voltage stability and power flow studies of distribution system including

VOLTAGE STABILITY AND POWER FLOW STUDIES OF DISTRIBUTION SYSTEM INCLUDING DISTRIBUTED GENERATION

By

Mostafa Hassan Mostafa Abdel-Gawad A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE in Electrical Power and Machines Engineering

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT June, 2016

VOLTAGE STABILITY AND POWER FLOW STUDIES OF DISTRIBUTION SYSTEM INCLUDING DISTRIBUTED GENERATION

By Mostafa Hassan Mostafa Abdel-Gawad

A Thesis Submitted to the Faculty of Engineering at Cairo University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE In Electrical Power and Machines Engineering

Under the Supervision of

Prof. Dr. Magdy El-Marsafawy

Dr. Mostafa El-Shahed

Professor of Electrical Power Systems Electrical Power and Machines Department Faculty of Engineering, Cairo University

Assistant Professor of Electrical Power Systems Electrical Power and Machines Department Faculty of Engineering, Cairo University

FACULTY OF ENGINEERING, CAIRO UNIVERSITY GIZA, EGYPT JUNE, 6102

Engineer: Date of Birth: Nationality: E-mail: Phone: Address: Registration Date: Awarding Date: Degree: Department: Supervisors:

Examiners: Title of Thesis:

Key Words:

Mostafa Hassan Mostafa Abdel-Gawad 1 / 12 / 1989 Egyptian [email protected] 01114741378 Owseem City, Giza, Egypt 1 / 10 / 2013 / / Master of Science Electrical Power and Machines Engineering Prof. Dr. Magdy El-Marsafawy Dr. Mostafa Elshahed

VOLTAGE STABILITY AND POWER FLOW STUDIES OF DISTRIBUTION SYSTEM INCLUDING DISTRIBUTED GENERATION Voltage stability, radial distribution networks, distributed generator, load model, power flow.

Summary: The distributed generation (DG) is more increased on power grids around the world. DG units have proven to have an effect on voltage profile, power flow, power quality, stability, reliability, and protection. The voltage instability occurs when increased load which propulsion power system to stability boundaries and lead to voltage collapse and power blackouts. Therefore, there is a need to study voltage stability of the system. Also, study how to prevent power system near to stability boundaries. In this thesis, the effect of penetration of distributed generation of a radial system on voltage stability, voltage profile, and power flow will be studied. The distributed generation studied in this thesis will give active and reactive power or active power only. Power flow is studied by calculating voltage profile of each bus and power losses of the distribution system. Voltage stability analysis is studied by calculating fast voltage stability index, line stability index, line stability factor, maximum load ability and plotting the P-V curves. This thesis is offering a study of the effect of load models on the calculation of voltage stability, voltage profile, and power flow. The optimal location and size of distributed generation to achieve minimum power losses and enhanced voltage stability are studied in this thesis by using genetic algorithm.

AUTHOR'S DECLARATION

This thesis is submitted to Cairo University in partial fulfillment of the requirement for the Master of Science degree in Electrical Engineering. No Part of this thesis has been submitted for a degree or a qualification at other university or institute. Finally, I understand that my thesis may be made electronically available to the public.

Name: Signature:

Mostafa Hassan Mostafa Abdel-Gawad

Mostafa Hassan Mostafa

Date:

June, 2016

Cairo University, Giza, Egypt, 2016 © Mostafa Hassan 2016

Acknowledgments First and foremost thanks to God. Without his help and blessing I would not have been able to finish this work. I am honored to record my deepest sense of gratitude and thanks to my supervisors Prof. Dr. Magdy El-Marsafawy and Dr. Mostafa Elshahed for the efforts they had exerted in this research, their helpful discussions, constructive criticism and the understanding they haves shown throughout this work. I do really appreciate very much their fruitful comments to this thesis. I also wish to acknowledge and present my sincere gratitude to Prof. Dr. Sherif Mohamed Wasfy for his continuous encouragement, care, and support. Very special thanks to my family, especially my parents, my brothers and my sisters for their patience, understanding and encouragement during the different phases of my work. They spared no effort until this work comes to existence. I would like to thank my fiancée (Kholoud Sarg) for understanding, encouragement and continuous support. Finally, I would like to thank my friends, especially Sherif Saed, Mohamed Saber, Islam Salah, Ahmed Abdelrahman and Mahmoud Alnahas for their encouragement and continuous support.

Thank you all!

i

Table of Contents Acknowledgments ........................................................................................................... i Table of Contents ........................................................................................................... ii List of Tables ................................................................................................................ vii List of Figure .................................................................................................................. x List of Abbreviation .................................................................................................... xiv Abstract

xv

Chapter 1

Introduction.............................................................................................. 1

1.1

Overview ........................................................................................................... 1

1.2

Problem Statement ............................................................................................ 1

1.3

Research Objectives .......................................................................................... 1

1.4

Thesis Outlines .................................................................................................. 2

Chapter 2

Literature survey ..................................................................................... 3

2.1

Introduction ....................................................................................................... 3

2.2

Definition of Distributed Generation ................................................................ 3

2.3

Types of DG ...................................................................................................... 3

2.3.1

Wind Turbine ............................................................................................. 4

2.3.2

Photovoltaic ............................................................................................... 5

2.3.3

Fuel cells .................................................................................................... 6

2.3.4

Reciprocating Internal Combustion Engine (ICE)..................................... 6

2.3.5

Micro-turbines ........................................................................................... 6

2.3.6

Gas Turbine................................................................................................ 6

2.3.7

Storage Devices ......................................................................................... 7

2.4

System Stability Overview................................................................................ 7

2.4.1

Rotor Angle stability.................................................................................. 8

2.4.2

Frequency Stability .................................................................................... 9

2.4.3

Voltage Stability ........................................................................................ 9

Chapter 3

System Analysis and Problem Formulation ........................................ 10

3.1

Load Flow Analysis ........................................................................................ 10

3.1.1 3.2

Voltage stability analysis ................................................................................ 12

3.2.1

3.3

Load Flow Solution ................................................................................. 12 Static Voltage Stability ............................................................................ 12

3.2.1.1

P-V and Q-V Curves. ....................................................................................... 12

3.2.1.2

Voltage Stability Indices ................................................................................. 15

Optimal sizing and siting of DG ..................................................................... 18 ii

3.3.1 3.3.1.1

Objective Function ......................................................................................... 19

3.3.1.2

Constraints ..................................................................................................... 19

3.3.2 3.4

Problem Formulation ............................................................................... 19

Optimization Techniques ......................................................................... 19

Load Modeling ................................................................................................ 20

3.4.1

Static Load Model .................................................................................... 20

Chapter 4

: Simulation Results and Discussions ................................................... 21

4.1

Introduction ..................................................................................................... 21

4.2

Single DG capable of delivering active and reactive power ........................... 21

4.2.1 4.2.1.1

Result of voltage stability indices without DG and with different DG size .... 23

4.2.1.2

Result of voltage profile without DG and with different DG size................... 27

4.2.1.3

Result of power flow without DG and with different DG size........................ 30

4.2.1.4

Result of P-V curve without DG and with different DG size........................... 31

4.2.2

4.3

IEEE 33 bus radial distribution system.................................................... 21

Practical radial distribution system .......................................................... 39

4.2.2.1


4.2.2.2


4.2.2.3


4.2.2.4


Single DG capable of delivering active power only ....................................... 50

4.3.1


1.1.4.4


1.1.4.4


1.1.4.1


1.1.4.1


4.3.2

Practical radial distribution system .......................................................... 66

4.3.2.1


4.3.2.2


4.3.3 4.3.3.1

Result of power flow without DG and with different DG size ................ 71 Result of P-V curve without DG and with different DG size........................... 72

4.4 Comparison between DG that given active and reactive power and DG that give active power only ............................................................................................... 76 4.4.0


1.1.4.4

Voltage Stability ............................................................................................. 76

1.1.4.4

Voltage Profile ................................................................................................ 77

iii

4.4.1.3

Power Flow..................................................................................................... 78

1.1.4.1

P-V Curve ........................................................................................................ 80

4.4.2

Practical radial distribution system in Japan............................................ 81

4.4.2.1

Voltage Stability ............................................................................................. 81

4.4.2.2

Voltage Profile ................................................................................................ 81

4.4.2.3

Power Flow..................................................................................................... 82

4.4.2.4

P-V Curve ........................................................................................................ 84

Chapter 5

Load Modeling ....................................................................................... 85

1.0

Introduction ..................................................................................................... 85

5.2

Industrial Load ................................................................................................ 85

5.2.1

Single DG capable of delivering active and reactive power .................... 85

5.2.1.1 Result of voltage stability indices without DG and with different DG size when load is industrial load ........................................................................................... 86 5.2.1.2 load

Result of voltage profile without DG and with different DG size at industrial 90

5.2.1.3

Result of power flow without DG and with different DG size at industrial load 93

5.2.2

Single DG capable of delivering active power only ................................ 94

5.2.2.1 Result of voltage stability indices without DG and with different DG size at industrial load ................................................................................................................ 95

5.3

5.2.2.2 load

Result of voltage profile without DG and with different DG size at industrial 99

5.2.2.3

Result of power flow without DG and with different DG size at industrial load 102

Residential Load............................................................................................ 103

5.3.1

Single DG capable of delivering active and reactive power .................. 103

5.3.1.1 Result of voltage stability indices without DG and with different DG size at residential load............................................................................................................. 103 5.3.1.2 load

Result of voltage profile without DG and with different DG size at residential 108

5.3.1.3 load

Result of power flow without DG and with different DG size at residential 111

5.3.2

Single DG capable of delivering active power only .............................. 112

5.3.2.1 Result of voltage stability indices without DG and with different DG size at residential load............................................................................................................. 112 5.3.2.2 load

Result of voltage profile without DG and with different DG size at residential 116

iv

5.3.2.3 load

5.4

Result of power flow without DG and with different DG size at residential 119

Commercial Load .......................................................................................... 120

5.4.1

Single DG capable of delivering active and reactive power .................. 120

5.4.1.1 Result of voltage stability indices without DG and with different DG size at commercial load ........................................................................................................... 120 5.4.1.2 load

Result of voltage profile without DG and with different DG size at commercial 125

5.4.1.3 load

Result of power flow without DG and with different DG size at commercial 128

5.4.2

Single DG capable of delivering active power only .............................. 129

5.4.2.1 Result of voltage stability indices without DG and with different DG size at commercial load ........................................................................................................... 129

5.5

5.4.2.2 load

Result of voltage profile without DG and with different DG size at commercial 133

5.4.2.3 load

Result of power flow without DG and with different DG size at commercial 136

Result comparison ......................................................................................... 137

Chapter 6

Optimal Sizing and Sitting of DG....................................................... 139

6.1

Introduction ................................................................................................... 139

6.2

Constant Load ............................................................................................... 139

6.2.1

Load flow and voltage stability analysis................................................ 139

6.2.2

Optimal location and size of DG unit to achieve losses minimization .. 143

6.2.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability .................................................................................... 147 6.3

Industrial Load .............................................................................................. 151

6.3.1


6.3.2



Residential Load............................................................................................ 163

6.4.1


6.4.2



Commercial Load .......................................................................................... 175

2.1.0


6.5.2

Optimal location and size of DG unit to achieve losses minimization .. 179 v

6.5.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability .................................................................................... 183 Chapter 7

Conclusions and Future Work ........................................................... 187

7.1

Conclusions ................................................................................................... 187

7.2

Recommendations and Future Work ............................................................. 188

References 189 Appendices 193 Appendix A.1 ........................................................................................................... 193 Appendix A.3 ........................................................................................................... 195

vi

List of Tables

Table ‎3.1: Load types and exponent values ................................................................... 20 Table ‎4.1: Rating of installed distributed generation..................................................... 23 Table ‎4.2: Values of fast voltage stability index (FVSI) at the different DG size ....... 24 Table ‎4.3: Values of the line stability index (Lmn) at the different DG size ................ 25 Table ‎4.4 Values of line stability factor (LQP) at the different DG size ....................... 26 Table ‎4.5: The effect of increasing size of DG on voltage of each bus ......................... 29 Table ‎4.6: The effect of increasing size of DG on power flow ..................................... 30 Table ‎4.7: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 31 Table ‎4.8: Rating of installed DG .................................................................................. 39 Table ‎4.9: Values of fast voltage stability index (FVSI) at the diverse DG size ........... 40 Table ‎4.10: Values of the line stability index (Lmn) at the diverse DG size ................ 41 Table ‎4.11: Values of line stability factor (LQP) at the diverse DG size ...................... 41 Table ‎4.12: The effect of increasing size of DG on voltage of each bus ....................... 44 Table ‎4.13: The effect of increasing size of DG on power flow ................................... 44 Table ‎4.14: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 45 Table ‎4.15: Rating of installed DG ................................................................................ 51 Table ‎4.16: Values of fast voltage stability index (FVSI) at the different DG size ..... 52 Table ‎4.17: Values of the line stability index (Lmn) at the different DG size .............. 53 Table ‎4.18: Values of line stability factor (LQP) at the diverse DG size ...................... 54 Table ‎4.19 The effect of increasing size of DG on voltage of each bus ........................ 57 Table ‎4.20: The effect of increasing size of DG on power flow ................................... 58 Table ‎4.21: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 59 Table ‎4.22: Rating of installed DG ................................................................................ 66 Table ‎4.23: Values of fast voltage stability index (FVSI) at the different DG size ...... 67 Table ‎4.24: Values of the line stability index (Lmn) at the different DG size ............. 68 Table ‎4.25: Values of line stability factor (LQP) at the different DG size .................... 68 Table ‎4.26: The effect of increasing size of DG on voltage of each bus ....................... 71 Table ‎4.27: The effect of increasing size of DG on power flow ................................... 71 Table ‎4.28: The Impact of Increasing Size of DG on Max Load Ability ...................... 72 Table ‎5.1: Rating of installed distributed generation..................................................... 85 Table ‎5.2 Values of fast voltage stability index (FVSI) at the different DG size at industrial load ................................................................................................................ 87 Table ‎5.3 :Values of the line stability index (Lmn) at the different DG size at industrial load ................................................................................................................................ 88 Table ‎5.4: Values of line stability factor (LQP) at the diverse DG size at industrial load ....................................................................................................................................... 89 Table ‎5.5: The effect of increasing size of DG on voltage of each bus ......................... 92 Table ‎5.6: The effect of increasing size of DG on power flow ..................................... 93 Table ‎5.7: Values of fast voltage stability index (FVSI) at the different DG size at industrial load ................................................................................................................ 96 Table ‎5.8: Values of the line stability index (Lmn) at the different DG size at industrial load ................................................................................................................................ 97 vii

Table ‎5.9: Values of line stability factor (LQP) at the different DG size at industrial load ................................................................................................................................ 98 Table ‎5.10: The effect of increasing size of DG on voltage of each bus ..................... 101 Table ‎5.11: The effect of increasing size of DG on power flow ................................. 102 Table ‎5.12: Values of fast voltage stability index (FVSI) at the different DG size at residential load ............................................................................................................. 105 Table ‎5.13: Values of the line stability index (Lmn) at the different DG size at residential load ............................................................................................................. 106 Table ‎5.14: Values of line stability factor (LQP) at the different DG size at residential load .............................................................................................................................. 107 Table ‎5.15 :The effect of increasing size of DG on voltage of each bus at residential load .............................................................................................................................. 110 Table ‎5.16: The effect of increasing size of DG on power flow ................................. 111 Table ‎5.17: Values of fast voltage stability index (FVSI) at the different DG size at residential load ............................................................................................................. 113 Table ‎5.18: Values of the line stability index (Lmn) at the different DG size at residential load ............................................................................................................. 114 Table ‎5.19: Values of line stability factor (LQP) at the different DG size at residential load .............................................................................................................................. 115 Table ‎5.20: The effect of increasing size of DG on voltage of each bus at residential load .............................................................................................................................. 118 Table ‎5.21: The effect of increasing size of DG on power flow at residential load .... 119 Table ‎5.22: Values of fast voltage stability index (FVSI) at the different DG size at commercial .................................................................................................................. 122 Table ‎5.23: Values of the line stability index (Lmn) at the different DG size at commercial load........................................................................................................... 123 Table ‎5.24: Values of line stability factor (LQP) at the different DG size at commercial load .............................................................................................................................. 124 Table ‎5.25: The effect of increasing size of DG on voltage of each bus at commercial load .............................................................................................................................. 127 Table ‎5.26: The effect of increasing size of DG on power flow at commercial load .. 128 Table ‎5.27: Values of fast voltage stability index (FVSI) at the different DG size at commercial load........................................................................................................... 130 Table ‎5.28: Values of the line stability index (Lmn) at the different DG size at commercial load........................................................................................................... 131 Table ‎5.29: Values of line stability factor (LQP) at the different DG size at commercial load .............................................................................................................................. 132 Table ‎5.30: The effect of increasing size of DG on voltage of each bus at commercial load .............................................................................................................................. 135 Table ‎5.31: The effect of increasing size of DG on power flow at commercial load .. 136 Table ‎5.32: Result of different load with DG give active and reactive power ............ 137 Table ‎5.33: Result of different load with DG give active power only ........................ 138 Table ‎6.1: Show load flow solution without DG ......................................................... 140 Table ‎6.2: Show value of fast voltage stability index without DG .............................. 141 Table ‎6.3: optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses ................................................................................................... 143 Table ‎6.4: Optimal DG size and location by genetic algorithm .................................. 145 Table ‎6.5: Show load flow solution with DG to achieve minimum losses only ......... 145 Table ‎6.6: show value of fast voltage stability index to achieve minimum losses ...... 146 Table ‎6.7: Optimal DG size and location by genetic algorithm .................................. 148 viii

Table ‎6.8: Show load flow solution with DG to achieve minimum losses and enhanced voltage stability............................................................................................................ 148 Table ‎6.9: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability............................................................................................ 149 Table ‎6.10: Show load flow solution without DG ....................................................... 152 Table ‎6.11: Show value of fast voltage stability index without DG ........................... 153 Table ‎6.12: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses ................................................................................................... 155 Table ‎6.13: Optimal DG size and location by genetic algorithm ................................ 157 Table ‎6.14: Show load flow solution with DG to achieve minimum losses................ 157 Table ‎6.15: show value of fast voltage stability index to achieve minimum losses .... 158 Table ‎6.16: Optimal DG size and location by genetic algorithm ................................ 160 Table ‎6.17: Show load flow solution with DG to achieve minimum losses and enhanced voltage stability............................................................................................................ 160 Table ‎6.18: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability............................................................................................ 161 Table ‎6.19: Show load flow solution without DG ....................................................... 164 Table ‎6.20: Show value of fast voltage stability index without DG ............................ 165 Table ‎6.21: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses ................................................................................................... 167 Table ‎6.22: Optimal DG size and location by genetic algorithm ................................ 169 Table ‎6.23: Show load flow solution with DG to achieve minimum losses only ....... 169 Table ‎6.24: show value of fast voltage stability index to achieve minimum losses .... 170 Table ‎6.25: Optimal DG size and location by genetic algorithm ................................ 172 Table ‎6.26: Show load flow solution with DG to achieve minimum losses and enhanced voltage stability............................................................................................................ 172 Table ‎6.27: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability............................................................................................ 173 Table ‎6.28: Show load flow solution without DG ....................................................... 176 Table ‎6.29: Show value of fast voltage stability index without DG ............................ 177 Table ‎6.30: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses ................................................................................................... 179 Table ‎6.31: Optimal DG size and location by genetic algorithm ................................ 181 Table ‎6.32: Show load flow solution with DG to achieve minimum losses only ....... 181 Table ‎6.33: show value of fast voltage stability index to achieve minimum losses .... 182 Table ‎6.34: Optimal DG size and location by genetic algorithm ................................ 184 Table ‎6.35: Show load flow solution with DG to achieve minimum losses and enhanced voltage stability............................................................................................................ 184 Table ‎6.36: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability............................................................................................ 185

ix

List of Figure Figure ‎2-1: Distributed Generation sources ..................................................................... 4 Figure ‎2-2: Types of wind turbines ................................................................................ 5 Figure ‎2-3: Open Cycle Gas Turbine Engine. ................................................................. 7 Figure ‎2-4: Classification of power system stability ....................................................... 8 Figure ‎3-1: A simple radial distribution network .......................................................... 10 Figure ‎3-2: Single line of power transmission .............................................................. 13 Figure ‎3-3: P-V curve or nose curve............................................................................. 14 Figure ‎3-4: Q-V characteristic curve ............................................................................ 14 Figure ‎3-5: Single line of power transmission concept ................................................ 15 Figure ‎3-6: Single line of power transmission concept ................................................. 17 Figure ‎4-1: 33 bus radial distribution systems ............................................................... 22 Figure ‎4-2 : The effect of increasing size of DG on the weakest voltage stability bus (bus 30) .......................................................................................................................... 27 Figure ‎4-3: The effect of increasing the size of DG on voltage of the weakest voltage stability bus (bus 30) ...................................................................................................... 27 Figure ‎4-4: The effect of increasing size of DG on voltage of each bus ....................... 28 Figure ‎4-5: The effect of increasing the size of DG on power losses ............................ 30 Figure ‎4-6: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 31 Figure ‎4-7: P-V Curves without DG............................................................................. 32 Figure ‎4-8: P-V Curves with DG (size 10% of the load) ............................................. 33 Figure ‎4-9: P-V Curves with DG (size 20% of the load) ............................................. 34 Figure ‎4-10: P-V Curves with DG (size 30% of the load) ........................................... 35 Figure ‎4-11: P-V Curves with DG (size 40% from the load) ....................................... 36 Figure ‎4-12: P-V Curves with DG (size 50% of the load) ........................................... 37 Figure ‎4-13: P-V Curves with DG (size 60% of the load) ........................................... 38 Figure ‎4-14: Practical radial 15 bus distribution system ............................................... 39 Figure ‎4-15: The effect of increasing size of DG on the weakest bus (bus 11) ............ 42 Figure ‎4-16: The effect of increasing the size of DG on voltage of the weakest bus (bus 11) .................................................................................................................................. 42 Figure ‎4-17: The effect of increasing size of DG on voltage of each bus ..................... 43 Figure ‎4-18: The effect of increasing the size of DG on power losses .......................... 45 Figure ‎4-19: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 46 Figure ‎4-20: P-V Curves without DG............................................................................ 46 Figure ‎4-21: P-V Curves with DG (size 10% of the load) ........................................... 47 Figure ‎4-22: P-V Curves with DG (size 20% of the load) ........................................... 47 Figure ‎4-23: P-V Curves with DG (size 30% of the load) ........................................... 48 Figure ‎4-24: P-V Curves with DG (size 40% of the load) ........................................... 48 Figure ‎4-25: P-V Curves with DG (size 50% of the load) ............................................ 49 Figure ‎4-26: P-V Curves with DG (size 60% of the load) ............................................ 49 Figure ‎4-27: P-V Curves with DG (size 70% of the load) ............................................ 50 Figure ‎4-28: The effect of increasing size of DG on the weakest bus (bus 30) ............ 55 Figure ‎4-29: The effect of increasing the size of DG on voltage of the weakest bus (bus 30) .................................................................................................................................. 55 Figure ‎4-30: The effect of increasing size of DG on voltage of each bus ..................... 56 x

Figure ‎4-31: The effect of increasing the size of DG on power losses .......................... 58 Figure ‎4-32: The effect of increasing size of DG on the maximum value of the loading parameter ....................................................................................................................... 59 Figure ‎4-33: P-V Curves without DG............................................................................ 60 Figure ‎4-34: P-V Curves with DG (size 10% of the load) ........................................... 61 Figure ‎4-35: P-V Curves with DG (size 20% of the load) ........................................... 62 Figure ‎4-36: P-V Curves with DG (size 30% of the load) ............................................ 63 Figure ‎4-37: P-V Curves with DG (size 40% of the load) ............................................ 64 Figure ‎4-38: P-V Curves with DG (size 50% of the load) ............................................ 65 Figure ‎4-39: The effect of increasing size of DG on the weakest bus (bus 11) ............ 67 Figure ‎4-40: The effect of increasing the size of DG on voltage of the weakest bus (bus 11) .................................................................................................................................. 69 Figure ‎4-41: The effect of increasing size of DG on voltage of each bus ..................... 70 Figure ‎4-42: The effect of increasing the size of DG on power losses .......................... 72 Figure ‎4-43: P-V Curves without DG........................................................................... 73 Figure ‎4-44: P-V Curves with DG 10% of load ........................................................... 73 Figure ‎4-45: P-V Curves with DG 20% of load ........................................................... 74 Figure ‎4-46: P-V Curves with DG 30% of load ........................................................... 74 Figure ‎4-47: P-V Curves with DG 40% of load ............................................................ 75 Figure ‎4-48: P-V Curves with DG 50% of load ............................................................ 75 Figure ‎4-49: P-V Curves with DG 60% of load ............................................................ 76 Figure ‎4-50: The impact of two type DG on voltage stability....................................... 77 Figure ‎4-51: The impact of two types of DG on Voltage profile at bus 30 ................... 78 Figure ‎4-52: The impact of two types of DG on power flow ........................................ 79 Figure ‎4-53: The impact of two types of DG on power losses ...................................... 79 Figure ‎4-54: The impact of two types of DG on max loading point ............................. 80 Figure ‎4-55: The impact of two types of DG on voltage stability ................................ 81 Figure ‎4-56: The impact of two types of DG on Voltage of weakest voltage stability bus (bus 11).................................................................................................................... 82 Figure ‎4-57: The impact of two types of DG on power flow ....................................... 83 Figure ‎4-58: The impact of two types of DG on power losses ..................................... 83 Figure ‎4-59: The impact of two types of DG on max loading point ............................. 84 Figure ‎5-1: The effect of increasing size of DG on the weakest voltage stability bus at industrial load ................................................................................................................ 86 Figure ‎5-2: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at industrial load ........................................................................................ 90 Figure ‎5-3: The effect of increasing the size of DG on active & reactive power losses 94 Figure ‎5-4: The effect of increasing size of DG on the weakest voltage stability bus at industrial load ................................................................................................................ 95 Figure ‎5-5: The effect of increasing the size of DG on voltage of the weakest bus voltage stability at industrial load .................................................................................. 99 Figure ‎5-6: The effect of increasing size of DG on voltage of each bus at industrial load ..................................................................................................................................... 100 Figure ‎5-7: The effect of increasing the size of DG on active & reactive power losses at industrial load .............................................................................................................. 102 Figure ‎5-8: The effect of increasing size of DG on the weakest bus (bus 30) ............ 104 Figure ‎5-9: The effect of increasing the size of DG on voltage of the weakest voltage stability bus (bus 30) at residential load ...................................................................... 108 Figure ‎5-10: The effect of increasing size of DG on voltage of each bus at residential load .............................................................................................................................. 109 xi

Figure ‎5-11: The effect of increasing the size of DG on power losses ........................ 111 Figure ‎5-12: The effect of increasing size of DG on the weakest voltage stability bus at residential load ............................................................................................................. 116 Figure ‎5-13: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at residential load .................................................................................... 116 Figure ‎5-14: The effect of increasing size of DG on voltage of each bus at residential load .............................................................................................................................. 117 Figure ‎5-15: The effect of increasing the size of DG on power losses at residential load ..................................................................................................................................... 119 Figure ‎5-16: The effect of increasing size of DG on the weakest voltage stability bus (bus 30) at commercial load ........................................................................................ 121 Figure ‎5-17: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at commercial load .................................................................................. 125 Figure ‎5-18: The effect of increasing size of DG on voltage of each bus at commercial load .............................................................................................................................. 126 Figure ‎5-19: The effect of increasing the size of on power losses at commercial load 128 Figure ‎5-20: The effect of increasing size of DG on the weakest voltage stability bus at commercial load........................................................................................................... 133 Figure ‎5-21: The effect of increasing the size of DG on voltage of the weakest bus voltage stability (bus 30) ............................................................................................. 133 Figure ‎5-22: The effect of increasing size of DG on voltage of each bus at commercial load .............................................................................................................................. 134 Figure ‎5-23: The effect of increasing the size of photovoltaic on power losses at commercial load........................................................................................................... 136 Figure ‎6-1: Voltage profile of IEEE 33 bus system .................................................... 142 Figure ‎6-2: Fast voltage stability index of IEEE 33 bus System ................................. 142 Figure ‎6-3: Optimum size of DG at each bus of IEEE 33 bus system ........................ 144 Figure ‎6-4: Total active and reactive power losses corresponding to optimum size at each bus of IEEE 33 bus system .................................................................................. 144 Figure ‎6-5: Voltage profile at each bus after install DG to achieve minimum losses . 146 Figure ‎6-6: FVSI of each line in IEEE 33 bus system after install optimal DG size and location ........................................................................................................................ 147 Figure ‎6-7: Voltage profile without DG and after install DG at bus 6 and bus 30 ...... 150 Figure ‎6-8: FVSI without DG and after install DG at bus 6 and bus 30 ..................... 150 Figure ‎6-9: Voltage profile of IEEE 33 bus system .................................................... 154 Figure ‎6-10: Fast voltage stability index of IEEE 33 bus System ............................... 154 Figure ‎6-11: Optimum size of DG at each bus of IEEE 33 bus system ...................... 156 Figure ‎6-12: Total active and reactive power losses corresponding to optimum size at each bus of IEEE 33 bus system .................................................................................. 156 Figure ‎6-13: Voltage profile at each bus after install DG to achieve minimum losses 158 Figure ‎6-14: FVSI of each line in IEEE 33 bus system after install optimal DG size and location ........................................................................................................................ 159 Figure ‎6-15: Voltage profile without DG and after install DG at bus 6 and bus 30 .... 162 Figure ‎6-16: FVSI without DG and after install DG at bus 6 and bus 30 ................... 162 Figure ‎6-17: Voltage profile of IEEE 33 bus system .................................................. 166 Figure ‎6-18: Fast voltage stability index of IEEE 33 bus System ............................... 166 Figure ‎6-19: Optimum size of DG at each bus of IEEE 33 bus system ..................... 168 Figure ‎6-20: Total active and reactive power losses corresponding to optimum size at each bus of IEEE 33 bus system .................................................................................. 168 Figure ‎6-21: Voltage profile at each bus after install DG to achieve minimum losses 170 xii

Figure ‎6-22: FVSI of each line in IEEE 33 bus system after install optimal DG size and location ........................................................................................................................ 171 Figure ‎6-23: Voltage profile without DG and after install DG at bus 6 and bus 30 .... 174 Figure ‎6-24: FVSI without DG and after install DG at bus 6 and bus 30 ................... 174 Figure ‎6-25: Voltage profile of IEEE 33 bus system .................................................. 178 Figure ‎6-26: Fast voltage stability index of IEEE 33 bus System ............................... 178 Figure ‎6-27: Optimum size of DG at each bus of IEEE 33 bus system ..................... 180 Figure ‎6-28: Total active and reactive power losses corresponding to optimum size at each bus of IEEE 33 bus system .................................................................................. 180 Figure ‎6-29: Voltage profile at each bus after install DG to achieve minimum losses 182 Figure ‎6-30: FVSI of each line in IEEE 33 bus system after install optimal DG size and location ........................................................................................................................ 183 Figure ‎6-31: Voltage profile without DG and after install DG at bus 6 and bus 30 .... 186 Figure ‎6-32: FVSI without DG and after install DG at bus 6 and bus 30 ................... 186

xiii

List of Abbreviation ABC

Artificial Bee Colony

BIBC

Bus Injection to Branch Current

BCBV

Branch Current to Bus Voltage

DG

Distributed Generation

GA

Genetic Algorithm

IEEE

Institute of Electrical and Electronics Engineers

KCL

Kirchhoff‟s‎Current‎Law‎

FVSI

Fast Voltage Stability Index

Lmn

Line Voltage Stability Index

LQP

Line Voltage Stability Factor

α‎

Voltage exponents of real loads

β‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎ Voltage exponents of reactive loads

xiv

Abstract The distributed generation (DG) is more increased on power grids around the world. DG units have proven to have an effect on voltage profile, power flow, power quality, stability, reliability, and protection. The voltage instability occurs when increased load which propulsion power system to stability boundaries and lead to voltage collapse and power blackouts. Therefore, there is a need to study voltage stability of the system. Also, study how to prevent power system near to stability boundaries. In this thesis, the effect of penetration of distributed generation of a radial system on voltage stability, voltage profile, and power flow will be studied. The distributed generation studied in this thesis will give active and reactive power or active power only. Power flow is studied by calculating voltage profile of each bus and power losses of the distribution system. Voltage stability analysis is studied by calculating fast voltage stability index, line stability index, line stability factor, maximum load ability and plotting the P-V curves. Normally a constant power load model is assumed in most of the studies. Such assumptions may lead to misleading results about deferral values. Load modeling has a large influence on the effect of distributed generation on voltage stability, voltage profile, and power flow. This thesis is offering a study of the effect of load models on the calculation of voltage stability, voltage profile, and power flow. The optimal location and size of distributed generation to achieve minimum power losses and enhanced voltage stability are studied in this thesis by using genetic algorithm. To show the validity of the proposed solutions and techniques, computer simulations are carried out on IEEE 33 bus radial distribution network and practical ‎radial ‎distribution‎‎system‎‎in ‎Japan and the simulation results are presented and discussed. All the required software is developed using MATLAB script files, Excel, PSAT.

xv

Chapter 1 Introduction 1.1 Overview Always, loads are far from the power plant, transmission lines and distribution systems are used to transport energy from power plants to loads. Load demand is growing, this increase needs new plant, transmission lines and distribution systems which more expensive. Therefore, distributed generation is used to increase the capacity power of grid and improve it. Distributed generation (DG) have many types such as wind turbine, photovoltaic, fuel cells, micro turbine and gas turbine. Distributed generation that gives active and reactive power or gives active power only have an effect on voltage profile, power flow, power quality, stability, reliability, protection and line losses. This will studied in this thesis.

1.2 Problem Statement The energy which transports from the power plant to load increased when load demand is increased. So, power losses in transmission line increase which causes a greater voltage drop at this line. This leads to declining voltage, weak in voltage stability and blackout.

1.3 Research Objectives The goal of this research studies the effect of the penetration of DG on power flow and voltage stability. Therefore, this research is targeting the following objectives: ● Provide survey about types of distributed generation, voltage stability and load modeling. ● Study power flow of radial system with different sizes of distributed generation. ●‎ Study voltage stability of the radial system with different sizes of distributed generation. ●‎ Study‎ the‎ effect‎ of‎ load‎ modeling‎ on‎ power‎ flow‎ and‎ voltage‎ stability with different sizes of distributed generation. ●‎ Determine the optimal location and size to minimize total power losses and to enhance voltage stability for each load modeling type.

1

1.4 Thesis Outlines The present thesis consists of seven chapters Chapter 1: A general introduction to the thesis topics and offered problem statement and research objective and thesis outlines. Chapter 2: Present a literature survey on the definition of distributed generation, types of DG, power system stability, voltage stability analysis and load modeling. Chapter 3: Present power system stability, voltage stability analysis, load modeling and problem formulation Chapter 4: Evaluate the effect size of distributed generation on voltage profile, power flow, and voltage stability when DG give active and reactive power or give active power only and Present comparison between two cases. Chapter 5: Evaluate the effect of load modeling distributed generation on voltage profile, power flow, and voltage stability. Chapter 6: Present the optimal size and location to minimize losses only and to enhance voltage stability with minimizing losses with different load model. Chapter 7: Present the thesis summary and contributions.

2

Chapter 2 Literature survey 2.1 Introduction This chapter gives a writing review on distribution generation, voltage stability and load modeling.

2.2 Definition of Distributed Generation In the light of the writing review, there is no steady description of Distributed Generation (DG), but generally, they are little-scale generation element situated near or at loads [1]. Distributed generation can be described as a slight scale generation element based on either burning such as reciprocating engines and turbines, or nonburning such as fuel cells, photovoltaic, wind turbines, etc [2]. These are situated near the end clients and are characterized as renewable or co-generation sources [2]. Distributed generation is described in IEEE [3] as‎“a‎slight wellspring of electric power generation or storage (commonly running from a kW to tens of MW) that is not a part of the main power plant and is situated near to‎ the‎ load”.‎ Distributed generation is described in IEEE [1] as‎ “an‎ electric power generation wellspring associated straightforwardly to the distribution system or on near‎to‎the‎client”.‎This description is the most general description because there is no limit on the DG size and capacity.

2.3 Types of DG There are many types of DG which can be categorized to dispatchable or nondispatchable. The DG is dispatchable when the operator can control the essential energy sources. The DG is non-dispatchable when the operator cannot control the essential energy sources like renewable energy sources. Types of DG source are shown in Figure 2-1 and are briefly discussed as follows.

3

Figure ‎2-1: Distributed Generation sources

2.3.1 Wind Turbine In the latest years, wind energy plays an important role in generating power from renewable energy. Wind energy is a sort of renewable green energy. Renewable energy is reaped from nature, and it is clean and free. The idea of operation for a wind turbine is the transformation the kinetic energy into mechanical energy and then changed into electrical energy, using AC generators such as induction and synchronous machine. A cluster of wind turbines mounted in a specific area is known as a wind farm. These wind farms are usually installed in a windy place, in light of the fact that the energy that can be created by a wind turbine firmly relies on upon wind speed. The efficiency of the wind turbine is 20% to 40%, and its power rating varies between 0.3 to 7 MW [4]. Wind turbines are categorized into four sorts: A, B, C, and D as shown in Figure 2-2 [5].

4

Figure ‎2-2: Types of wind turbines Type A usage a constant velocity wind turbine with a Squirrel Cage Induction Generator (SCIG). Type B usages a variable velocity wind turbine with a Wound Rotor Induction Generator (WRIG). Type C usages a Doubly Fed Induction Generator (DFIG) with a wound rotor induction generator (WRIG). Type D usages a full variable velocity wind turbine with generator, linked to the network through a full load frequency converter. Type of generator is a Wound Rotor Synchronous Generator (WRSG) or a Permanent Magnet Synchronous Generator (PMSG) [5].

2.3.2 Photovoltaic The primary part of a photovoltaic is solar cells. The solar cell is produced using semiconductor materials, for example, monocrystalline and polycrystalline silicon. It uses semiconductors to transform sunlight into electric energy. Photovoltaic are similar to electronics devices in using diodes, transistors, and integrated circuits [6]. Photovoltaic (PV) systems use to transform of sunlight into electricity without any combustion engine. PV module rating related to a number of PV cells and type of connection parallel or series. PV panels installed at ground or roof or can be attached motorized tracking units which track the sun to increase electrical energy.The photovoltaic rating is from 0.3 kW to many megawatts in the big system [7]. The efficiency of photovoltaic is low less than 20% [8]. PV systems are the most expensive DG types [9]. Power electronics converters used to connect photovoltaic DG to grid with Maximum Power Point Tracking (MPPT) [10]. Photovoltaic work with MPPT by used several methods, for example, voltage feedback, the perturb and observe method, linear line approximation, fuzzy logic control, neural network method, and practical measure method [11].

5

2.3.3 Fuel cells Fuel cells (FCs) are used to transform the chemical energy into direct current electrical energy without burning [12]. There are many types of fuel cells such as solid oxide fuel cells (SOFC), polymer electrolyte membrane fuel cells (PEMFC) and molten carbonate fuel cells (MCFC) are most likely be used for DG applications [13][16]. A fuel cell is similar to a battery in constructing by two electrodes with an ionconductive electrolyte inserted between them. A fuel cell‎isn‟t‎similar to a battery in it does not a requirement to be charged. The efficiency of the fuel cell is about 40-60% [17].The benefits of fuel cells are high efficiency, little emission, and silent operation [17]. Boost converter used to increase the output voltage of fuel cells and then used a dc-ac converter. The chief challenge of the marketing of fuel cells is the high investment cost [18].

2.3.4 Reciprocating Internal Combustion Engine (ICE) Reciprocating internal combustion engines (ICEs) transform heat into rotary motion which drives a generator. ICE is one of the most DG type used and the smallest expensive one [19]. A generator which used in reciprocating internal combustion engine is a synchronous or an induction generator. ICE can be linked to the network without any power electronics converter. Drawbacks of ICEs are great maintenance, fuel cost, harmful emissions and a great noise [20], [21].

2.3.5 Micro-turbines Micro-turbines are essentially a grouping of a small generator and a small turbine. The micro-turbines rating are from few kilowatts to megawatts [22]. Microturbines work with less vibration and low noise, require low maintenance, and run on a variety of fuels [23]. So, the micro turbine is one the important DG today. They are diverse the traditional burning turbines. Microturbine rotates at very great velocity from 50,000 to 120,000 rpm [24]. So, microturbines generate a very high-frequency power from 1500 to 4000 Hz [23]. Therefore, power electronics converter used to link microturbine with grid [25].

2.3.6 Gas Turbine Gas turbines are increased, due to their lesser emission and greater efficiency. A gas turbine consists of a compressor, with a burning chamber and a turbine operating under the Brayton cycle [26], [27]. Figure 2-3 shows open cycle gas turbine engine. The maintenance cost is lesser than for reciprocating engines.

6

.

.

Figure ‎2-3: Open Cycle Gas Turbine Engine.

2.3.7 Storage Devices Stability, power quality, and reliability of power system are increased when used storage devices [28]. Sorts of storage devices are batteries, flywheels, super-capacitors, and superconducting magnetic energy storage. Power electronics converter used to link this type of DG with the grid.

2.4 System Stability Overview In the operation of a power system, at any given time, there must be a balance between the electricity supply and the demand. A power system should, therefore, be able to maintain this balance under both normal conditions (steady-state) and after disturbances‎(transient).‎The‎stability‎of‎a‎power‎system‎is‎defined‎as‎“a‎property‎of‎a‎ power system that enables it to remain in a state of equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance”‎[29]. The operating condition of a power system is described according to physical quantities, such as the magnitude and phase angle of the voltage at each bus, and the active/reactive power flowing in each line. If these quantities are constant over time, the system is in steady state; if they are not constant, the system is considered to be in disturbance [30]. The disturbances can be small or large depending on their origin and magnitude. For instance, small variations in load and generation are types of small disturbances, but faults, large changes in load, and loss of generating units are types of large disturbances [30]. The stability of a power system can be classified as shown in Figure 2-4into [31]: rotor angle stability, voltage stability, and frequency stability. In basic terms, distribution system networks are designed to receive power from the transmission line and then distribute it to customers. Thus, real power and reactive power both flow in one direction. However, when DG units are installed in distribution systems, the directions of the real and reactive power may be reversed. Therefore, the penetration of DG units into distribution systems affects the stability of the system, and as the penetration level increases, stability becomes a significant issue. Any fault 7

occurring in the distribution system might cause voltage and angle instability [32]. In distribution systems with embedded DG units, the main factors that influence stability are the control strategies of the DG units, the energy storage systems, the types of load in the system, the location of faults, and the inertia constant of the motor [33].

Figure ‎2-4: Classification of power system stability

2.4.1 Rotor Angle stability Rotor‎ angle‎ stability‎ is‎ “the‎ ability‎ of‎ interconnected‎ synchronous‎ machines‎ in‎ a‎ power system to remain in synchronism under normal operating conditions and after being subjected‎ to‎ a‎ disturbance”‎ [29]. Instability occurs in the form of increasing angular swings of some generators, which leads to the loss of synchronism. Therefore, machine characteristics and modeling are helpful in the study of the rotor angle stability [29]. In distributed generation, rotor angle stability has been studied in both transmission and distribution systems. Reference [34] investigated the impact of high penetration levels of DG units on the transient stability of a transmission power system. The researchers examined transient stability by making scenarios of faults in all possible branches, and concluded that the penetration level of the units affects the power flow in the transmission lines, and hence, the transient stability of the transmission. The author of [35] studied the impact of distributed generation technology (such as inverter-based and rotating-based DG units) on the transient stability of a power system. This study found that transient stability is strongly dependent on the technology used in the DG units.

8

2.4.2 Frequency Stability Frequency stability is defined as the capability of a power system to keep the frequency inside an acceptable range following a system upset that results in a significant imbalance between generation and load [29].

2.4.3 Voltage Stability Voltage stability is defined as the capability of a power system to continue steady acceptable voltages at all buses in the system under ordinary conditions and after being subjected to a disturbance [36]. Voltage stability can be attained by sufficient generation and transmission of energy. Generation and transmission units have definite capacities that are peculiar to them. These limits should not be exceeded in a healthy power system. Voltage stability problem arises when the system is heavily loaded that causes to go beyond limitations of power system. A power system enters a state of voltage instability when a disturbance, increase in load demand power or change in system condition causes a progressive and uncontrollable decline in voltage. The main factor causing instability is the inability of the power system to meet the demand for reactive power [29] and [37].

9

Chapter 3 System Analysis and Problem Formulation 3.1 Load Flow Analysis Load flow analysis can be obtained by using the developed method by J.H.Teng [38]. This method depends on two matrices, the bus injection to branch current (BIBC) matrix and the branch current to the bus voltage (BCBV) matrix. This method is very efficient when dealing with the radial distribution system. The developed method will be described in this part.

Figure ‎3-1: A simple radial distribution network Figure 3-1 shows a simple radial distribution network which is used to illustrate this method. is the branch current and is the bus injection current. Apparent power load at each bus is expressed by: (3.1) Active and reactive powers load in each bus and node voltage current injection

(

)

used to obtain the (3.2)

Where is bus voltage at the iteration is current injection of bus, at the iteration Kirchhoff‟s‎Current‎Law‎(KCL) can be used to obtain the relation between the bus current injections and branch current. 10

(3.3) } Equation 3.3 can be rewritten as follows:

(3.4) [

[

]

][ ]

Equation 3.4 can be arranged in general form as follows: [

]

[

][ ]

(3.5)

Where BIBC is the bus-injection to the branch-current (BIBC) matrix. The branch currents are related to bus voltages by equation (3.6):

(3.6) } Where is the impedance between bus and bus . The equation 3.6 can be rewrite as following:

(3.7) [ ]

[ ]

[

][

]

The voltage drop from each bus to the reference bus is obtained as

(3.8) [ ]

[ ]

[

][

]

General form as following: [

]

[

][

]

Where BCBV is the branch current to the bus-voltage matrix. 11

(3.9)

By combining equations (3.5) and (3.9) [ Where

]

[

][

]

[

][

][ ]

is a multiplication matrix of

and

[

][ ]

(3.10)

matrices.

3.1.1 Load Flow Solution The following equations are used to solve load flow equations. ( [

)

(3.2)

]

(3.11) (3.12)

Where is bus voltage at the iteration is current injection of bus, at the

iteration

3.2 Voltage stability analysis There are two methods to analyze voltage stability: static and dynamic [36]. This thesis is concerned of static analysis of voltage stability.

3.2.1 Static Voltage Stability The static voltage stability is assessed by i) P-V and Q-V curves ii) Voltage stability indices The next subsection introduces overview about these techniques. 3.2.1.1 P-V and Q-V Curves. P-V and Q-V curves are created by carrying out a large number of power flows using power flow methods. PV and QV curves are a traditional method for explaining the voltage instability.

12

Figure ‎3-2: Single line of power transmission Consider the simplified two-bus model in Figure 3-6. Active and reactive power reach to load can be calculated by using load flow equation [36]. (3.13) (3.15) Where is the active power load is the reactive power load is the line reactance is the load bus voltage δ‎‎is the angle difference between the supply voltage and the receiving voltage. Solving (3.14) and (3.15) √

(3.16)

√

Equation (3.16) produces two solutions of voltages, signified by the upper and lower parts of the PV-curve, these solution points are moving on a P-V curve until they merge into a critical loading point as shown in Figure 3.3.The upper voltage solution, which is corresponding‎to‎“+”‎sign‎in equation (3.16) is stable, while the lower voltage, corresponding‎ to‎ “-”‎ sign,‎ is‎ unstable‎ [36].‎ The‎ top‎ of‎ the‎ “nose‎ curve”‎ is‎ called‎ the‎ maximum load ability point or voltage collapse point. The stability margin can be defined by the distant from the operating point to the voltage collapse point, it is the most widely accepted index for the proximity of voltage collapse.

13

Figure ‎3-3: P-V curve or nose curve Often, a more suitable characteristic for a certain side of voltage stability analysis is the Q-V curves in figure 3.4. QV curves represent a plot of reactive power versus voltage for a specific bus. These can be used for evaluating the requirements for reactive power compensation since they show the sensitivity and variation of bus voltages with respect to reactive power injections or absorptions. A positive Q-V region since an increase in Q is accompanied by an increase in V is indicative of stable operation and a negative Q-V region since an increase in Q represents a decrease in V is indicative of unstable operation [29]. In conclusion, The V-Q sensitivity can judges that a system is voltage unstable if, for at least one bus in the system, the bus voltage magnitude decreases as the reactive power injection in the same bus is increased.

Figure ‎3-4: Q-V characteristic curve 14

3.2.1.2

Voltage Stability Indices

In general, it is beneficial to evaluate voltage stability of power systems by means of voltage stability indices, scalar magnitudes that can be observed as system parameters change. Operators can use these indices to distinguish how close the system is to voltage collapse in an intuitive manner and react accordingly. After a literature research on voltage stability indices detailed and complete classification of these indices was noticed. Although some comparison papers between indices have been found in [39 - 43]. The voltage stability analysis in this thesis will be focused on Fast Voltage stability index (FVSI), Line Stability Index (Lmn), Line Stability Factor (LQP). By using these voltages stability indices can measure the level of stability of system and thereby suitable deed may be taken if the indices show a poor level of stability. The line, which the values of the stability indices are near to one, is more sensitive to the voltage instability. 3.2.1.2.1 Fast Voltage Stability Index (FVSI) Fast voltage stability index shortened by FVSI is used to forecast the voltage stability condition in the system. Figure 3.5 illustrates a single line of an interconnected network. The FVSI is derived in [44], [45] and [46].

I

,

+ Figure ‎3-5: Single line of power transmission concept Where = voltage on sending and receiving buses = active and reactive power on the sending bus = active and reactive power on the receiving buses = apparent power on the sending and receiving buses = angle difference between sending and receiving buses Z= + = line impedance between sending bus and receiving bus The current flows from sending bus and receiving bus given by

15

,

is reference voltage The apparent power of receiving bus given by

Separating the real and imaginary parts

Solve equations (3.23) and (3.22) to get voltage of receiving bus

(

)

̅ √[(

)

]

The discriminant is set greater than or equal to zero to make system stability

[(

)

]

(

)

Since 𝛅 is normally very small then, 𝛅 = 0 R sin𝛅

and X cos𝛅

X

The fast voltage stability index (FVSI) can be defined by

16

The line that has index value closest to 1 will be the most critical line and may lead to the system instability. To rightly a secure condition the value of FVSI should be below 1.00. 3.2.1.2.2 Line stability Index(Lmn) line stability index is derived in [45], [46], [47]. The formulation begins with the current equation in a power system. Figure 2-10 illustrates a single line of a power transmission concept.

+ Figure ‎3-6: Single line of power transmission concept | || |

| |

| || |

| |

From these power equations, one can separate real and reactive power | || |

(

| || |

Putting

| |

)

| |

into equation 3.31 and solving it for

√[

]

Now for Z sin = X, we have √[

]

17

The following conditions, which can be used as a stability condition: [

]

[

]

is termed the line stability index of that line. The stability condition is used to find the stability index for each line connected between two busbars in an interconnected network. Based on the stability indices of lines, voltage collapse can be accurately predicted. As long as the stability index L,, remains less than I, the system is stable and when this index exceeds the value 1, the whole system loses its stability and voltage collapse occurs. Thus the proposed method can be used in voltage collapse prediction. 3.2.1.2.3 Line stability factor (LQP) Line stability factor is derived in [46] and [47]. The power equation can be represented as;

(

)

The line stability factor is obtained by setting the discriminate of the reactive power roots at bus 1 to be greater than or equal to zero. Line stability factor is defined by the following condition, (

)(

)

Where: X = line reactance, Qj = reactive power at the receiving end, Vi= sending end voltage, Pi=active sending end power. LQP must be less than unity to maintain a stable system.

3.3 Optimal sizing and siting of DG The chief profit from development analysis is to find the suitable location and size of a DG and avoid installation them non-optimally which may result in an increasing in system losses, voltage problems, etc. The optimization issue is defined by how to find the optimal size and location of DG unit to satisfy the preferred objective function subject to certain operating constraints.

18

3.3.1 Problem Formulation In order to formulate the problem, two things must be thought about. These two things are the objective functions that want to be optimized and the other is the constraints that can confine this objective. 3.3.1.1 Objective Function Several studies recommended DG siting and sizing to minimizing the system power loss while DG placement to enhance the voltage stability. I. Via Losses Minimization Mathematically, the objective function is formulated as follows: To Minimize:

=∑

Where is the no. of branches, respectively.

, and

are the

branch resistance and current

II. Via Voltage Stability Index Minimization The objective of the allocation technique is to minimize the maximum value of the voltage stability indices mentioned in equation (3.27), (3.35) and (3.37). Mathematically, the objective function is formulated as follows: To Minimize: [FVSI min], [Lmn min], [LQP min] 3.3.1.2

Constraints

i) Voltage constraints: For DG:

| |

(3.38)

Where =1,‎2,‎3…n.‎And‎n‎is‎the‎number‎of‎buses. ii) Maximum DG size: ∑

(3.39)

3.3.2 Optimization Techniques In this work a single DG capable of delivering active power only is considered. The Genetic Algorithm (GA) is used to solve the allocation problems under the constrained objective function mentioned in equations (3.38) and (3.39).

19

3.4 Load Modeling In conventional load flow studies, it is presumed that active and reactive power demands are specified constant values, regardless of the amplitude of voltages in the same bus. In actual distribution systems operation, different categories and types of loads such as residential, industrial and commercial loads might be present. The nature of these types of loads is such that their active and reactive powers are dependent on the voltage of the system. Moreover, load characteristics have significant effects on load flow solutions and other subsequent calculations [48]. Distribution system loads present different behavior to grid voltage variations. For example, active and reactive power consumption by fluorescent lamps are highly affected by the voltage magnitude, while personal computers are less sensitive to voltage variations [49]. Static load models are the most commonly used in load flow analysis in distribution networks.

3.4.1 Static Load Model This model expresses the reactive and active power as a function of the magnitude of bus bar voltage. The load models can be mathematically expressed as | | | | Where, = Real power injections at bus = Reactive power injections at bus = Real load at bus at nominal voltage = Reactive load at bus at nominal voltage α‎=‎Voltage exponents of real loads β‎=‎Voltage exponents of reactive loads = Voltage of th node Practical voltage dependent load models, i.e., residential, industrial, and commercial, given in [50] have been adopted for investigations. In a constant power model, conventionally‎used‎in‎ power‎ ﬂow‎studies,‎ is assumed. The values of the real and reactive exponents used in the present work for industrial, residential, and commercial loads are given in Table [50]. Table ‎3.1: Load types and exponent values Load Type

α

β

Constant Load

0

0

Industrial Load

0.18

6.00

Residential Load

0.92

4.04

Commercial Load

1.51

3.40

20

Chapter 4 : Simulation Results and Discussions 4.1 Introduction In this thesis, all simulations have been executed by MATLAB (m-file), PSAT program and Excel to run the load flow, calculate power losses, voltage stability index and draw a P-V curve of each bus. In this thesis, there are two cases ●‎Single‎DG‎capable‎of‎delivering‎active‎and‎reactive power ●‎Single‎DG‎capable‎of‎delivering‎active‎power‎only

4.2 Single DG capable of delivering active and reactive power In this part, the results will be presented as follow: ●‎Results of voltage stability indices without DG and with different DG size ●‎Results of voltage profile without DG and with different DG size ●‎Results of power flow without DG and with different DG size ●‎Results of P-V curve without DG and with different DG size. All simulations in this part were executed on ●‎IEEE‎33‎bus‎radial‎distribution system ●‎Practical‎radial‎distribution‎system‎in‎Japan.

4.2.1 IEEE 33 bus radial distribution system In this part, all simulations were executed on IEEE 33 bus radial distribution system shown in Figure 4.1. The network substation voltage is 12.66 KV, base MVA=100 and total load of 3.7 MW and 2.3 MVAR. The system‟s data can be found in [45] and given in Appendix A.

21

Figure ‎4-1: 33 bus radial distribution systems

22

4.2.1.1 Result of voltage stability indices without DG and with different DG size Voltage stability indices described in section 3.2 are applied on IEEE 33 bus radial system. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 4.2. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 4.3. Values of line stability factor (LQP) at the diverse DG size are shown in Table 4.4. According to values of voltage stability indices without the DG in Table 4.2, 4.3 and 4.4 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 4.1. From Tables 4.2, 4.3 and 4.4 notice that the values of voltage stability indices at each line are nearer to zero when installing the DG unit in bus 30. So, voltage stability enhanced at each bus. Also, when increases the size of DG, voltage stability of each bus more enhanced. Figure 4.2 demonstrations the effect of increasing the size of DG on the weakest voltage stability line (bus 29 to bus 30).

Table ‎4.1: Rating of installed distributed generation Rating of wind turbine 10% of the load 20% of the load 30% of the load 40% of the load 50% of the load 20% of the load

Active Power (MWatt) 0.3715 0.743 1.1145 1.486 1.8575 6.66

23

Reactive Power (MVAR) 0.23 0.46 0.69 0.92 1.15 0..4

Table ‎4.2: Values of fast voltage stability index (FVSI) at the different DG size Line

FVSI without DG

1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11 11 to 12 12 to 13 13 to 14 14 to 15 15 to 16 16 to 17 17 to 18 2 to 19 19 to 20 20 to 21 21 to 22 3 to 23 23 to 24 24 to 25 6 to 26 26 to 27 27 to 28 28 to 29 29 to 30 30 to 31 31 to 32 32 to 33

0.000341 0.001224 0.001870 0.000741 0.000881 0.001869 0.006656 0.001224 0.001200 0.000587 0.001272 0.003070 0.002646 0.000351 0.000929 0.001598 0.001801 0.000329 0.003040 0.000839 0.001494 0.001251 0.009608 0.009739 0.000347 0.000488 0.001192 0.003253 0.021936 0.004005 0.001861 0.000890

FVSI with DG 10 % of load 0.000341 0.001223 0.001862 0.000736 0.000873 0.001837 0.006544 0.001203 0.001179 0.000577 0.001250 0.003016 0.002599 0.000345 0.000912 0.001569 0.001769 0.000329 0.003038 0.000838 0.001493 0.001245 0.009567 0.009698 0.000341 0.000479 0.001168 0.003158 0.021145 0.003846 0.001786 0.000854



24




Table ‎4.3: Values of the line stability index (Lmn) at the different DG size Line

Lmn without DG


0.000340 0.001216 0.001860 0.000737 0.000884 0.001873 0.006625 0.001227 0.001203 0.000586 0.001270 0.003080 0.002650 0.000352 0.000929 0.001600 0.001801 0.000329 0.003046 0.000839 0.001494 0.001250 0.009639 0.009752 0.000346 0.000486 0.001188 0.003241 0.021763 0.004015 0.001861 0.000889

Lmn with with DG 10 % of load 0.000340 0.001216 0.001853 0.000732 0.000875 0.001841 0.006514 0.001206 0.001182 0.000576 0.001247 0.003026 0.002603 0.000345 0.000913 0.001572 0.001769 0.000329 0.003044 0.000838 0.001493 0.001246 0.009598 0.009710 0.000340 0.000477 0.001162 0.003143 0.020995 0.003855 0.001787 0.000854



25




Table ‎4.4 Values of line stability factor (LQP) at the different DG size Line


LQP without DG 7.56E-05 0.000252 0.000385 0.000152 0.000376 0.001712 0.000655 0.000421 0.000422 5.63E-05 0.000125 0.001174 0.001678 0.000156 0.000323 0.001026 0.000686 0.000157 0.001364 0.000487 0.000951 0.000398 0.003690 0.003713 7.15E-05 0.000100 0.000522 0.001404 0.004519 0.001987 0.001072 0.000632

LQP with LQP with LQP with LQP with DG 10 % DG 20 % DG 30 % DG 40 % of load of load of load of load 7.45E-05 7.36E-05 7.28E-05 7.21E-05 0.000252 0.000251 0.000251 0.000251 0.000383 0.000382 0.000380 0.000379 0.000151 0.000150 0.000149 0.000148 0.000373 0.000369 0.000366 0.000363 0.001684 0.001657 0.001632 0.001608 0.000644 0.000634 0.000624 0.000615 0.000413 0.000407 0.000400 0.000394 0.000415 0.000408 0.000402 0.000396 5.53E-05 5.44E-05 5.35E-05 5.27E-05 0.000123 0.000121 0.000119 0.000117 0.001154 0.001135 0.001116 0.001099 0.001648 0.001620 0.001594 0.001570 0.000153 0.000150 0.000148 0.000146 0.000317 0.000312 0.000307 0.000302 0.001007 0.000990 0.000974 0.000959 0.000674 0.000662 0.000651 0.000641 0.000157 0.000157 0.000156 0.000156 0.001364 0.001363 0.001362 0.001361 0.000484 0.000484 0.000483 0.000483 0.000950 0.000950 0.000949 0.000949 0.000396 0.000395 0.000393 0.000392 0.003675 0.003660 0.003646 0.003632 0.003697 0.003682 0.003668 0.003654 7.06E-05 6.92E-05 6.84E-05 6.74E-05 9.87E-05 9.69E-05 9.53E-05 9.38E-05 0.000511 0.000501 0.000492 0.000484 0.001363 0.001325 0.001290 0.001258 0.004356 0.004207 0.004072 0.003947 0.001908 0.001836 0.001771 0.001711 0.001029 0.000990 0.000955 0.000923 0.000606 0.000583 0.000562 0.000543

26

LQP with DG 50 % of load 7.16E-05 0.000251 0.000377 0.000148 0.000360 0.001585 0.000606 0.000389 0.000390 5.19E-05 0.000115 0.001083 0.001546 0.000144 0.000297 0.000944 0.000631 0.000156 0.001360 0.000483 0.000948 0.000390 0.003619 0.003640 6.65E-05 9.24E-05 0.000475 0.001228 0.003831 0.001656 0.000893 0.000526

LQP with DG 60 % of load 7.037E-05 0.0002513 0.0003765 0.0001472 0.0003577 0.0015648 0.0005987 0.0003838 0.0003852 5.128E-05 0.0001141 0.0010688 0.0015252 0.0001419 0.0002937 0.0009314 0.0006227 0.0001566 0.0013600 0.0004829 0.0009481 0.0003893 0.0036071 0.0036281 6.536E-05 9.113E-05 0.0004683 0.0012002 0.0037260 0.0016062 0.0008662 0.0005099

Voltage Stability Indices value of Line 29

0.025

0.02

0.015 FVSI Lmn

0.01

LQP 0.005

0 0%

10%

20% 30% 40% Penetration Level of DG from Load

50%

60%

Figure ‎4-2 : The effect of increasing size of DG on the weakest voltage stability bus (bus 30) 4.2.1.2 Result of voltage profile without DG and with different DG size Table 4.5 and Figure 4.4 demonstrate the effect of increasing the size of DG unit on the voltage of each bus. From Table 4.5, the voltage of each bus enhanced when the DG installed at the bus .1. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 4.3 demonstrates the effect of increasing the size of DG unit on the voltage profile of the weakest voltage stability bus (bus .1). The voltage at bus 30 changes from 0.9251 to 1.025095 when the DG generates 60% from the load. So, the voltage at bus 30 is enhanced by 0.0999. This change shows that the voltage at bus 30 enhanced due to installing DG.

Voltage Magnitude at Bus 30

1.04 1.02 1 0.98 0.96 0.94 0.92 0.9 0%

10%

20%

30%

40%

50%

60%

Penetration level of DG from Load

Figure ‎4-3: The effect of increasing the size of DG on voltage of the weakest voltage stability bus (bus 30)

27

Figure ‎4-4: The effect of increasing size of DG on voltage of each bus

28

Table ‎4.5: The effect of increasing size of DG on voltage of each bus Voltage Bus Voltage at Bus 1 Voltage at Bus 2 Voltage at Bus 3 Voltage at Bus 4 Voltage at Bus 5 Voltage at Bus 6 Voltage at Bus 7 Voltage at Bus 8 Voltage at Bus 9 Voltage at Bus 10 Voltage at Bus 11 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 61 Voltage at Bus 60 Voltage at Bus 66 Voltage at Bus 6. Voltage at Bus 64 Voltage at Bus 61 Voltage at Bus 62 Voltage at Bus 63 Voltage at Bus 64 Voltage at Bus 65 Voltage at Bus .1 Voltage at Bus .0 Voltage at Bus .6 Voltage at Bus ..

Without DG 1 0.997032 0.982938 0.975457 0.968060 0.949660 0.946174 0.941331 0.935063 0.929415 0.928544 0.927045 0.920933 0.918667 0.917255 0.915887 0.913860 0.913253 0.996503 0.992926 0.992221 0.991584 0.979352 0.972681 0.969356 0.947730 0.945167 0.933727 0.925509 0.921952 0.917791 0.916875 0.916591

DG 10 % of load 1 0.997357 0.985000 0.978801 0.972738 0.957688 0.954233 0.949432 0.943220 0.937623 0.936760 0.935274 0.929217 0.926971 0.925572 0.924217 0.922208 0.921607 0.996829 0.993252 0.992548 0.991911 0.981421 0.974765 0.971447 0.956452 0.954858 0.947672 0.942667 0.940826 0.936749 0.935852 0.935574

DG 20 % of load 1 0.997669 0.986979 0.982011 0.977229 0.965392 0.961967 0.957206 0.951047 0.945498 0.944642 0.943169 0.937163 0.934937 0.933550 0.932206 0.930215 0.929619 0.997141 0.993565 0.992861 0.992224 0.983408 0.976765 0.973454 0.964823 0.964160 0.961059 0.959137 0.958946 0.954947 0.954067 0.953794

29

DG 30 % of load 1 0.997969 0.988884 0.985102 0.981553 0.972810 0.969412 0.964690 0.958580 0.953076 0.952227 0.950766 0.944810 0.942602 0.941226 0.939893 0.937918 0.937327 0.997441 0.993867 0.993163 0.992526 0.985320 0.978690 0.975386 0.972882 0.973116 0.973948 0.974998 0.976394 0.972468 0.971604 0.971336

DG 40 % of load 1 0.998259 0.990724 0.988087 0.985728 0.979971 0.976599 0.971912 0.965850 0.960389 0.959547 0.958097 0.952187 0.949996 0.948631 0.947309 0.945350 0.944763 0.997732 0.994158 0.993455 0.992818 0.987167 0.980550 0.977252 0.980662 0.981763 0.986391 0.990310 0.993241 0.989382 0.988533 0.988270

DG 50 % of load 1 0.998540 0.992504 0.990975 0.989769 0.986898 0.983551 0.978900 0.972883 0.967462 0.966626 0.965187 0.959322 0.957147 0.955793 0.954481 0.952536 0.951954 0.998012 0.994440 0.993737 0.993100 0.988954 0.982349 0.979057 0.988190 0.990130 0.998433 1.005128 1.009545 1.005749 1.004913 1.004655

DG 60 % of load 1 0.998807 0.994200 0.993726 0.993617 0.993502 0.990178 0.985559 0.979584 0.974202 0.973372 0.971943 0.966120 0.963960 0.962615 0.961313 0.959382 0.958804 0.998280 0.994709 0.994005 0.993369 0.990656 0.984062 0.980776 0.995365 0.998103 1.009915 1.019262 1.025094 1.021356 1.020533 1.020279

4.2.1.3

Result of power flow without DG and with different DG size

Table 4.6 demonstrations the effect of increasing the size of DG unit on power flow. From Table 4.6 it is observed that there is reduced in real & reactive power generated by The Electric Company due to installing the DG unit at bus 30. Furthermore, power losses get reduced obviously. But when DG size reaches to a certain size power losses is increased. From result analysis, optimum DG size needed to limit the best DG size to get the best minimization power losses. Table ‎4.6: The effect of increasing size of DG on power flow

0% 10%

Pintake MWatt 3.91753 3.4891

Qintake MVAR 2.4351 2.1673

MWatt 1 0.3715

20%

3.07737

1.9112

30%

2.680467

40% 50% 60%

2.29687 1.92529 1.5733

MVAR 1 0.23

Pl MWatt 3.715 3.715

Ql MVAR 2.3 2.3

Plosses KWatt 202.5 145.6

0.746

0.46

3.715

2.3

105.4

1.6653

1.1145

0.69

3.715

2.3

80

1.4288 1.2 0.9798

1.486 1.8575 2.22

0.92 1.15 0..4

3.715 3.715 3.715

2.3 2.3 2.3

67.9 67.8 78.3

250

200 Power Losses (KWatt)

DG%

150 Power losses

100

50

0 0%

10%

20%

30%

40%

50%

60%

Penetration Level of DG from Load

Figure ‎4-5: The effect of increasing the size of DG on power losses

30

4.2.1.4 Result of P-V curve without DG and with different DG size Figure 4-6 to 4-13 demonstrations the effect of increasing size of DG unit on P-V curve of each bus. Table 4.7 demonstrations the effect of increasing the size of DG unit on the maximum value of the loading parameter of the power system. The maximum value of the loading parameter of power system increased when increase size of DG. Maximum load ability changes from 3.6136 to 4.373 when the DG generates 60% from the load. Maximum load ability is developed by 0.7594. This change shows that Maximum load ability enhanced due to install DG. Table ‎4.7: The effect of increasing size of DG on the maximum value of the loading parameter DG 0% 10% 20% 30% 40% 50% 60%

Max. Load Ability 3.6136 3.7823 3.9293 4.0542 4.1713 4.2761 4.373

4.6

Max Loading Point

4.4 4.2 4 3.8 3.6 3.4 3.2 3 0%

10%

20%

30%

40%

50%

60%


Figure ‎4-6: The effect of increasing size of DG on the maximum value of the loading parameter

31

Voltage Magnitude(P.U)

1 0.9 0.8 0.7

0.5

1

2.5

3

3.5

V_{Bus1} V_{Bus10} V_{Bus11} V_{Bus12} V_{Bus13} V_{Bus14} V_{Bus15} V_{Bus16} V_{Bus17} V_{Bus18} V_{Bus19} V_{Bus2} V_{Bus20} V_{Bus21} V_{Bus22} V_{Bus23} V_{Bus24} V_{Bus25} V_{Bus26} V_{Bus27} V_{Bus28} V_{Bus29} V_{Bus3} V_{Bus30} V_{Bus31} V_{Bus32} V_{Bus33} V_{Bus4} V_{Bus5} V_{Bus6} V_{Bus7} V_{Bus8} V_{Bus9}

32

0.6 0.5 0.4 0.3 0.2 0.1 0 0

1.5 2 Total Loading Level  (P.U)

Figure ‎4-7: P-V Curves without DG

Voltage Magnitude (P.U)

1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5

V_{Bus1}

V_{Bus10}

V_{Bus11}

V_{Bus12} V_{Bus13}

V_{Bus14}

V_{Bus15}

V_{Bus16}

V_{Bus17}

V_{Bus18}

V_{Bus19}

V_{Bus2} V_{Bus20}

V_{Bus21}

V_{Bus22}

V_{Bus23}

V_{Bus24}

V_{Bus25}

V_{Bus26}

V_{Bus27} V_{Bus28}

V_{Bus29}

V_{Bus3}

V_{Bus30}

V_{Bus31}

V_{Bus32}

V_{Bus33}

V_{Bus4} V_{Bus5}

V_{Bus6}

V_{Bus7}

V_{Bus8}

33

1

0.8

0.6

0.4

0.2

0

Total Loading Parameter  (p.u.)

Figure ‎4-8: P-V Curves with DG (size 10% of the load)


1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5

V_{Bus1} V_{Bus10}

V_{Bus11} V_{Bus12} V_{Bus13} V_{Bus14} V_{Bus15} V_{Bus16} V_{Bus17} V_{Bus18} V_{Bus19} V_{Bus2} V_{Bus20} V_{Bus21} V_{Bus22} V_{Bus23}

V_{Bus24} V_{Bus25} V_{Bus26} V_{Bus27} V_{Bus28} V_{Bus29} V_{Bus3} V_{Bus30} V_{Bus31} V_{Bus32} V_{Bus33} V_{Bus4} V_{Bus5} V_{Bus6}

V_{Bus7} V_{Bus8}

34

1

0.8

0.6

0.4

0.2

0




1.4

1.2

0.5

1

1.5

2

2.5

3

3.5

4

V_{Bus1}

V_{Bus10} V_{Bus11}

V_{Bus12}

V_{Bus13} V_{Bus14}

V_{Bus15}

V_{Bus16} V_{Bus17}

V_{Bus18}

V_{Bus19} V_{Bus2}

V_{Bus20}

V_{Bus21} V_{Bus22}

V_{Bus23}

V_{Bus24}

V_{Bus25} V_{Bus26}

V_{Bus27}

V_{Bus28} V_{Bus29}

V_{Bus3}

V_{Bus30} V_{Bus31}

V_{Bus32}

V_{Bus33} V_{Bus4}

V_{Bus5}

V_{Bus6} V_{Bus7}

V_{Bus8}

35

1

0.8

0.6

0.4

0.2

0 0




1.4

1.2

0.5

1

1.5

2

2.5

3

3.5

4

V_{Bus1}

V_{Bus10} V_{Bus11}

V_{Bus12}

V_{Bus13}

V_{Bus14} V_{Bus15}

V_{Bus16}

V_{Bus17}

V_{Bus18} V_{Bus19}

V_{Bus2}

V_{Bus20}

V_{Bus21} V_{Bus22}

V_{Bus23}

V_{Bus24}

V_{Bus25} V_{Bus26}

V_{Bus27}

V_{Bus28}

V_{Bus29} V_{Bus3}

V_{Bus30}

V_{Bus31}

V_{Bus32} V_{Bus33}

V_{Bus4}

V_{Bus5}

V_{Bus6} V_{Bus7}

V_{Bus8}

36

1

0.8

0.6

0.4

0.2

0 0


Figure ‎4-11: P-V Curves with DG (size 40% from the load)


1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5

4


37

1

0.8

0.6

0.4

0.2

0




1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5

4


38

1

0.8

0.6

0.4

0.2

0



4.2.2 Practical radial distribution system Figure 4.13 demonstrations a single line diagram of a practical radial distribution system in the Kumamoto area in Japan. The network substation voltage is 6.6 KV, base MVA=10 and total load of 6.229 MW and 2.624 MVAR. The system‟s‎ data‎ can‎ be‎ found in [53] and given in Appendix A.2.

Figure ‎4-14: Practical radial 15 bus distribution system

Table ‎4.8: Rating of installed DG Rating of wind turbine 10% from the load 20% from the load 30% from the load 40% from the load 50% from the load 60% from the load 70% from the load

Active Power (MWatt) 0.063236 0.126472 0.189708 0.252944 0.31618 0.379416 0.442652 39

Reactive Power (MVAR) 0.026238 0.052477 0.078715 0.104953 0.131191 0.157429 0.183667

4.2.2.1 Result of voltage stability indices without DG and with different DG size Voltage stability indices described in section 3.2 are applied in the practical radial distribution system. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 4.9. Values of the line stability index (Lmn) at the diverse DG size are shown in Table 4.10. Values of line stability factor (LQP) at the diverse DG size are shown in Table 4.11. According to the values of voltage stability indices without the DG in Table 4.9, 4.10 and 4.11 it is found that the line which starts from the bus 10 to the bus 11 is the weakest line. So the DG unit is installed at bus 11. The DG unit is varied from 0 to 50% from load to demonstrate the effect of the DG size on voltage stability Indices. Rating of the installed DG is limited in Table 4.8. From Tables 4.9, 4.10 and 4.11 notices that values of voltage stability indices at each line are nearer to zero when installing the DG unit in bus 11. So, voltage stability enhanced at all buses. Also, when increases the size of DG, voltage stability of each bus more enhanced. Figure 4.15 demonstrations the effect of increasing the size of DG on the weakest line (bus 10 to bus 11).

Table ‎4.9: Values of fast voltage stability index (FVSI) at the diverse DG size Line

FVSI without DG

1 to 2 2 to 3 3 to 4 3 to 12 4 to 5 4 to 7 5 to 6 7 to 8 8 to 9 9 to 10 10 to 11 12 to 13 13 to 14

0.000632 4.05E-05 0.001319 0.000777 0.00033 0.00109 0.000215 0.000628 0.000335 0.000236 0.044479 0.000117 0.000795

FVSI with DG 10 % of load 0.000632 4.02E-05 0.001310 0.000771 0.000326 0.001078 0.000213 0.000619 0.000328 0.000230 0.043382 0.000116 0.000789



40





Table ‎4.10: Values of the line stability index (Lmn) at the diverse DG size Line


Lmn without DG 0.000636 4.05E-05 0.001328 0.000779 0.000300 0.001208 0.000196 0.000631 0.000336 0.000236 0.044631 0.000117 0.000797

Lmn with DG 10 % of load 0.000636 4.02E-05 0.001318 0.000773 0.000297 0.001193 0.000194 0.000621 0.000329 0.000231 0.043473 0.000117 0.000792







Table ‎4.11: Values of line stability factor (LQP) at the diverse DG size Line

LQP without DG

LQP with LQP with LQP with LQP with LQP with LQP with LQP with DG 10 % DG 20 % DG 30 % DG 40 % DG 50 % DG 60 % DG 70 % of load of load of load of load of load of load of load


0.000631 3.93E-05 0.001270 0.000915 0.000296 0.001098 0.000199 0.000634 0.000325 0.000226 0.042492 0.000107 0.000693

0.000631 3.90E-05 0.001261 0.000907 0.000293 0.001085 0.000196 0.000624 0.000319 0.000221 0.041444 0.000106 0.000688

0.000631 3.87E-05 0.001253 0.000899 0.000290 0.001074 0.000194 0.000615 0.000313 0.000216 0.040494 0.000105 0.000683

0.000631 3.85E-05 0.001245 0.000893 0.000287 0.001064 0.000193 0.000607 0.000308 0.000212 0.039088 0.000105 0.000679

41

0.000631 3.83E-05 0.001238 0.000887 0.000285 0.001054 0.000191 0.000599 0.000303 0.000208 0.038836 0.000104 0.000675

0.000631 3.80E-05 0.001231 0.000881 0.000282 0.001046 0.000189 0.000592 0.000298 0.000204 0.038107 0.000104 0.000671

0.000631 3.79E-05 0.001225 0.000876 0.000280 0.001038 0.000188 0.000586 0.000294 0.000201 0.037434 0.000103 0.000668

0.000631 3.78E-05 0.001220 0.000872 0.000278 0.001030 0.000186 0.000580 0.000290 0.000198 0.036812 0.000102 0.000665

0.047

Voltage Stability Indices value

0.045 0.043 FVSI

0.041

Lmn LQP

0.039 0.037 0.035 0%

10%

20% 30% 40% 50% Penetration Level of DG from Load

60%

70%

Figure ‎4-15: The effect of increasing size of DG on the weakest bus (bus 11) 4.2.2.2 Result of voltage profile without DG and with different DG size Table 4.16 and Figure 4.17 demonstrate the effect of increasing the size of DG unit on the voltage of each bus. From Table 4.12, the voltage of each bus enhanced when the DG installed at the bus 11. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 4.16 demonstrates the effect of increasing the size of DG on the voltage profile of the weakest bus (bus 11). The voltage at bus 11 changes from 0.91582 to 0.9974 when the DG generates 70% from the load. So, the voltage at bus 11 is enhanced by 0.08158. This change shows that the voltage at bus 30 enhanced due to installing DG.


1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0%

10%

20%

30%

40%

50%

60%

70%


Figure ‎4-16: The effect of increasing the size of DG on voltage of the weakest bus (bus 11) 42


43

Table ‎4.12: The effect of increasing size of DG on voltage of each bus Bus

Voltage at Bus 1 Voltage at Bus 2 Voltage at Bus 3 Voltage at Bus 4 Voltage at Bus 5 Voltage at Bus 6 Voltage at Bus 7 Voltage at Bus 8 Voltage at Bus 9 Voltage at Bus 10 Voltage at Bus 11 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15

4.2.2.3

Withou DG t 10% of load DG 1 1 0.9793 0.9828 0.9787 0.9823 0.9680 0.9732 0.9676 0.9728 0.9674 0.9726 0.9559 0.9631 0.9428 0.9520 0.9329 0.9438 0.9279 0.9395 0.9158 0.9294 0.9768 0.9803 0.9754 0.9790 0.9739 0.9775 0.9736 0.9772

DG 20% of load

DG 30% of load

DG 40% of load

DG 50% of load

DG 60% of load

DG 70% of load

1 0.9860 0.9856 0.9781 0.9777 0.9775 0.9698 0.9607 0.9539 0.9505 0.9423 0.9836 0.9823 0.9808 0.9805

1 0.9890 0.9886 0.9826 0.9822 0.9820 0.9760 0.9688 0.9635 0.9608 0.9545 0.9867 0.9853 0.9838 0.9836

1 0.9917 0.9914 0.9868 0.9864 0.9862 0.9818 0.9764 0.9725 0.9706 0.9660 0.9895 0.9882 0.9866 0.9864

1 0.9942 0.9940 0.9907 0.9903 0.9901 0.9873 0.9836 0.9811 0.9798 0.9770 0.9921 0.9908 0.9892 0.9890

1 0.9966 0.9964 0.9944 0.9940 0.9938 0.9924 0.9904 0.9892 0.9886 0.9875 0.9945 0.9932 0.9917 0.9914

1 0.9987 0.9986 0.9978 0.9974 0.9972 0.9972 0.9968 0.9968 0.9969 0.9974 0.9967 0.9954 0.9939 0.9937

Result of power flow without DG and with different DG size

Table 4.13 demonstrations the effect of increasing the size of DG unit on power flow. From Table 4.13, it is observed that there is reduced in real & reactive power generated by The Electric Company due to install the DG unit at bus 11. Furthermore, power losses get reduced obviously. But when DG size reaches to a certain size power losses is increased. From result analysis, optimum DG size needed to limit the best DG size to get the best minimization power losses. Table ‎4.13: The effect of increasing size of DG on power flow DG% 0% 10% 20% 30% 40% 50% 60% 70%

Pintake MWatt 6.3236 5.6629 5.0087 4.3604 3.7174 3.0794

Qintake MVAR 2.6238 2.1604 1.7364 1.3483 0.9930 0.6683

Pdg MWatt 0 0.6323 1.2647 1.8970 2.5294 3.1618

0.244611 0.181711

0.03718 0.01020

0.37941 0.44265

Qdg MVAR 0 0.2623 0.5247 0.7871 1.0495 1.3119

Pl MWatt 6.22 6.22 6.22 6.22 6.22 6.22 0.157429 6.22 0.183667 6.22 44

Ql MVAR 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6

Plosses KWatt 94 66 44 28 17 12 11.27 14.6

100 90

Power Losses (KWatt)

80 70 60 50 Power losses

40 30 20 10 0 0%

10%

20%

30%

40%

50%

60%

70%


Figure ‎4-18: The effect of increasing the size of DG on power losses 4.2.2.4 Result of P-V curve without DG and with different DG size Figure 4.19, 4.20, 4.21, 4.22, 4.23, 4.24, 4.25, 4.26 and 4.27 demonstrations the effect of increasing size of DG on P-V curve of each bus. Table 4.16 demonstrations the effect of increasing the size of DG on the maximum value of the loading parameter of the power system. The maximum value of the loading parameter of power system increased when increase size of DG. Maximum load ability changes from 2.6291 to 3.2069 when the DG generates 70% from the load. Maximum load ability is developed by 0.5778. This change shows that Maximum load ability enhanced due to install DG. Table ‎4.14: The effect of increasing size of DG on the maximum value of the loading parameter DG 0% 10% 20% 30% 40% 50% 60% 70%

Max. Load Ability 2.7122 2.7277 2.7493 2.7593 2.7809 2.7916 2.8129 2.8243

45

2.84

Max Loading Point

2.82 2.8 2.78 2.76 2.74 2.72 2.7 0%

10%


60%

70%


1.4

VBus1 VBus10

Voltage Magnitude(p.u)

1.2

VBus11 VBus12

1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1

1.5 Total Loading Level  (p.u.)

2


46

2.5

1.4 VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

0 0

VBus8 VBus9 0.5

1


2

2.5


1.4 VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

0 0

VBus8 VBus9 0.5

1


2

2.5


47

1.4 VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

0 0

VBus8 VBus9 0.5

1


2

2.5


1.4 VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

0 0

VBus8 VBus9 0.5

1


2

2.5

Figure ‎4-24: P-V Curves with DG (size 40% of the load) 48

1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5


1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5

Figure ‎4-26: P-V Curves with DG (size 60% of the load) 49

1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5


4.3 Single DG capable of delivering active power only In this part, the results will be presented as follow ●‎Result‎of‎voltage‎stability‎indices‎without‎DG and with different DG size ●‎Result‎of‎voltage‎profile‎without‎DG and with different DG size ●‎Result‎of‎power‎flow‎without‎DG and with different DG size ●‎Result of P-V curve without DG and with different DG size

4.3.1 IEEE 33 bus radial distribution system In this part, all simulations execute on IEEE 33 bus radial distribution system shown in Figure 4.1. The network substation voltage is 12.66 KV, base MVA=100 and total load of 3.7 MW and 2.3 MVAR. The system‟s‎ data‎ can‎ be‎ found‎ in‎ [53] and given in Appendix A.

50

4.3.1.1 Result of voltage stability indices without DG and with different DG size Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive bus to voltage collapse. The most sensitive bus related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 4.16. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 4.17. Values of line stability factor (LQP) at the diverse DG size are shown in Table 4.18. According to values of voltage stability indices without the DG in Table 4.16, 4.17, 4.18 it is found that bus 30 is the weakest bus. So, the DG unit is installed at bus 30.The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in the Table 4.15. From Tables 4.16, 4.17 and 4.18 notices that the values of voltage stability indices at each line are nearer to zero when installing DG in bus 30. So, voltage stability enhanced at all buses. Also, Voltage stability more enhanced at all buses when to increase the size of DG. Figure 4.28 demonstrations the effect of increasing the size of DG on the weakest bus (bus 30). The value of FVSI at bus 30 changes from 0.0219 to 0.018599, the value of LQP changes from 0.00451 to 0.003831 and the value of Lmn changes from 0.0217 to 0.01851 when the DG generates 50 % from the load. These changes show that the weakest bus (bus 30) enhanced due to installing DG. Table ‎4.15: Rating of installed DG Rating of DG 10% penetration level 20% penetration level 30% penetration level 40% penetration level 50% penetration level

of load of load of load of load of load

Active Power(MWatt) 0.3715 0.743 1.1145 1.486 1.8575

51

Reactive Power(MVAR) 0 0 0 0 0

Table ‎4.16: Values of fast voltage stability index (FVSI) at the different DG size Line


FVSI without DG 0.0003412 0.0012241 0.0018702 0.0007415 0.0008818 0.0018691 0.0066564 0.0012244 0.0012000 0.0005875 0.0012725 0.0030703 0.0026468 0.0003519 0.0009296 0.0015985 0.0018019 0.0003297 0.0030407 0.0008393 0.0014940 0.0012510 0.0096084 0.0097399 0.0003472 0.0004882 0.0011927 0.0032535 0.0219368 0.0040056 0.0018615 0.0008900

FVSI with DG 10% of load 0.0003412 0.0012236 0.0018644 0.0007377 0.0008755 0.0018469 0.0065768 0.0012096 0.0011853 0.0005803 0.0012567 0.003032 0.0026134 0.0003474 0.0009177 0.0015781 0.0017788 0.0003295 0.0030392 0.0008389 0.0014933 0.0012471 0.0095781 0.0097088 0.0003431 0.0004819 0.0011754 0.0031870 0.0213881 0.0038941 0.0018092 0.0008650


52






Lmn without DG 0.0003406 0.0012164 0.0018604 0.0007375 0.0008846 0.0018731 0.0066259 0.0012279 0.0012030 0.0005866 0.0012700 0.0030806 0.0026509 0.0003522 0.0009299 0.0016008 0.0018015 0.0003296 0.0030466 0.0008393 0.0014940 0.0012501 0.0096396 0.0097522 0.0003460 0.0004860 0.0011881 0.0032413 0.0217632 0.0040150 0.0018617 0.0008897

Lmn with DG 10% of load 0.0003404 0.0012131 0.0018515 0.0007325 0.0008746 0.0018508 0.0065470 0.0012130 0.0011883 0.0005793 0.0012542 0.0030421 0.0026173 0.0003477 0.0009181 0.0015803 0.0017784 0.0003295 0.0030451 0.0008389 0.0014933 0.0012482 0.0096091 0.0097210 0.0003416 0.0004790 0.0011645 0.0031619 0.0211664 0.0039030 0.0018094 0.0008647


53




Table ‎4.18: Values of line stability factor (LQP) at the diverse DG size Line


LQP without DG 7.565E-05 0.0002522 0.0003852 0.0001528 0.0003768 0.0017126 0.0006558 0.0004211 0.0004228 5.634E-05 0.0001254 0.0011749 0.0016786 0.0001564 0.0003235 0.0010264 0.0006863 0.0001572 0.0013649 0.0004847 0.0009515 0.0003983 0.0036909 0.0037138 7.154E-05 0.0001005 0.0005223 0.0014042 0.0045192 0.0019872 0.0010728 0.0006323

LQP with DG 10% of load 7.461E-05 0.0002521 0.0003840 0.0001520 0.0003741 0.0016923 0.0006479 0.0004160 0.0004176 5.564E-05 0.0001238 0.0011602 0.0016574 0.0001544 0.0003194 0.0010132 0.0006775 0.0001571 0.0013642 0.0004844 0.0009510 0.0003970 0.0036792 0.0037019 7.103E-05 9.922E-05 0.0005147 0.0013754 0.0044061 0.0019317 0.0010427 0.0006144


54





0.025

0.02

0.015

FVSI Lmn

0.01

LQP

0.005

0 0%

10%

20% 30% 40% Penetration Level of DG from Load

50%

Figure ‎4-28: The effect of increasing size of DG on the weakest bus (bus 30) 4.3.1.2 Result of voltage profile without DG and with different DG size Table 4.19 and Figure 4.30 demonstrate the effect of increasing the size of DG on the voltage of each bus. From Table 4.19, the voltage of each bus enhanced when the DG installed at the bus .1. Furthermore, the voltage at each bus more enhanced when increases the size of DG generation. Figure 4.29 demonstrates the effect of increasing the size of DG on the voltage profile of the weakest bus (bus .1). The voltage at bus 30 changes from 0.9219 to 1.0095 when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.08759. This change shows that the voltage at bus 30 enhanced due to installing DG.

Voltage Magnitude of bus 30 (Per Unit)

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0.91 0%

10%

20% 30% Penetration Level of DG from Load

40%

50%

Figure ‎4-29: The effect of increasing the size of DG on voltage of the weakest bus (bus 30)

55


56

Table ‎4.19 The effect of increasing size of DG on voltage of each bus

Voltage at Bus 1 Voltage at Bus 2 Voltage at Bus 3 Voltage at Bus 4 Voltage at Bus 5 Voltage at Bus 6 Voltage at Bus 7 Voltage at Bus 8 Voltage at Bus 9 Voltage at Bus 10 Voltage at Bus 11 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 61 Voltage at Bus 60 Voltage at Bus 66 Voltage at Bus 6. Voltage at Bus 64 Voltage at Bus 61 Voltage at Bus 62 Voltage at Bus 63 Voltage at Bus 64 Voltage at Bus 65 Voltage at Bus .1 Voltage at Bus .0 Voltage at Bus .6 Voltage at Bus ..

Without DG 1 0.997032 0.982938 0.975457 0.968060 0.949660 0.946174 0.941331 0.935063 0.929415 0.928544 0.927045 0.920933 0.918667 0.917255 0.915887 0.913860 0.913253 0.996503 0.992926 0.992221 0.991584 0.979352 0.972681 0.969356 0.947730 0.945167 0.933727 0.925509 0.921952 0.917791 0.916875 0.916591

DG 10% of load 1 0.997274 0.984478 0.977957 0.971560 0.955345 0.951881 0.947068 0.940840 0.935228 0.934362 0.932873 0.926800 0.924548 0.923145 0.921786 0.919772 0.919169 0.996746 0.993169 0.992465 0.991828 0.980898 0.974238 0.970918 0.953937 0.952104 0.943423 0.937304 0.935053 0.930951 0.930049 0.929769

DG 20% of load 1 0.997508 0.985962 0.980366 0.974933 0.96081 0.957376 0.952592 0.946401 0.940824 0.939964 0.938483 0.932447 0.930209 0.928815 0.927464 0.925463 0.924864 0.996980 0.993404 0.992700 0.992063 0.982388 0.975738 0.972423 0.959916 0.958790 0.952774 0.948688 0.947707 0.943660 0.942770 0.942494

57

DG 30% of load 1 0.997733 0.987395 0.982693 0.978192 0.966101 0.962678 0.957921 0.951766 0.946222 0.945366 0.943894 0.937894 0.935669 0.934283 0.932940 0.930951 0.930355 0.997205 0.993630 0.992926 0.992289 0.983826 0.977185 0.973876 0.965687 0.965245 0.961807 0.959696 0.959952 0.955957 0.955078 0.954806

DG 40% of load 1 0.997951 0.988780 0.98494 0.981343 0.971205 0.967801 0.963070 0.956950 0.951436 0.950585 0.949122 0.943155 0.940943 0.939565 0.938230 0.936251 0.935659 0.997423 0.993849 0.993145 0.992509 0.985216 0.978585 0.975280 0.971265 0.971488 0.970549 0.970359 0.971820 0.967874 0.967006 0.966737

DG 50% of load 1 0.998162 0.990120 0.987121 0.984396 0.976144 0.972758 0.968053 0.961965 0.956481 0.955635 0.954179 0.948245 0.946045 0.944674 0.943346 0.941379 0.940790 0.997634 0.994061 0.993357 0.992721 0.986561 0.979940 0.976639 0.976666 0.977534 0.979022 0.980703 0.983341 0.979442 0.978584 0.978319

4.3.1.3 Result of power flow without DG and with different DG size Table 4.20 demonstrations the effect of increasing the size of DG on power flow. From Table 4.20, it is observed that there is reduced in real power generated by Electric Company due to installing the DG at bus 30. Also, power losses decrease but when DG size reaches to a certain size power losses increase. From result analysis, optimum DG size needed to limit the best DG size to get the best minimization power losses. Table ‎4.20: The effect of increasing size of DG on power flow Pintake (MWatt)

Qintake (MVAR)

Pl (MWatt)

Ql (MVAR)

Plosses (KWatt)

(MWatt)

Without DG

3.917

2.435

0

0

3.715

2.3

202.5

10%

3.5

2.4105

0.3715

0

3.715

2.3

165

20%

3.11

2.393

0.743

0

3.715

2.3

139

30%

2.7239

2.3844

1.114

0

3.715

2.3

123.4

40%

2.346

2.3819

1.486

0

3.715

2.3

117.6

50%

1.978

2.3856

18575

0

3.715

2.3

120.8

10%

20%

Total Power Losses (KWatt)

250

200

150

100

50

0 0%

30%

40%

50%

DG Size

Figure ‎4-31: The effect of increasing the size of DG on power losses

58

4.3.1.4 Result of P-V curve without DG and with different DG size Figure 4.32 to 4.38 demonstrations the effect of increasing size of DG on P-V curve of each bus. Table 4.21 demonstrations the effect of increasing the size of DG on the maximum value of the loading parameter of the power system. The maximum value of the loading parameter of power system increased when increase size of DG. Maximum load ability changes from 3.6136 to 4.2761 when the DG generates 50% from the load. Maximum load ability is developed by 0.6625. This change shows that Maximum load ability enhanced due to install DG. From result analysis when DG size reaches a certain size the change in maximum load ability is small. Table ‎4.21: The effect of increasing size of DG on the maximum value of the loading parameter

Max Loading Point

DG 0% 10% 20% 30% 40% 50%

Max. Load Ability 3.6136 3.7305 3.8255 3.9073 3.9915 4.0662

4.1 4.05 4 3.95 3.9 3.85 3.8 3.75 3.7 3.65 3.6 3.55 0%

10%

20%

30%

40%

50%

60%

DG size from load


59

Voltage Magnitude(P.U)

1 0.9 0.8 0.7

0.5

1

2.5

3

3.5


60

0.6 0.5 0.4 0.3 0.2 0.1 0 0

1.5 2 Total Loading Level  (P.U)



1.4

1.2

0.5

1

1.5

2

2.5

3

3.5

V_{Bus1}

V_{Bus10} V_{Bus11} V_{Bus12} V_{Bus13} V_{Bus14} V_{Bus15} V_{Bus16} V_{Bus17} V_{Bus18} V_{Bus19}

V_{Bus2} V_{Bus20} V_{Bus21} V_{Bus22} V_{Bus23} V_{Bus24} V_{Bus25} V_{Bus26} V_{Bus27} V_{Bus28} V_{Bus29}


V_{Bus9}

61

1

0.8

0.6

0.4

0.2

0 0




1.4

1.2

0.5

1

1.5

2

2.5

3

3.5

V_{Bus1}




V_{Bus9}

62

1

0.8

0.6

0.4

0.2

0 0




1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5


63

1

0.8

0.6

0.4

0.2

0




1.4

1.2

0.5

1

1.5

2

2.5

3

3.5

V_{Bus1}




V_{Bus9}

64

1

0.8

0.6

0.4

0.2

0 0




1.4

1.2

0

0.5

1

1.5

2

2.5

3

3.5

4


65

1

0.8

0.6

0.4

0.2

0



4.3.2 Practical radial distribution system Figure 4.13 demonstrations a single line diagram of a practical radial distribution system in the Kumamoto area in Japan. The load on the bus 11 is the largest in the system. The network substation voltage is 6.6 KV, base MVA=10 and total load of 6.229 MW and 2.624 MVAR. The system‟s‎data‎can‎be‎found‎in‎[54] and given in Appendix A.2. 4.3.2.1 Result of voltage stability indices without DG and with different DG size Voltage stability indices described in section 3.2 are applied in the practical radial distribution system. This study is executed to distinguish the most sensitive bus to voltage collapse. The most sensitive bus related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 4.23. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 4.24. Values of line stability factor (LQP) at the diverse DG size are shown in Table 4.25. According to the values of voltage stability indices without the DG in Table 4.23, 4.24 and 4.25 it is found that bus 11 is the weakest bus. So the DG unit is installed at bus 11. The DG unit is varied from 0 to 50% from load to demonstrate the effect of the DG on voltage stability Indices. Rating of the installed wind turbine is limited in the Table 4.22. From Tables 4.23, 4.24 and 4.25 notice that values of voltage stability indices at each bus & line are nearer to zero when installing DG in bus 11. So, voltage stability enhanced at all buses. Also, when increases the size of DG, voltage stability more enhanced at all buses. Figure 4.35 demonstrations the effect of increasing the size of DG on the weakest line (bus 10 to bus 11).

Table ‎4.22: Rating of installed DG Rating of wind turbine 10% of the load 20% of the load 30% of the load 40% of the load 50% of the load 60% of the load

Active Power (MWatt) 0.063236 0.126472 0.189708 0.252944 0.31618 0.379416

66

Reactive Power (MVAR) 0 0 0 0 0 0

0.045


0.044 0.043 0.042

FVSI Lmn

0.041

LQP 0.04 0.039 0.038 0%

10%


60%

Figure ‎4-39: The effect of increasing size of DG on the weakest bus (bus 11) Table ‎4.23: Values of fast voltage stability index (FVSI) at the different DG size

Line

1 to 2 2 to 3 3 to 4 3 to 12 4 to 5 4 to 7 5 to 6 7 to 8 8 to 9 9 to 10 10 to 11 12 to 13 13 to 14 14 to 15

FVSI without DG 0.0006328 4.057E-05 0.0013196 0.0007774 0.0003301 0.0010900 0.0002153 0.0006286 0.0003352 0.0002363 0.0444795 0.0001177 0.0007953 0.0003916

FVSI with DG 10% of load 0.0006328 4.048E-05 0.0013164 0.0007755 0.0003288 0.0010857 0.0002145 0.0006251 0.0003327 0.0002342 0.0440629 0.0001174 0.0007934 0.0003906



67





1 to 2 2 to 3 3 to 4 3 to 12 4 to 5 4 to 7 5 to 6 7 to 8 8 to 9 9 to 10 10 to 11 12 to 13 13 to 14 14 to 15

Lmn without DG 0.0006367 4.058E-05 0.0013283 0.0007793 0.0003006 0.0012083 0.0001961 0.0006316 0.0003362 0.0002366 0.0446318 0.0001179 0.0007970 0.0003914

Lmn with DG 10% of load 0.0006362 4.048E-05 0.0013238 0.0007774 0.0002993 0.0012011 0.0001954 0.0006272 0.0003334 0.0002344 0.0441518 0.0001176 0.0007950 0.0003904






Table ‎4.25: Values of line stability factor (LQP) at the different DG size Line

1 to 2

LQP without DG 0.0096787

LQP with DG 10% of load 0.0079047

LQP with DG 20% of load 0.0063349

LQP with LQP with DG 30% of DG 40% load of load 0.0049651 0.0037905

2 to 3 3 to 4 3 to 12

3.932E-05 3.9237E-05 3.916E-05 3.9100E-05 3.905E-05 0.0012707 0.0012676 0.0012651 0.0012630 0.0012614 0.0009150 0.0009123 0.0009102 0.0009084 0.0009071

4 to 5 4 to 7 5 to 6 7 to 8

0.0002964 0.0010983 0.0001992 0.0006341

0.0002952 0.0010938 0.0001984 0.0006304

0.0002942 0.0010899 0.0001977 0.0006272

0.0002934 0.0010867 0.0001971 0.0006244

0.0002927 0.0010841 0.0001966 0.0006221

8 to 9 0.0003257 9 to 10 0.0002264 10 to 11 0.0424929

0.0003233 0.0002244 0.0420949

0.0003211 0.0002227 0.0417424

0.0003193 0.0002211 0.0414321

0.0003177 0.0002198 0.0411609

12 to 13 0.0001074 13 to 14 0.0006930 14 to 15 2.453E-05

0.0001071 0.0006913 2.447E-05

0.0001069 0.0001067 0.0001066 0.0006899 0.0006888 0.0006879 2.442E-05 2.4389E-05 2.435E-05

68

LQP with LQP with DG 50% DG 60% of load of load 0.0028074 0.0006317 3.902E-05 3.900E-05 0.0012603 0.0012596 0.0009061 0.0009056 0.0002921 0.0002917 0.0010820 0.0010805 0.0001962 0.0001960 0.0006202 0.0006187 0.0003163 0.0003152 0.0002187 0.0002177 0.0409266 0.0407271 0.0001065 0.0001064 0.0006873 0.0006870 2.433E-05 2.432E-05

4.3.2.2 Result of voltage profile without DG and with different DG size Table 4.26 and Figure 4.41 demonstrate the effect of increasing the size of DG on the voltage of each bus. From Table 3.26, the voltage of each bus enhanced when the DG installed at the bus 11. Furthermore, the voltage at each bus more enhanced when increases the size of DG generation. Figure 4.40 demonstrates the effect of increasing the size of DG on the voltage profile of the weakest bus (bus 11). The voltage at bus 11 changes from 0.91582 to 0.939655 when the DG generates 60% from the load. So, the voltage at bus 11 is enhanced by 0.023835. This change shows that the voltage at bus 30 enhanced due to installing DG.

0.945


0.94 0.935 0.93 0.925 0.92 0.915 0.91 0%

10%

20%

30%

40%

50%

60%


Figure ‎4-40: The effect of increasing the size of DG on voltage of the weakest bus (bus 11)

69


70

Table ‎4.26: The effect of increasing size of DG on voltage of each bus

Voltage at Bus 1 Voltage at Bus 2 Voltage at Bus 3 Voltage at Bus 4 Voltage at Bus 5 Voltage at Bus 6 Voltage at Bus 7 Voltage at Bus 8 Voltage at Bus 9 Voltage at Bus 10 Voltage at Bus 11 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15

Without DG 1 0.97939 0.97876 0.96805 0.96765 0.96744 0.95599 0.94282 0.93298 0.92793 0.91582 0.97680 0.97545 0.97391 0.97367

DG 10% of load 1 0.98054 0.97995 0.96995 0.96955 0.96934 0.95866 0.94630 0.93706 0.93231 0.92090 0.97799 0.97665 0.97510 0.97487

DG 20% of load 1 0.98149 0.98093 0.97157 0.97117 0.97096 0.96099 0.94938 0.94070 0.93624 0.92551 0.97898 0.97764 0.97610 0.97586

DG 30% DG 40% DG 50% of load of load of load 1 1 1 0.9822 0.9828 0.9832 0.9817 0.9823 0.9827 0.9729 0.9740 0.9749 0.9725 0.9736 0.9745 0.9723 0.9734 0.9743 0.9630 0.9647 0.9661 0.9520 0.9544 0.9564 0.9439 0.9467 0.9492 0.9397 0.9428 0.9455 0.9296 0.9334 0.9367 0.9797 0.9803 0.9808 0.9784 0.9790 0.9794 0.9769 0.9775 0.9779 0.9766 0.9772 0.9777

DG 60% of load 1 0.98348 0.98302 0.97558 0.97518 0.97497 0.96720 0.95805 0.95128 0.94783 0.93965 0.98108 0.97973 0.97820 0.97796

4.3.3 Result of power flow without DG and with different DG size Table 4.27 demonstrations the effect of increasing the size of DG on power flow. From Table 4.27, it is observed that there is reduced in real power generated by Electric Company due to installing the DG at bus 11. Furthermore, power losses get reduced obviously. But when DG size reaches to a certain size power losses is increased. From result analysis, optimum DG size needed to limit the best DG size to get the best minimization power losses. Table ‎4.27: The effect of increasing size of DG on power flow Pintake (MWatt)

Qintake (MVAR)

(MWatt)

Without DG

6.323

2.623

0

0

6.22

2.62

94

10%

5.669

2.468

0.632

0

6.22

2.62

73.1

20%

5.020

2.343

1.264

0

6.22

2.62

56.5

30%

4.376

2.246

1.897

0

6.22

2.62

44.5

40%

3.736

2.175

2.529

0

6.22

2.62

37

50%

3.101

2.132

3.161

0

6.22

2.62

33.9

60%

0.2469

0.211456

0.37941

0

6.22

2.62

35.05

71

Pl Ql (MWatt) (MVAR)

Plosses (KWatt)

100 90 Total Power Losses (KWatt)

80 70 60 50 40 30 20 10 0 0%

10%

20%

30%

40%

50%

60%


Figure ‎4-42: The effect of increasing the size of DG on power losses 4.3.3.1 Result of P-V curve without DG and with different DG size The maximum value of the loading parameter of the system increases when increase penetration level of installed DG but when DG size reaches to a certain level, the maximum value of the loading parameter decreases. From result analysis, optimum DG size is needed to reach the best value of the loading parameter of the system. Figure 4.43 to 49 demonstrations the effect of increasing size of DG on P-V curve of each bus. Table 4.64 demonstrations the effect of increasing the size of DG on the maximum value of the loading parameter of the power system. The maximum value of the loading parameter of the system is increasing when to increase the size of installed DG but when DG size reaches to a certain level, the maximum value of the loading parameter decreases. From result analysis, optimum DG size is needed to reach the best value of the loading parameter of the system. Table ‎4.28: The Impact of Increasing Size of DG on Max Load Ability DG 0% 10% 20% 30% 40% 50% 60%

Max. Load Ability 2.7122 2.7241 2.7405 2.7469 2.753 2.7588 2.7755

72

1.4

VBus1 VBus10


1.2

VBus11 VBus12

1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5

Figure ‎4-43: P-V Curves without DG 1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

0 0

VBus8 VBus9 0.5

1


2

Figure ‎4-44: P-V Curves with DG 10% of load

73

2.5

1.4

VBus1 VBus10


1.2

VBus11 VBus12

1

VBus13 VBus14

0.8

VBus15 VBus2

0.6

VBus3 VBus4

0.4

VBus5 VBus6

0.2

VBus7 VBus8

0 0

0.5

1


2

2.5

Figure ‎4-45: P-V Curves with DG 20% of load 1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5


74

1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5


1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 0 0

VBus9 0.5

1


2

2.5


75

1.4

VBus1 VBus10

1.2

VBus11


VBus12 1

VBus13 VBus14

0.8

VBus15 VBus2 VBus3

0.6

VBus4 VBus5

0.4

VBus6 VBus7

0.2

VBus8 VBus9

0 0

0.5

1


2

2.5


4.4 Comparison between DG that given active and reactive power and DG that give active power only This part outlines the comparison between single DG capable of delivering active and reactive power and single DG capable of delivering active power only by voltage stability, voltage profile, power flow & the max value of a loading parameter of the system. All simulations in this part execute on IEEE 33 bus radial distribution system & practical radial distribution system in Japan.

4.4.1 IEEE 33 bus radial distribution system 4.4.1.1

Voltage Stability

Tables 4.2, 4.3, 4.4, 4.16, 4.17, 4.18 shows that line between bus 29 & bus 30 (L_(2930))is weakest voltage stability line. So, compare between DG that gives active and reactive power & DG that give active power only by calculating voltage stability indices at the weakest voltage stability line (LineL_ (29-30)). Figure 4.50 shows the impact of the penetration level of two type of DG on voltage stability indices in Line L_(29-30). Figure 4.50 shows that the voltage stability indices improved in the case of the installation DG that gives active and reactive power better than the installation DG that gives active power only.

76

FVSI with DG (P&Q)

Lmn with DG (P&Q)

LQP with DG (P&Q)

FVSI with DG (P)

Lmn with DG (P)

LQP with DG( P)

0.025

0.02

0.015

0.01

0.005

0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-50: The impact of two type DG on voltage stability 4.4.1.2 Voltage Profile Tables 4.6, 4.3, 4.4, 4.16, 4.17, 4.18 shows that Bus 30 is the weakest voltage stability bus. So, Compare between two types of DG by calculating voltage profile at the weakest voltage stability bus (bus 30). Figure 4.51 shows the impact of the penetration level of two types of the voltage of bus 30. Figure 4.51 shows that the voltage profile improved in the case of the installation DG that gives active and reactive power better than the installation DG that gives active power only.

77

Voltage at bus 30 With DG (P&Q)

Voltage at bus 30 With DG (P)

1.02 1 Voltage at Bus 30

0.98 0.96 0.94 0.92 0.9 0.88 0.86 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-51: The impact of two types of DG on Voltage profile at bus 30 4.4.1.3

Power Flow

Figure 4.52 shows the impact of the penetration level of two types of DG on real & reactive intake by the main generator. Figure 4.52 shows that real power intake by the main generator in the case of the installation DG that gives active and reactive power equal real power intake by the main generator in case of the installation DG that gives active power only. Also, shows that reactive power intake by the main generator in the case of the installation DG that gives active and reactive power less than reactive power intake by the main generator in case of the installation DG that gives active power only. Figure 4.53 shows the impact of the penetration level of two types DG on power losses. Figure 4.53 shows that power losses in the case of the installation DG that give active and reactive power less than power losses in case of the installation DG that give active power only.

78

0.045 𝑃_𝑖𝑛𝑡𝑎𝑘𝑒 (P&Q)

0.04 0.035

Q_𝑖𝑛𝑡𝑎𝑘𝑒(P&Q)

0.03 𝑃_𝑖𝑛𝑡𝑎𝑘𝑒 (P)

0.025 0.02

Q_𝑖𝑛𝑡𝑎𝑘𝑒 (P)

0.015 0.01 0.005 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-52: The impact of two types of DG on power flow

0.0025

power losses (P.U)

0.002 Power Losses (P&Q)

0.0015

Power Losses (P)

0.001

0.0005

0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-53: The impact of two types of DG on power losses

79

4.4.1.4

P-V Curve

Figure 4.54 shows the impact of the penetration level of two types of DG on max loading point. Figure 4.54 shows that max loading point in the case of the installation DG that gives active and reactive power greater than in the case of the installation DG that gives active power only. When reach a certain level in the case of DG that gives active power only max loading point decrease.

Max loading point (lamada) (P&Q) Max loading point (lamada)(P)

Max loading point(lamada)

4.4 4.2 4 3.8 3.6 3.4 3.2 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-54: The impact of two types of DG on max loading point

80

4.4.2 Practical radial distribution system in Japan

4.4.2.1

Voltage Stability

Tables 4.9, 4.10, 4.11, 4.23, 4.24 and 4.25 shows that line between bus 10 & bus 11( is weakest voltage stability line. So, compare between two types DG that given active and reactive power & DG that give active power only by calculating voltage stability indices at the weakest line (Line ). Figure 4.55 shows the impact of the penetration level of two types of DG on voltage stability indices in . Figure 4.55 shows that the voltage stability indices improved in the case of the installation DG that gives active and reactive power better than the installation DG that gives active power only. 0.046 FVSI with DG (P&Q)

0.044

Lmn with DG (P&Q)

0.042

LQP with DG (P&Q)

0.04 0.038

FVSI with DG (P)

0.036

Lmn with DG (P)

0.034 0%

10%

20%

30%

40%

50%

LQP with DG( P)

DG Penetration

Figure ‎4-55: The impact of two types of DG on voltage stability 4.4.2.2 Voltage Profile Tables 4.9, 4.10, 4.11, 4.23, 4.24 and 4.25 shows that Bus 11 is the weakest voltage stability bus. So, compare between two types of DG by calculating voltage at the weakest voltage stability bus (bus 11). Figure 4.56 shows that the voltage of the weakest voltage stability bus improved in the case of the installation DG that gives active and reactive power better than the installation DG that gives reactive power only.

81

0.99 0.98 0.97

Voltage at Bus 11

0.96 0.95 Voltage at bus 11 With DG (P&Q)

0.94 0.93 0.92

Voltage at bus 11 With DG (P)

0.91 0.9 0.89 0.88 0%

10%

20% 30% DG Size

40%

50%

Figure ‎4-56: The impact of two types of DG on Voltage of weakest voltage stability bus (bus 11)

4.4.2.3 Power Flow Figure 4.57 shows the impact of the penetration level of two types of DG on real & reactive power intake by the main generator. Figure 4.57 shows that real power intake by the main generator in the case of the installation DG that gives active and reactive power equal real power intake by the main generator in case of the installation DG that gives active power only. Also, shows that reactive power intake by the main generator in the case of the installation DG that gives active and reactive power less than reactive power intake by the main generator in case of the installation DG that gives active power only. Figure 4.58 shows the impact of the penetration level of two types of DG on power losses. Figure 4.58 shows that power losses in the case of the installation DG that give active and reactive power less than power losses in case of the installation DG that give active power only.

82

0.7 𝑃_𝑖𝑛𝑡𝑎𝑘𝑒 (P&Q)

0.6 0.5

Q_𝑖𝑛𝑡𝑎𝑘𝑒(P&Q)

0.4

𝑃_𝑖𝑛𝑡𝑎𝑘𝑒 (P)

0.3

Q_𝑖𝑛𝑡𝑎𝑘𝑒 (P)

0.2 0.1 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-57: The impact of two types of DG on power flow

0.01 0.009

power losses (P.U)

0.008 0.007 Power Losses (P&Q)

0.006 0.005

Power Losses (P)

0.004 0.003 0.002 0.001 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-58: The impact of two types of DG on power losses

83

4.4.2.4

P-V Curve

Figure 4.59 shows the impact of the penetration level of two types of DG on max loading point. Figure 4.59 shows that max loading point in the case of the installation DG that gives active and reactive power greater than in the case of the installation DG that gives active power only. When reach a certain level in the case of DG that gives active power only max loading point decrease.

3.2

Max loading point(lamada)

3.1 3

Max loading point (lamada) (P&Q)

2.9 2.8

Max loading point (lamada)(P)

2.7 2.6 2.5 2.4 2.3 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎4-59: The impact of two types of DG on max loading point

84

Chapter 5 Load Modeling 5.1 Introduction From Load modeling explained in section 2.8, the load is divided into the constant load, residential load, industrial load and commercial load. In this chapter simulate each type and study the voltage stability indices, power flow & voltage profile for various load models and compare them. All studies in this chapter carry out IEEE 33 bus radial distribution system.

5.2 Industrial Load In industrial load, the reactive and active power is depending on the magnitude of bus voltage.‎The‎value‎of‎α‎=‎0.18‎and‎the‎value‎of‎β‎=‎6. | | | | Distributed generation has two cases ●‎Single‎DG‎capable‎of‎delivering‎active‎and‎reactive‎power ●‎Single‎DG‎capable‎of‎delivering active power only

5.2.1 Single DG capable of delivering active and reactive power In this part, the results will be presented as follow ●‎Result‎of‎voltage‎stability‎indices‎without‎DG‎and‎with‎different‎DG‎size ●‎Result‎of‎voltage‎profile‎without‎DG‎and‎with‎different DG size ●‎Result‎of‎power‎flow‎without‎DG‎and‎with‎different‎DG‎size ●‎Result‎of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1. Table ‎5.1: Rating of installed distributed generation Rating of wind turbine 10% of the load 20% of the load 30% of the load 40% of the load 50% of the load

Active Power (MWatt) 0.3715 0.743 1.1145 1.486 1.8575

85

Reactive Power (MVAR) 0.23 0.46 0.69 0.92 1.15

5.2.1.1 Result of voltage stability indices without DG and with different DG size when load is industrial load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.2. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.3. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.4. According to values of voltage stability indices without the DG in Table 5.2, 5.3 and 5.4 it is found that the line which starts from bus 29 to bus 30 is the weakest voltage stability line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 5.1. From Tables 5.2, 5.3 and 5.4 notice that the values of voltage stability indices at each line are increasing when installing the DG unit in bus 30. So, voltage stability is worse on each bus. Also, when increases the size of DG, voltage stability of each bus more worse. This occurs due to that the industrial load at each bus dependent on the voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when installed DG in distributed systems. Figure 5.1 demonstrations the effect of increasing the size of wind turbines on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.01411 to 0.01969, the value of LQP changes from 0.00291 to 0.004056 and the value of Lmn changes from 0.014056 to 0.019596 when the DG generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to install DG at bus 30.

Voltage Stability Indices value of bus 30

0.025

0.02

0.015 FVSI Lmn

0.01

LQP 0.005

0 0%

10%

20%

30% 40% DG Size from Load

50%

60%

Figure ‎5-1: The effect of increasing size of DG on the weakest voltage stability bus at industrial load

86

Table ‎5.2 Values of fast voltage stability index (FVSI) at the different DG size at industrial load Line


FVSI without DG 0.0003356 0.0011129 0.0016279 0.0006186 0.0006657 0.0013788 0.0047645 0.0008451 0.0008009 0.0003895 0.0008361 0.0019478 0.0016557 0.0002181 0.0005715 0.0009716 0.0010907 0.0003231 0.0029174 0.0008018 0.0014219 0.0011110 0.0082044 0.0081507 0.0002579 0.0003575 0.0008228 0.0021409 0.0141098 0.0025143 0.0011611 0.0005541



87




Table ‎5.3 :Values of the line stability index (Lmn) at the different DG size at industrial load Line


Lmn without DG 0.0003354 0.0011136 0.0016270 0.0006183 0.0006718 0.0013819 0.0047619 0.0008492 0.0008044 0.0003893 0.0008356 0.0019580 0.0016587 0.0002184 0.0005720 0.0009732 0.0010906 0.0003231 0.0029234 0.0008018 0.0014219 0.0011103 0.0082380 0.0081647 0.0002575 0.0003567 0.0008237 0.0021412 0.0140556 0.0025226 0.0011614 0.0005539



88




Table ‎5.4: Values of line stability factor (LQP) at the diverse DG size at industrial load Line


LQP without DG 6.922E-05 0.0002293 0.0003353 0.0001275 0.0002845 0.0012635 0.0004695 0.0002918 0.0002823 3.735E-05 8.241E-05 0.0007457 0.0010502 9.725E-05 0.0001990 0.0006246 0.0004155 0.0001540 0.0013096 0.0004630 0.0009056 0.0003537 0.0031516 0.0031101 5.315E-05 7.361E-05 0.0003604 0.0009241 0.0029068 0.0012498 0.0006693 0.0003945

LQP with DG 10% of load 6.934E-05 0.0002317 0.0003401 0.0001300 0.0002947 0.0013006 0.0004834 0.0003003 0.0002907 3.847E-05 8.488E-05 0.0007681 0.0010818 0.0001001 0.0002050 0.0006433 0.0004280 0.0001542 0.0013111 0.0004636 0.0009067 0.0003563 0.0031750 0.0031330 5.494E-05 7.642E-05 0.0003825 0.0009911 0.0031305 0.0013406 0.0007184 0.0004231


89




5.2.1.2 Result of voltage profile without DG and with different DG size at industrial load Table 5.5 and Figure 5.2 demonstrate the effect of increasing the size of DG on the voltage of each bus. From Table 5.5, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.3 demonstrates the effect of increasing the size of DG on the voltage of the weakest voltage stability bus (bus 30). The voltage at bus 30 changes from 0.9324 to 1.0096 when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.0772. This change shows that the voltage at bus 30 enhanced due to installing DG. Voltage Magnitude (P.U) at bus 30

1.02 1

0.98 0.96 0.94 0.92 0.9

0.88 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-2: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at industrial load

90

Figure ‎5-2: The effect of increasing size of DG on voltage of each bus at industrial load

91

Table ‎5.5: The effect of increasing size of DG on voltage of each bus Without DG Voltage at Bus 1 Voltage at Bus 2 Voltage at Bus 3 Voltage at Bus 4 Voltage at Bus 5 Voltage at Bus 6 Voltage at Bus 7 Voltage at Bus 8 Voltage at Bus 9 Voltage at Bus 10 Voltage at Bus 11 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 12 Voltage at Bus 13 Voltage at Bus 14 Voltage at Bus 15 Voltage at Bus 61 Voltage at Bus 60 Voltage at Bus 66 Voltage at Bus 6. Voltage at Bus 64 Voltage at Bus 61 Voltage at Bus 62 Voltage at Bus 63 Voltage at Bus 64 Voltage at Bus 65 Voltage at Bus .1 Voltage at Bus .0 Voltage at Bus .6 Voltage at Bus ..

1 0.9972519 0.9843177 0.9775965 0.9709750 0.9551857 0.9524046 0.9478673 0.9422548 0.9372250 0.9364142 0.9350188 0.9296121 0.9276903 0.9264283 0.9252011 0.9234799 0.9229449 0.9967301 0.9932019 0.9925093 0.9918839 0.9808818 0.9745228 0.9713612 0.9535198 0.9513164 0.9420246 0.9353832 0.9323827 0.9287967 0.9280230 0.9277962

DG 10% of load 1 0.9975375 0.9861299 0.9805430 0.9751033 0.9621639 0.9593386 0.9548103 0.9491889 0.9441495 0.9433404 0.9419479 0.9365303 0.9345977 0.9333346 0.9321069 0.9303772 0.9298413 0.9970155 0.9934865 0.9927936 0.9921680 0.9826911 0.9763251 0.9731601 0.9611275 0.9598051 0.9542536 0.9504436 0.9490190 0.9453920 0.9446062 0.9443730

DG 20% of load 1 0.9978120 0.9878720 0.9833756 0.9790720 0.9688638 0.9659944 0.9614739 0.9558426 0.9507927 0.9499850 0.9485951 0.9431656 0.9412219 0.9399576 0.9387291 0.9369907 0.9364537 0.9972899 0.9937601 0.9930670 0.9924412 0.9844302 0.9780574 0.9748892 0.9684329 0.9679583 0.9659965 0.9649062 0.9649990 0.9613259 0.9605268 0.9602868

92

DG 30% of load 1 0.9980764 0.9895506 0.9861051 0.9828965 0.9753119 0.9723986 0.9678849 0.9622428 0.9571815 0.9563750 0.9549875 0.9495451 0.9475903 0.9463244 0.9450949 0.9433476 0.9428095 0.9975542 0.9940237 0.9933304 0.9927044 0.9861061 0.9797266 0.9765551 0.9754650 0.9758081 0.9773002 0.9788286 0.9803860 0.9766622 0.9758488 0.9756015

DG 40% of load 1 0.9983318 0.9911716 0.9887409 0.9865896 0.9815308 0.9785737 0.9740659 0.9684120 0.9633387 0.9625333 0.9611477 0.9556917 0.9537256 0.9524580 0.9512273 0.9494709 0.9489316 0.9978095 0.9942782 0.9935848 0.9929585 0.9877242 0.9813382 0.9781635 0.9822484 0.9833818 0.9882039 0.9922593 0.9952335 0.9914546 0.9906259 0.9903711

DG 50% of load 1 0.9985789 0.9927396 0.9912908 0.9901626 0.9875396 0.9845388 0.9800361 0.9743697 0.9692836 0.9684792 0.9670953 0.9616251 0.9596474 0.9583780 0.9571458 0.9553803 0.9548396 0.9980564 0.9945245 0.9938308 0.9932044 0.9892896 0.9828971 0.9797193 0.9888038 0.9907026 0.9987415 1.0052399 1.0095872 1.0057491 1.0049042 1.0046416

5.2.1.3 Result of power flow without DG and with different DG size at industrial load Table 5.6 demonstrations the effect of increasing the size of DG unit on power flow. From Table 5.6, it is observed that there is reduced in real & reactive power generated by The Electric Company due to installing the DG unit and there is an increase in total load due to improving voltage of each bus. Furthermore, power losses get reduced but when to reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.3 demonstrate the effect of increasing size of DG on power losses. Table ‎5.6: The effect of increasing size of DG on power flow

0

Pl(M Watt) 3.684

Ql(MV AR) 1.718

Plosses( KWatt) 161

Qlosses( KVAR) 107

0.37

0.23

3.689

1.808

118

78

1.500

0.74

0.46

3.693

1.901

87

59

2.652

1.355

1.11

0.69

3.697

1.996

69

48

40%

2.277

1.22

1.48

0.92

3.701

2.095

62

44

50%

1.912

1.094

1.85

1.15

3.705

2.196

64

48

Pintake (MWatt) 3.846

Qintake (MVAR) 1.825

(MWatt)

(M VAR)

0

10%

3.436

1.657

20%

3.038

30%

Without DG

93

Active Power losses

Reactive Power Losses

0.0018 0.0016

Losses (P.U)

0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-3: The effect of increasing the size of DG on active & reactive power losses

5.2.2 Single DG capable of delivering active power only In this part, the results will be presented as follow ●‎Results of voltage stability indices without DG and with different DG size ●‎Results of voltage profile without DG and with different DG size ●‎Results of power flow without DG and with different DG size ●‎Results of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1.

94

5.2.2.1 Result of voltage stability indices without DG and with different DG size at industrial load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.7. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.8. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.9. According to values of voltage stability indices without the DG in Table 5.7, 5.8 and 5.9 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 5.1. From Tables 5.7, 5.8 and 5.9 notice that the values of voltage stability indices at each line are increasing when installing the DG unit in bus 30. So, voltage stability is worse on each bus. Also, when increases the size of DG, voltage stability of each bus more worse. This occurs due to that the industrial load at each bus dependent on the voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when installed DG in distributed systems. Figure 5.4 demonstrations the effect of increasing the size of DG on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.01411 to 0.0179, the value of LQP changes from 0.00291 to 0.003688 and the value of Lmn changes from 0.01405 to 0.01758 when the DG generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to installing DG.

0.02


0.018 0.016 0.014 0.012 FVSI

0.01

Lmn

0.008

LQP

0.006 0.004 0.002 0 0%

10%

20%


50%

60%

Figure ‎5-4: The effect of increasing size of DG on the weakest voltage stability bus at industrial load

95

Table ‎5.7: Values of fast voltage stability index (FVSI) at the different DG size at industrial load

Line 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11 11 to 12 12 to 13 13 to 14 14 to 15 15 to 16 16 to 17 17 to 18 2 to 19 19 to 20 20 to 21 21 to 22 3 to 23 23 to 24 24 to 25 6 to 26 26 to 27 27 to 28 28 to 29 29 to 30 30 to 31 31 to 32 32 to 33

FVSI without DG

FVSI with DG 10% of load





0.0003356 0.0011129 0.0016279 0.0006186 0.0006657 0.0013788 0.0047645 0.0008451 0.0008009 0.0003895 0.0008361 0.0019478 0.0016557 0.0002181 0.0005715 0.0009716 0.0010907 0.0003231 0.0029174 0.0008018 0.0014219 0.0011110 0.0082044 0.0081507 0.0002579 0.0003575 0.0008228 0.0021409 0.0141098 0.0025143 0.0011611 0.0005541

0.0003360 0.0011218 0.0016459 0.0006279 0.0006825 0.0014078 0.0048657 0.0008631 0.0008181 0.0003979 0.0008540 0.0019898 0.0016914 0.0002228 0.0005839 0.0009925 0.0011142 0.0003234 0.0029200 0.0008026 0.0014231 0.0011173 0.0082508 0.0081969 0.0002642 0.0003673 0.0008576 0.0022468 0.0148652 0.0026422 0.0012201 0.000582

0.0003364 0.0011304 0.0016633 0.0006369 0.0006989 0.0014360 0.0049643 0.0008807 0.0008348 0.0004060 0.0008715 0.0020307 0.0017261 0.0002274 0.0005959 0.0010130 0.0011372 0.0003237 0.0029224 0.0008032 0.0014243 0.0011234 0.0082956 0.0082414 0.0002703 0.0003770 0.0008921 0.0023526 0.0156225 0.0027701 0.0012791 0.0006104

0.0003368 0.0011388 0.0016802 0.0006456 0.0007149 0.0014635 0.0050605 0.0008978 0.0008511 0.0004139 0.0008885 0.0020706 0.0017600 0.0002319 0.0006076 0.0010329 0.0011596 0.0003240 0.0029248 0.0008038 0.0014255 0.0011292 0.0083389 0.0082844 0.0002763 0.0003865 0.0009264 0.0024582 0.0163813 0.0028979 0.0013381 0.0006386

0.016264 0.001146 0.001696 0.000654 0.000730 0.001490 0.005154 0.000914 0.000866 0.000421 0.000905 0.002109 0.001793 0.000236 0.000619 0.000524 0.001181 0.000324 0.002927 0.000804 0.001426 0.001134 0.008380 0.008326 0.000282 0.000395 0.000960 0.002563 0.017141 0.003025 0.001397 0.000666

0.0003376 0.0011547 0.0017125 0.0006624 0.0007459 0.0015166 0.0052459 0.0009308 0.0008824 0.0004292 0.0009213 0.0021475 0.0018252 0.0002405 0.0006302 0.0010713 0.0012027 0.0003244 0.0029293 0.0008051 0.0014277 0.0011403 0.0084212 0.0083662 0.0002879 0.0004050 0.0009942 0.0026688 0.0179033 0.0031531 0.0014559 0.0006948

96

Table ‎5.8: Values of the line stability index (Lmn) at the different DG size at industrial load Line

Lmn without DG

Lmn with DG 10% of load






0.000335 0.001113 0.001627 0.000618 0.000671 0.001381 0.004761 0.000849 0.000804 0.000389 0.000835 0.001958 0.001658 0.000218 0.000572 0.000973 0.001090 0.000323 0.002923 0.000801 0.001421 0.001110 0.008238 0.008164 0.000257 0.000356 0.000823 0.002141 0.014055 0.002522 0.001161 0.000553

0.0003357 0.0011191 0.0016412 0.0006261 0.0006854 0.0014108 0.0048618 0.0008672 0.0008215 0.0003976 0.0008534 0.0019998 0.0016944 0.0002231 0.0005843 0.0009942 0.0011141 0.0003233 0.0029260 0.0008025 0.0014231 0.0011189 0.0082842 0.0082107 0.0002634 0.0003659 0.0008533 0.002236 0.0147622 0.0026503 0.0012204 0.0005821

0.0003507 0.0010782 0.0016548 0.0006336 0.0006985 0.0014391 0.0049591 0.0008847 0.0008381 0.0004057 0.0008708 0.0020406 0.0017291 0.0002277 0.0005963 0.0010146 0.0011371 0.0003236 0.0029284 0.0008032 0.0014243 0.0011249 0.0083287 0.0082551 0.0002692 0.0003749 0.0008824 0.0023313 0.0154679 0.0027780 0.0012793 0.0006102

0.0003361 0.0011292 0.0016679 0.0006407 0.0007112 0.0014666 0.0050540 0.0009017 0.0008543 0.0004136 0.0008878 0.0020804 0.0017630 0.0002321 0.0006080 0.0010346 0.0011594 0.0003239 0.0029308 0.0008038 0.0014255 0.0011307 0.0083718 0.0082980 0.0002748 0.0003837 0.0009111 0.0024254 0.0161728 0.0029055 0.0013383 0.0006384

0.0162206 0.0011337 0.0016803 0.0006477 0.0007234 0.0014935 0.0051465 0.0009183 0.0008702 0.0004213 0.0009043 0.0021192 0.0017960 0.0002365 0.0006195 0.0010540 0.0011812 0.0003241 0.0029330 0.0008045 0.0014266 0.0011363 0.0084133 0.0083395 0.0002803 0.0003923 0.0009393 0.0025188 0.0168767 0.0030329 0.0013972 0.0006665

0.0003365 0.0011379 0.0016922 0.0006543 0.0007353 0.0015197 0.0052368 0.0009346 0.0008856 0.0004288 0.0009204 0.0021570 0.0018282 0.0002407 0.0006306 0.0010730 0.0012025 0.0003244 0.0029352 0.0008051 0.0014276 0.0011418 0.0084536 0.0083796 0.0002856 0.0004007 0.0009670 0.0026116 0.0175796 0.0031602 0.0014560 0.0006945

97

Table ‎5.9: Values of line stability factor (LQP) at the different DG size at industrial load Line

LQP without DG

LQP with DG 10% of load






6.922E-05 0.0002293 0.0003353 0.0001275 0.0002845 0.0012635 0.0004695 0.0002918 0.0002823 3.735E-05 8.241E-05 0.0007457 0.0010502 9.725E-05 0.0001990 0.0006246 0.0004155 0.0001540 0.0013096 0.0004630 0.0009056 0.0003537 0.0031516 0.0031101 5.315E-05 7.361E-05 0.0003604 0.0009241 0.0029068 0.0012498 0.0006693 0.0003945

6.931E-05 0.0002311 0.0003390 0.0001294 0.0002917 0.0012900 0.0004794 0.0002979 0.0002883 3.81E-05 8.418E-05 0.0007617 0.0010728 9.931E-05 0.0002033 0.0006380 0.0004245 0.0001542 0.0013108 0.0004634 0.0009064 0.0003557 0.0031695 0.0031275 5.443E-05 7.564E-05 0.0003756 0.0009698 0.0030624 0.0013127 0.0007033 0.0004143

6.940E-05 0.0002329 0.0003426 0.0001312 0.0002987 0.0013159 0.0004891 0.0003038 0.0002942 3.893E-05 8.590E-05 0.0007773 0.0010948 0.0001013 0.0002074 0.0006511 0.0004332 0.0001543 0.0013119 0.0004638 0.0009072 0.0003576 0.0031867 0.0031444 5.569E-05 7.763E-05 0.0003907 0.0010154 0.0032184 0.0013756 0.0007373 0.0004341

6.948E-05 0.0002346 0.0003460 0.0001330 0.0003055 0.0013411 0.0004986 0.0003095 0.0002999 3.969E-05 8.758E-05 0.0007926 0.0011162 0.0001032 0.0002115 0.0006638 0.0004417 0.0001544 0.0013129 0.0004642 0.0009079 0.0003595 0.0032033 0.0031607 5.693E-05 7.959E-05 0.0004057 0.0010609 0.0033747 0.0014384 0.0007713 0.0004539

0.0033547 0.0002363 0.0003494 0.0001348 0.0003122 0.0013657 0.0005078 0.0003152 0.0003055 4.043E-05 8.921E-05 0.0008074 0.0011372 0.0001052 0.0002155 0.0006762 0.0004500 0.0001545 0.0013139 0.0004646 0.0009086 0.0003613 0.0032193 0.0031764 5.813E-05 8.151E-05 0.0004206 0.0011064 0.0035313 0.0015013 0.0008052 0.0004737

6.96E-05 0.0002379 0.0003527 0.0001365 0.0003188 0.0013897 0.0005168 0.0003206 0.0003109 4.115E-05 9.081E-05 0.0008219 0.0011576 0.0001070 0.0002194 0.0006883 0.0004581 0.0001546 0.0013149 0.0004649 0.0009093 0.0003630 0.0032349 0.0031916 5.931E-05 8.34E-05 0.0004353 0.0011518 0.0036882 0.0015641 0.0008391 0.0004935

98

5.2.2.2 Result of voltage profile without DG and with different DG size at industrial load Table 5.10 and Figure 5.5 demonstrate the effect of increasing the size of DG on the voltage of each bus. From Table 5.10, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.6 demonstrates the effect of increasing the size of DG on the voltage of the weakest voltage stability bus (bus 30). The voltage at bus 30 changes from 0.93238275 to 0.98660642 when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.05422. This change shows that the voltage at bus 30 enhanced due to installing DG.


0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0%

10%

20%

30%

40%

50%

60%

DG Size

Figure ‎5-5: The effect of increasing the size of DG on voltage of the weakest bus voltage stability at industrial load

99

Figure ‎5-6: The effect of increasing size of DG on voltage of each bus at industrial load

100

Table ‎5.10: The effect of increasing size of DG on voltage of each bus


Without DG 1 0.997251 0.984317 0.977596 0.970975 0.955185 0.952404 0.947867 0.942254 0.937225 0.936414 0.935018 0.929612 0.927690 0.926428 0.925201 0.923479 0.922944 0.996730 0.993201 0.992509 0.991883 0.980881 0.974522 0.971361 0.953519 0.951316 0.942024 0.935383 0.932382 0.928796 0.928023 0.927796

10% DG

20% DG

30% DG

40% DG

50% DG

1 0.9974696 0.9856997 0.9798436 0.9741239 0.9601886 0.9573760 0.9528452 0.9472265 0.9421900 0.9413804 0.9399871 0.9345727 0.9326432 0.9313805 0.9301530 0.9284257 0.9278901 0.9969477 0.9934188 0.9927261 0.9921005 0.9822615 0.9758972 0.9727331 0.9590025 0.9574712 0.9505940 0.9457913 0.9439987 0.9403848 0.9396028 0.9393716

1 0.997678 0.987027 0.982003 0.977151 0.964990 0.962146 0.957621 0.951996 0.946952 0.946144 0.944753 0.939330 0.937393 0.936129 0.934901 0.933168 0.932632 0.997156 0.993627 0.992934 0.992308 0.983587 0.977217 0.974051 0.964268 0.963386 0.958836 0.955815 0.955199 0.951555 0.950764 0.950528

1 0.997879 0.988304 0.984082 0.980067 0.969606 0.966731 0.962212 0.956579 0.951528 0.950720 0.949331 0.943900 0.941955 0.940690 0.939462 0.937722 0.937185 0.997357 0.993827 0.993134 0.992508 0.984862 0.978487 0.975318 0.969332 0.969079 0.966776 0.965484 0.966015 0.962339 0.961539 0.961299

1 0.998073 0.989534 0.986085 0.982877 0.974047 0.971143 0.966628 0.960988 0.955929 0.955122 0.953734 0.948294 0.946342 0.945076 0.943847 0.942102 0.941564 0.997550 0.994020 0.993327 0.992701 0.986090 0.979710 0.976539 0.974208 0.974566 0.974436 0.974825 0.976476 0.972766 0.971956 0.971711

1 0.998259 0.990720 0.988016 0.985589 0.978326 0.975392 0.970881 0.965234 0.960167 0.959361 0.957974 0.952525 0.950565 0.949298 0.948068 0.946317 0.945778 0.997737 0.994206 0.993512 0.992886 0.987273 0.980889 0.977715 0.978909 0.979860 0.981833 0.983859 0.986606 0.982860 0.982040 0.981790

101

5.2.2.3 Result of power flow without DG and with different DG size at industrial load Table 5.11 demonstrations the effect of increasing the size of DG unit on power flow. From Table 5.11, it is observed that there is reduced in real power generated by The Electric Company due to install the DG unit at bus 30 and there is increase in reactive power generated by The Electric Company and the total load due to improve voltage of each bus. Furthermore, power losses get reduced but when reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.7 demonstrate the effect of increasing size of DG on active and reactive power losses. Table ‎5.11: The effect of increasing size of DG on power flow

0

Pl(M Watt) 3.684

Ql (MVAR) 1.718

Plosses( KWatt) 161

Qlosses (KVAR) 107

0.371

0

3.688

1.781

129

86

1.918

0.743

0

3.691

1.844

109

73

2.678

1.977

1.114

0

3.694

1.909

98

67

40%

2.308

2.042

1.486

0

3.697

1.974

97

68

50%

1.947

2.115

1.857

0

3.699

2.040

105

75

Pintake (MWatt) 3.846

Qintake( MVAR) 1.825

(M Watt)

(MVAR)

0

10%

3.446

1.867

20%

3.057

30%

Without DG

Power Losses (P.U)

Active Power losses

Reactive Power losses

0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-7: The effect of increasing the size of DG on active & reactive power losses at industrial load 102

5.3 Residential Load In residential load, the reactive and active power is depending on magnitude of bus voltage. The value of‎α‎=‎0.92‎and‎the‎value‎of‎β‎=‎4.04. | | | | Distributed generation has two cases ●‎Single‎DG‎capable‎of‎delivering‎active‎and‎reactive‎power ●‎Single‎DG‎capable‎of‎delivering‎active‎power‎only

5.3.1 Single DG capable of delivering active and reactive power In this part, the results will be presented as follow ●‎Result‎of‎voltage‎stability‎indices‎without‎DG‎and‎with‎different‎DG‎size ●‎Result‎of‎voltage‎profile‎without‎DG‎and‎with‎different‎DG‎size ●‎Result‎of‎power‎flow‎without‎DG‎and‎with‎different‎DG‎size ●‎Result‎of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1. 5.3.1.1 Result of voltage stability indices without DG and with different DG size at residential load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.12. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.13. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.14. According to values of voltage stability indices without the DG in Table 5.12, 5.13 and 5.14 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 5.1. From Tables 5.12, 5.13 and 5.14 notice that the values of voltage stability indices at each line are increasing when installed the DG unit in bus 30. So, voltage stability is worse at each bus. Also, when increases the size of DG, voltage stability of each bus more worsen. This occurs due to that the residential load at each bus dependent on voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when 103

installed DG in distributed systems. Figure 5.8 demonstrations the effect of increasing the size of DG on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.0141098 to 0.01934, the value of LQP changes from 0.00291 to 0.00399 and the value of Lmn changes from 0.01405 to 0.0193 when the wind turbine generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to installing DG.


0.025

0.02

0.015 FVSI Lmn

0.01

LQP 0.005

0 0%

10%

20%


50%

60%

Figure ‎5-8: The effect of increasing size of DG on the weakest bus (bus 30)

104

Table ‎5.12: Values of fast voltage stability index (FVSI) at the different DG size at residential load Line


FVSI without DG 0.0003374 0.0011485 0.0017028 0.0006559 0.0007284 0.0015169 0.0052953 0.0009503 0.0009103 0.0004435 0.0009547 0.0022503 0.0019202 0.0002537 0.0006665 0.0011370 0.0012779 0.0003252 0.0029568 0.0008137 0.0014449 0.0011543 0.0086332 0.0086315 0.0002832 0.0003943 0.0009242 0.0024378 0.0161726 0.0029040 0.0013432 0.0006413



105




Table ‎5.13: Values of the line stability index (Lmn) at the different DG size at residential load Line


Lmn without DG 0.000335 0.001113 0.001627 0.000618 0.000671 0.001381 0.004761 0.000849 0.000804 0.000389 0.000835 0.001958 0.001658 0.000218 0.000572 0.000973 0.001090 0.000323 0.002923 0.000801 0.001421 0.001110 0.008238 0.008164 0.000257 0.000356 0.000823 0.002141 0.014055 0.002522 0.001161 0.000553



106




Table ‎5.14: Values of line stability factor (LQP) at the different DG size at residential load Line




LQP with DG 20% of load 0.0002272 0.0012143 0.0002744 0.0002869 0.0007903 0.0009406 0.0003579 0.0022713 0.0011460 0.0001015 0.0001934 0.0031959 0.0017946 0.0013257 0.0013758 0.0043366 0.0014466 0.0016144 0.0019845 0.0007046 0.0013823 0.0004582 0.0021202 0.0035528 0.0003975 0.0007788 0.0004245 0.0011253 0.0035923 0.0015112 0.0008295 0.0004896

107




5.3.1.2 Result of voltage profile without DG and with different DG size at residential load Table 5.15 and Figure 5.9 demonstrate the effect of increasing the size of DG on voltage of each bus. From Table 5.15, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.10 demonstrates the effect of increasing the size of DG on the voltage of the weakest voltage stability bus (bus 30). The voltage at bus 30 changes from 0.9324 to 1.0099when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.077519. This change shows that the voltage at bus 30 enhanced due to install DG.

1.02


1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0%

10%

20%

30%

40%

50%

60%

DG Size from load

Figure ‎5-9: The effect of increasing the size of DG on voltage of the weakest voltage stability bus (bus 30) at residential load

108

Figure ‎5-10: The effect of increasing size of DG on voltage of each bus at residential load

109

Table ‎5.15 :The effect of increasing size of DG on voltage of each bus at residential load


Without DG

DG 10% of load

DG 20% of load

DG 30% of load

DG 40% of load

DG 50% of load

1 0.997251 0.984317 0.977596 0.970975 0.955185 0.952404 0.947867 0.942254 0.937225 0.936414 0.935018 0.929612 0.927690 0.926428 0.925201 0.923479 0.922944 0.996730 0.993201 0.992509 0.991883 0.980881 0.974522 0.971361 0.953519 0.951316 0.942024 0.935383 0.932382 0.928796 0.928023 0.927796

1 0.997555 0.986240 0.980705 0.975319 0.962272 0.959332 0.954929 0.949386 0.944411 0.943626 0.942277 0.936928 0.934987 0.933747 0.932545 0.930813 0.930284 0.997033 0.993503 0.992810 0.992183 0.982812 0.976456 0.973297 0.961230 0.959899 0.954127 0.950151 0.948700 0.945072 0.944281 0.944042

1 0.997826 0.987964 0.983509 0.979249 0.968955 0.965981 0.961569 0.956004 0.951007 0.950221 0.948870 0.943497 0.941544 0.940300 0.939093 0.937351 0.936820 0.997304 0.993774 0.993080 0.992453 0.984532 0.978168 0.975005 0.968518 0.968035 0.965902 0.964683 0.964753 0.961074 0.960270 0.960025

1 0.998089 0.989631 0.986222 0.983050 0.975415 0.972408 0.967988 0.962400 0.957383 0.956595 0.955241 0.949846 0.947881 0.946632 0.945421 0.943668 0.943135 0.997567 0.994036 0.993342 0.992715 0.986195 0.979823 0.976656 0.975564 0.975901 0.977284 0.978732 0.980274 0.976543 0.975725 0.975475

1 0.998344 0.991247 0.988851 0.986735 0.981672 0.978632 0.974204 0.968594 0.963557 0.962768 0.961411 0.955993 0.954017 0.952763 0.951548 0.949786 0.949251 0.997821 0.994290 0.993595 0.992968 0.987808 0.981428 0.978257 0.982389 0.983521 0.988310 0.992340 0.995310 0.991526 0.990695 0.990439

1 0.998591 0.992816 0.991403 0.990312 0.987743 0.984671 0.980235 0.974604 0.969546 0.968756 0.967397 0.961957 0.959968 0.958711 0.957492 0.955719 0.955182 0.998068 0.994536 0.993842 0.993214 0.989373 0.982986 0.979812 0.989012 0.990916 0.999008 1.005545 1.009902 1.006066 1.005222 1.004960

110

5.3.1.3 Result of power flow without DG and with different DG size at residential load Table 5.16 demonstrations the effect of increasing the size of wind turbine unit on power flow. From Table 5.16, it is observed that there is reduced in real & reactive power generated by The Electric Company due to install the DG unit at bus 30. There is increase in total load due to improve voltage of each bus. Furthermore, power losses get reduced but when reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.11 demonstrate the effect of increasing size of wind turbine on power losses. Table ‎5.16: The effect of increasing size of DG on power flow

Without DG

Pintake( MWatt) 3.723

Qintake( MVAR) (MWatt) 1.99 0

0

Pl (MWatt) 3.564

Ql(MV AR) 1.885

Plosses( KWatt) 159

Qlosses( KVAR) 105

(M VAR)

10%

3.331

1.80

0.371

0.23

3.586

1.953

116

77

20%

2.951

1.619

0.743

0.46

3.608

2.021

86

58

30%

2.583

1.447

1.114

0.69

3.629

2.090

68

47

40%

2.224

1.283

1.486

0.92

3.649

2.159

61

44

50%

1.874

1.126

1.857

1.15

3.668

2.229

63

47

Power Losses (P.U)

Active Power losses


0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-11: The effect of increasing the size of DG on power losses 111

5.3.2 Single DG capable of delivering active power only In this part, the results will be presented as follow ●‎Results of voltage stability indices without DG and with different DG size ●‎Results of voltage profile without DG and with different DG size ●‎Results of power flow without DG and with different DG size ●‎Results of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1. 5.3.2.1 Result of voltage stability indices without DG and with different DG size at residential load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.17. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.18. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.19. According to values of voltage stability indices without the DG in Table 5.17, 5.18 and 5.19 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 5.1. From Tables 5.17, 5.18 and 5.19 notice that the values of voltage stability indices at each line are increasing when installed the DG unit in bus 30. Also, when increases the size of DG, voltage stability of each bus more worsen. This occurs due to that the residential load at each bus dependent on voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when installed DG in distributed systems. Figure 5.12 demonstrations the effect of increasing the size of DG on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.01411 to 0.0179, the value of LQP changes from 0.00291 to 0.00369 and the value of Lmn changes from 0.0141 to 0.0176 when the DG generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to installing DG.

112

Table ‎5.17: Values of fast voltage stability index (FVSI) at the different DG size at residential load Line


FVSI without DG 0.000335 0.001112 0.001627 0.000618 0.000665 0.001378 0.004764 0.000845 0.000800 0.000389 0.000836 0.001947 0.001655 0.000218 0.000571 0.000971 0.001090 0.000323 0.002917 0.000801 0.001421 0.001111 0.008204 0.008150 0.000257 0.000357 0.000822 0.002140 0.014109 0.002514 0.001161 0.000554



113




Table ‎5.18: Values of the line stability index (Lmn) at the different DG size at residential load Line


Lmn without DG 0.000335 0.001113 0.001627 0.000618 0.000671 0.001381 0.004761 0.000849 0.000804 0.000389 0.000835 0.001958 0.001658 0.000218 0.000572 0.000973 0.001090 0.000323 0.002923 0.000801 0.001421 0.001110 0.008238 0.008164 0.000257 0.000356 0.000823 0.002141 0.014055 0.002522 0.001161 0.000553



114




Table ‎5.19: Values of line stability factor (LQP) at the different DG size at residential load Line



LQP with DG 10% of load 6.922E-05 0.0002293 0.0003353 0.0001275 0.0002845 0.0012635 0.0004695 0.0002918 0.0002823 3.7357E-05 8.2413E-05 0.0007457 0.0010502 9.7252E-05 0.0001990 0.0006246 0.0004155 0.0001540 0.0013096 0.0004630 0.0009056 0.0003537 0.0031516 0.0031101 5.3151E-05 7.3616E-05 0.0003604 0.0009241 0.0029068 0.0012498 0.0006693 0.0003945


115


LQP with DG 40% of load 0.0033547 0.0002363 0.0003494 0.0001348 0.0003122 0.0013657 0.0005078 0.0003152 0.0003055 4.043E-05 8.921E-05 0.0008074 0.0011372 0.0001052 0.0002155 0.0006762 0.0004500 0.0001545 0.0013139 0.0004646 0.0009086 0.0003613 0.0032193 0.0031764 5.813E-05 8.151E-05 0.0004206 0.0011064 0.0035313 0.0015013 0.0008052 0.0004737



0.02 0.018 0.016 0.014 0.012 0.01

FVSI

0.008

Lmn

0.006

LQP

0.004 0.002 0 0%

10%

20%

30%

40%

50%

60%

DG Size from Load

Figure ‎5-12: The effect of increasing size of DG on the weakest voltage stability bus at residential load 5.3.2.2 Result of voltage profile without DG and with different DG size at residential load Table 5.20 and Figure 5.13 demonstrate the effect of increasing the size of DG on voltage of each bus. From Table 5.20, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.14 demonstrates the effect of increasing the size of DG on the voltage of the weakest voltage stability bus (bus 30). The voltage at bus 30 changes from 0.93238 to 0.9866 when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.0542. This change shows that the voltage at bus 30 enhanced due to install DG. Voltage Magnitude at Bus 30

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0%

10%

20%

30% DG Size from load

40%

50%

60%

Figure ‎5-13: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at residential load 116

Figure ‎5-14: The effect of increasing size of DG on voltage of each bus at residential load

117

Table ‎5.20: The effect of increasing size of DG on voltage of each bus at residential load


Without DG 1 0.997251 0.984317 0.977596 0.970975 0.955185 0.952404 0.947867 0.942254 0.937225 0.936414 0.935018 0.929612 0.927690 0.926428 0.925201 0.923479 0.922944 0.996730 0.993201 0.992509 0.991883 0.980881 0.974522 0.971361 0.953519 0.951316 0.942024 0.935383 0.932382 0.928796 0.928023 0.927796

10% DG

20% DG

30% DG

40% DG

50% DG

1 0.997251 0.984317 0.977596 0.970975 0.955185 0.952404 0.947867 0.942254 0.937225 0.936414 0.935018 0.929612 0.927690 0.926428 0.925201 0.923479 0.922944 0.996730 0.993201 0.992509 0.991883 0.980881 0.974522 0.971361 0.953519 0.951316 0.942024 0.935383 0.932382 0.928796 0.928023 0.927796

1 0.997678 0.987027 0.982003 0.977151 0.964990 0.962146 0.957621 0.951996 0.946952 0.946144 0.944753 0.939330 0.937393 0.936129 0.934901 0.933168 0.932632 0.997156 0.993627 0.992934 0.992308 0.983587 0.977217 0.974051 0.964268 0.963386 0.958836 0.955815 0.955199 0.951555 0.950764 0.950528

1 0.997879 0.988304 0.984082 0.980067 0.969606 0.966731 0.962212 0.956579 0.951528 0.950720 0.949331 0.943900 0.941955 0.940690 0.939462 0.937722 0.937185 0.997357 0.993827 0.993134 0.992508 0.984862 0.978487 0.975318 0.969332 0.969079 0.966776 0.965484 0.966015 0.962339 0.961539 0.961299

1 0.998073 0.989534 0.986085 0.982877 0.974047 0.971143 0.966628 0.960988 0.955929 0.955122 0.953734 0.948294 0.946342 0.945076 0.943847 0.942102 0.941564 0.997550 0.994020 0.993327 0.992701 0.986090 0.979710 0.976539 0.974208 0.974566 0.974436 0.974825 0.976476 0.972766 0.971956 0.971711

1 0.998259 0.990720 0.988016 0.985589 0.978326 0.975392 0.970881 0.965234 0.960167 0.959361 0.957974 0.952525 0.950565 0.949298 0.948068 0.946317 0.945778 0.997737 0.994206 0.993512 0.992886 0.987273 0.980889 0.977715 0.978909 0.979860 0.981833 0.983859 0.986606 0.982860 0.982040 0.981790

118

5.3.2.3 Result of power flow without DG and with different DG size at residential load Table 5.21 demonstrations the effect of increasing the size of DG unit on power flow. From Table 5.21, it is observed that there is reduced in real power generated by The Electric Company due to install the DG unit at bus 30. There is increase in reactive power generated by The Electric Company and the total load due to improve voltage of each bus. Furthermore, power losses get reduced but when reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.15 demonstrate the effect of increasing size of DG on active and reactive power losses. Table ‎5.21: The effect of increasing size of DG on power flow at residential load Pintake( MWatt)

Qintake( MVAR)

(M Watt)

Without DG

3.846

1.825

0

10%

3.446

1.867

20%

3.057

30%

Qlosses( MVAR) 107

Pl(MWa tt)

Ql(MV AR)

Plosses( KWatt)

0

3.684

1.718

161

0.371

0

3.688

1.781

129

86

1.918

0.743

0

3.691

1.844

109

73

2.678

1.977

1.114

0

3.694

1.909

98

67

40%

2.308

2.042

1.486

0

3.697

1.974

97

68

50%

1.947

2.115

1.857

0

3.699

2.040

Power Losses (P.U)

Active Power losses

105

75


0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-15: The effect of increasing the size of DG on power losses at residential load

119

5.4 Commercial Load In commercial load, the reactive and active power is depending on magnitude of bus voltage.‎The‎value‎of‎α‎=‎1.51‎and‎the‎value‎of‎β‎=‎3.4. | | | | Distributed generation has two cases ●‎Single‎DG‎capable‎of‎delivering‎active‎and‎reactive‎power ●‎Single‎DG‎capable‎of‎delivering‎active‎power‎only

5.4.1 Single DG capable of delivering active and reactive power In this part, the results will be presented as follow ●‎Results of voltage stability indices without DG and with different DG size ●‎Results of voltage profile without DG and with different DG size ●‎Results of power flow without DG and with different DG size ●‎Results of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1. 5.4.1.1 Result of voltage stability indices without DG and with different DG size at commercial load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.22. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.23. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.24. According to values of voltage stability indices without the DG in Table 5.22, 5.23 and 5.24 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 4.1. From Tables 5.22, 5.23 and 5.24 notice that the values of voltage stability indices at each line are increasing when installed the DG unit in bus 30. Also, when increases the size of DG, voltage stability of each bus more worsen. This occurs due to that the commercial load at each bus dependent on voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when installed DG in distributed systems. Figure 5.16 demonstrations the effect of increasing the size of DG on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.0169 to 0.01922, the 120

value of LQP changes from 0.00348 to 0.00396 and the value of Lmn changes from 0.01684 to 0.01913 when the DG generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to installing DG.


0.025

0.02

0.015 FVSI Lmn

0.01

LQP 0.005

0 0%

10%

20%


50%

60%

Figure ‎5-16: The effect of increasing size of DG on the weakest voltage stability bus (bus 30) at commercial load

121

Table ‎5.22: Values of fast voltage stability index (FVSI) at the different DG size at commercial Line


FVSI without DG 0.000338 0.001160 0.001728 0.000668 0.000750 0.001566 0.005486 0.000988 0.000950 0.000463 0.000998 0.002361 0.002017 0.000266 0.000701 0.001198 0.001347 0.000325 0.002970 0.000817 0.001452 0.001169 0.008780 0.008797 0.000292 0.000407 0.000961 0.002547 0.016936 0.003049 0.001411 0.000673



122




Table ‎5.23: Values of the line stability index (Lmn) at the different DG size at commercial load Line


Lmn without DG 0.000337 0.001156 0.001723 0.000666 0.000754 0.001569 0.005471 0.000991 0.000952 0.000462 0.000996 0.002370 0.002020 0.000267 0.000701 0.001199 0.001308 0.000325 0.002975 0.000817 0.001448 0.001170 0.008810 0.008760 0.000291 0.000406 0.000959 0.002542 0.016839 0.003056 0.001411 0.000674



123




Table ‎5.24: Values of line stability factor (LQP) at the different DG size at commercial load Line


LQP without DG 6.97E-05 0.000239 0.000356 0.000137 0.000320 0.001435 0.000540 0.000340 0.000334 4.44E-05 9.83E-05 0.000903 0.001279 0.000118 0.000244 0.000769 0.000513 0.000155 0.001333 0.000472 0.000925 0.000372 0.003372 0.003354 6.02E-05 8.39E-05 0.000420 0.001099 0.003489 0.001512 0.000813 0.000478



124




5.4.1.2 Result of voltage profile without DG and with different DG size at commercial load Table 5.25 and Figure 5.17 demonstrate the effect of increasing the size of DG on voltage of each bus. From Table 5.25, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.6 demonstrates the effect of increasing the size of DG on the voltage of the weakest voltage stability bus (bus 30). The voltage at bus 30 changes from 0.9327 to 1.0101 when the photovoltaic generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.0773. This change shows that the voltage at bus 30 enhanced due to install DG.


1.02 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 0%

10%

20%

30%

40%

50%

60%

DG Size

Figure ‎5-17: The effect of increasing the size of DG on voltage of the weakest voltage stability bus at commercial load

125

Figure ‎5-18: The effect of increasing size of DG on voltage of each bus at commercial load

126

Table ‎5.25: The effect of increasing size of DG on voltage of each bus at commercial load


Without DG

10% DG

20% DG

30% DG

40% DG

50% DG

1 0.9973101 0.9846815 0.9781428 0.9717087 0.9559602 0.9530341 0.9487682 0.9433711 0.9385262 0.9377684 0.9364658 0.9312590 0.9293577 0.9281541 0.9269878 0.9252934 0.9247797 0.9967888 0.9932665 0.9925739 0.9919480 0.9812837 0.9749808 0.9718495 0.9543134 0.9521326 0.9425987 0.9357671 0.9327719 0.9292551 0.9284869 0.9282533

1 0.997585 0.986432 0.980993 0.975704 0.962784 0.959825 0.955537 0.950104 0.945226 0.944464 0.943155 0.937912 0.935996 0.934784 0.933611 0.931903 0.931386 0.997064 0.993541 0.992848 0.992222 0.983028 0.976714 0.973577 0.961759 0.960448 0.954676 0.950696 0.949267 0.945682 0.944898 0.944659

1 0.997852 0.988124 0.983747 0.979566 0.969376 0.966384 0.962074 0.956607 0.951697 0.950931 0.949615 0.944338 0.942407 0.941188 0.940007 0.938286 0.937766 0.997330 0.993806 0.993113 0.992487 0.984715 0.978390 0.975247 0.968951 0.968481 0.966342 0.965116 0.965199 0.961549 0.960749 0.960504

1 0.998110 0.989763 0.986415 0.983306 0.975757 0.972734 0.968402 0.962901 0.957961 0.957191 0.955869 0.950558 0.948612 0.947386 0.946198 0.944465 0.943941 0.997588 0.994063 0.993370 0.992743 0.986348 0.980012 0.976865 0.975913 0.976257 0.977633 0.979073 0.980623 0.976908 0.976093 0.975842

1 0.998361 0.991353 0.989003 0.986935 0.981945 0.978891 0.974539 0.969005 0.964034 0.963261 0.961933 0.956589 0.954629 0.953396 0.952201 0.950456 0.949928 0.997839 0.994313 0.993619 0.992992 0.987933 0.981587 0.978434 0.982665 0.983800 0.988584 0.992610 0.995581 0.991803 0.990973 0.990717

1 0.998604 0.992898 0.991519 0.990462 0.987957 0.984873 0.980501 0.974935 0.969935 0.969158 0.967823 0.962448 0.960474 0.959234 0.958033 0.956275 0.955745 0.998082 0.994555 0.993861 0.993235 0.989473 0.983117 0.979959 0.989225 0.991128 0.999222 1.005761 1.010114 1.006274 1.005429 1.005167

127

5.4.1.3 Result of power flow without DG and with different DG size at commercial load Table 5.26 demonstrations the effect of increasing the size of DG unit on power flow. From Table 5.26, it is observed that there is reduced in real & reactive power generated by The Electric Company due to install the DG unit at bus 30. There is increase in total load due to improve voltage of each bus. Furthermore, power losses get reduced but when reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.18 demonstrate the effect of increasing size of wind turbine on power losses. Table ‎5.26: The effect of increasing size of DG on power flow at commercial load Pintake( MWatt)

Qintake( MVAR)

(M Watt)

(M VAR)

Pl(M Watt)

Ql(M VAR)

Plosses( KWatt)

Qlosses( KVAR)

Without DG

3.630

2.051

0

0

3.47

1.94

154

102

10%

3.252

1.852

0.371

0.23

3.51

2.00

113

75

20%

2.885

1.662

0.743

0.46

3.54

2.06

84

57

30%

2.529

1.480

1.114

0.69

3.57

2.12

66

46

40%

2.183

1.306

1.486

0.92

3.60

2.18

59

43

50%

1.845

1.138

1.857

1.15

3.64

2.24

62

46

Power Losses (P.U)

Active Power losses


0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

DG Size

Figure ‎5-19: The effect of increasing the size of on power losses at commercial load

128

5.4.2 Single DG capable of delivering active power only In this part, the results will be presented as follow ●‎Results of voltage stability indices without DG and with different DG size ●‎Results of voltage profile without DG and with different DG size ●‎Results of power flow without DG and with different DG size ●‎Results of P-V curve without DG and with different DG size. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 3.2.1. 5.4.2.1 Result of voltage stability indices without DG and with different DG size at commercial load Voltage stability indices described in section 3.2 are applied on the system under study. This study is executed to distinguish the most sensitive line to voltage instability. The most sensitive line related to maximum values of voltage stability indices. Values of fast voltage stability index (FVSI) at the diverse DG size are shown in Table 5.27. The values of the line stability index (Lmn) at the diverse DG size are shown in Table 5.28. Values of line stability factor (LQP) at the diverse DG size are shown in Table 5.29. According to values of voltage stability indices without the DG in Table 5.27, 5.28 and 5.29 it is found that the line which starts from bus 29 to bus 30 is the weakest line. So, the DG unit is installed at bus 30. The DG size is varied from 0 to 50% from load to demonstrate the effect of the DG size on Voltage Stability Indices. Rating of the installed DG is defined in Table 5.1. From Tables 5.27, 5.28 and 5.29 notice that the values of voltage stability indices at each line are increasing when installed the DG unit in bus 30. Also, when increases the size of DG, voltage stability of each bus more worsen. This occurs due to that the commercial load at each bus dependent on voltage of bus. Load at each bus increased when voltage bus is improved. So, voltage stability is worse when installed DG in distributed systems. Figure 5.19 demonstrations the effect of increasing the size of DG on the weakest voltage instability bus (bus 30). The value of FVSI at bus 30 changes from 0.0169 to 0.0185, the value of LQP changes from 0.00348 to 0.00382 and the value of Lmn changes from 0.0168 to 0.0182 when the DG generates 50 % from the load. These changes show that the weakest voltage stability bus (bus 30) worse due to installing DG.

129

Table ‎5.27: Values of fast voltage stability index (FVSI) at the different DG size at commercial load Line

FVSI without DG


0.000338 0.001160 0.001728 0.000668 0.000750 0.001566 0.005486 0.000988 0.000950 0.000463 0.000998 0.002361 0.002017 0.000266 0.000701 0.001198 0.001347 0.000325 0.002970 0.000817 0.001452 0.001169 0.008780 0.008797 0.000292 0.000407 0.000961 0.002547 0.016936 0.003049 0.001411 0.000673

FVSI with DG10% of load 0.000338 0.001165 0.001737 0.000673 0.000759 0.001577 0.005525 0.000995 0.000957 0.000466 0.001005 0.002378 0.002032 0.000268 0.000706 0.001206 0.001356 0.000326 0.002970 0.000818 0.001452 0.001171 0.008797 0.008813 0.000294 0.000411 0.000978 0.002597 0.017274 0.003101 0.001435 0.000685


130




Table ‎5.28: Values of the line stability index (Lmn) at the different DG size at commercial load Line


Lmn without DG 0.000337 0.001156 0.001723 0.000666 0.000754 0.001569 0.005471 0.000991 0.000952 0.000462 0.000996 0.002370 0.002020 0.000267 0.000701 0.001199 0.001347 0.000325 0.002975 0.000817 0.001452 0.001168 0.008810 0.008808 0.000291 0.000406 0.000959 0.002542 0.016839 0.003056 0.001411 0.000673



131




Table ‎5.29: Values of line stability factor (LQP) at the different DG size at commercial load Line


LQP without DG 6.97E-05 0.000239 0.000356 0.000137 0.000320 0.001435 0.000540 0.000340 0.000334 4.44E-05 9.83E-05 0.00090 0.001279 0.000118 0.000244 0.000769 0.000513 0.000155 0.001333 0.000472 0.000925 0.000372 0.003372 0.003354 6.02E-05 8.39E-05 0.000420 0.001099 0.003489 0.001512 0.000813 0.000478



132





0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0

FVSI Lmn LQP

0%

10%

20%

30%

40%

50%

60%

DG Size from Load

Figure ‎5-20: The effect of increasing size of DG on the weakest voltage stability bus at commercial load 5.4.2.2 Result of voltage profile without DG and with different DG size at commercial load Table 5.30 and Figure 5.20 demonstrate the effect of increasing the size of DG on voltage of each bus. From Table 5.30, the voltage of each bus enhanced when the DG installed at the bus 30. Furthermore, the voltage at each bus more enhanced when increases the size of DG unit. Figure 5.21 demonstrates the effect of increasing the size of DG on the voltage profile of each bus. The voltage at bus 30 changes from 0.9328 to 0.9868 when the DG generates 50% from the load. So, the voltage at bus 30 is enhanced by 0.05414. This change shows that the voltage at bus 30 enhanced due to install DG. Voltage Magnitude at Bus 30

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0%

10%

20%

30%

40%

50%

60%

DG Size

Figure ‎5-21: The effect of increasing the size of DG on voltage of the weakest bus voltage stability (bus 30) 133

Figure ‎5-22: The effect of increasing size of DG on voltage of each bus at commercial load

134

Table ‎5.30: The effect of increasing size of DG on voltage of each bus at commercial load


Without DG 1 0.997310 0.984681 0.978142 0.971708 0.955960 0.953034 0.948768 0.943371 0.938526 0.937768 0.936465 0.931259 0.929357 0.928154 0.926987 0.925293 0.924779 0.996788 0.993266 0.992573 0.991948 0.981283 0.974980 0.971849 0.954313 0.952132 0.942598 0.935767 0.932771 0.929255 0.928486 0.928253

DG 10% of load 1 0.997519 0.986008 0.980304 0.974740 0.960819 0.957869 0.953587 0.948165 0.943297 0.942536 0.941229 0.935996 0.934084 0.932875 0.931703 0.930000 0.929483 0.996997 0.993474 0.992781 0.992155 0.982606 0.976295 0.973159 0.959644 0.958126 0.951013 0.946031 0.944236 0.940672 0.939893 0.939656

DG 20% of load 1 0.997720 0.987290 0.982393 0.977672 0.965511 0.962539 0.958241 0.952794 0.947903 0.947140 0.945828 0.940571 0.938648 0.937433 0.93625 0.934544 0.934025 0.997199 0.993675 0.992982 0.992356 0.983884 0.977564 0.974425 0.964795 0.963918 0.959153 0.955971 0.955347 0.951738 0.950948 0.950706

135

DG 30% of load 1 0.997915 0.988531 0.984414 0.980509 0.970048 0.967053 0.962741 0.957270 0.952357 0.951591 0.950274 0.944994 0.943060 0.941841 0.940659 0.93893 0.938416 0.99739 0.993869 0.993176 0.992550 0.985120 0.978792 0.975649 0.969777 0.969525 0.967038 0.965610 0.966132 0.962478 0.961677 0.961432

DG 40% of load 1 0.998104 0.989732 0.986373 0.983259 0.974440 0.971423 0.967097 0.961602 0.956668 0.955899 0.954578 0.949275 0.947331 0.946107 0.944921 0.943190 0.942666 0.997582 0.994057 0.993364 0.992737 0.986317 0.979982 0.976834 0.974601 0.974958 0.974685 0.974970 0.976612 0.972914 0.972103 0.971854

DG 50% of load 1 0.998287 0.990896 0.988271 0.985927 0.978696 0.975658 0.971317 0.965800 0.960846 0.960074 0.958749 0.953423 0.951470 0.950240 0.949050 0.947310 0.946785 0.997765 0.994239 0.993546 0.992919 0.987477 0.981134 0.977983 0.979279 0.980228 0.982110 0.984069 0.986809 0.983068 0.982247 0.981994

5.4.2.3 Result of power flow without DG and with different DG size at commercial load Table 5.31 demonstrations the effect of increasing the size of DG unit on power flow. From Table 5.31, it is observed that there is reduced in real power generated by The Electric Company due to install the DG unit at bus 30. There is increase in reactive power generated by The Electric Company and the total load due to improve voltage of each bus. Furthermore, power losses get reduced but when reach certain DG size active and reactive power losses increased. So, optimization technique used to limit the best size and location. Figure 5.22 demonstrate the effect of increasing size of DG on active and reactive power losses. Table ‎5.31: The effect of increasing size of DG on power flow at commercial load Pintake( MWatt)

Qintake( MVAR)

(M Watt)

Without DG

3.630

2.051

0

10%

3.255

2.074

20%

2.889

30%

Qlosses( KVAR) 102

Pl(MWa tt)

Ql(MV AR)

Plosses( KWatt)

0

3.475

1.948

154

0.371

0

3.500

1.989

126

84

2.103

0.743

0

3.524

2.029

108

73

2.532

2.138

1.114

0

3.547

2.070

100

40%

2.183

2.18

1.486

0

3.57

2.110

99

69

50%

1.842

2.226

1.857

0

3.592

2.149

107

76

Active Power losses

68


0.0018 0.0016 0.0014 0.0012 0.001 0.0008 0.0006 0.0004 0.0002 0 0%

10%

20%

30%

40%

50%

Figure ‎5-23: The effect of increasing the size of photovoltaic on power losses at commercial load 136

5.5 Result comparison The result of different load can be collected in Table 5-30 and Table 5-31.this result in two tables is at the same size DG (30% penetration level) discussed as following: Constant Load: When the installed DG, active and reactive power which take from electric company decrease. Also, active and reactive power losses decrease. Residential, Industrial, and Commercial Load: when the installed DG gives active and reactive power, the active and reactive power that takes from electric company is decrease. Also, active and reactive power losses decrease. Active and reactive load increase due to improve voltage profile of system. When the installed DG gives active power only, active power that takes from electric company is decrease but reactive power that takes from electric company is increase. Active and reactive power losses decrease. Active and reactive load increase due to improve voltage profile of system. Table ‎5.32: Result of different load with DG give active and reactive power Pintake Constant

Residential

Industrial

Commercial

Qintake 0.024351

0.03715

0.037239

0.016654 0.007697 0.01991

0.03715 0 0.035646

With DG

0.025831

0.014478

Difference Without DG With DG Difference Without DG With DG Difference

0.011408

0.005432

0.038465

0.018254

0.026529 0.011936

Without DG With DG Difference Without DG

Ql 0.023

Plosses 0.002025

0.001351

0.023 0

0.0008 0.001225

0.000554 0.000797

0.018852

0.001592

0.001059

0.036291

0.020902

0.00068

0.000476

-0.000645 0.036849

-0.00205 0.01718

0.000912 0.001616

0.000583

0.013552 0.004702

0.036979 -0.00013

0.019969 -0.002789

0.000695 0.000921

0.000483 0.000592

0.036303

0.020511

0.034755

0.019483

0.001548

0.001029

0.025296 0.011007

0.014806 0.005705

0.035771 -0.001016

0.021241 -0.001758

0.000669 0.000879

0.000465 0.000564

0.039175 0.026805 0.01237

137

Pl

Qlosses

0.001075

Table ‎5.33: Result of different load with DG give active power only Pintake

Constant

Residential

Industrial

Commercial

Qintake 0.024351

Without DG

0.039175

With DG

0.027239

0.023844

Difference Without DG

0.011936

0.000507

0.037239

0.01991

With DG

0.025965

0.02096

Difference Without DG

0.011274

-0.00105 0.018254

With DG Difference Without DG With DG Difference

Pl

Ql

Plosses

Qlosses

0.03715

0.023

0.002025

0.001351

0.03715

0.023

0.001234

0.000844

0 0.03564 6

0

0.000791

0.000507

0.018852

0.001592

0.001059

0.36104

0.02027

0.001006

0.00069

-0.00141

0.000586

0.000369

0.01718

0.001616

0.001075

0.019094

0.000984

0.000676

0.026781

0.01977

-0.32539 0.03684 9 0.03694

0.011684

-0.001516

-9.3E-05

-0.00191

0.000632

0.000399

0.036303

0.020511

0.03475

0.019483

0.001548

0.001029

0.025329 0.010974

0.021388 -0.000877

0.03547 -0.00071

0.020702 -0.00121

0.001001 0.000547

0.000686 0.000343

0.038465

Where: Pintake: is total active power generated by the electric company Qintake: is total reactive power generated by the electric company Pl: total active load of system Ql: total reactive load of system Plosses: total active power losses of system Qlosses: total reactive power losses of system

138

Chapter 6 Optimal Sizing and Sitting of DG 6.1 Introduction From Load modeling explained in section 3.3, load is divided into constant load, residential load, industrial load and commercial load. In this chapter simulate each type and study the optimal location and size of DG to achieve minimum losses and enhanced voltage stability. In this work a single DG capable of delivering active power only is considered. The Genetic Algorithm (GA) is used to solve the allocation problems under the constrained objective function. All simulations in this part execute on IEEE 33 bus radial distribution system that explained in section 4.4.

6.2 Constant Load In constant load, the reactive and active‎power‎aren‟t depending on magnitude of bus voltage. In this part, the results will be presented as follow: ●‎ Load flow and voltage stability analysis ●‎Optimal location and size of DG unit to achieve losses minimization ●‎Optimal location and size of DG unit to achieve losses minimization and enhanced voltage stability

6.2.1 Load flow and voltage stability analysis Table 6.1 and Table 6.2 show the load flow solution and the value of the FVSI of each line in the network. Figure 6.2 shows the voltage profile of each bus, found from running the load flow program. The result of load flow which obtained from load flow program is same result in [55], [56]. This is show that load flow program which used in this thesis is correct. From this analysis we can note that: 1. The bus having the minimum value of voltage magnitude is bus 18. 2. The line having maximum value of FVSI is line from bus 29 to bus 30. So, this line is the most sensitive to voltage instability. 3. Total active power losses equal 202.5311 KW and total reactive power power losses equal 135.1284 KVAR.

139

Table ‎6.1: Show load flow solution without DG Bus No.

Voltage Mag.(P.U)

Voltage Angle (deg.)

Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.913253516

-0.4993

2

0.997032347

0.0145

19

0.996503983

0.0037

3

0.982938535

0.0961

20

0.992926387

-0.0633

4

0.975457308

0.1617

21

0.992221884

-0.0827

5

0.968060486

0.2283

22

0.991584465

-0.1030

6

0.949660219

0.1339

23

0.979352811

0.0651

7

0.946174846

-0.0964

24

0.972681659

-0.0236

8

0.941331315

-0.0603

25

0.969356672

-0.0673

9

0.935063191

-0.1333

26

0.947730956

0.1734

10

0.929415882

-0.2007

27

0.945167216

0.2295

11

0.928544734

-0.1931

28

0.933727659

0.3125

12

0.927045419

-0.1816

29

0.925509575

0.3904

13

0.920933414

-0.2729

30

0.921952163

0.4956

14

0.918667063

-0.3516

31

0.917791001

0.4112

15

0.917255002

-0.3892

32

0.916875582

0.3882

16

0.915887326

-0.4125

33

0.916591939

0.3805

17

0.913860474

-0.4897

140

Table ‎6.2: Show value of fast voltage stability index without DG Line

Line Number

FVSI

Line

Line Number

FVSI

1 to 2

1

0.000341216

2 to 19

18

0.000329749

2 to 3

2

0.001224196

19 to 20

19

0.003040758

3 to 4

3

0.001870258

20 to 21

20

0.00083933

4 to 5

4

0.000741505

21 to 22

21

0.001494074

5 to 6

5

0.000881882

3 to 23

22

0.001251037

6 to 7

6

0.001869122

23 to 24

23

0.009608412

7 to 8

7

0.006656411

24 to 25

24

0.009739918

8 to 9

8

0.00122441

6 to 26

25

0.000347254

9 to 10

9

0.001200083

26 to 27

26

0.000488256

10 to 11

10

0.000587592

27 to 28

27

0.001192794

11 to 12

11

0.001272535

28 to 29

28

0.003253578

12 to 13

12

0.00307032

29 to 30

29

0.021936812

13 to 14

13

0.002646866

30 to 31

30

0.004005633

14 to 15

14

0.000351913

31 to 32

31

0.001861539

15 to 16

15

0.000929604

32 to 33

32

0.000890046

16 to 17

16

0.001598511

17 to 18

17

0.00180197

141

Figure ‎6-1: Voltage profile of IEEE 33 bus system

Fast Voltage Stability Index 0.025

Value of FVSI

0.02 0.015 0.01

0.005 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Line Number Figure ‎6-2: Fast voltage stability index of IEEE 33 bus System

142

6.2.2 Optimal location and size of DG unit to achieve losses minimization Genetic algorithm used to obtain the optimal location and size of DG. Table 6.3 show the optimum DG size at each bus of IEEE 33 bus system to achieve minimum active and reactive power losses. Also, Figure 6.2 shows the optimum DG size at each bus of IEEE bus system. Figure 6.3 shows the total active and reactive power losses of IEEE 33 bus system when installed optimum DG at each bus. Table ‎6.3: optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses Bus No. 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000 15.0000 16.0000 17.0000 18.0000 19.0000 20.0000 21.0000 22.0000 23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 29.0000 30.0000 31.0000 32.0000 33.0000

Size 3.9999 3.6298 3.1594 2.8914 2.5750 2.4410 2.0849 1.7304 1.5086 1.4730 1.4104 1.2097 1.1491 1.0859 1.0145 0.9037 0.8513 1.7180 0.4809 0.4238 0.3413 2.4632 1.7066 1.2994 2.4368 2.2712 1.6411 1.6414 1.5360 1.3473 1.2923 1.2257

MW-Losses 192.6818 152.5917 140.1600 128.2913 103.8423 104.8560 109.5014 116.1183 120.0345 120.7458 122.1921 127.3698 129.1723 131.8153 135.2112 141.0758 144.1962 197.7831 199.9616 200.0667 200.4061 161.7340 165.6117 171.1120 105.6897 108.0338 115.6683 115.6683 117.5093 123.4804 125.8178 129.5218 143

KVAR-Losses 129.9370 108.7338 102.0565 95.6821 74.7821 77.2629 76.1979 79.4658 81.4363 81.5341 81.8607 85.4528 87.4537 89.3538 91.3275 97.6372 99.3303 133.4123 133.6353 133.6554 133.9046 114.3772 115.7296 118.4729 75.5479 76.6234 81.5620 81.5632 82.0026 86.6507 88.8000 93.3879

Optimum size of DG at each bus 4.5 4

Optimum Size of DG

3.5 3 2.5 2 1.5 1 0.5 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Figure ‎6-3: Optimum size of DG at each bus of IEEE 33 bus system

Total active power losses (KW)

Total reactive power losses (KVAR)

250 200 150 100 50 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number

Figure ‎6-4: Total active and reactive power losses corresponding to optimum size at each bus of IEEE 33 bus system 144

Table 6.4 summarizes the optimal DG size and location to achieve minimum losses by genetic algorithm. The optimal location to achieve minimum losses is found at bus 6. The optimal size of DG is 2.575 MWatt. Total active power losses and reactive power losses are 103.84 KWatt and 74.78 KVAR. The value of maximum fast voltage stability index is 0.0203 at bus 30. Table 6.5 and Table 6.6 show load flow study and value of fast voltage stability index of IEEE 33 bus system when installed optimal size DG (2.575 MWatt) at optimal location (Bus 6). Table ‎6.4: Optimal DG size and location by genetic algorithm Optimization bus 6

Plosses (KWatt) 103.8423

Qlosses (KVAR) 74.7821

FVSI(30)

Pdg(MWatt)

0.0203

2.5750

Table ‎6.5: Show load flow solution with DG to achieve minimum losses only Bus No.

Voltage Mag.(P.U)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1

0.9986 0.9928 0.9915 0.9906 0.9862 0.9828 0.9782 0.9721 0.9667 0.9659 0.9644 0.9586 0.9564 0.9550 0.9537 0.9518

Voltage Angle (deg.) 0 0.0575 0.3694 0.6063 0.8509 1.4283 1.2151 1.2484 1.1808 1.1185 1.1255 1.1361 1.0518 0.9792 0.9444 0.9230 0.8518

145

Bus No.

Voltage Mag.(P.U)


18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0.9512 0.9981 0.9945 0.9938 0.9931 0.9893 0.9827 0.9794 0.9843 0.9819 0.9709 0.9630 0.9596 0.9556 0.9547 0.9544

0.8429 0.0467 -0.0201 -0.0394 -0.0597 0.3391 0.2521 0.2093 1.4649 1.5169 1.5937 1.6657 1.7629 1.6850 1.6638 1.6566

Table ‎6.6: show value of fast voltage stability index to achieve minimum losses Line 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11 11 to 12 12 to 13 13 to 14 14 to 15 15 to 16 16 to 17 17 to 18

Line Number

FVSI

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.0003 0.0012 0.0018 0.0007 0.0008 0.0017 0.0062 0.0011 0.0011 0.0005 0.0012 0.0028 0.0024 0.0003

15 16 17

0.0009 0.0015 0.0017

Line 2 to 19 19 to 20 20 to 21 21 to 22 3 to 23 23 to 24 24 to 25 6 to 26 26 to 27 27 to 28 28 to 29 29 to 30 30 to 31 31 to 32 32 to 33

Line Number 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

FVSI 0.0003 0.0030 0.0008 0.0015 0.0012 0.0094 0.0095 0.0003 0.0005 0.0011 0.0030 0.0203 0.0037 0.0017 0.0008

Voltage Magnitude (per unit)

Votage of Each Bus 1.01 1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233 Bus Number

Figure ‎6-5: Voltage profile at each bus after install DG to achieve minimum losses

146

Fast Voltge Stability Index 0.025

Value of FVSI

0.02 0.015 0.01 0.005 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Line Number

Figure ‎6-6: FVSI of each line in IEEE 33 bus system after install optimal DG size and location

6.2.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability Table 6.2 shows that line which start from bus 29 to bus 30 is the worst voltage stability line because it has the large FVSI value. So, the best location of DG to enhanced voltage stability is bus 30. Genetic algorithm used to obtain optimal size of DG to achieve minimum active and reactive power losses at bus 30. Table 6.7 summarizes the optimal DG size and location to achieve minimum losses and enhanced voltage stability by genetic algorithm. The optimal location to achieve minimum losses is found at bus 30. The optimal size of DG is 1.5357 Mwatt. Total active and reactive power losses are 117.51 kwatt and 82 KVAR. The value of maximum fast voltage stability index is 0.0199 after install optimal size DG. Table 6.8 and Table 6.9 show load flow study and value of fast voltage stability index of IEEE 33 bus system when installed optimal size DG (1.5357 MWatt) at bus 30 to enhanced voltage stability. Figure 6.7 and Figure 6.8 clarifies the positive impact of DG integration on the voltage profile‎improvement‎and‎voltage‎stability‎enhancement‎for‎all‎system„s‎buses.‎Comparing‎ the results obtained after integrating DG and obtained without the DG (network base case) shows a significant decrease in the network losses, improve in voltage stability index and voltage magnitude. When install DG at bus 6, maximum FVSI change from 0.0219 to 0.0203. When install DG at bus 30, maximum FVSI change from 0.0219 to 0.0199.So, IEEE 33 bus system more enhanced voltage stability when install DG at bus 30. 147

Table ‎6.7: Optimal DG size and location by genetic algorithm Optimization bus 30


Qlosses (KVAR) 82

FVSI(30)

Pdg(MWatt)

0.0199

1.5357

Table ‎6.8: Show load flow solution with DG to achieve minimum losses and enhanced voltage stability

Bus No.

Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9364

0.3134

2

0.9980

0.04

19

0.9975

0.0292

3

0.9890

0.2589

20

0.9939

-0.0377

4

0.9852

0.4272

21

0.9932

-0.057

5

0.9818

0.6010

22

0.9925

-0.0773

6

0.9719

0.9169

23

0.9854

-0.0773

7

0.9685

0.6972

24

0.9788

0.1407

8

0.9637

0.7316

25

0.9755

0.0975

9

0.9576

0.5977

26

0.9720

1.0145

10

0.9521

0.5977

27

0.9723

1.1517

11

0.9513

0.6049

28

0.9717

1.7715

12

0.9498

0.6158

29

0.9718

2.25

13

0.9438

0.5289

30

0.9734

2.495

14

0.9416

0.4540

31

0.9694

2.4193

15

0.9403

0.4182

32

0.9686

2.3987

16

0.9389

0.3960

33

0.9683

2.3917

17

0.9369

0.3226

148

Table ‎6.9: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability Line Number

FVSI

Line

Line Number

FVSI

1 to 2 2 to 3 3 to 4

1

0.0003

2 3

0.0012 0.0018

2 to 19 19 to 20 20 to 21

18 19

0.0003 0.0030

20 21

0.0008 0.0015

4 to 5 5 to 6

4 5

0.0007 0.0009

21 to 22 3 to 23

22

0.0012

6 to 7 7 to 8 8 to 9

6 7 8

0.0018 0.0064 0.0012

23 to 24 24 to 25

23

0.0095

24

0.0096

6 to 26

25 26

0.0003 0.0005

9 to 10 10 to 11

9 10

0.0011 0.0006

26 to 27 27 to 28 28 to 29

27 28

0.0011 0.0030

11 to 12

11

0.0012

12 to 13

12

0.0029

29 to 30

29

0.0199

13 to 14

13

0.0025

30 to 31

0.0003 0.0009 0.0015

31 to 32

0.0036 0.0017

32 to 33

32

0.0008

16 to 17

14 15 16

30 31

14 to 15

17 to 18

17

0.0017

Line

15 to 16

149

Voltage profile when DG at bus 30


Voltage profile without DG

1.02 1

Voltage Magnitude

0.98 0.96 0.94 0.92 0.9 0.88 0.86 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number

Figure ‎6-7: Voltage profile without DG and after install DG at bus 6 and bus 30

FVSI when DG at bus 30


FVSI without DG

0.025

Value of FVSI

0.02

0.015

0.01

0.005

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Bus Number

Figure ‎6-8: FVSI without DG and after install DG at bus 6 and bus 30

150

6.3 Industrial Load In industrial load, the reactive and active power is depending on magnitude of bus voltage.‎The‎value‎of‎α‎=‎0.18‎and‎the‎value‎of‎β‎=‎6. | | | | In this part, the results will be presented as follow ●‎ Load flow and voltage stability analysis ●‎Optimal location and size of DG unit to achieve losses minimization ●‎Optimal location and size of DG unit to achieve losses minimization and enhanced voltage stability

6.3.1 Load flow and voltage stability analysis Table 6.10 and Table 6.11 show the load flow solution and the value of the FVSI of each line in the network. From this analysis we can note that: 1. The bus having the minimum value of voltage magnitude is bus 18. 2. The line having maximum value of FVSI is line from bus 29 to bus 30. So, this line is the most sensitive to voltage instability. 3. Total power losses equal 161.5869 KW and total active power losses equal 107.4842 KVAR.

151


Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9229

-1.1311

2

0.9973

-0.0045

19

0.9967

-0.0156

3

0.9843

-0.0248

20

0.9932

-0.0853

4

0.9776

-0.0273

21

0.9925

-0.1051

5

0.9710

-0.0312

22

0.9919

-0.1259

6

0.9552

-0.2726

23

0.9809

-0.0662

7

0.9524

-0.5084

24

0.9745

-0.1739

8

0.9479

-0.5106

25

0.9714

-0.2277

9

0.9423

-0.6250

26

0.9535

-0.2591

10

0.9372

-0.7309

27

0.9513

-0.2389

11

0.9364

-0.7311

28

0.9420

-0.2844

12

0.9350

-0.7328

29

0.9354

-0.3045

13

0.9296

-0.8651

30

0.9324

-0.2592

14

0.9277

-0.9548

31

0.9288

-0.3699

15

0.9264

-0.9993

32

0.9280

-0.3984

16

0.9252

-1.0308

33

0.9278

-0.4078

17

0.9235

-1.1173

152


Line Number

Line

Line Number

1 to 2

1

0.000335628

2 to 19

18

0.00032319

2 to 3

2

0.00111294

19 to 20

19

0.002917495

3 to 4

3

0.001627951

20 to 21

20

0.000801861

4 to 5

4

0.000618671

21 to 22

21

0.001421955

5 to 6

5

0.000665773

3 to 23

22

0.001111098

6 to 7

6

0.001378884

23 to 24

23

0.008204436

7 to 8

7

0.004764588

24 to 25

24

0.008150747

8 to 9

8

0.000845137

6 to 26

25

0.000257981

9 to 10

9

0.000800977

26 to 27

26

0.000357527

10 to 11

10

0.000389598

27 to 28

27

0.000822823

11 to 12

11

0.000836106

28 to 29

28

0.00214099

12 to 13

12

0.001947851

29 to 30

29

0.014109823

13 to 14

13

0.001655781

30 to 31

30

0.002514338

14 to 15

14

0.000218181

31 to 32

31

0.001161103

15 to 16

15

0.000571573

32 to 33

32

0.000554155

16 to 17

16

0.00097161

17 to 18

17

0.001090705

FVSI

153

FVSI

Voltage Of Each Bus 1.02


1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Figure ‎6-9: Voltage profile of IEEE 33 bus system

Fast Voltage Stability Index 0.016 0.014

Value of FVSI

0.012 0.01

0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


154

6.3.2 Optimal location and size of DG unit to achieve losses minimization Genetic algorithm used to obtain the optimal location and size of DG. Table 6.12 show the optimum DG size at each bus of IEEE 33 bus system to achieve minimum active and reactive power losses. Also, Figure 5.11 shows the optimum DG size at each bus of IEEE bus system. Figure 6.12 shows the total active and reactive power losses of IEEE 33 bus system when installed optimum DG at each bus. Table ‎6.12: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses Bus No. 2.0000 3.0000 4.0000 5.0000 6.0000 7.0000 8.0000 9.0000 10.0000 11.0000 12.0000 13.0000 14.0000 15.0000 16.0000 17.0000 18.0000 19.0000 20.0000 21.0000 22.0000 23.0000 24.0000 25.0000 26.0000 27.0000 28.0000 29.0000 30.0000 31.0000 32.0000 33.0000

Size 3.7772 3.3096 2.8615 2.6087 2.3147 2.2024 1.8874 1.5728 1.3747 1.3428 1.2860 1.1061 1.0517 0.9954 0.9305 0.8312 0.7828 1.5911 0.4604 0.4073 0.3288 2.2699 1.5922 1.2172 2.1846 2.0289 1.6310 1.4392 1.3403 1.1823 1.1359 1.0795

MW-Losses 153.3323 120.2532 110.6955 101.512 82.4172 82.9269 86.1755 91.1126 94.0317 94.5821 95.7110 99.7339 101.1278 103.2253 105.9769 110.7128 113.2853 157.5205 159.2323 159.3157 159.6203 127.1159 129.6391 134.1900 84.2566 86.5963 92.2628 94.7779 96.6801 100.8502 102.5521 105.3060 155

KVAR-Losses 103.3086 86.6396 81.8776 77.3145 59.8924 60.2922 59.6668 62.0076 63.3975 63.5148 63.8353 66.5594 68.0166 69.5164 71.1188 76.2339 77.6320 106.0550 106.0986 106.1058 106.3297 90.5141 90.8748 93.0339 60.7812 62.0003 65.4855 66.4527 67.1980 70.2562 71.7881 75.2565

Figure ‎6-11: Optimum size of DG at each bus of IEEE 33 bus system



180 160 140 120 100 80 60 40 20 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number





FVSI(30) 0.0202

Pdg(MWatt) 2.3147

Table ‎6.14: Show load flow solution with DG to achieve minimum losses Bus No.

Voltage Mag.(P.U)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1

0.9986 0.9927 0.9912 0.99 0.9827 0.9827 0.9782 0.9675 0.9675 0.9667 0.9653 0.9579 0.9579 0.9566 0.9554 0.9536

Voltage Angle (deg.) 0 0.0419 0.2708 0.4518 0.6388 1.0673 0.8495 0.8622 0.7701 0.6849 0.6874 0.6903 0.5805 0.5006 0.4613 0.4345 0.3568

157

Bus No.

Voltage Mag.(P.U)


18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0.9530 0.9980 0.9945 0.9938 0.9932 0.9892 0.9828 0.9796 0.9840 0.9817 0.9720 0.9650 0.9619 0.9582 0.9574 0.9572

0.3453 0.0308 -0.0382 -0.0579 -0.0786 0.2332 0.1328 0.0827 1.0894 1.1214 1.1251 1.1413 1.2048 1.1103 1.0856 1.0774


FVSI 0.00033829 0.001167711 0.001738887 0.000676257 0.000773455 0.001562699 0.00540692 0.000959493 0.000909732 0.000442485 0.000949875 0.002214242 0.001881893 0.000248023 0.00064985 0.001104692


FVSI 0.000324896 0.002932916 0.000806098 0.001429466 0.00114938 0.008487934 0.008432593 0.0002926 0.000405523 0.000932216 0.002424361 0.015981441 0.002848536 0.00131535 0.000627751

0.001240157

Votage of Each Bus 1.01

Voltage Magnitude (per unit)

1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233 Bus Number


158

Fast Voltge Stability Index 0.018 0.016 Value of FVSI

0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Line Number


6.3.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability Table 6.11 shows that line which start from bus 29 to bus 30 is the worst voltage stability line because it has the large FVSI value. So, the best location of DG to enhanced voltage stability is bus 30. Genetic algorithm used to obtain optimal size of DG to achieve minimum active and reactive power losses at bus 30. Table 6.16 summarizes the optimal DG size and location to achieve minimum losses and enhanced voltage stability by genetic algorithm. The optimal location to achieve minimum losses and enhanced voltage stability is found at bus 30. The optimal size of DG is 1.3403 Mwatt. Total active and reactive power losses are 96.6801 kwatt and 67.198 KVAR. The value of maximum fast voltage stability index is 0.0199 after install optimal size DG. Table 6.17 and Table 6.18 show load flow study and value of fast voltage stability index of IEEE 33 bus system when installed optimal size DG (1.3403 MWatt) at bus 30 to enhanced voltage stability. Figure 6.15 and Figure 6.16 clarifies the positive impact of DG integration on the voltage profile improvement and voltage stability enhancement‎for‎all‎system„s‎buses.‎Comparing‎ the results obtained after integrating DG and obtained without the DG (network base case) shows a significant decrease in the network losses, improve in voltage stability index and voltage magnitude. When install DG at bus 6, maximum FVSI change from 0.0215 to 0.0202. When install DG at bus 30, maximum FVSI change from 0.0215 to 0.0199.So, IEEE 33 bus system more enhanced voltage stability when install DG at bus 30. 159

Table ‎6.16: Optimal DG size and location by genetic algorithm Optimization bus 30



FVSI(30)

Pdg(MWatt)

0.0199

1.3403


Bus No.

Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9399

-0.1956

2

0.9980

0.0253

19

0.9975

0.0142

3

0.9891

0.1657

20

0.9939

-0.0551

4

0.9853

0.2825

21

0.9933

-0.0748

5

0.9818

0.4032

22

0.9926

-0.0956

6

0.9723

0.5861

23

0.9856

0.1265

7

0.9694

0.3605

24

0.9792

0.0229

8

0.9649

0.3666

25

0.9761

-0.0288

9

0.9593

0.2647

26

0.9723

0.6643

10

0.9542

0.1704

27

0.9724

0.7748

11

0.9534

0.1717

28

0.9715

1.2696

12

0.9520

0.1726

29

0.9712

1.6549

13

0.9466

0.0530

30

0.9724

1.8565

14

0.9446

-0.0312

31

0.9687

1.7678

15

0.9434

-0.0728

32

0.9679

1.7444

16

0.9421

-0.1016

33

0.9677

1.7366

17

0.9404

-0.1831

160


FVSI

Line

1 to 2 2 to 3 3 to 4

1

0.000337138

2 3

0.001143773 0.001690223

2 to 19 19 to 20 20 to 21

4 to 5 5 to 6

4 5

0.000650865 0.000724522

21 to 22 3 to 23

6 to 7 7 to 8

0.001479985

8 to 9

6 7 8

9 to 10 10 to 11

9 10

0.000860803 0.000418689

26 to 27 27 to 28

11 to 12

11

28 to 29

12 to 13

12

0.000898686 0.002094412

27 28

29 to 30

29

13 to 14

13

0.001780191

30 to 31

14 to 15

0.0002346 0.000614642

31 to 32 32 to 33

32

16 to 17

14 15 16

30 31

17 to 18

17

Line

15 to 16

0.005117821 0.000908036

Line Number 18 19 20 21

FVSI 0.000324158 0.002926246 0.000804265

22

0.001426217 0.001132715

23 to 24 24 to 25

23

0.008364534

24

6 to 26

25 26

0.008309914 0.000279905

0.001044841 0.001172942

161

0.00039226 0.000947153 0.002522314 0.016843312 0.002975563 0.001373981 0.000655725




1.02

Voltage Magnitude (Per Unit)

1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number



Voltage profile when DG at Bus 6


Voltage Magnitude (Per Unit)

1.02 1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number


162

6.4 Residential Load In residential load, the reactive and active power is depending on magnitude of bus voltage.‎The‎value‎of‎α‎=‎0.92‎and‎the‎value‎of‎β‎=‎4.04. | | | | In this part, the results will be presented as follow ●‎Load flow and voltage stability analysis ●‎Optimal location and size of DG unit to achieve losses minimization ●‎Optimal location and size of DG unit to achieve losses minimization and enhanced voltage stability

6.4.1 Load flow and voltage stability analysis Table 6.19 and Table 6.20 show the load flow solution and the value of the FVSI of each line in the network. Figure 6.17 shows the voltage profile of each bus, found from running the load flow program. Figure 6.18 shows the fast voltage stability of each line. From this analysis we can note that: 1. The bus having the minimum value of voltage magnitude is bus 18 2. The line having maximum value of FVSI is line from bus 29 to bus 30. So, this line is the most sensitive to voltage instability 3. Total active power losses equal 159.2 KW and total reactive power losses equal 105.9 KVAR

163


Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9235

-0.8186

2

0.9973

0.0031

19

0.9968

-0.0079

3

0.9845

0.0231

20

0.9932

-0.0759

4

0.9778

0.0469

21

0.9925

-0.0953

5

0.9712

0.0701

22

0.9919

-0.1158

6

0.9553

-0.1014

23

0.9810

-0.0128

7

0.9524

-0.3216

24

0.9747

-0.1097

8

0.9480

-0.3089

25

0.9715

-0.1577

9

0.9425

-0.4002

26

0.9537

-0.0789

10

0.9376

-0.4845

27

0.9515

-0.0463

11

0.9368

-0.4817

28

0.9419

-0.0401

12

0.9354

-0.4783

29

0.9351

-0.0218

13

0.9301

-0.5861

30

0.9321

0.0432

14

0.9282

-0.6655

31

0.9285

-0.0502

15

0.9270

-0.7043

32

0.9277

-0.0748

16

0.9258

-0.7305

33

0.9275

-0.0829

17

0.9240

-0.8074

164


Line Number

Line

Line Number

FVSI

1 to 2

1

0.000337473

2 to 19

18

0.000325286

2 to 3

2

0.001148555

19 to 20

19

0.002956891

3 to 4

3

0.001702838

20 to 21

20

0.000813799

4 to 5

4

0.000655908

21 to 22

21

0.001444903

5 to 6

5

0.000728451

3 to 23

22

0.001154328

6 to 7

6

0.001516901

23 to 24

23

0.008633225

7 to 8

7

0.005295374

24 to 25

24

0.008631566

8 to 9

8

0.000950376

6 to 26

25

0.000283297

9 to 10

9

0.000910341

26 to 27

26

0.00039439

10 to 11

10

0.000443525

27 to 28

27

0.000924299

11 to 12

11

0.000954772

28 to 29

28

0.002437871

12 to 13

12

0.002250304

29 to 30

29

0.016172692

13 to 14

13

0.001920274

30 to 31

30

0.002904072

14 to 15

14

0.000253741

31 to 32

31

0.00134322

15 to 16

15

0.000666507

32 to 33

32

0.000641367

16 to 17

16

0.001137064

17 to 18

17

0.001277938

FVSI

165



1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number



Value of FVSI

0.014 0.012 0.01

0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


166

6.4.2 Optimal location and size of DG unit to achieve losses minimization Genetic algorithm used to obtain the optimal location and size of DG. Table 6.21 show the optimum DG size at each bus of IEEE 33 bus system to achieve minimum active and reactive power losses. Also, Figure 6.19 shows the optimum DG size at each bus of IEEE bus system. Figure 6.20 shows the total active and reactive power losses of IEEE 33 bus system when installed optimum DG at each bus. Table ‎6.21: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses Bus No. Size MW-Losses KVAR losses 2.0000 3.6070 151.7396 102.1057 3.0000 3.1998 121.4197 87.0066 4.0000 2.7743 112.7432 82.7539 5.0000 2.5417 104.2480 78.5954 62.1245 6.0000 2.2860 86.0304 7.0000 2.1724 86.5928 62.7078 8.0000 1.8578 89.8834 62.0839 9.0000 1.5438 94.7389 64.3876 10.0000 1.3490 97.5350 65.7154 11.0000 1.3173 98.0565 65.8188 12.0000 1.2618 99.1293 66.1157 13.0000 1.0844 102.9326 68.6962 14.0000 1.0306 104.2472 70.0790 15.0000 0.9739 106.2498 71.5044 16.0000 0.9087 108.8674 73.0205 17.0000 0.8082 113.3631 77.8489 18.0000 0.7598 115.7903 79.1543 19.0000 1.5260 155.5033 104.5439 20.0000 0.4512 156.9900 104.5195 21.0000 0.3993 157.0624 104.5199 22.0000 0.3228 157.3506 104.7337 23.0000 2.1979 127.5019 90.3603 24.0000 1.5535 129.4493 90.3906 25.0000 1.1884 133.6329 92.3486 26.0000 2.1567 87.7792 62.9445 27.0000 2.0024 89.9885 64.0673 28.0000 1.6119 95.2051 67.3047 29.0000 1.4262 97.4111 68.1152 30.000 1.3295 99.1270 68.7316 31.0000 1.1691 103.2309 71.7474 32.0000 1.1212 104.8961 73.2388 33.0000 1.0619 107.5942 76.5974

167

Optimum size of DG at each bus 4

Optimum Size of DG

3.5 3 2.5 2 1.5 1 0.5 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33




180 160 140 120 100 80 60 40 20 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number





FVSI(30)

Pdg(MWatt)

0.0202

2.2860


Voltage Mag.(P.U)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 0.9986 0.9926 0.9911 0.9899 0.9853 0.9822 0.9778 0.9722 0.9671 0.9663 0.9650 0.9596 0.9576 0.9563 0.9551 0.9533

Voltage Bus Angle No. (deg.) 0 18 0.0459 19 0.2960 20 0.4901 21 0.6904 22 1.1500 23 0.9398 24 0.9608 25 0.8818 26 0.8090 27 0.8133 28 0.8192 29 0.7240 30 0.6500 31 0.6141 32 0.5905 33 0.5185

169

Voltage Mag.(P.U) 0.9528 0.9980 0.9945 0.9938 0.9932 0.9892 0.9828 0.9796 0.9836 0.9813 0.9714 0.9642 0.9611 0.9574 0.9566 0.9564

Voltage Angle (deg.) 0.5086 0.0350 -0.0327 -0.0521 -0.0724 0.2622 0.1693 0.1232 1.1773 1.2164 1.2501 1.2888 1.3639 1.2796 1.2572 1.2497


FVSI 0.000339229 0.001184397 0.001768739 0.000689364 0.000794456 0.001615074 0.005641125 0.001012525 0.000969972 0.000472554 0.001017358 0.002398293 0.002046334 0.000270417 0.00071034 0.001211832 0.001361985


FVSI 0.000326139 0.002964661 0.000815936 0.001448697 0.001173948 0.008780305 0.008778627 0.000301719 0.00042004 0.000983985 0.002594962 0.017217432 0.003091953 0.001430067 0.000682826

Votage of Each Bus 1.01 Voltage Magnitude (per unit)

1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233 Bus Number


170

Value of FVSI

Fast Voltge Stability Index 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Line Number


6.4.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability Table 6.2 shows that line which start from bus 29 to bus 30 is the worst voltage stability line because it has the large FVSI value. So, the best location of DG to enhanced voltage stability is bus 30. Genetic algorithm used to obtain optimal size of DG to achieve minimum active and reactive power losses at bus 30. Table 6.25 summarizes the optimal DG size and location to achieve minimum losses and enhanced voltage stability by genetic algorithm. The optimal location to achieve minimum losses is found at bus 30. The optimal size of DG is 1.3297 Mwatt. Total active and reactive power losses are 99.127 kwatt and 68.7323 KVAR. The value of maximum fast voltage stability index is 0.0199 after install optimal size DG. Table 6.26 and Table 6.27 show load flow study and value of fast voltage stability index of IEEE 33 bus system when installed optimal size DG (1.397 MWatt) at bus 30 to enhanced voltage stability. Figure 6.23 and Figure 6.24 clarifies the positive` impact of DG integration on the voltage profile improvement and voltage stability enhancement for all‎system„s‎buses.‎Comparing‎ the results obtained after integrating DG and obtained without the DG (network base case) shows a significant decrease in the network losses, improve in voltage stability index and 171

voltage magnitude. When install DG at bus 6 , maximum FVSI change from 0.0219 to 0.0203. When install DG at bus 30 , maximum FVSI change from 0.0219 to 0.0199.So, IEEE 33 bus system more enhanced voltage stability when install DG at bus 30. Table ‎6.25: Optimal DG size and location by genetic algorithm Optimization bus 30



FVSI(30) 0.0199

Pdg(MWatt) 1.3297


Bus No.

Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9400

0.0087

2

0.9980

0.0299

19

0.9975

0.0190

3

0.9891

0.1948

20

0.9940

-0.0488

4

0.9854

0.3264

21

0.9933

-0.0682

5

0.9818

0.4623

22

0.9926

-0.0886

6

0.9722

0.6830

23

0.9857

0.1601

7

0.9693

0.4685

24

0.9793

0.0654

8

0.9648

0.4859

25

0.9761

0.0185

9

0.9593

0.4015

26

0.9722

0.7651

10

0.9543

0.3237

27

0.9723

0.8809

11

0.9535

0.3273

28

0.9711

1.3957

12

0.9521

0.3322

29

0.9707

1.7957

13

0.9467

0.2315

30

0.9719

2.0053

14

0.9448

0.1552

31

0.9682

1.9242

15

0.9435

0.1180

32

0.9674

1.9026

16

0.9423

0.0933

33

0.9671

1.8953

17

0.9406

0.0192

172


FVSI

Line

1 to 2 2 to 3 3 to 4

1

0.000338472

2 3

0.001168862 0.001740161

2 to 19 19 to 20 20 to 21

4 to 5 5 to 6

4 5

0.000674828 0.000765162

21 to 22 3 to 23

6 to 7 7 to 8

0.001571934

8 to 9

6 7 8

9 to 10 10 to 11

9 10

0.000943769 0.000459798

26 to 27 27 to 28

11 to 12

11

28 to 29

12 to 13

12

0.000989856 0.002333269

27 28

29 to 30

29

13 to 14

13

0.001990946

30 to 31

14 to 15

0.00026309 0.000691081

31 to 32 32 to 33

32

16 to 17

14 15 16

30 31

17 to 18

17

Line

15 to 16

0.005489176 0.000985215

Line Number 18 19 20 21

FVSI 0.000325772 0.002961314 0.000815015

22

0.001447063 0.001165477

23 to 24 24 to 25

23

0.008716803

24

6 to 26

25 26

0.008715133 0.000295665

0.001178982 0.001325058

173

0.000414216 0.0010013 0.002667354 0.017770306 0.003163071 0.001462944 0.00069852



Voltage profile without DG 1.02

Voltage Magnitude

1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number


1.02

Voltage profile when DG at bus 30 Voltage profile without DG


Voltage Magnitude

1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number


174

6.5 Commercial Load In commercial load, the reactive and active power is depending on magnitude of bus voltage.‎The‎value‎of‎α‎=‎1.51‎and‎the‎value‎of‎β‎=‎3.40. | | | | In this part, the results will be presented as follow ●‎Load flow and voltage stability analysis ●‎Optimal location and size of DG unit to achieve losses minimization ●‎Optimal location and size of DG unit to achieve losses minimization and enhanced voltage stability

6.5.1 Load flow and voltage stability analysis Table 6.28 and Table 6.29 show the load flow solution and the value of the FVSI of each line in the network. Figure 6.25 shows the voltage profile of each bus, found from running the load flow program. From this analysis we can note that: 1. The bus having the minimum value of voltage magnitude is bus 18. 2. The line having maximum value of FVSI is line from bus 29 to bus 30. So, this line is the most sensitive to voltage instability. 3. Total power losses equal 154.8474 KW and total active power losses equal 102.8791 KVAR.

175


Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9248

-0.6557

2

0.9973

0.0066

19

0.9968

-0.0042

3

0.9847

0.0457

20

0.9933

-0.0713

4

0.9781

0.0819

21

0.9926

-0.0906

5

0.9717

0.1179

22

0.9919

-0.1108

6

0.9560

-0.0175

23

0.9813

0.0126

7

0.9530

-0.2272

24

0.9750

-0.0786

8

0.9488

-0.2075

25

0.9718

-0.1237

9 10 11

0.9434 0.9385 0.9378

-0.2864 -0.3589 -0.3548

26 27 28

0.9543 0.9521 0.9426

0.0090 0.0472 0.0785

12

0.9365

-0.3490

29

0.9358

0.1154

13

0.9313

-0.4432

30

0.9328

0.1891

14

0.9294

-0.5163

31

0.9293

0.1056

15

0.9282

-0.5517

32

0.9285

0.0834

16

0.9270

-0.5749

33

0.9283

0.0760

17

0.9253

-0.6459

176

Table ‎6.29: Show value of fast voltage stability index without DG

Line

Line Number

Line

Line Number

FVSI

1 to 2

1

0.000338105

2 to 19

18

0.000325981

2 to 3

2

0.001160953

19 to 20

19

0.002970006

3 to 4

3

0.001728743

20 to 21

20

0.000817766

4 to 5

4

0.000668881

21 to 22

21

0.001452534

5 to 6

5

0.000750998

3 to 23

22

0.00116905

6 to 7

6

0.001566258

23 to 24

23

0.008780665

7 to 8

7

0.00548669

24 to 25

24

0.008797138

8 to 9

8

0.000988581

6 to 26

25

0.000292317

9 to 10

9

0.000950268

26 to 27

26

0.000407575

10 to 11

10

0.000463157

27 to 28

27

0.000961389

11 to 12

11

0.00099806

28 to 29

28

0.002547525

12 to 13

12

0.002361791

29 to 30

29

0.016936992

13 to 14

13

0.002017759

30 to 31

30

0.00304927

14 to 15

14

0.000266866

31 to 32

31

0.001411002

15 to 16

15

0.0007016

32 to 33

32

0.000673826

16 to 17

16

0.0011984

17 to 18

17

0.001347344

FVSI

177



1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number



Value of FVSI

0.014 0.012 0.01

0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32


178

6.5.2 Optimal location and size of DG unit to achieve losses minimization Genetic algorithm used to obtain the optimal location and size of DG. Table 5.30 show the optimum DG size at each bus of IEEE 33 bus system to achieve minimum active and reactive power losses. Also, Figure 6.27 shows the optimum DG size at each bus of IEEE bus system. Figure 6.28 shows the total active and reactive power losses of IEEE 33 bus system when installed optimum DG at each bus. Table ‎6.30: Optimum DG size at each bus of IEEE 33 bus system and total active and reactive power losses Bus No. Size MW-Losses MVAR 2.0000 3.4750 147.9058 99.4397 3.0000 3.1052 119.7314 85.5540 4.0000 2.6951 111.7742 81.7164 5.0000 2.4757 103.8857 77.9158 6.0000 2.2462 86.6091 62.3344 7.0000 2.1335 87.1784 62.9299 8.0000 1.8221 90.4111 62.3345 9.0000 1.5115 95.1095 64.5612 10.0000 1.3208 97.7691 65.8190 11.0000 1.2899 98.2625 65.9162 12.0000 1.2355 99.2799 66.1974 13.0000 1.0615 102.8714 68.6345 14.0000 1.0090 104.1097 69.9384 15.0000 0.9523 106.0143 71.2884 16.0000 0.8876 108.5004 72.7240 17.0000 0.7871 112.7618 77.2834 18.0000 0.7389 115.0560 78.5094 19.0000 1.4762 151.3579 101.6538 20.0000 0.4433 152.6818 101.5808 21.0000 0.3932 152.7462 101.5775 22.0000 0.3182 153.0218 101.7831 23.0000 2.1373 125.2115 88.5061 24.0000 1.5202 126.747 88.3020 25.0000 1.1643 130.6469 90.1079 26.0000 2.1182 88.2873 63.1096 27.0000 1.9653 90.3982 64.1692 28.0000 1.5824 95.3055 67.2043 29.0000 1.4023 97.3192 67.9132 30.0000 1.3079 98.9086 68.4590 31.0000 1.1477 102.8549 71.3497 32.0000 1.0994 104.4546 72.7747 33.0000 1.0398 107.0518 75.9941

179

Optimum size of DG at each bus 4

Optimum Size of DG

3.5 3 2.5 2 1.5 1 0.5 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33




180 160 140 120 100 80 60 40 20 0 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number





FVSI(30) 0.0202

Pdg(MWatt) 2.2463


Voltage Mag.(P.U)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

1 0.9986 0.9926 0.9910 0.9898 0.9851 0.9820 0.9776 0.9721 0.9671 0.9663 0.9650 0.9596 0.9577 0.9564 0.9552 0.9535

Voltage Bus Angle No. (deg.) 0 18 0.0473 19 0.3047 20 0.5029 21 0.7074 22 1.1762 23 0.9713 24 0.9960 25 0.9241 26 0.8579 27 0.8629 28 0.8703 29 0.7829 30 0.7126 31 0.6787 32 0.6569 33 0.5884

181

Voltage Mag.(P.U) 0.9530 0.9980 0.9945 0.9938 0.9932 0.9892 0.9828 0.9796 0.9834 0.9811 0.9712 0.9641 0.9609 0.9573 0.9565 0.9563

Voltage Angle (deg.) 0.5793 0.0365 -0.0304 -0.0497 -0.0699 0.2728 0.1838 0.1398 1.2058 1.2481 1.2959 1.3452 1.4254 1.3468 1.3257 1.3186


FVSI 0.000339539 0.001189951 0.00177867 0.000693739 0.000801576 0.001633146 0.005722313 0.001031001 0.000991046 0.000483035 0.001040922 0.002463214 0.002104319 0.000278323 0.000731726 0.00124982 0.001405177


FVSI 0.00032655 0.002975184 0.000819192 0.001455066 0.001182202 0.008879417 0.008896078 0.000304852 0.000425044 0.001002205 0.00265549 0.017656774 0.003178884 0.001470986 0.00070247

Votage of Each Bus 1.01 Voltage Magnitude (per unit)

1 0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 1 2 3 4 5 6 7 8 9 101112131415161718192021222324252627282930313233 Bus Number


182

Value of FVSI

Fast Voltge Stability Index 0.02 0.018 0.016 0.014 0.012 0.01 0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Line Number


6.5.3 Optimal size and location of DG unit to achieve losses minimization and enhanced voltage stability Table 6.2 shows that line which start from bus 29 to bus 30 is the worst voltage stability line because it has the large FVSI value. So, the best location of DG to enhanced voltage stability is bus 30. Genetic algorithm used to obtain optimal size of DG to achieve minimum active and reactive power losses at bus 30. Table 6.34 summarizes the optimal DG size and location to achieve minimum losses and enhanced voltage stability by genetic algorithm. The optimal location to achieve minimum losses is found at bus 30. The optimal size of DG is 1.3080 Mwatt. Total active and reactive power losses are 98.9086 kwatt and 68.4593 KVAR. The value of maximum fast voltage stability index is 0.0199 after install optimal size DG. Table 6.35 and Table 6.36 show load flow study and value of fast voltage stability index of IEEE 33 bus system when installed optimal size DG (1.3080 MWatt) at bus 30 to enhanced voltage stability. Figure 6.31 and Figure 6.32 clarifies the positive impact of DG integration on the voltage profile improvement and voltage stability enhancement for all system„s‎buses.‎Comparing‎ the results obtained after integrating DG and obtained without the DG (network base case) shows a significant decrease in the network losses, improve in voltage stability index and voltage magnitude. When install DG at bus 6 , maximum FVSI change from 0.0219 to

183

0.0203. When install DG at bus 30 , maximum FVSI change from 0.0219 to 0.0199.So, IEEE 33 bus system more enhanced voltage stability when install DG at bus 30. Table ‎6.34: Optimal DG size and location by genetic algorithm Optimization bus 30



FVSI(30)

Pdg(MWatt)

0.0199

1.3080


Bus No.

Voltage Mag.(P.U)


Bus No.

Voltage Mag.(P.U)


1

1

0

18

0.9406

0.1060

2

0.9980

0.0318

19

0.9975

0.0209

3

0.9892

0.2064

20

0.9940

-0.0460

4

0.9854

0.3437

21

0.9933

-0.0653

5

0.9820

0.4853

22

0.9926

-0.0855

6

0.9724

0.7208

23

0.9857

0.1739

7

0.9693

0.5139

24

0.9794

0.0840

8

0.9650

0.5364

25

0.9763

0.0395

9

0.9595

0.4614

26

0.9723

0.8039

10

0.9546

0.3924

27

0.9724

0.9209

11

0.9539

0.3971

28

0.9710

1.4391

12

0.9525

0.4038

29

0.9705

1.8413

13

0.9472

0.3134

30

0.9716

2.0525

14

0.9453

0.2419

31

0.9680

1.9757

15

0.9441

0.2073

32

0.9671

1.9551

16

0.9429

0.1849

33

0.9669

1.9482

17

0.9412

0.1154

184

Table ‎6.36: show value of fast voltage stability index to achieve minimum losses and enhanced voltage stability Line 1 to 2 2 to 3 3 to 4 4 to 5 5 to 6 6 to 7 7 to 8 8 to 9 9 to 10 10 to 11 11 to 12

Line Number

FVSI

Line

Line Number

2 to 19

18

3

0.000338918 0.001177345 0.001756978

19 to 20 20 to 21

19 20

4 5

0.00068293 0.000779179

6 7

0.001603819 0.005618999

21 to 22 3 to 23 23 to 24

21 22 23

8 9 10

0.001012402 0.000973167 0.00047432

24 to 25 6 to 26

24 25

11

0.001022129 0.002418748

26 to 27 27 to 28 28 to 29

26 27 28

29 to 30

29

30 to 31

30

31 to 32 32 to 33

31 32

1 2

12 to 13

12

13 to 14 14 to 15 15 to 16 16 to 17

13 14 15 16

17 to 18

17

0.002066369 0.0002733 0.000718518 0.001227277 0.001379822

185

FVSI 0.000326304 0.002972944 0.000818575 0.001453971 0.001176505 0.008836646 0.008853225 0.000301072 0.000421741 0.001019848 0.002717271 0.018089503 0.003228414 0.00149391 0.000713417

1.02

Voltage profile when DG at bus 30 Voltage profile without DG


Voltage Magnitude

1 0.98 0.96 0.94 0.92 0.9 0.88 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 Bus Number




FVSI without DG

0.02 0.018 0.016 Value of FVSI

0.014 0.012 0.01

0.008 0.006 0.004 0.002 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 Bus Number


186

Chapter 7 Conclusions and Future Work 7.1 Conclusions This thesis is directed to power flow study and the voltage stability analysis of radial distribution system including distributed generator (DG). The following points should be concluded from the research work conducted in the thesis: i) ii)

The bus having the maximum value of fast voltage stability, line stability factor and line stability factor is the most sensitive bus to voltage instability. The system becomes closer to voltage instability problem due to increase load demand. This problem can be solved by adding DG.

iii)

Voltage stability more enhanced, voltage profile more improved, total power losses more decreased and maximum load ability more increase when increase the penetration level of distributed generation which give active and reactive power make. But if distributed generation is from type that give active power only. When increase penetration level of this DG type occurs voltage stability enhanced, voltage profile improved, total power losses decreased and maximum load ability increase but when reach a certain size total power losses increase and maximum load ability decrease.

iv)

When compare between distributed generation that give active and reactive power and distributed generation that give active power. Distributed generation that give active and reactive power is better than distributed generation that gives active power. Distributed generation effect on voltage stability, voltage profile, and power flow according to type of load modeling. The optimal size and location of distributed generation depend on objective function and constrain and load modeling.

v) vi)

187

7.2 Recommendations and Future Work i) ii) iii) iv) v)

Study the effect of adding more than one distributed generation on radial system on voltage stability, voltage profile, and power flow. Utilize renewable energy as a distributed generation unit such as wind and solar energy. In order to achieve more accurate results of the realistic behavior strategy, it can be implemented on the recently daily load curve. Study the effect of distributed generation on rotor angle stability and frequency stability. Study the effect of distributed generation on dynamic voltage stability.

188

References [1]‎T.‎Ackermann,‎G.‎Andersson,‎and‎L.‎Sder, "Distributed generation: a definition," Electr. Power Syst. Res., vol. 57, pp. 195-204, 2001. [2]J.Momoh,‎G.D.Boswell,‎“Improving‎power‎Grid‎‎Efficiency‎using‎‎‎‎Distributed‎ Generation”‎Proceedings‎of‎‎the‎7th‎international‎conference‎on‎power‎system‎operation‎ and planning, pp.11-17, Jan., 2007 [3] P. Dondi, D. Bayoumi, C. Haederli, D. Julian, and M. Suter, "Network integration of distributed power generation," J. Power Sources, vol. 106, pp. 1-9, 2002. [4] Rashid Al-Abri "Voltage Stability Analysis with High Distributed Generation (DG) Penetration" Waterloo, Ontario, Canada, 2012 [5] Enercon, "http://www.enercon.de/en/_home.htm or http://www.metaefficient.com/news/new-record-worlds-largest-wind-turbine-7megawatts.html," Enercon Energy for the World [6] T. Ackermann, Wind Power in Power Systems: John Wiley & Sons, 2005. [7] T. Markvart, Solar Electricity, 2nd ed.: John Wiley & Sons, 1997. [8] K. Emery, "The rating of photovoltaic performance," IEEE Trans. Electron Devices, vol. 46, pp. 1928-1931, 1999. [9] F. Blaabjerg, C. Zhe, and S. B. Kjaer, "Power electronics as efficient interface in dispersed power generation systems," IEEE Trans. Power Electron., vol. 19, pp. 11841194, 2004. [10]‎A.‎Goetzberger,‎and‎V.‎U.‎Hoffmann,‎“Photovoltaic‎Solar‎Energy‎Generation”‎ Springer Series in Applied Science, 2005.}. [11] L. Li-Shiang, H. Wen-Chieh, F. Ya-Tsung, and C. Yu-An, "Novel grid-connected photovoltaic generation system," in Electric Utility Deregulation and Restructuring and Power Technologies (DRPT) 2008, pp. 2536-2541. [12] T. Esram and P. L. Chapman, "Comparison of photovoltaic array maximum power point tracking techniques," IEEE Trans. Energy Convers., vol. 22, pp. 439-449, 2007. [13] D. M. Ali, "A simplified dynamic simulation model (prototype) for a stand-alone Polymer Electrolyte Membrane (PEM) fuel cell stack," in Proc. International Middle-East, Power System Conference, MEPCON, pp. 480-485, 2008. [14]‎C.Wang,‎M.H.Nehrir,‎and‎S.R.Shaw,‎“Dynamic‎Models‎and‎Model‎Validation‎for‎ PEM‎Fuel‎Cells‎Using‎Electrical‎Circuits,”‎IEEE‎Transaction‎on‎Energy‎Conversion,‎ Vol.20, No.2, PP.442-451, June 2005. [15] O.Yamamoto,‎“Solid‎Oxide‎Fuel‎Cells‎Fundamental‎Aspects‎and‎Prospects,”‎ Electrochimica Acta, Vol.45, No. (15-16), PP. 2423-2435, 2000. 189

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[45]‎I.‎Musirin,‎and‎T.‎K.‎A.‎Rahman,‎”Novel‎Fast‎Voltage‎Stability‎Index‎(FVSI)‎for‎ Voltage‎Stability‎Analysis‎in‎Power‎Transmission‎System”,‎,Proc.‎of‎Student‎Conference on Research and Development, Shah Alam, Malaysia, July 2002. [46]‎I.‎Musirin;‎T.‎K.‎A.‎Rahman‎“On-Line Voltage Stability Based Contingency Ranking Using‎Fast‎Voltage‎Stability‎Index‎(FVSI)”‎Transmission‎and‎Distribution‎Conference‎and‎ Exhibition 2002: Asia Pacific. IEEE/PES. [47]‎I‎Musirin‎and‎T‎K‎Abdul‎Rahman,‎“On-Line Voltage Stability Index for Voltage Collapse‎Prediction.‎in‎Power‎System,”‎presented‎at‎Brunei‎International‎Conference‎on‎ Engineering and Technology 2001 (BICET200 I), Brunei. October 2001. [48] Mostafa H Mostafa, Mostafa A Elshahed and Magdy M Elmarsfawy "Power Flow Study and Voltage Stability Analysis for Radial System with Distributed Generation" International Journal of Computer Applications (0975 – 8887) Volume 137 – No.9, March 2016 [49]‎A‎Mohamed,‎G‎B‎Jasmon‎and‎S‎Yusoff,‎“A‎Static‎Voltage‎Collapse‎Indicator‎Using‎ Line‎Stability‎Factors,”‎Journal‎of‎Industrial‎Technology,‎Vol.‎7,‎No.‎I.‎pp‎73-85. Pt C, (1989) [50] M. H. Haque, "Load Flow Solution of Distribution Systems with Voltage Dependent Load Models", Electric Power Systems Research, Volume 36, Issue 3, pp.151–156, March 1996. [51]‎L.‎M.‎Vargas‎Rios,‎“Local‎Voltage‎Stability‎Assessment‎for‎Variable‎Load‎ Characteristics”‎Master‟s‎thesis,‎Univ.‎British‎Columbia,‎Vancouver,‎BC,‎Canada, 2009. [Online]. Available: https://circle.ubc.ca/handle/2429/21424. [52]‎IEEE‎Task‎Force‎on‎Load‎Representation‎for‎Dynamic‎Performance,‎“Bibliography‎ on‎load‎models‎for‎power‎ﬂow‎and‎dynamic‎performance‎simulation,”‎IEEE‎Trans.‎Power‎ Syst., vol. 10, no. 1, pp. 523–538, Feb. 1995. [53]‎M.‎E.‎Baran‎and‎F.‎F.‎Wu,‎“Network‎reconfiguration in distribution systems for loss reduction‎and‎load‎balancing”,‎IEEE‎Transaction‎on‎Power‎Delivery,‎Vol.‎4,‎No.‎2,‎pp.‎ 1401–1407, Apr. 1989. [54]‎S.‎Li‎K.‎Tomsovic‎and‎T.‎Hiyama‎‎“Load‎Following‎Functions‎Using‎Distributed‎ Energy Rtsources”,‎IEEE,‎Apr.‎2000. [55] M. Ettehadi, H.Ghasemi, and S. Vaez-Zadeh,‎“Voltage‎Stability-Based DG Placement in‎Distribution‎Networks”,‎IEEE‎Transactions‎on‎Power‎Delivery,‎Vol.‎28,‎No.‎1,‎pp.‎171178, Jan. 2013. [56]‎R.‎Vemana,‎and‎Dr.‎M.‎Sridhar,‎”‎A‎particle swarm optimization to optimal shunt capacitor‎placement‎in‎radial‎distribution‎systems‎”,‎International‎Journal‎of‎Advanced‎ Research in Electrical,Electronics and Instrumentation Engineering, Vol. 2, No. 10, pp. 4887 - 4895, October 2013.

192

Appendices Appendix A.1 Table A.1 Line Data of 33 Node Radial Distribution Network Branch Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Sending -end Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 19 20 21 3 23 24 6 26 27 28 29 30 31 32

Receiving-end Node 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

193

Branch Resistance(Ω) 0.0922 0.4930 0.3660 0.3811 0.8190 0.1872 0.7114 1.0300 1.0040 0.1996 0.3744 1.4680 0.5416 0.5910 0.7463 1.2890 0.7320 0.1640 1.5042 0.4095 0.7089 0.4512 0.8980 0.8960 0.2030 0.2842 1.0590 0.8042 0.5075 0.9744 0.3105 0.3410

Branch Reactance(Ω) 0.0470 0.2511 0.1864 0.1941 0.7070 0.6188 0.2351 0.7400 0.7400 0.0650 0.1238 1.1550 0.7129 0.5260 0.5450 1.7210 0.5740 0.1565 1.3554 0.4784 0.9373 0.3083 0.7091 0.7011 0.1034 0.1447 0.9337 0.7006 0.2585 0.9630 0.3619 0.5302

Table A.2 Node Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Load Data of IEEE33 Node Radial Distribution Network (KW)

(KVAR)

0 100 90 120 60 60 200 200 60 60 45 60 60 120 60 60 60 90 90 90 90 90 90 420 420 60 60 60 120 200 150 210 60

0 60 40 80 30 20 100 100 20 20 30 35 35 80 10 20 20 40 40 40 40 40 50 200 200 25 25 20 70 600 70 100 40

BASE KV = 12.66 and BASE MVA=100

194

Appendix A.3 Load Data of Japan Radial Distribution Network Branch Number 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Sending Node 1 2 3 3 4 4 5 7 8 9 10 12 13 14

Receiving Node 2 3 4 12 5 7 6 8 9 10 11 13 14 15

R (P.U)

X(P.U)

B(P.U)

0.003145 0.00033 0.006667 0.027502 0.005785 0.008001 0.014141 0.008999 0.00700 0.003666 0.008999 0.039653 0.039653 0.016070

0.075207 0.001849 0.030808 0.127043 0.014949 0.036961 0.036547 0.041575 0.032346 0.016940 0.041575 0.102984 0.102984 0.004153

0 0.00150 0.03525 0 0.00250 0.03120 0 0 0.00150 0.00350 0.00200 0 0 0

(P.U) 0.0208 0.0495 0.0958 0.0132 0.0442 0.0638 0.0113 0.0323 0.0213 0.0208 0.2170 0.0029 0.0161 0.0139

BASE VOLTAGE = 66 KV, BASE MVA = 10 MVA

195

(P.U) 0.0021 0.0051 0.0098 0.0014 0.0045 0.0066 0.0012 0.0033 0.0022 0.0029 0.2200 0.0003 0.0016 0.0014

‫مهخص انرضانت‬ ‫يضداد اعرخذاو انًٕنذ انًٕصع فٗ شثكاخ انقٕٖ انكٓشتيح نًا نّ يٍ ذاشيش كثيش ػهٗ انعٓذ انكٓشتٗ نهًُظٕيح ٔعشياٌ‬ ‫ٔظٕدج انطاقح ٔاػرًاديح ٔحًايح انًُظٕيح انكٓشتيح‪ٔ .‬تغثة صيادج االحًال انكٓشتيح يحذز ػذو اعرقشاس نهعٓذ انكٓشتٗ‬ ‫داخم شثكح انرٕصيغ انكٓشتٗ ال ٌ صيادج االحًال انكٓشتيح ذذفغ يُظٕيح انقشٖ انكٓشتيح انٗ حذٔد اعرقشاسْا يًا يٕدٖ‬ ‫انٗ َقص فٗ انعٓذ انكٓشتٗ ٔاالَقطاػاخ انكٓشتيح‪ .‬نزنك َحراض انٗ دساعح اعرقشاس انعٓذ انكٓشتٗ نهًُظٕيح ٔايضا‬ ‫دساعح كيفيح يُغ ٔصٕل انًُظٕيح انكٓشتيح انٗ حذٔد اعرقشاسْا‪.‬‬ ‫ظْٕش ْزِ ان شعانح ْٗ دساعح ذاشيش انًٕنذ انًٕصع ٔعؼرّ ػهٗ اذضاٌ انعٓذ انكٓشتٗ ٔانعٓذ انكٓشتٗ نهًُظٕيح‬ ‫ٔعشياٌ انطاقح فٗ َظى انرٕصيغ انشؼاػيح‪ .‬فٗ ْزِ انشعانح ذى اعرخذاو انًٕنذ انًٕصع انزٖ يؼطٗ قذسج فؼانح ٔقذسج غيش‬ ‫فؼانح فٗ َفظ انٕقد ٔايضا انًٕنذ انًٕصع انزٖ يؼطٗ قذسج فؼانح فقظ‪ .‬يرى دساعح عشياٌ انطاقح نهًُظٕيح انكٓشتيح ػٍ‬ ‫طشيق حغاب انعٓذ انكٓشتٗ نكم قضية ٔانفقذ انكٓشتٗ فٗ انُظاو انرٕصيؼٗ‪ .‬ذحهيم اعرقشاس انعٓذ يرى ػٍ طشيق‬ ‫حغاب يؼايم اعرقشاس انعٓذ ٔيؼايم اعقشاس انخظ ٔقإٌَ اعرقشاس انخظ ٔحغاب اقصٗ قذسج نالحًال انكٓشتيح ٔسعى‬ ‫انؼالقح تيٍ انقذسج انفؼانح ٔانعٓذ‪.‬‬ ‫فٗ يؼظى انذساعاخ ذًصم االحًال انكٓشتيح تٕاعطح قذسج شاترح ْزا يؤدٖ انٗ َرائط غيش دقيقح‪ٔ .‬قذ ٔظذ اٌ ذًصيم‬ ‫االحًال نّ ذاشيش كثيش ػهٗ ذاشيش انًٕنذ انًٕصع ػهٗ اعقشاس انعٓذ انكٓشتٗ ٔظٓذ انًُظٕيح ٔعشياٌ انطاقح‪ .‬نزنك فٗ‬ ‫ْزج انشعانح ذى دساعح ذاشيش االحًال ػهٗ حغاتاخ اعرقشاس انعٓذ ٔظٓذ انًُظٕيح ٔانفقذ انكٓشتٗ‪ٔ .‬ايضا ذى دساعح‬ ‫افضم يكاٌ ٔعؼّ نهًٕنذ انًٕصع نرحقيق اقم فقذ فٗ انطاقح ٔاحغٍ اعرقشاس نهعٓذ تاعرخذاو انخٕسصيياخ‪.‬‬ ‫ٔقذ ذى ذٕضيح انرقُياخ انًقرشحح ػٍ طشيق ذطثيقٓا ػهٗ يُظٕيح انرٕصيغ انكٓشتٗ انًُشٕسج فٗ ‪ ْٗٔ IEEE‬شثكح‬ ‫ذٕصيغ راخ ‪ ..‬قضية ذٕصيغ ٔايضا ذى ذطثيقٓا ػهٗ يُظٕيح ذٕصيغ شؼاػيح ػًهيح ْٔٗ ظضء يٍ شثكح انياتاٌ‪ٔ .‬ذًد‬ ‫انًحاكاِ انحاعٕتيح ػٍ طشيق ‪ٔ .Matlab, PSAT, Excell‬قذ ذى ػشض انُرائط ٔذقيًٓا‪.‬‬

‫وحخكىن انرضانت مه ضبؼت فصىل وباالضافت انً انمراجغ وهً ‪:‬‬ ‫انفصم األول‪:‬‬

‫يؼذ تًصاتح يقذيح ٔ ذًٓيذ نًٕضٕع انثحس ٔػشض انًشكهح َٔظشج ػايح ػٍ انشعانّ ٔاْذافٓا ٔيا‬ ‫يحرٕيّ كم فصم‪.‬‬

‫انفصم انثاوً‪ :‬يخصص ْزا انفصم إلػطاء نًحح ػايح ػٍ انًٕضٕع نهقاسئ ٔ يُاقشح انقضايا األعاعيح انًرؼهقح‬ ‫تانًٕنذ انًٕصع ٔإَاػّ ٔاعرقشاس انُظى انكٓشتيح‪.‬‬ ‫انفصم انثانث ‪:‬‬

‫يخصص ْزا انفصم إلػطاء ذحهيم ػٍ االَظًح انكٓشتيح ٔػشض انًشكهحٔذًصيم االحًال انكٓشتيح‪.‬‬

‫انفصم انرابغ‪:‬‬

‫يؼشض ْ زا انفصم ذقيى نراشيش انًٕنذ انًٕصع ٔعؼرّ ػهٗ انعٓذ انكٓشتٗ ٔعشياٌ انطاقح ٔاعرقشاس‬ ‫انعٓذ فٗ حانح اٌ انًٕنذ انًٕصع يؼطٗ قذسج فؼانح ٔغيش فؼانح فٗ َفظ انٕقد أ يؼطٗ قذسج فؼانح‬ ‫فقظ ٔقذ ذى فٗ ْزا انفصم انًقاسَح تيٍ حانرٗ انًٕنذ انًٕصع‪.‬‬

‫انفصم انخامص‪ :‬فٗ ْزا انفصم يرى ػشض ٔذقيى ذاشيش االحًال انكٓشتيح ػهٗ ذاشيش انًٕنذ انًٕصع ػهٗ ظٓذ انًُظٕيح‬ ‫ٔعشياٌ انطاقح ٔاعرقشاس انعٓذ‬ ‫انفصم انطادش‪ :‬في ْزا انفصم يرى دساعح افضم يكاٌ ٔعؼّ نهًٕنذ انًٕصع نرقهيم انفقذ انكٓشتٗ فقظ‪ٔ .‬ايضا دساعح‬ ‫افضم يكاٌ ٔعؼح نرحقيق افضم ذقهيم نهفقذ انكٓشتٗ ٔذؼضيض اعرقشاس انعٓذ‪ٔ .‬ذرى ْزِ انذساعح ػهٗ‬ ‫ظًيغ إَاع االحًال انكٓشتيح‪.‬‬ ‫انفصم انطابغ‪ :‬ذى ػشض االعرُراظاخ انشئيغيح نهشعانح ٔانرٕصياخ انًقرشحح نهذساعاخ انًغرقثهيح انرٗ يًكٍ انحاقٓا‬ ‫فٗ يعال ْزا انثحس‪.‬‬ ‫‪196‬‬

‫يُٓــــــــــــــــــذط‪6‬‬ ‫ذاسيــخ انًيــــالد‪6‬‬

‫مصطفى حسن مصطفى عبدالجواد‬ ‫‪0545 / 06 / 0‬‬

‫انعُغيـــــــــــــــح‪6‬‬

‫مصرى‬

‫ذاسيخ انرغعيم‪:‬‬

‫‪610. / 01 / 0‬‬

‫ذــــاسيخ انًُــــح‪:‬‬

‫‪/‬‬

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‫انقغـــــــــــــــــــــى‪:‬‬

‫هندسة القوى واالالت الكهربية‬

‫انذسظــــــــــــــــــــح‪:‬‬

‫ماجيستير العموم‬

‫انًششفٌٕ ‪:‬‬

‫أ‪.‬د مجدى المرصفاوى‬ ‫د‪ .‬مصطفى الشاهد‬

‫انًًرحُـــــــٌٕ ‪:‬‬ ‫ػُـــــٕاٌ انشعانــح ‪:‬‬

‫دراضت اضخقرار انجهذ وضريان انقىي نىظاو انخىزيغ انكهربيت انمحخىيت‬

‫ػهً انمىنذ انمىزع‬ ‫انكهًاخ انذانح ‪6‬‬

‫ذؼضيض اعرقشاس انعٓذ‪ ،‬شثكاخ انرٕصيغ انشؼاػيح‪ ،‬انًٕنذ انًٕصع‪ ،‬ذًصم االحًال‬ ‫انكٓشتيح ٔ عشياٌ انقٕٖ‪.‬‬

‫يهخـــــص انثحــــــس ‪:‬‬ ‫يضداد اعرخذاو انًٕنذ انًٕصع فٗ شثكاخ انقٕٖ انكٓشتيح نًا نّ يٍ ذاشيش كثيش ػهٗ انعٓذ انكٓشتٗ نهًُظٕيح ٔعشياٌ‬ ‫ٔظٕدج انطاقح ٔاػرًاديح ٔحًايح انًُظٕيح انكٓشتيح‪ٔ .‬تغثة صيادج االحًال انكٓشتيح يحذز ػذو اعرقشاس نهعٓذ انكٓشتٗ‬ ‫داخم شثكح انرٕصيغ انكٓشتٗ الٌ صيادج االحًال انكٓشتيح ذذفغ يُظٕيح انقشٖ انكٓشتيح انٗ حذٔد اعرقشاسْا يًا يٕدٖ‬ ‫انٗ َقص فٗ انعٓذ انكٓشتٗ ٔاالَقطاػاخ انكٓشتيح‪ .‬نزنك َحراض انٗ دساعح اعرقشاس انعٓذ انكٓشتٗ نهًُظٕيح ٔايضا‬ ‫دساعح كيفيح يُغ ٔصٕل انًُظٕيح انكٓشتيح انٗ حذٔد اعرقشاسْا‪.‬‬ ‫ظْٕش ْزِ انشعانح ْٗ دساعح ذاشيش انًٕنذ انًٕصع ٔعؼرّ ػهٗ اذضاٌ انعٓذ انكٓشتٗ ٔانعٓذ انكٓشتٗ نهًُظٕيح‬ ‫ٔعشياٌ انطاقح فٗ َظى انرٕصيغ انشؼاػيح‪ .‬فٗ ْزِ انشعانح ذى اعرخذاو انًٕنذ انًٕصع انزٖ يؼطٗ قذسج فؼانح ٔقذسج غيش‬ ‫فؼانح فٗ َفظ انٕقد ٔايضا انًٕنذ انًٕصع انزٖ يؼطٗ قذسج فؼانح فقظ‪ .‬يرى دساعح عشياٌ انطاقح نهًُظٕيح انكٓشتيح ػٍ‬ ‫طشيق حغاب انعٓذ انكٓشتٗ نكم قضية ٔانفقذ انكٓشتٗ فٗ انُظاو انرٕصيؼٗ‪ .‬ذحهيم اعرقشاس انعٓذ يرى ػٍ طشيق‬ ‫حغاب يؼايم اعرقشاس انعٓذ ٔيؼايم اعقشاس انخظ ٔقإٌَ اعرقشاس انخظ ٔحغاب اقصٗ قذسج نالحًال انكٓشتيح ٔسعى‬ ‫انؼالقح تيٍ انقذسج انفؼانح ٔانعٓذ‪.‬‬ ‫فٗ يؼظى انذساعاخ ذًصم االحًال انكٓشتيح تٕاعطح قذسج شاترح ْزا يؤدٖ انٗ َرائط غيش دقيقح‪ٔ .‬قذ ٔظذ اٌ ذًصيم‬ ‫االحًال نّ ذاشيش كثيش ػهٗ ذاشيش انًٕنذ انًٕصع ػهٗ اعقشاس انعٓذ انكٓشتٗ ٔظٓذ انًُظٕيح ٔعشياٌ انطاقح‪ .‬نزنك فٗ‬ ‫ْزج انشعانح ذ ى دساعح ذاشيش االحًال ػهٗ حغاتاخ اعرقشاس انعٓذ ٔظٓذ انًُظٕيح ٔانفقذ انكٓشتٗ‪ٔ .‬ايضا ذى دساعح‬ ‫افضم يكاٌ ٔعؼّ نهًٕنذ انًٕصع نرحقيق اقم فقذ فٗ انطاقح ٔاحغٍ اعرقشاس نهعٓذ تاعرخذاو انخٕسصيياخ‪.‬‬

‫‪197‬‬

‫دراضت اضخقرار انجهذ وضريان انقىي نىظاو انخىزيغ انكهربيت انمحخىيت‬ ‫ػهً انمىنذ انمىزع‬ ‫إػذاد‬

‫مصطفً حطه مصطفً ػبذانجىاد‬ ‫رضانت مقذمت انً كهيت انهىذضت ‪ -‬جامؼت انقاهرة‬ ‫كجسء مه مخطهباث انحصىل ػهً درجت ماجيطخير انؼهىو‬ ‫فً‬ ‫هىذضت انقىي واآلالث انكهربيت‬

‫ححج اشراف‬

‫أ‪.‬د‪ .‬مجذي انمرصفاوي‬

‫د‪ .‬مصطفً انشاهذ‬

‫اعرار تقغى ُْذعح انقٕٖ اآلالخ انكٓشتيح‬ ‫كهيح انُٓذعح – ظايؼح انقاْشج‬

‫اعرار يغاػذ تقغى ُْذعح انقٕٖ اآلالخ انكٓشتيح‬ ‫كهيح انُٓذعح – ظايؼح انقاْشج‬

‫كهيت انهىذضت – جامؼت انقاهرة‬ ‫انجيسة – جمهىريت مصر انؼربيت‬ ‫‪2016‬‬

‫‪198‬‬

‫دراضت اضخقرار انجهذ وضريان انقىي نىظاو انخىزيغ انكهربيت انمحخىيت‬ ‫ػهً انمىنذ انمىزع‬

‫إػذاد‬

‫مصطفً حطه مصطفً ػبذانجىاد‬ ‫رضانت مقذمت انً كهيت انهىذضت ‪ -‬جامؼت انقاهرة‬ ‫كجسء مه مخطهباث انحصىل ػهً درجت ماجيطخير انؼهىو‬ ‫فً‬ ‫هىذضت انقىي واآلالث انكهربيت‬

‫كهيت انهىذضت – جامؼت انقاهرة‬ ‫انجيسة – جمهىريت مصر انؼربيت‬ ‫‪2016‬‬

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