44 49.00 31.00 14.00 29.44 57.00 31.00 14.00 26.67 76.00 30.00 15.00 29.44 50.00 29.00 14.00 26.67 77.00 29.00 14.00 28.33 74.00 28.00 14.00 28.89 76.00 30.00 14.00 30.56 69.00 32.00 15.00 29.44 72.00 32.00 14.00 28.89 83.00 31.00 14.00 30.00 72.00 30.00 13.00 28.89 81.00 38.00 18.00 27.78 70.00 30.00 12.00 28.33 71.00 38.00 18.00 26.67 78.00 30.00 13.00 28.89 53.00 29.00 12.00

138

Table B.8: Load Model Data for September 2 pm


(C0) (%) MW MVAR 1998

41.11 37.00 46.00 21.00 40.56 35.00 45.00 20.00 38.33 26.00 42.00 19.00 39.44 36.00 44.00 19.00 37.78 35.00 43.00 19.00 38.89 26.00 41.00 19.00 37.78 42.00 42.00 19.00 41.67 18.00 39.00 17.00 40.56 41.00 45.00 20.00 41.11 35.00 45.00 20.00 38.33 41.00 42.00 18.00 40.00 31.00 36.00 16.00 41.11 18.00 38.00 16.00 41.67 20.00 41.00 18.00 37.78 33.00 38.00 18.00 38.89 36.00 44.00 20.00 42.78 12.00 42.00 19.00 39.44 33.00 42.00 19.00 40.56 19.00 42.00 19.00 38.33 29.00 41.00 19.00

1999 44.44 12.00 47.00 20.00 40.56 30.00 46.00 20.00 40.00 44.00 46.00 20.00 40.00 25.00 44.00 20.00 40.56 23.00 44.00 19.00 42.22 13.00 42.00 19.00 38.33 28.00 41.00 18.00 36.67 31.00 41.00 18.00 37.22 27.00 41.00 18.00 37.78 25.00 40.00 18.00 37.78 22.00 38.00 17.00 37.22 27.00 36.00 16.00 36.11 32.00 38.00 18.00 35.56 41.00 37.00 17.00 35.56 41.00 36.00 16.00 42.78 11.00 36.00 16.00 36.11 27.00 33.00 15.00 37.22 27.00 34.00 16.00 37.22 39.00 37.00 17.00 38.89 26.00 41.00 18.00 36.67 40.00 37.00 17.00

139

Continuation of Table B.8: Load Model Data for September 2 pm


(C0) (%) MW MVAR 2000

38.33 12.00 39.00 17.00 36.11 28.00 40.00 17.00 38.89 16.00 38.00 17.00 37.22 33.00 39.00 18.00 37.22 22.00 36.00 16.00 37.22 26.00 38.00 16.00 40.00 13.00 38.00 16.00 37.78 24.00 37.00 16.00 38.89 17.00 37.00 16.00 38.33 20.00 38.00 17.00 38.33 19.00 37.00 16.00 38.89 22.00 39.00 17.00 40.00 10.00 38.00 16.00 40.56 9.00 36.00 16.00 36.11 35.00 38.00 17.00 35.56 44.00 38.00 16.00 39.44 12.00 35.00 15.00 36.67 32.00 36.00 16.00 39.44 20.00 35.00 16.00 37.78 19.00 36.00 16.00 37.22 30.00 38.00 17.00

2001 40.00 29.00 41.00 17.00 40.56 15.00 38.00 17.00 40.00 17.00 37.00 17.00 41.67 12.00 37.00 17.00 43.89 9.00 38.00 16.00 39.44 24.00 38.00 16.00 38.33 18.00 37.00 18.00 37.78 29.00 36.00 16.00 36.67 30.00 36.00 18.00 37.78 27.00 37.00 17.00 35.00 48.00 35.00 16.00 34.44 42.00 34.00 17.00 37.22 39.00 35.00 17.00 37.22 33.00 37.00 18.00 40.00 10.00 36.00 16.00 40.00 18.00 38.00 17.00 41.11 11.00 38.00 18.00 41.67 9.00 36.00 15.00 40.00 19.00 38.00 18.00 40.00 20.00 36.00 14.00 38.89 26.00 34.00 16.00 41.11 18.00 35.00 15.00

140

Appendix C

ERROR BARS PLOTS

141

Figure C.1: Error Bar for the Active Power Model for 1998 June at 2 am

142

Figure C.2: Error Bar for the Reactive Power Model for 1998 June at 2 am

143

Figure C.3: Error Bar for the Active Power Model for 1998 June at 2 pm

144

Figure C.4: Error Bar for the Reactive Power Model for 1998 June at 2 pm

145


146


147


148


149


150


151


152


153


154


155


156


157

Figure C.17: Error Bar for the Active Power Model for 1998 July at 2 am

158

Figure C.18: Error Bar for the Reactive Power Model for 1998 July at 2 am

159

Figure C.19: Error Bar for the Active Power Model for 1998 July at 2 pm

160

Figure C.20: Error Bar for the Reactive Power Model for 1998 July at 2 pm

161


162


163


164


165


166


167


168


169


170


171


172


173

Figure C.33: Error Bar for the Active Power Model for 1998 August at 2 am

174

Figure C.34: Error Bar for the Reactive Power Model for 1998 August at 2 am

175


176


177


178


179


180


181

Figure C.41: Error Bar for the Active Power Model for 1998 September at 2 am

182

Figure C.42: Error Bar for the Reactive Power Model for 1998 September at 2 am

183

Figure C.43: Error Bar for the Active Power Model for 1998 September at 2 pm

184

Figure C.44: Error Bar for the Reactive Power Model for 1998 September at 2 pm

185


186


187


188


189


190


191


192


193


194


195


196


197

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200

Vita

• Khaled Hamed Abdullah Al-Ghamdi

• Born in Al-Baha, Saudi Arabia in Rajab 1392H.

• Received Degree of Bachelor of Science in Electrical Engineering, with third

honors, from King Fahd University of Petroleum and Minerals, Dhahran, Saudi

Arabia in January 1997.

• Working in the Saudi Electricity Company-Eastern Region Branch (SEC-ERB),

Dammam, Saudi Arabia as Planning Engineer, System Planning Department.

Documents

Environmental Impact on Residential Load Modelingeprints.kfupm.edu.sa/10554/1/10554.pdf · 2011-04-06 · Environmental Impact on Residential Load Modeling Khaled Hamed Al-Ghamdi