Smart Integration of Distributed Renewable
Generation and Battery Energy Storage
Duong Quoc Hung
Bachelor of Electrical and Electronics Engineering
Master Engineering in Electric Power System Management
A thesis submitted for the degree of Doctor of Philosophy at
The University of Queensland in 2014
The School of Information Technology and Electrical Engineering
ABSTRACT
Renewable energy (i.e., biomass, wind and solar) and Battery Energy Storage (BES) are
emerging as sustainable solutions for electricity generation. In the last decade, the smart
grid has been introduced to accommodate high penetration of such renewable resources
and make the power grid more efficient, reliable and resilient. The smart grid is formulated
as a combination of power systems, telecommunication communication and information
technology. As an integral part of the smart grid, a smart integration approach is presented
in this thesis. The main idea behind the smart integration is locating, sizing and operating
renewable-based Distributed Generation (DG) resources and associated BES units in
distribution networks strategically by considering various technical, economical and
environmental issues. Hence, the aim of the thesis is to develop methodologies for strategic
planning and operations of high renewable DG penetration along with an efficient usage of
BES units.
The first contribution of the thesis is to present three alternative analytical expressions
to identify the location, size and power factor of a single DG unit with a goal of
minimising power losses. These expressions are easily adapted to accommodate different
types of renewable DG units for minimizing energy losses by considering the time-varying
demand and different operating conditions of DG units. Both dispatchable and nondispatchable renewable DG units are investigated in the study. Secondly, a methodology is
also introduced in the thesis for the integration of multiple dispatchable biomass and
nondispatchable wind units. The concept behind this methodology is that each
nondispatchable wind unit is converted into a dispatchable source by adding a biomass unit
with sufficient capacity to retain the energy loss at a minimum level. Thirdly, the thesis
studies the determination of nondispatchable photovoltaic (PV) penetration into
distribution systems while considering time-varying voltage-dependent load models and
probabilistic generation. The system loads are classified as an industrial, commercial or
residential type or a mix of them with different normalised daily patterns. The Beta
probability density function model is used to describe the probabilistic nature of solar
irradiance. An analytical expression is proposed to size a PV unit. This expression is based
on the derivation of a multiobjective index (IMO) that is formulated as a combination of
ii
three indices, namely active power loss, reactive power loss and voltage deviation. The
IMO is minimised in determining the optimal size and power factor of a PV unit. Fourthly,
the thesis discusses the integration of PV and BES units considering optimal power
dispatch. In this work, each nondispatchable PV unit is converted into a dispatchable
source by adding a BES unit with sufficient capacity. An analytical expression is proposed
to determine the optimal size and power factor of PV and BES units for reducing energy
losses and enhancing voltage stability. A self-correction algorithm is then developed for
sizing multiple PV and BES units. Finally, the thesis presents a comprehensive framework
for DG planning. In this framework, analytical expressions are proposed to efficiently
capture the optimal power factor of each DG unit with a standard size for minimising
energy losses and enhancing voltage stability. The decision for the optimal location, size
and number of DG units is obtained through a benefit-cost analysis over a given planning
horizon. Here, the total benefit includes energy sales, loss reduction, network investment
deferral and emission reduction, while the total cost is a sum of capital, operation and
maintenance expenses.
The study reveals that the time-varying demand and generation models play a
significant role in renewable DG planning. Depending on the characteristics of demand
and generation, a distribution system would accommodate up to an estimated 48% of the
nondispatchable renewable DG penetration. A higher penetration level could be obtained
for dispatchable DG technologies such as biomass and a hybrid of PV and BES units. More
importantly, the study also indicates that optimal power factor operation could be one of
the aspects to be considered in the strategy of smart renewable DG integration. A
significant energy loss reduction and voltage stability enhancement can be achieved for all
the proposed scenarios with DG operation at optimal power factor when compared to DG
generation at unity power factor which follows the current standard IEEE 1547.
Consequently, the thesis recommends an appropriate modification to the grid code to
reflect the optimal or near optimal power factor operation of DG as well as BES units. In
addition, it is shown that inclusion of energy loss reduction together with other benefits
such as network investment deferral and emission reduction in the analysis would recover
DG investments faster.
iii
DECLARATION BY AUTHOR
This thesis is composed of my original work, and contains no material previously
published or written by another person except where due reference has been made in the
text. I have clearly stated the contribution by others to jointly-authored works that I have
included in my thesis.
I have clearly stated the contribution of others to my thesis as a whole, including
statistical assistance, survey design, data analysis, significant technical procedures,
professional editorial advice, and any other original research work used or reported in my
thesis. The content of my thesis is the result of work I have carried out since the
commencement of my research higher degree candidature and does not include a
substantial part of work that has been submitted to qualify for the award of any other
degree or diploma in any university or other tertiary institution. I have clearly stated which
parts of my thesis, if any, have been submitted to qualify for another award.
I acknowledge that an electronic copy of my thesis must be lodged with the University
Library and, subject to the General Award Rules of The University of Queensland,
immediately made available for research and study in accordance with the Copyright Act
1968.
I acknowledge that copyright of all material contained in my thesis resides with the
copyright holder(s) of that material. Where appropriate I have obtained copyright
permission from the copyright holder to reproduce material in this thesis.
iv
PUBLICATIONS DURING CANDIDATURE
Book (1):
1.
N. Mithulananthan and D.Q. Hung, “Smart integration of distributed generation”,
under preparation.
Published International Journal Articles (7):
2.
D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Determining PV penetration
for distribution systems with time-varying load models, IEEE Transactions on Power
Systems, early access, DOI: 10.1109/TPWRS.2014.2314133 (ERA 2010: ranked A*,
impact factor: 3.530).
3.
D.Q. Hung, N. Mithulananthan, and R.C. Bansal, “An optimal investment planning
framework for multiple DG units in industrial distribution systems”, Applied Energy,
volume 124, pages 67-72, July 2014 (ERA 2010: ranked A, impact factor: 5.261).
4.
D.Q. Hung, and N. Mithulananthan, “Loss reduction and loadability enhancement
with DG: A dual-index analytical approach”, Applied Energy, volume 115, pages
233-241, February 2014 (ERA 2010: ranked A, impact factor: 5.261).
5.
D.Q. Hung, N. Mithulananthan, and R.C. Bansal, “Integration of PV and BES units
in commercial distribution systems considering energy losses and voltage stability”,
Applied Energy, volume 113, pages 1162-1170, January 2014 (ERA 2010: ranked A,
impact factor: 5.261).
6.
D.Q. Hung, N. Mithulananthan and R. C. Bansal, “Analytical strategies for
renewable distributed generation integration considering energy loss minimization,”
Applied Energy, volume 105, pages 75-85, May 2013 (ERA 2010: ranked A, impact
factor: 5.261).
7.
D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Optimal placement of
dispatchable and nondispatchable renewable DG units in distribution networks for
minimising energy loss,” International Journal of Electrical Power and Energy
Systems, volume 55, pages 179-186, February 2014 (ERA 2010: ranked C, impact
factor: 3.432).
8.
D.Q. Hung, N. Mithulananthan, and R.C. Bansal, “A combined practical approach
for distribution system loss reduction”, International Journal of Ambient Energy, in
Press, DOI: 10.1080/01430750.2013.829784.
v
Submitted International Journal Articles (1):
9.
D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Probabilistic voltage profile
optimization with electric vehicles and PV units in commercial systems,” under
preparation, to be submitted to IEEE Transactions on Power Systems.
International Conference Papers (7)
10.
D.Q. Hung, and N. Mithulananthan, “Assessing the impact of loss reduction on
distributed generation investment decisions,” in Proceedings of 23nd Australasian
Universities Power Engineering Conference, Tasmania, Australia, 29 September - 3
Oct. 2013.
11.
D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Placement of photovoltaic and
battery energy storage units in distribution systems considering energy loss,” in
Proceedings of International Smart Grid Conference & Exhibition, Seoul, Korean, 811 July 2013.
12.
D.Q. Hung and N. Mithulananthan, "A Simple approach for distributed generation
integration considering benefits for DNO," in Proceedings of IEEE International
Conference on Power Systems Technology, Auckland, New Zealand, 30 October - 2
November 2012.
13.
D.Q. Hung and N. Mithulananthan, “A dual-index based analytical approach for DG
planning considering power losses,” in Proceedings of 22nd Australasian Universities
Power Engineering Conference, Bali, Indonesia, 26-29 September 2012.
14.
D.Q. Hung and N. Mithulananthan, "An optimal operating strategy of DG unit for
power loss reduction in distribution systems," in Proceedings of 7th IEEE
International Conference on Industrial and Information Systems, Chennai, India, 0609 August 2012.
15.
D.Q. Hung and N. Mithulananthan, “Alternative analytical approaches for renewable
DG allocation for energy loss minimization,” in Proceedings of IEEE Power and
Energy Society General Meeting, USA, 22-26 July 2012.
16.
D.Q. Hung and N. Mithulananthan, “Community energy storage and capacitor
allocation in distribution systems,” in Proceedings of 21st Australasian Universities
Power Engineering Conference, Brisbane, Australia, 25-28 September 2011.
vi
PUBLICATIONS INCLUDED IN THIS THESIS
1. D.Q. Hung, N. Mithulananthan and R. C. Bansal, “Analytical strategies for renewable
distributed generation integration considering energy loss minimization,” Applied
Energy, volume 105, pages 75-85, May 2013 – Partially incorporated as Chapters 2 and
4.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (15%)
Reviewed the paper (15%)
R. C. Bansal
Discussion on results (5%)
Reviewed the paper (5%)
2. D.Q. Hung, and N. Mithulananthan “Loss reduction and loadability enhancement with
DG: A dual-index analytical approach”, Applied Energy, volume 115, pages 233-241,
February 2014 – Partially incorporated as Chapter 4.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (20%)
Reviewed the paper (20%)
vii
3. D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Optimal placement of
dispatchable and nondispatchable renewable DG units in distribution networks for
minimising energy loss,” International Journal of Electrical Power and Energy
Systems, volume 55, pages 179-186, February 2014 – Partially incorporated as Chapters
2 and 5.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (15%)
Reviewed the paper (15%)
Kwang Y. Lee
Discussion on results (5%)
Reviewed the paper (5%)
4. D.Q. Hung, N. Mithulananthan, and Kwang Y. Lee, “Determining PV penetration for
distribution systems with time-varying load models, IEEE Transactions on Power
Systems, early access, DOI: 10.1109/TPWRS.2014.2314133 – Incorporated as
Chapters 2, 3 and 6.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (15%)
Reviewed the paper (15%)
Kwang Y. Lee
Discussion on results (5%)
Reviewed the paper (5%)
viii
5. D.Q. Hung, N. Mithulananthan, and R.C. Bansal, “Integration of PV and BES units in
commercial distribution systems considering energy losses and voltage stability”,
Applied Energy, volume 113, pages 1162-1170, January 2014 – Incorporated as
Chapters 2, 3 and 7.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (15%)
Reviewed the paper (15%)
R. C. Bansal
Discussion on results (5%)
Reviewed the paper (5%)
6. D.Q. Hung, N. Mithulananthan, and R.C. Bansal, “An optimal investment planning
framework for multiple DG units in industrial distribution systems”, accepted for
publication in Applied Energy, volume 124, pages 67-72, July 2014 – Partially
incorporated as Chapters 2, 3 and 8.
Contributor
Statement of contribution
Duong Quoc Hung
Programming, simulation and modelling (100%)
Result interpretation and discussion (80%)
Wrote the paper (80%)
N. Mithulananthan
Discussion on results (15%)
Reviewed the paper (15%)
R. C. Bansal
Discussion on results (5%)
Reviewed the paper (5%)
ix
Contributions by Others to the Thesis
No contributions by others.
Statement of Parts of the Thesis Submitted to Qualify for the Award of another
Degree
None.
x
ACKNOWLEDGEMENTS
One of the most rewarding achievements in my life to date is the completion of my
doctoral dissertation at The University of Queensland, which is one of the world’s top
universities. I would like to take this opportunity to convey my immense gratitude to all
those persons who have given their valuable support and assistance.
First and foremost, I would like to express my sincere gratitude and profound respect to
my supervisor Dr. N. Mithulananthan for his understanding, continuous intellectual
support, invaluable advice and constant encouragement of my endeavours throughout my
study. He was very generous with his time and knowledge, and assisted me enthusiastically
in each step to complete the thesis. I am also grateful to him for his important advice on
my future career.
I am profoundly indebted to my associate supervisor Prof. R.C. Bansal from University
of Pretoria for his help, suggestions and enlightening discussions towards my research.
Thanks also go to Prof. Kwang Y. Lee from Baylor University for his constructive
comments and guidance.
I would like to acknowledge the financial support of the Government of Australia
through the International Postgraduate Research Scholarship and The University of
Queensland through the UQ Centennial Scholarship.
I would also like to extend thanks to all my colleagues and staffs from the Power and
Energy Group of The University of Queensland for their help during my study.
Last but not least, special thanks go to my whole family, especially my beloved parents,
wife and son, who have been an important and indispensable source of motivation and
inspiration. I love my family. This thesis is dedicated to them.
“Live a good, honourable life. Then when
you get older and think back, you’ll be able
to enjoy it a second time.”
xi
KEYWORDS
Battery energy storage, biomass, distributed generation planning, distribution system,
energy loss, optimal power factor, photovoltaic, voltage deviation, voltage stability, wind.
Australian and New Zealand Standard Research Classifications (ANZSRC)
ANZSRC code: 090607, Power and Energy Systems Engineering (excl. Renewable
Power), 70%
ANZSRC code: 090608, Renewable Power and Energy Systems Engineering (excl.
Solar Cells), 30%
Fields of Research (FoR) Classification
FoR code: 0906, Electrical and Electronic Engineering, 100%
xii
TABLE OF CONTENTS
1
2
Introduction
1.1
Background ......................................................................................................... 1
1.2
Research Objectives ............................................................................................ 2
1.3
Thesis Outline ..................................................................................................... 3
Literature Review
4
2.1
Introduction......................................................................................................... 4
2.2
Technologies of DG and BES............................................................................. 4
2.3
3
1
2.2.1
Solar Photovoltaic................................................................................... 4
2.2.2
Wind Turbines ........................................................................................ 5
2.2.3
Biomass Gas Turbines ............................................................................ 5
2.2.4
Battery Energy Storage........................................................................... 6
Renewable DG Integration.................................................................................. 6
2.3.1
Technical Benefits .................................................................................. 7
2.3.2
Environmental Benefits ........................................................................ 12
2.3.3
Economical Benefits ............................................................................. 13
2.4
Renewable DG Integration with BES ............................................................... 15
2.5
Grid Codes for DG Integration ......................................................................... 16
2.6
Summary ........................................................................................................... 16
Load and Generation Modelling and Test Systems
18
3.1
Introduction....................................................................................................... 18
3.2
Load Modelling................................................................................................. 18
3.3
Generation Modelling ....................................................................................... 19
3.3.1
Dispatchable Generation....................................................................... 19
xiii
3.4
3.5
4
3.3.2
Nondispatchable Generation................................................................. 20
3.3.3
DG Penetration Level ........................................................................... 22
3.3.4
Generation Criteria ............................................................................... 22
Software Tools and Test Systems ..................................................................... 22
3.4.1
33-Bus Test System .............................................................................. 22
3.4.2
69-Bus One Feeder Test System........................................................... 23
3.4.3
69-Bus Four Feeder Test System.......................................................... 24
Summary ........................................................................................................... 24
Analytical Expressions for Renewable DG Integration
25
4.1
Introduction....................................................................................................... 25
4.2
Load and Renewable DG Modelling ................................................................ 26
4.3
4.4
4.2.1
Load Modelling .................................................................................... 26
4.2.2
Renewable DG Modelling .................................................................... 27
Problem Formulation ........................................................................................ 28
4.3.1
Power Loss............................................................................................ 28
4.3.2
Impact of the Size and Power Factor of DG on Power Losses............. 32
4.3.3
Energy Loss .......................................................................................... 33
Proposed Methodology ..................................................................................... 33
4.4.1
Approach 1 (A1) ................................................................................... 33
4.4.2
Approach 2 (A2) ................................................................................... 35
4.4.3
Approach 3 (A3) ................................................................................... 37
4.4.4
Computational Procedure ..................................................................... 39
4.5
Exhaustive Load Flow Solution........................................................................ 42
4.6
Case Study......................................................................................................... 42
4.6.1
Test System........................................................................................... 42
xiv
4.6.2
4.7
5
Summary ........................................................................................................... 54
Wind and Biomass Integration for Energy Loss Reduction
56
5.1
Introduction....................................................................................................... 56
5.2
Load and Renewable DG Modelling ................................................................ 57
5.2.1
Load Modelling .................................................................................... 57
5.2.2
Renewable DG Modelling .................................................................... 57
5.3
Problem Formulation ........................................................................................ 58
5.4
Proposed Methodology ..................................................................................... 59
5.5
5.6
6
Numerical Results................................................................................. 42
5.4.1
Expression for Sizing DG at Predefined Power Factor ........................ 59
5.4.2
Proposed Expressions for Sizing DG at Optimal Power Factor ........... 60
5.4.3
Computational Procedure ..................................................................... 61
Case Study......................................................................................................... 65
5.5.1
Test System........................................................................................... 65
5.5.2
DG Placement without Considering Power Factor Limit..................... 66
5.5.3
Biomass versus Wind ........................................................................... 70
5.5.4
Voltage Profiles .................................................................................... 70
5.5.5
Power Factor Impact on Energy Loss................................................... 71
Summary ........................................................................................................... 73
Multi-Objective PV Integration
74
6.1
Introduction....................................................................................................... 74
6.2
Load and Solar PV Modelling .......................................................................... 75
6.2.1
Load Modelling .................................................................................... 75
6.2.2
Solar PV Modelling .............................................................................. 75
6.2.3
Combined Generation-Load Model ...................................................... 78
xv
6.3
6.4
6.5
6.6
7
Problem Formulation ........................................................................................ 78
6.3.1
Impact Indices....................................................................................... 78
6.3.2
Multiobjective Index............................................................................. 81
Proposed Analytical Approach ......................................................................... 83
6.4.1
Sizing PV .............................................................................................. 83
6.4.2
Computational Procedure ..................................................................... 85
Case Study......................................................................................................... 86
6.5.1
Test Systems ......................................................................................... 86
6.5.2
Location Selection ................................................................................ 88
6.5.3
Sizing with Respect to Indices.............................................................. 91
6.5.4
PV Penetration and Energy Losses....................................................... 93
Summary ........................................................................................................... 95
PV and BES Integration for Energy Loss and Voltage Stability
96
7.1
Introduction....................................................................................................... 96
7.2
Load and Generation Modelling ....................................................................... 97
7.3
7.4
7.2.1
Load Modelling .................................................................................... 97
7.2.2
Nondispatchable PV Modelling............................................................ 97
7.2.3
Dispatchable BES Modelling ............................................................... 98
Problem Formulation ........................................................................................ 98
7.3.1
Conceptual Design................................................................................ 98
7.3.2
Impact Indices..................................................................................... 100
7.3.3
Multiobjective Index........................................................................... 101
7.3.4
Energy Loss and Voltage Stability ..................................................... 102
Proposed Methodology ................................................................................... 104
7.4.1
Proposed Analytical Expressions ....................................................... 104
xvi
7.4.2
7.5
7.6
8
Case Study....................................................................................................... 108
7.5.1
Test System......................................................................................... 108
7.5.2
Numerical Results............................................................................... 109
Summary ......................................................................................................... 116
Benefit and Cost Analyses for Biomass Integration
117
8.1
Introduction..................................................................................................... 117
8.2
Load and DG Modelling ................................................................................. 118
8.3
8.4
8.5
8.6
9
Self-Correction Algorithm.................................................................. 106
8.2.1
Load Modelling .................................................................................. 118
8.2.2
DG Modelling..................................................................................... 119
Problem Formulation ...................................................................................... 119
8.3.1
Impact Indices..................................................................................... 119
8.3.2
Multiobjective Index........................................................................... 120
8.3.3
Technical Constraints ......................................................................... 121
8.3.4
Energy Loss and Voltage Stability ..................................................... 121
8.3.5
Benefit and Cost Analysis .................................................................. 122
Proposed Methodology ................................................................................... 124
8.4.1
Optimal Power Factor......................................................................... 124
8.4.2
Computational Procedure ................................................................... 127
Case Study....................................................................................................... 127
8.5.1
Test System......................................................................................... 127
8.5.2
Assumptions and Constraints ............................................................. 128
8.5.3
Numerical Results............................................................................... 129
Summary ......................................................................................................... 137
Conclusions
138
xvii
9.1
Summary ......................................................................................................... 138
9.2
Contributions................................................................................................... 141
9.3
Future Research............................................................................................... 142
Bibliography
143
Appendix A
155
Appendix B
160
xviii
LIST OF FIGURES
2.1
Overall DG benefits...................................................................................................... 7
3.1
The 33-bus test distribution system............................................................................ 23
3.2
The 69-bus test distribution system (one feeder). ...................................................... 23
3.3
The 69-bus test distribution system (four feeders). .................................................... 24
4.1
Normalized daily load demand curve......................................................................... 27
4.2
Normalized daily wind and PV output curves............................................................ 28
4.3
Impact of the size and power factor of a DG unit on system active power loss. ....... 32
4.4
Daily curves for (a) demand and (b) system power losses without a DG unit........... 43
4.5
Daily curves at bus 61: (a) dispatchable biomass DG output and (b) system
power losses with a dispatchable biomass DG unit.................................................... 45
4.6
Daily curves at bus 61: (a) nondispatchable biomass DG output and (b) system
power losses with a nondispatchable biomass DG unit.............................................. 47
4.7
Daily curves at bus 61: (a) wind DG output and (b) system power losses with a
wind DG unit. ............................................................................................................. 48
4.8
Daily curves at bus 61: (a) PV DG output and (b) system power losses with a
PV DG unit. ................................................................................................................ 49
4.9
Maximum and actual penetration for scenarios 2-5. .................................................. 51
4.10 Annual energy loss reduction for scenarios 2-5. ........................................................ 51
4.11 Voltage profiles at extreme periods for scenarios 1-5................................................ 51
4.12 DG placement with different power factors for scenarios 2-3. .................................. 53
4.13 DG placement with different power factors for scenarios 4-5. .................................. 54
5.1
Normalized hourly load demand curve. ..................................................................... 57
5.2
Normalized hourly wind output curve........................................................................ 58
5.3
Hourly optimal generation curve of biomass DG unit. .............................................. 62
5.4
Hourly optimal generation curve of nondispatchable wind DG unit. ........................ 64
5.5
Hourly optimal generation curve of wind-biomass DG mix. ..................................... 65
5.6
Hourly load demand and power loss curves (scenario 1)........................................... 67
xix
5.7
Hourly optimal generation curve of biomass DG units (scenario 2).......................... 67
5.8
Hourly optimal generation curve of wind DG units (scenario 3). .............................. 68
5.9
Hourly optimal generation curve of wind-biomass DG mix (scenario 4). ................. 68
5.10 Hourly power loss curve in scenarios 1-4. ................................................................. 68
5.11 Hourly percentage power loss reduction in scenarios 2-4.......................................... 70
5.12 Voltage profile at extreme periods (period 59) for scenarios 1-4. ............................. 71
5.13 Impact of the power factor of DG units on energy loss reduction. ............................ 73
6.1
Normalized daily demand curve for various customers. ............................................ 75
6.2
PDF for solar irradiance at hours 8, 12 and 16........................................................... 77
6.3
Expected output of a PV module at hours 8, 12 and 16. ............................................ 77
6.4
A radial distribution system: (a) without PV and (b) with PV. .................................. 79
6.5
The 69-bus test distribution system............................................................................ 87
6.6
The 33-bus test distribution system............................................................................ 87
6.7
Expected PV output for hours: (a) 6-10, (b) 11-15 and (c) 16-19. ............................. 89
6.8
Normalized daily expected PV output........................................................................ 90
6.9
PV size with respect to IMO at various locations at average load level for the
industrial load model: (a) 69-bus system and (b) 33-bus system. .............................. 90
6.10 Hourly expected PV outputs at bus 61 for the 69-bus system for different timevarying load models. .................................................................................................. 91
6.11 Hourly expected IMO curves for the 69-bus system with a PV at bus 61 for
different time-varying load models. ........................................................................... 92
6.12 PV size and indices for the 69-bus system with PV at bus 61 for different timevarying load models. .................................................................................................. 92
6.13 PV penetration levels in the 69- and 33-bus systems. ................................................ 94
7.1
Conceptual model of grid-connected PV-BES system: (a) Connection diagram
and (b) Charging and discharging characteristics of BES and PV output.................. 99
7.2
Hybrid PV-BES system impact on maximum loadability and voltage stability
margin....................................................................................................................... 103
7.3
Daily PV-BES outputs, power factor and index curves for scenario 1: (a) PVBES outputs, (b) Power factor of PV-BES units, (c) Indices with three PV-BES
units. ......................................................................................................................... 110
xx
7.4
Daily charging and discharging curves of BES unit at bus 12 for scenario 1. ......... 112
7.5
PV-BES impact on energy loss. ............................................................................... 115
7.6
PV-BES impact on maximum loadability and voltage stability margin. ................. 115
7.7
Voltage profiles at extreme periods for all scenarios. .............................................. 115
8.1
Nominalised Load duration curve. ........................................................................... 118
8.2
Single line diagram of the 69-bus test distribution system with DG units............... 130
8.3
Indices (ILP, ILQ and IMO) for the system with various numbers of DG units
over planning horizon............................................................................................... 131
8.4
Losses of the system with and without DG units over planning horizon................. 132
8.5
Voltage stability margin curves for all scenarios over planning horizon................. 133
8.6
NPV at various average DG utilization factors for different scenerios over
planning horizon....................................................................................................... 136
8.7
Percentage ratio of the total demand plus loss to the thermal transformer limit
over planning horizon............................................................................................... 136
xxi
LIST OF TABLES
3.1
Load types and exponents for voltage-dependent loads............................................. 19
4.1
Dispatchable biomass DG placement ......................................................................... 45
4.2
Nondispatchable biomass DG placement................................................................... 47
4.3
Nondispatchable wind DG placement ........................................................................ 48
4.4
Nondispatchable PV DG placement ........................................................................... 49
5.1
Optimal DG placement without considering power factor limit ................................ 69
5.2
Optimal DG placement without considering power factor limit ................................ 69
5.3
Optimal DG placement considering power factor limit ............................................. 72
5.4
Optimal DG placement considering power factor limit ............................................. 72
6.1
PV allocation in the 69- and 33-Bus Systems ............................................................ 93
6.2
Energy loss reduction over a day for 69 and 33-Bus Systems ................................... 94
7.1
PV-BES placement with optimal lagging and unity power factors.......................... 111
7.2
Sizing PV and BES units at optimal lagging power factor (Scenario 1).................. 113
7.3
Sizing PV and BES units at unity power factor (Scenario 2)................................... 113
7.4
Energy loss and voltage stability.............................................................................. 116
8.1
Economic input data. ................................................................................................ 128
8.2
Location, size and power factor of DG units............................................................ 130
8.3
Energy loss and voltage stability over planning horizon.......................................... 133
8.4
Analysis of the present value benefit and cost for different scenarios over
planning horizon....................................................................................................... 135
8.5
Comparison of different scenarios over planning horizon. ...................................... 135
A.1 System data of 33-bus test distribution system ........................................................ 155
A.2 System data of 69-bus test distribution system (one feeder).................................... 156
A.3 System data of 69-bus test distribution system (four feeder) ................................... 158
xxii
B.1 Mean and Standard Deviation of Solar Irradiance ................................................... 160
B.2 Characteristics of the PV module ............................................................................. 160
xxiii
ABBREVIATIONS
ABC
Artificial Bee Colony algorithm
A1, A2, A3
Analytical approach 1, 2 and 3, respectively
BES
Battery Energy Storage
CP
Critical Point
CPF
Continuous Power Flow
CO2
Carbon dioxide
DFIG
Doubly-Fed Induction Generator
DG
Distributed Generation
ELF
Exhaustive Load Flow
GA
Genetic Algorithm
GSA
Gravitational Search Algorithm
HSA
Harmony Search Algorithm
IGA
Immune-Genetic Algorithm
MTLBO
Modified Teaching-Learning Based Optimization
NOx
Nitrogen oxide
OPF
Optimal Power Flow
PDF
Probability Density Function
PSO
Particle Swarm Optimization
PV
Photovoltaic
PV-BES
PV and BES system
SA
Simulated Annealing
SCA
Self-Correction Algorithm
SO2
Sulphur dioxide
VSM
Voltage Stability Margin
xxiv
NOMENCLATURE
AEy
Actual annual emission of the system with DG units (TonCO2)
ALossy
Actual annual energy loss of the system with DG units (MWh)
AIMO
Average multi-objective index
AVSM
Average voltage stability margin of the system
B
Present value benefit over a planning horizon ($)
BCR
Benefit and cost ratio
C
Present value cost over a planning horizon ($)
CDG
Capital cost of DG ($/kW)
CEy
Cost of each ton of generated CO2 ($/TonCO2)
CF
Capacity factor
CLossy
Loss value ($/MWh)
d
Discount rate
E BESk
Total energy stored in the BES unit at bus k
unit
E PV
Amount of PV module generated energy
EIy
Emission incentive ($/year)
Eloss
Total annual system energy loss, MWh
GRID
E PVk
Amount of PV energy delivering to the grid at bus k
E( PV + BES )
Energy amount of a combination of PV and BES units
ILP , ILQ
Active and reactive power loss indices, respectively
IMO
Multi-objective index
I ai
Active current of branch i
I ak
Active current of DG unit at bus k
Ii
Current magnitude of branch i, I i = I ai + I ri
I ri
Reactive current of branch i
I rk
Reactive current of DG unit at bus k
IRR
Internal rate of return
IVD
Voltage deviation index
LF
Load factor
2
xxv
2
LIy
Loss incentive ($/year)
n
Number of branches
N
Number of buses
ND
Network deferral benefit ($/kW)
NPV
Net present value
Ny
Planning horizon (years)
OMy
Annual operation, maintenance and fuel costs ($/year)
opf DGi
Optimal power factor of DG unit at bus i
pf DGi
Power factor of DG unit at bus i
CH
DISCH
PBESk
and PBESk
Charge and discharge power of the BES unit at bus k, respectively
Pbi , Qbi
Active and reactive power flow through branch i respectively
PDGi , QDGi , S DGi
Active, reactive and apparent power sizes of DG unit, respectively at
bus i
PDi , QDi
Active and reactive power of load, respectively at bus i
Pi , Qi
Net active and reactive power injections, respectively at bus i
Pk , Qk
Active and reactive power of the combination of PV and BES units at
bus k
PL , QL
Total system active and reactive power losses without DG unit (MW),
respectively
PLDG , QLDG
Total system active and reactive power losses with DG unit (MW),
respectively
unit
PPV
Maximum output of a PV module unit
p.u. demand(t)
Demand in p.u. at period t
p.u. DG ouput(t)
DG output in p.u. at period t
Ri , X i
Resistance and reactance of branch i
Ry
Annual energy sales ($/year)
TEy
Annual emission target level of the system without DG (TonCO2)
TLossy
Annual energy loss target level of the system without DG (MWh)
VD
Voltage deviation
Vi , δ i
Voltage and angle, respectively at bus i
xxvi
Z ij
ijth element of impedance matrix ( Z ij = rij + jxij )
α ij , βij
Loss coefficients
δ
Growth rate of demand a year
∆AVSM
An increase in the average voltage stability margin
∆E
Energy loss reduction
∆Ploss
System loss reduction due to DG injection, kW
∆t
Time duration, hour
λmax
Maximum loading
ρ
Probability of the solar irradiance
η BES
Round trip efficiency ( η BES = η c × η d )
ηc , η d
Charge and discharge efficiencies of the BES unit
xxvii
CHAPTER 1
INTRODUCTION
1.1
Background
Distributed Generation (DG) based on renewable resources such as solar, wind, ocean,
hydro, biomass and geothermal heat are considered as green power because of the
negligible impact on greenhouse gas emissions. Such sources have emerged as an
alternative energy solution to mitigate the dependence on fossil fuels since the mid-1970s
after the first oil crisis [1]. However, during this period, due to its high energy production
costs along with utility and government disincentives, renewable DG remained relatively
dormant until the mid-2000s [2].
There has been a renewed interest in the deployment of renewable DG since the mid2000s when the issue of global warming came to the forefront of concerns by many parts
of the world [2]. In addition, the technical and economical benefits, government incentives,
and advancement in the technologies have lead to a significantly increased interest in the
usage of renewable DG worldwide. For example, as of 2010, renewable energy supplied an
approximately 16.7% of the global energy consumption [3]. Among all renewable
technologies, solar photovoltaic (PV) grew the fastest with a yearly increase of 58%
worldwide during the period of late 2006 to 2011 and achieved just over 102 GW of the
global installed capacity in 2012 [4]. It is expected that this figure could increase to more
than 423 GW by 2017. This resource is popularly used in Germany and Italy. Wind energy
is growing globally at a yearly rate of 30%, and was just more than 282 GW of the global
capacity at the end of 2012 [3]. Such a resource is popularly used in Europe, Asia, and the
United States.
1
CHAPTER 1. INTRODUCTION
2
From the utilities’ perspective, intermittent renewable DG units (e.g., wind and solar)
located close to loads in distribution systems can create several economical, technical and
environmental benefits. However, the high penetration of such resources, together with
demand variations has introduced many challenges to distribution networks such as power
fluctuations, high losses, voltage rise and low voltage stability [5]. Consequently, in the
last decade, the grid codes in many countries such as the United State, Germany, the
United Kingdom, Denmark, Australia and Spain have been modified to accommodate such
resources [6]. This modification has also aimed at modernizing the electric power grid to
satisfy the demand for higher energy efficiency, reliability and security of the system.
Meanwhile, the concept of the smart grid has been introduced as an important part of this
modification to facilitate high penetration of renewable DG [7]. The smart grid is a
complicated infrastructure as a combination of power systems, telecommunication
communication and information technology. As an integral part of the smart grid, a smart
integration approach is presented in this thesis. The main idea behind the smart integration
is to accommodate and operate renewable DG and associated Battery Energy Storage
(BES) units in distribution networks strategically by considering various technical,
economical and environmental issues.
1.2
Research Objectives
The goal of the thesis is to develop methodologies for strategically planning and operating
renewable DG units along with an efficient usage of BES sources in distribution networks.
This thesis also aims to show how to operate renewable DG units behind the idea of the
optimal power factor to maximize technical and economical benefits. The main objectives
of the research can be highlighted as follows:
1. Develop analytical approaches to locate and size different types of single renewable
DG units with optimal power factor operation for minimising energy losses while
considering the time-varying characteristics of demand and generation.
2. Develop a methodology to locate and size multiple dispatchable biomass and
nondispatchable wind units for minimising energy losses.
3. Develop a methodology to determine intermittent PV penetration for distribution
systems with time-varying load models and probabilistic generation with objectives
of reducing active and reactive power losses and voltage deviation.
CHAPTER 1. INTRODUCTION
3
4. Propose a methodology for sizing hybrid PV and BES units with optimal power
dispatch for reducing energy losses and enhancing voltage stability.
5. Propose a comprehensive framework for biomass DG investment planning with
optimal power factor operation which considers all economical, technical and
environmental aspects over a given planning horizon.
1.3
Thesis Outline
This thesis is organised as follows:
Chapter 2 provides background knowledge about DG and BES technologies, which are
needed to better comprehend this thesis. This chapter also includes an overall literature
review on current approaches for DG and BES integration in distribution systems. Chapter
3 describes the modelling of loads and renewable generation used in the next chapters. The
software tools and test systems used throughout this research is also introduced in this
chapter.
Chapter 4 introduces the idea of optimal DG power factor operation. This introduction
provides a foundation for developing the methodologies with different applications
presented in the next chapters. Three alternative analytical approaches are then presented
in this chapter to accommodate a single renewable DG unit for minimising energy losses
while considering the time-varying characteristics of demand and generation. Chapter 5
presents a methodology to integrate multiple nondispatchable and dispatchable renewable
DG units for minimising energy losses.
Chapter 6 presents a methodology to determine the penetration of PV in distribution
systems with time-varying load models while considering the probabilistic characteristic of
generation. Chapter 7 discusses the integration of hybrid PV and BES units with optimal
power dispatch for reducing energy losses and enhancing static voltage stability. Chapter 8
reports a comprehensive framework for biomass DG planning that considers economical,
technical and environmental aspects.
Finally, Chapter 9 concludes with a summary of the research in this thesis. The
contributions and directions for further research are also presented in this chapter.
CHAPTER 2
LITERATURE REVIEW
2.1
Introduction
This chapter provides an overview of DG and BES technologies. Secondly, it
systematically reports a comprehensive literature review on different issues of DG
integration in distribution systems from the perspective of utilities, covering energy losses,
voltage stability, voltage profiles, network investment deferral, environment, and energy
sales. Thirdly, the issues of renewable DG integration with BES units in distribution
systems are thoroughly reviewed in this chapter. Finally, major limitations and gaps drawn
from the survey are highlighted in this chapter.
2.2
Technologies of DG and BES
DG can be defined as “small-scale generating units located close to the loads that are being
served” [8]. It is possible to classify DG technologies into two broad categories: nonrenewable and renewable energy resources [9]. The former comprises reciprocating
engines, combustion gas turbines, micro-turbines, fuel cells, and micro Combined Heat and
Power (CHP) plants. The latter includes biomass, wind, solar PV, geothermal and tide
power plants. The next subsections provide a brief overview of the technologies of solar
PV, wind and biomass to be considered in this research.
2.2.1 Solar Photovoltaic
Solar PV technologies use some of the properties of semiconductors to directly convert
4
CHAPTER 2. LITERATURE REVIEW
5
sunlight into electricity [1]. The advantages are that these technologies are characterized by
zero emissions, silent operation, and a long life service. They also require low maintenance
and no fuel costs. In addition, solar energy is redundant and inexhaustible. However, it is
weather-dependent, intermittent and unavailable during the night. Given a high PV
penetration level together with demand variations, power distribution systems would
experience power fluctuations along with unexpected voltage rise, high losses and low
voltage stability. Another drawback is that PV technologies require a high-capital
investment cost.
2.2.2 Wind Turbines
Wind turbines are devices that convert kinetic energy from the wind into electricity. They
can be classified into two types: vertical axis wind turbines and horizontal axis wind
turbines [1]. Like solar PV, wind turbines are emissions free and require no fuel costs.
Wind energy is also redundant and inexhaustible. However, the main challenges are that
wind turbines have an unpredictable and intermittent output, and a high-capital investment
cost. In addition, the simultaneous occurrence of excessive wind generation and low
demand could lead to the possibility of encountering voltage rise, high losses and low
voltage stability in power distribution systems.
2.2.3 Biomass Gas Turbines
Biomass power plants can generate electricity using a steam cycle where biomass raw
materials such as waste are converted into steam in a boiler [1]. The resulting steam is then
used to spin a turbine which is connected to a generator. Alternatively, biomass materials
can be converted to biogas. This biogas can be cleaned and upgraded to natural gas
standards when it becomes bio methane. The biogas can be used in a gas turbine, pistondriven engine or fuel cells to generate electricity. The advantage is that as a renewable
energy source, biomass-based power plants produce low emission.
As reported in [10], gas turbines have smaller sizes than any other source of rotating
power and provide higher reliability than reciprocating engines. They also have superior
response to load variations and excellent steady state frequency regulation when compared
to steam turbines or reciprocating engines. In addition, gas turbines require lower
maintenance and produce lower emissions than reciprocating engines.
CHAPTER 2. LITERATURE REVIEW
6
2.2.4 Battery Energy Storage
In addition to the wind, solar PV and biomass presented above, energy storage is also
considered in this thesis. This source is becoming a crucial component in the distribution
system, especially in the smart grid, to enhance the reliability, efficiency and sustainability.
More importantly, energy storage can support to accommodate a high penetration level of
intermittent renewable DG.
Energy storage is being developed in a variety of solutions such as batteries, flywheels,
ultracapacitors and superconducting energy storage systems. Among them, Battery Energy
Storage (BES) has recently emerged as one of the most promising near-term storage
technologies for power applications [11]. There are a number of leading battery
technologies such as lead-acid, nickel cadmium, nickel-metal hydride and lithium iron.
Among them, the lead-acid battery is the oldest, most mature technology, and low
investment costs [12]. Another advantage is that it can be designed for bulk energy storage
or for rapid charge and discharge; however, it is limited in terms of low energy efficiency
and short cycle life [11]. The rest of the battery technologies also present promise for
energy storage applications. These technologies have higher energy density capabilities
than lead-acid batteries, but they are currently not cost-effective for higher power
applications [11].
2.3
Renewable DG Integration
From the perspective of utilities, DG units can bring multiple technical benefits to
distribution networks such as loss reduction, voltage profile improvement, voltage
stability, network upgrade deferral and reliability while supplying energy sales as a
primary task. These can be classified into three major categories: economic, technical and
environmental benefits, as illustrated in Figure 2.1. In addition, DG units can participate
into the competitive market to provide ancillary services such as spinning reserve, voltage
regulation, reactive power support and frequency control [13-15]. However, the
inappropriate planning and operations of these resources may lead to high losses, voltage
rise and low system stability as a result of reverse power flow [5, 16]. Consequently, it is
necessary to develop proper methodologies to accommodate renewable DG resources.
DG planning considering various technical, economical and environmental issues has
CHAPTER 2. LITERATURE REVIEW
7
been discussed considerably over the last fifty-years [17]. The aim of researches is to bring
a wide variety of benefits shown in Figure 2.1 to distribution systems while satisfying
technical constraints such as penetration levels, bus voltages and feeder thermal capacity.
Some of the relevant methodologies found in the literature are reported below.
DG
integration
Loss reduction
Voltage
stability
Technical
benefit
Environmental
benefit
Economical
benefit
Voltage profile
Reliability
Network
upgrade
deferral
Figure 2.1. Overall DG benefits.
2.3.1 Technical Benefits
Energy Losses
The distribution system is well-known for its high R/X ratio and significant voltage drops
that could cause substantial power losses along the feeders. It is added that the distribution
loss is normally higher than the transmission loss. For instance, a study in [18] has showed
that an American Electric Power’s distribution system incurred a loss in the range of 6-8%
when compared to the transmission loss of 2.5-7.5%. This figure would be higher in radial
distribution systems with a high R/X ratio. Consequently, distribution loss reduction has
been one of the greatest challenges to power distribution utilities worldwide. It is necessary
to study the loss reduction at the distribution system level.
The system loss reduction at the distribution system level could be one of the major
benefits due to its impact on the utilities’ revenue. In addition, as a key consideration for
CHAPTER 2. LITERATURE REVIEW
8
DG planning, the loss reduction can lead to positive impacts on system capacity release,
voltage profiles and voltage stability [19]. DG planning methods for minimising losses can
be classified into two groups, namely power and energy losses.
The optimal DG placement and sizing issues for minimising power losses in distribution
networks have attracted great attention in recent years. Most traditional methods have
assumed that DG units are dispatchable and placed at the peak load [20]. Typical examples
for such researches are analytical methods [21-25], numerical approaches [19, 26, 27] and
a wide range of heuristic algorithms such as Simulated Annealing (SA) [28], Genetic
Algorithm (GA) [29], Particle Swarm Optimization (PSO) [30, 31], Artificial Bee Colony
(ABC) algorithm [32], Modified Teaching-Learning Based Optimization (MTLBO) [33],
and Harmony Search Algorithm (HSA) [34]. However, such traditional methods may not
address a practical case of the time-varying characteristics of demand and renewable
generation (e.g., nondispatchable wind output) as the optimum DG size at the peak demand
may not remain at other loading levels. Hence, the energy loss minimization may not be
optimal.
Recently, there are two major approaches based on time-series and probabilistic models
found in the literature to estimate energy losses in the presence of DG, especially
intermittent renewable resources. For the first model, few studies have presented
renewable DG integration for minimising energy losses that considers the time-varying
characteristics of demand and generation. For example, wind DG units were sized using a
GA-based approach [35] and an Optimal Power Flow (OPF)-based method [26], but the
locations were not considered in these works. For the second model, a probabilistic
planning method was introduced to accommodate renewable resources mix (i.e. biomass,
wind and solar) while considering the time-varying demand and probabilistic generation
[27]. The loads were assumed to follow the hourly load profile of IEEE-RTS system [36].
The probabilistic nature of wind speed and solar irradiance was respectively described
using the Weibull and Beta Probability Density Function (PDF) models [37, 38]. Biomass
DG units were assumed to have constant rated outputs without associated uncertainties. A
combined generation-load model was proposed to incorporate the DG output powers as
multistate variables in the problem planning. In addition, a planning method that considers
the probability of both demand and generation for locating and sizing wind and PV-based
DG units were also reported in [19, 39]. In general, the time-series or probabilistic
CHAPTER 2. LITERATURE REVIEW
9
planning method can provide a more accurate result than the traditional planning approach
presented earlier. In addition, the relevant literature review shows that most of the existing
studies have assumed that DG units operate at pre-specified power factor, normally unity
power factor under the current standard IEEE 1547. In such researches, only the location
and size have been considered, while the optimal power factor for each DG unit that would
be a crucial part for minimising energy losses has been neglected. Depending on the
characteristics of loads served, each DG unit that can deliver both active and reactive
power at optimal power factor may have positive impacts on energy loss reduction.
Voltage Stability
The voltage stability at the transmission system level has been studied considerably over
the last thirty-years [40]. Voltage instability normally occurs under heavily loaded system
conditions together with deficient reactive power support and this may lead to voltage
collapse. At the distribution system level, the voltage instability has been identified for the
last decade. For instance, a voltage instability problem in a power distribution network that
was widespread to a corresponding power transmission network caused a major blackout in
the S/SE Brazilian system in 1997 [41]. Another study has reported that under critical
loading conditions in a certain industrial area, the distribution network experienced voltage
collapse [42]. In recent years, due to high intermittent renewable penetration, sharply
increased loads and the demand for higher system security, it is necessary to study the
voltage stability at the distribution system level.
The DG placement and sizing of DG units for enhancing voltage stability in the
distribution system are a new concept, but this topic has attracted the interest of some
recent research efforts. Like the DG allocation for minimising power losses, most
traditional methods for enhancing voltage stability have assumed that DG units are
dispatchable and placed at the peak load. Typical examples of such studies are iterative
techniques based on Continuous Power Flow (CPF) [43, 44], a hybrid of model analysis
and CPF [45], a power stability index-based method [46], a numerical approach [47] and
heuristic algorithms such as SA [28] and PSO [48-50]. Although well-suited to
accommodate dispatchable DG units such as gas turbines, the approaches presented above
may not solve a practical scenario that considers the time-characteristics of the varying
demand and nondispatchable renewable DG output.
CHAPTER 2. LITERATURE REVIEW
10
Recently, a probabilistic planning approach was successfully developed for renewable
DG allocation (i.e., biomass, wind and solar) that considers the varying-time demand and
probabilistic generation [51]. This model was presented in the previous study in [27] to
accommodate renewable DG units for minimising energy losses. In [51], a sensitivity
technique was used for searching the candidate buses to effectively reduce the search
space. However, studies [22, 47, 52] indicated that sensitivity techniques may not be
effective to capture the candidate buses for DG installation on radial distribution feeders
with goals of minimising losses and enhancing voltage stability. Using these techniques
would also potentially limit DG penetration levels in the feeders since the most sensitive
buses are normally found at the end of feeders as reported in [25, 34, 43-45, 51, 52].
Another limitation of the study in [51] as well as [28, 43-50] is that the optimal power
factor for each DG unit was not considered. Depending on the nature of loads served, DG
operation at optimal power factor may have positive impacts on the voltage stability.
Voltage Profiles
The voltage profile issue of distribution systems, which is relevant to power quality, is
normally less important than the energy loss from the viewpoint of utilities. However, in
recent years, it appears that due to high intermittent renewable DG penetration, there has
been an increasing interest in the voltage profile issue at the distribution system level [53].
The voltage profile is normally considered together with technical respects and system
constraints, which can be formulated as a multiobjective, for determining the location and
size of DG units. For example, exhaustive load flow analyses were adopted to address
multiobjective index [54, 55]. This index is defined as a combination of impact indices by
assigning a weight for each one. These impact indices are related to active and reactive
power losses, voltage drops, conductor capacity and short-circuit currents. Similarly, a
study in [56] proposed a hybrid of PSO and Gravitational Search Algorithm (PSO-GSA).
The aim is to minimize the multiobjective index, which is a combination of different
indices related to power losses, voltage profiles, MVA capacity, emissions, and the number
of DG units. Overall, a constant load model was assumed in the works presented above.
However, the importance of the voltage-dependent load models also needs to be examined.
Recently, few studies [29, 57, 58] indicated that the voltage-dependent load models (i.e.,
industrial, residential and commercial) considerably affect the DG penetration planning
CHAPTER 2. LITERATURE REVIEW
11
when compared to the constant load model. The research in [29] presented a multiobjective
optimization planning using GA to allocate a DG unit in distribution networks with
different load models. The multiobjective index is a combination of various impact indices
related to active and reactive power losses, system MVA capacity and voltage profiles. It
was shown that DG allocation with different types load models can produce dissimilar
outcomes in terms of locations and sizes. Similarly, a multiobjective planning approach
was developed using PSO for multiple DG allocation in distribution networks with
different load models [58]. The multiobjective index is a combination of different indices
related to active and reactive power losses, voltage profiles, MVA capacity and short
circuit levels. However, the above works assumed that DG units are dispatchable and
allocated at the peak load demand. Although a research in [59] indicated the effect of timevarying load models on energy loss assessment in a distribution system with wind DG
units, the optimal location and size were not addressed. Another study in [60] reported that
time-varying voltage-dependent load models have a critical impact on the location and size
of DG. The benefit is the energy sales from DG, while the costs are related to DG
investment, operation and imported energy. However, nondispatchable renewable DG that
considers time-varying load models and probabilistic generation was not reported in this
work.
Network Upgrade Deferral
The network upgrade deferral is the ability to defer the required investment on reinforcing
feeders and transformers due to DG connection. In the last decade, it has been reported that
the network upgrade deferral is an attractive option for DG planning to meet load growth
[61-63]. The study in [61] showed that depending on technologies adopted, DG units have
diverse impacts on the network deferral. For example, due to their intermittency, wind
units have the ability to release the overloads of power networks less than CHP units. In
addition, the report in [62] indicated that DG operation at lagging power factor, which
delivers both active and reactive power, obtains a higher benefit than DG generation at
unity and leading power factor. However, the importance of the location and size of DG
units needs to be considered.
The issues of locating and sizing DG units for deferring the distribution network
investment are normally evaluated with other associated aspects such as technical and
CHAPTER 2. LITERATURE REVIEW
12
economical benefits and system constraints. For example, DG placement for maximizing
the benefits of network upgrade deferral and loss reduction were reported using different
approaches: hybrid GA-OPF [64], ordinal optimization [65] and Immune-Genetic
Algorithm (IGA) [66]. Moreover, an OPF-based method was proposed for distribution
system planning in the presence of DG over a given planning horizon [67]. The objective is
to minimize the costs related to feeder reinforcement, operation and energy losses.
Similarly, a multiyear multiperiod OPF-based method was successfully developed for DG
planning considering the network investment deferral [68, 69]. Another study in [70]
developed a GA-based multiobjective framework to locate and size DG units to find the
best compromise between the network upgrade deferral and the costs related to energy
losses, unserved energy, and imported energy. In addition, a recent study in [71] proposed
a GA-based approach to place and size renewable DG units (i.e., biomass, wind and solar)
for maximizing the benefits from deferring network investments and reducing energy
losses and interruption costs. The probability of renewable energy and the variability of
demand were also incorporated in this approach.
In addition to the benefits presented above, reliability is another technical benefit that
DG can bring to distribution systems. However, it was not considered in this thesis.
2.3.2 Environmental Benefits
The global climate change agreements such as Kyoto Protocol aim at reducing greenhouse
gas emissions. Three main components to emissions from electricity production are namely
carbon dioxide (CO2), nitrogen oxide (NOX) and sulphur dioxide (SO2). These components
are emitted from the centralized power plants due to burning fossil fuels. Emissions can be
lowered by increasing the amount of clean and renewable energy DG resources in power
systems, thereby reducing the usage of electricity generated from centralized power plants
[72]. For example, a British study estimated that CHP-based power plants reduced an
estimated 41% of CO2 emission in 1999 [17]. Similarly, a report on the Danish power
system showed that the usage of DG contributed an emission reduction of 30% during the
period of 1998-2001. However, DG technologies adopted may have a significant impact on
the amount of emission reduction. For example, renewable DG technologies such as
biomass, wind and solar PV produce low or zero emissions when compared to nonrenewable DG technologies, which consume fossil fuels, such as fuel cells, natural gas
CHAPTER 2. LITERATURE REVIEW
13
turbine engines and micro-turbines. It is clear that increasing DG penetration in
distribution systems can reduce emissions. However, this could be limited by technical and
economical aspects and system constraints.
The literature shows that different approaches have been developed for locating and
sizing DG units for maximizing emission reduction associated with technical and
economical benefits while satisfying system constraints. For example, a honey bee mating
optimization approach was proposed to reduce the emission while minimising the DG
installation and operation costs, voltage deviation and energy loss [73]. Similarly, a
multiobjective planning model based on an IGA approach was presented to reduce the
emission while minimising the costs related to DG installation and operation, network
reinforcement and imported electricity [74]. In a similar study [75], a multiobjective
planning model was developed to make a trade-off between emission and cost reductions.
The cost is related to DG investment and operation, energy loss and imported energy.
However, the limitation of studies [73-75] is that DG units were assumed to operate as a
dispatchable source without associated uncertainties. In contrast to these works, a GAbased multiobjective model was developed for wind DG planning that considers the
uncertainty of generation [76]. The objective is to improve the reliability while minimising
the costs related to DG investment and operation, and emission penalty.
2.3.3 Economical Benefits
In addition to the technical and environmental benefits from DG units thoroughly
discussed above, it is necessary to consider a comprehensive work through their cost and
benefit analysis including the energy sales. The monetary values converted from the
technical and environmental benefits from DG units are also included in the analysis.
The literature review presented in the previous subsections shows that considerable
works have presented DG planning. However, most of them have considered the cost
analysis only. In addition, a study in [77] presented an approach to determine the location
and number of DG units. The objective is to minimize the fuel cost and power losses. A
planning framework was also developed for PV integration by reducing the investment,
operation and imported energy costs [78]. Moreover, heuristic approaches were proposed
to locate and size DG units with an objective of minimising the costs of investment,
CHAPTER 2. LITERATURE REVIEW
14
operation, imported energy and energy losses [79, 80]. With the same objective, a research
in [81] presented a DG planning approach using PSO. However, the importance of the
benefit of DG units also needs to be considered in the analysis.
A study in [82] presented a dynamic programming algorithm to place and size DG units
through the cost and benefit analysis. The total cost is a sum of DG investment, operation
and maintenance costs, while the total benefit is a sum of the benefits arising from
reducing the power loss, imported energy and unserved energy. However, it seems that
inclusion of the DG energy sales in the analysis may provide a more precise result.
Few studies have reported comprehensive frameworks for DG investemnt planning on
the basis of the cost and benefit analysis including the energy sales from DG. For instance,
a study in [8] presented a heuristic approach to locate and size DG units by maximizing the
utility’s profit as a function of the benefit and cost. The benefit is the energy sales, whereas
the costs are related to DG investment, operation, imported energy, unserved energy, and
energy losses. A research in [83] developed a GA-based cost and benefit method to
accommodate DG units. The benefit is the energy sales, while the cost includes DG
investment and energy loss costs. In addition, a heuristic approach was introduced to locate
and size DG units through the cost and benefit analysis [84]. The benefit is the energy
sales, while the costs are related to DG investment and operation, substation and feeder
investments, imported energy and unserved energy.
In conclusion, the above review shows that numerous methodologies have developed
for DG integration in distribution systems, considering different respects: technical,
economical and environmental benefits. However, most of them have assumed that DG
units operate at a pre-defined power factor. Depending on the nature of loads served, DG
operation at optimum power factor may have positive impacts on system losses, voltage
stability, and system capacity release. Moreover, a comprehensive benefit-cost study on
multiple DG allocation with optimal power factor that considers the issues of energy loss
and voltage stability has not been reported in the literature. In addition, the importance of
time-varying voltage-dependent load models also needs to be considered in the analysis to
obtain a more realistic result.
CHAPTER 2. LITERATURE REVIEW
2.4
15
Renewable DG Integration with BES
Unlike conventional technologies-based DG units such as reciprocating engines and gas
turbines, PV sources are time and weather-dependent, intermittent and nondispatchable.
Advances in dispatchable BES technologies provide an opportunity to make these
nondispatchable PV sources dispatchable like conventional generators [85, 86]. Over the
last fifteen-years, a hybrid PV and BES system has been designed for stand-alone
applications [87-89]. In recent years, the hybrid of BES and PV system has been utilized as
one of the most viable solutions in grid-connected applications to mitigate the impacts of
PV intermittency, increase PV penetration and provide multiple benefits for utilities,
customers and PV owners. This topic has attracted the interest of numbers of recent
research efforts [85, 90-98]. A hybrid PV-BES system was developed for demand-side
applications to enhance the system electrical efficiency [92, 93]. An optimal charging and
discharging schedule of BES units utilized in a grid-connected PV system was presented
for peak load shaving [94]. A study in [95] proposed a methodology to determine the size
of BES units for power arbitrage and peak shaving used in a grid-connected PV system.
Authors in [96] presented a methodology to size BES units for increasing PV penetration
in a residential system with the objectives of voltage regulation and reductions in peak
power and annual cost. A strategy for charging and discharging BES units was proposed
for mitigating sudden changes in PV outputs and supporting evening peak load in
residential systems [97]. A concept to regulate voltages in distribution systems with high
PV penetration by controlling the output of customer-side BES units was reported in [90].
In this concept, a distribution utility is permitted to control the output of BES units during
a specific time period in exchange for subsidizing a part of BES investment costs. BES
units are sized and controlled to eliminate the power fluctuation of PV outputs [85, 98].
Finally, an optimal charging and discharging schedule of BES units on a hourly basis was
developed to mitigate the intermittency of PV-based DG outputs by minimising energy
losses [91]. Overall, the above review shows that considerable works have discussed the
charging and discharging schedules and size of BES units utilized in grid-connected PV
systems. However, most of the studies presented have assumed that the size of PV units
utilized in hybrid PV-BES systems is pre-defined and the optimal power factor dispatch for
each hybrid PV-BES unit over all periods is neglected as well. Depending on the
characteristics of loads served, each PV-BES hybrid unit that can deliver active and
CHAPTER 2. LITERATURE REVIEW
16
reactive power at optimal power factor may have positive impacts on minimising energy
loss and stabilizing the bus voltages of distribution systems.
2.5
Grid Codes for DG Integration
Under the recommendation of the current standard IEEE 1547, most of the DG units are
normally designed to operate at unity power factor [99]. Consequently, the inadequacy of
reactive power support for voltage regulation may exist in distribution networks, given a
high DG penetration level. Conventional devices such as switchable capacitors, voltage
regulators and tap changers are actually employed for automatic voltage regulation, but
they are not fast enough to compensate for transient events [100, 101]. It is likely that the
shortage of reactive power support may be an immediate concern at the distribution system
level in the future. On the other hand, depending on time and weather variability, the
simultaneous occurrence of excess intermittent renewable generation (i.e., wind and solar
PV) and low demand would lead to loss of voltage regulation along with unexpected
voltage-rise on the feeders due to reverse power flows [102]. As a fast response device, the
inverter-based PV unit is allowed to inject or absorb reactive power to stabilize load
voltages as per the new German grid code [103] while supplying energy as a primary task
[101, 104]. Other technologies such as synchronous machines used in biomass power
plants, and Doubly-Fed Induction Generators (DFIGs) or full converter synchronous
machines employed in wind farms are also capable of controlling reactive power while
supplying active power [105].
2.6
Summary
This chapter provided a brief overview of technologies of DG and associated BES in
distribution networks. It also reported a comprehensive literature review on renewable DG
integration in distribution systems. The concept and application of a hybrid PV and BES
system were also reviewed in this chapter. The literature review presented in this chapter
showed that traditional DG planning approaches have assumed that DG units are
dispatchable and placed at the peak demand. However, such approaches may not solve a
practical case of intermittent renewable DG units (e.g., wind and solar PV). Moreover, in
most existing studies, DG units have been assumed to operate at pre-specified power factor
under the current standard IEEE 1547, normally unity power factor. Furthermore, this
CHAPTER 2. LITERATURE REVIEW
17
chapter also showed that renewable DG planning that considers time-varying load models
and probabilistic generation has not been reported in the literature. In addition, a
comprehensive benefit-cost study on DG allocation with optimal power factor has not been
discussed in the literature.
CHAPTER 3
LOAD AND GENERATION MODELLING AND
TEST SYSTEMS
3.1
Introduction
As discussed in Chapter 2, an accurate modelling of the time-varying load models can help
in determining the penetration of renewable DG in a distribution system precisely. In
addition, the generation characteristics of intermittent renewable resources: wind and solar
depend on meteorological conditions (e.g., weather and temperature).
In this chapter, different time-varying voltage dependent load models are first defined.
The generation characteristics of renewable DG (i.e., solar PV, wind and biomass) and
BES are next presented. Finally, three different distribution test systems used throughout in
this study are also described.
3.2
Load Modelling
The time-varying voltage-dependent load model or the time-varying load model is defined
as a load model which is dependent on the time and voltage. Accordingly, the voltage
dependent load model in [106] which incorporates time-varying loads at period t can be
expressed as follows:
np
nq
Pk (t ) = Pok (t ) × Vk (t ) ; Qk (t ) = Qok (t ) × Vk (t )
18
(3.1)
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
19
where Pk and Qk are respectively the active and reactive power injections at bus k, Pok
and Qok are respectively the active and reactive load at bus k at nominal voltage; Vk is the
voltage at bus k; np and nq are, respectively, the active and reactive load voltage exponents
as given in Table 3.1 [106].
Table 3.1. Load types and exponents for voltage-dependent loads
Load types
3.3
np
nq
Constant
0
0
Industrial
0.18
6.00
Residential
0.92
4.04
Commercial
1.51
3.40
Generation Modelling
Renewable resources (i.e., solar, wind and biomass) and BES are considered in this thesis.
They can be classified into two categories: dispatchable and nondispatchable generation as
far as their capability of energy delivery is concerned. DG units are considered as a
dispatchable source, if its output power can be controlled at a fixed output automatically,
typically by varying the rate of fuel consumption. This includes generation technologies
such as biomass-based gas turbines and small hydro power plants. In contrast, DG units are
considered as a nondispatchable source, if its output power cannot be automatically
controlled and totally depends on weather conditions (e.g., wind speed and solar
irradiance). Solar PV and wind turbines are examples of such generation technologies.
3.3.1 Dispatchable Generation
Biomass
As discussed in Chapter 2, biogas produced from biomass raw materials is used to run gas
turbines. These gas turbines are synchronous machines and can be dispatched according to
the load demand curve.
Battery Energy Storage
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
20
The BES unit is assumed to be connected to an AC system via bidirectional DC/AC
converters that can be dispatched in all four quadrants over all given periods [107]. It can
operate at any desired power factor (lagging/leading) to charge or discharge active power.
In other words, the BES unit can operate as a load during charging periods and a generator
during discharging periods. It can inject or absorb reactive power as well.
3.3.2 Nondispatchable Generation
Solar Irradiance
The probabilistic nature of solar irradiance can be described using the Beta Probability
Density Function (PDF) as reported in [37]. This model has been employed in many PV
studies such as [27, 39, 91, 108]. Over each period (1 hour in this study), the PDF for solar
irradiance s can be expressed as follows:
 Γ(α + β ) (α −1)
(1 − s )( β −1) 0 ≤ s ≤ 1,α , β ≥ 0
s

f b ( s ) =  Γ(α )Γ( β )
0
otherwise

(3.2)
where f b (s ) is the Beta distribution function of s, s is the random variable of solar
irradiance (kW/m2); α and β are parameters of f b (s ) , which are calculated using the
mean ( µ ) and standard deviation ( σ ) of s as follows:
 µ (1 + µ )
β = (1 − µ )

σ
2
µ×β

− 1 ; α =
.
1− µ

The output power from the PV module at solar irradiance s, PPVo (s ) can be expressed as
follows [27, 39, 91]:
PPVo ( s ) = N × FF × V y × I y
where
FF =
VMPP × I MPP
; Vy = Voc − K v × Tcy
Voc × I sc
 N − 20 
I y = s[I sc + K i × (Tcy − 25)] ; Tcy = TA + s OT
.
 0 .8 
(3.3)
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
21
Here, N are the number of modules; Tcy and TA are respectively cell and ambient
temperatures (oC); K i and K v are respectively current and voltage temperature
coefficients (A/oC and V/oC); N OT is the nominal operating temperature of cell in oC; FF
is fill factor; Voc and I sc are respectively the open circuit voltage (V) and short circuit
current (A); VMPP and I MPP are respectively the voltage and current at maximum power
point.
Wind Speed
The probabilistic nature of the wind speed can be described using the Weibull PDF [27],
[44]. Over each period (1 hour in this study), the PDF for wind speed v can be expressed as
follows:
f w (v ) =
k v
 
cc
k −1
  v k 
exp −   
  c  
(3.4)
where f w (v) is the Weibull distribution function of v, v is the random variable of wind
speed (m/s); k = 2 is the shape index, c ≈ 1.128vm is the Rayleigh scale index; vm is the
mean value of wind speed that is calculated using the historical data for each time period.
The output power at wind speed v ( Pwo ) can be expressed as follows [109]:
0

2
3
a + a v + a2v + a3v
Pwo (v ) =  0 1
 Prated
0

0 ≤ v ≤ vci
vci ≤ v ≤ vr
vr ≤ v ≤ vco
(3.5)
vco ≤ v
where vci , vr , and vco are cut in, rated and cut out speed of the wind turbine, respectively;
Prated is the rating of wind turbine; a0 , a1 , a2 and a3 are the coefficients calculated using
any standard curve fitting technique such as ‘polyfit’ routine in Matlab [109].
Biomass
The biomass-based gas turbines can be assumed to generate a constant output power at its
rated value without associated uncertainties.
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
22
3.3.3 DG Penetration Level
The DG penetration level is the ratio of the total amount of DG energy exported to a
network and its total energy consumption [110].
3.3.4 Generation Criteria
As reported in Section 2.5, most of the DG units are normally designed to operate at unity
power factor under the recommendation of the standard IEEE 1547, [99]. This study
assumes that inverter-based PV units are allowed to inject or absorb reactive power in
compliance with the new German grid code [103]. Biomass gas turbines are modelled as
synchronous machines. Wind farms are modelled as Doubly-Fed Induction Generators
(DFIGs) or full converter synchronous machines. Such machines are also capable of
controlling reactive power while delivering active power [105]. The relationship between
the active and reactive power of a DG unit ( PDG and QDG ) can be expressed as [24]:
QDG = aPDG
(
where, a = ± tan cos
−1
( pf DG )) ;
(3.6)
a is positive for the DG unit supplying reactive power and
negative for the DG unit consuming reactive power; and pf DG is the operating power
factor of the DG unit.
3.4
Software Tools and Test Systems
In this thesis, the study tools, which will be presented in the next chapters, including
methodologies and algorithms have been developed for renewable DG integration. These
tools have been coded in MATLAB environment. A variety of test distribution systems,
ranging from 33 buses to 69 buses have been employed throughout in this thesis. Such
systems have been commonly used by several previous studies found in the literature. A
brief description of each system is provided below.
3.4.1 33-Bus Test System
Figure 3.1 shows a single line diagram of the 12.66 kV, 33-bus test radial distribution
system. It has one feeder with four different laterals, 32 branches and a total peak load of
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
23
3715 kW and 2300 kVAr. The total loss of the base case system is 211.20 kW. The
complete load data are given in Table A.1 (Appendix A) [111]. This system has been used
in Chapters 6 and 7.
Figure 3.1. The 33-bus test distribution system.
3.4.2 69-Bus One Feeder Test System
A single line diagram of the 12.66 kV, 69-bus test radial distribution system is shown in
Figure 3.2. It has one feeder with eight laterals, 68 branches, a total peak load of 3800 kW
and 2690 kVAr and its corresponding loss of 224.93 kW. Its complete load data are
provided in Table A.2 (Appendix A) [112]. This system has been used in Chapters 4 and 6.
Figure 3.2. The 69-bus one feeder test distribution system.
CHAPTER 3. LOAD AND GENERATION MODELLING AND TEST SYSTEMS
24
3.4.3 69-Bus Four Feeder Test System
Figure 3.3 shows a single line diagram of the 11 kV, 69-bus test radial distribution system,
which is fed by a 6 MVA 33/11 kV transformer [113]. This system consists of four feeders
with 68 branches, a total peak load of 4.47 MW and 3.06 MVAr and its corresponding loss
of 227.53 kW. The complete load data of this system are provided in Table A.3 (Appendix
A) [113]. This system has been used in Chapters 5 and 8.
S/S - 1
2
Legend
3
Substation
4
Bus
Feeder 2
Feeder 1
1
16
17
10
Line
11
5
24
23
18
25
19
26
Tie-line
68
12
20
27
7
13
21
28
8
14
22
29
9
15
50
66
37
48
47
64
67
38
49
63
65
62
36
61
43
35
34
56
46
55
42
45
41
33
54
Feeder 3
44
32
31
30
39
53
60
40
52
59
58
57
51
Feeder 4
69
6
S/S - 2
Figure 3.3. The 69-bus four feeders test distribution system [113].
3.5 Summary
This chapter provided a definition of time-varying voltage-dependent load models and
modelling of dispatchable and nondispatchable resources. Three test distribution systems
used in the research were also explained in this chapter.
CHAPTER 4
ANALYTICAL EXPRESSIONS FOR RENEWABLE
DG INTEGRATION
4.1
Introduction
As discussed in Chapter 2, the energy loss is one of the major concerns at the distribution
system level due to its impact on the utilities’ revenue. The loss reduction can reduce
power flows on distribution feeders, thereby resulting in positive impacts on system
capacity release, voltage profiles and voltage stability [19]. From the utilities’ perspective,
DG units located close to loads can significantly reduce energy losses in distribution
systems. However, the high penetration level of intermittent renewable DG units (i.e., wind
and solar) together with demand variations has introduced many challenges to distribution
systems such as power fluctuations, voltage rise, high losses and low voltage stability as a
result of reverse power flow [5].
Under the current standard IEEE 1547, renewable DG units are not allowed to supply
reactive power [99]. Consequently, it is likely that the shortage of reactive power support
may be an immediate concern at the distribution system level in the future with a high
penetration level of renewable DG units. Given the fact that not only does the active
power, but also the reactive power injection from renewable DG units play a significant
role in enhancing system performances such as energy savings, voltage profiles, system
capacity release and loadability. Depending on the nature of distribution systems, the
former or the latter may be dominant. In addition, it could be highlighted that the lack of
25
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
26
attention to reactive power support at the DG planning stage would potentially result in an
increase in investment costs used to add reactive power resources and other devices at the
operation stage. However, the redundancy of reactive power can lead to reverse power
flow, thereby leading to high losses, voltage rise, low system stability, etc. To address this
issue, it becomes necessary to study the optimal power factor of DG units, to which the
active and reactive power injections are optimized simultaneously.
As reported in Chapter 2, most of the existing studies have assumed that DG units
operate at a pre-specified power factor, normally unity power factor. In these researches,
only the location and size have been considered, while the optimal power factor for each
DG unit that would be a crucial part for minimising energy losses has been neglected.
Recently, a rule of thumb for DG operation has been developed for minimising power
losses [24, 25]. For this rule, it is recommended that the power factor of DG units should
be equal to the system load factor; however, the power factor is assumed to be the same for
all buses in these studies. Overall, the review of relevant literature has showed that
determining the power factor of renewable DG for each location that considers the timevarying characteristics of demand and generation for minimising energy losses has not
been reported. Depending on the characteristics of loads served, each DG unit which can
deliver both active and reactive power at optimal power factor may have positive impacts
on energy loss reduction.
This chapter presents three alternative analytical approaches to determine the optimum
size and operating strategy of a single DG unit to reduce power losses and a methodology
to identify the best location. These approaches are easily adapted to accommodate different
types of renewable DG units (i.e., biomass, wind and solar PV) for minimising energy
losses while considering the time-varying demand and possible operating conditions of DG
units. The proposed approaches are tested in the 69-bus one feeder test distribution system
(Figure 3.2) with different renewable DG scenarios.
4.2
Load and Renewable DG Modelling
4.2.1 Load Modelling
The distribution system under the study is assumed to follow the nominalised 24-hour load
profile of the IEEE-RTS system as shown in Figure 4.1 [36]. The time-varying constant P
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
27
and Q load model defined in Equation (3.1) is incorporated in the load characteristics. The
load factor (LF) or the average load level of the system can be estimated as the area under
the load curve in p.u. divided by the total duration. This can be expressed as follows:
24
LF = ∑
t =1
p.u. demand (t )
24
(4.1)
Load demand (p.u.)
1.0
0.9
0.8
0.7
0.6
0.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 4.1. Normalized daily load demand curve.
4.2.2 Renewable DG Modelling
In this study, three types of renewable DG units described in Chapter 3, namely biomass,
wind and solar PV are considered. The biomass DG output can be dispatched according to
the nominalised load curve illustrated in Figure 4.1. The outputs of wind and PV-based DG
are assumed to follow the nominalised average output curve depicted in Figure 4.2 [21,
114]. Each curve provides an hourly generation output as a percentage of the daily peak
output itself. The capacity factor ( CF ) of each type of DG is estimated as the ratio of the
area under the output curve in p.u. to the total duration as follows:
24
CF = ∑
t =1
p.u. DG output (t )
24
(4.2)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
1.0
Wind
PV
0.8
Output (p.u.)
28
0.6
0.4
0.2
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 4.2. Normalized daily wind and PV output curves.
4.3
Problem Formulation
4.3.1 Power Loss
Elgerd’s Loss Formula
The total active and reactive power losses (i.e., PL and QL) in a distribution system with N
buses can be calculated by “exact loss formula” as follows [115]:
N
N
PL = ∑∑ [α ij (Pi Pj + Qi Q j ) + β ij (Qi Pj − Pi Q j )]
(4.3)
i =1 j =1
N
N
QL = ∑∑ [γ ij (Pi Pj + Qi Q j ) + ξ ij (Qi Pj − Pi Q j )]
(4.4)
i =1 j =1
where
α ij =
rij
rij
cos(δ i − δ j ) ; β ij =
sin (δ i − δ j ) ;
ViV j
ViV j
γ ij =
xij
xij
cos(δ i − δ j ) ; ξij =
sin (δ i − δ j ) ;
ViV j
ViV j
Vi ∠δ i is the complex voltage at the bus ith; rij + jxij = Z ij is the ijth element of impedance
matrix [Z bus ] ; Pi and Pj are respectively the active power injections at buses i and j; Qi
and Q j are respectively the reactive power injections at buses i and j.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
29
The total active and reactive power injections at bus i where a DG unit is installed are
respectively given as follows [24]:
Pi = PDGi − PDi
(4.5)
Qi = QDGi − QDi = ai PDGi − QDi
(4.6)
where QDGi = ai PDGi , PDGi and QDGi are respectively the active and reactive power
−1
injections from the DG unit at bus i, ai = ( sign ) tan(cos ( pf DGi )) with sign = +1 : the DG
unit injecting reactive power, sign = −1 : the DG unit consuming reactive power; PDi and
QDi are respectively the active and reactive power of a load at bus i; pf DGi is the operating
power factor of the DG unit at bus i.
Substituting Equations (4.5) and (4.6) into Equations (4.3) and (4.4), we obtain the total
active and reactive power losses with a DG unit (i.e., PLDG and QLDG, respectively)
described as follows:
N N α (( P
ij
DGi − PDi )Pj + (ai PDGi − QDi )Q j ) 
PLDG = ∑∑ 

i =1 j =1  + β ij ((ai PDGi − QDi )Pj − ( PDGi − PDi )Q j )
(4.7)
N N γ (( P
ij
DGi − PDi )Pj + (ai PDGi − QDi )Q j ) 
QLDG = ∑∑ 

i =1 j =1  + ξij ((ai PDGi − QDi )Pj − (PDGi − PDi )Q j )
(4.8)
Branch Current Loss Formula
Alternatively, the total active and reactive power losses in a distribution system with n
braches can be calculated as follows [116]:
n
PL = ∑ I i Ri
2
(4.9)
i =1
n
QL = ∑ I i X i
2
(4.10)
i =1
where Ri and X i is respectively the resistance and reactance of branch i. I i is the current
magnitude; this current has two components: active ( I a ) and reactive ( I r ) which can be
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
30
obtained from a load flow solution. Hence, Equations (4.9) and (4.10) is respectively
rewritten as [116]:
n
PL = ∑
2
I ai Ri
i =1
n
n
+ ∑ I ri Ri
2
(4.11)
i =1
n
QL = ∑ I ai X i + ∑ I ri X i
2
i =1
2
(4.12)
i =1
When the active and reactive currents of a DG unit (i.e., I ak and I rk ) are injected at bus
k, Equations (4.11) and (4.12) can be rewritten as:
k
PLDG = ∑ (I ai + I ak ) Ri +
2
i =1
k
QLDG = ∑ (I ai + I ak ) X i +
2
i =1
n
k
n
i =1
i =k +1
∑ I ai Ri + ∑ (I ri + ak I ak )2 Ri + ∑ I ri Ri
2
i = k +1
n
k
∑ I ai X i + ∑ (I ri + ak I ak ) X i +
2
i = k +1
i =1
2
2
(4.13)
∑ I ri X i
(4.14)
n
2
i =k +1
Let a k = −( sign ) tan(cos −1 ( PFDGk )) , where sign = +1 for the DG unit injecting
reactive power; sign = −1 for the DG unit consuming reactive power. The relationship
between I rk and I ak at bus k can be expressed as follows:
I rk = ak I ak
(4.15)
Substituting Equation (4.15) into Equations (4.13) and (4.14), we obtain:
k
PLDG = ∑ (I ai + I ak ) Ri +
2
i =1
k
QLDG = ∑ (I ai + I ak ) X i +
2
i =1
n
k
n
i =1
i = k +1
∑ I ai Ri + ∑ (I ri + ak I ak )2 Ri + ∑ I ri Ri
2
i = k +1
n
k
n
i =1
i = k +1
2
∑ I ai X i + ∑ (I ri + ak I ak )2 X i + ∑ I ri X i
i = k +1
2
2
(4.16)
(4.17)
Branch Power Loss Formula
The total active and reactive power losses in a distribution system with n braches can be
obtained from Equations (4.9) and (4.10) as [117]:
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
n
PL = ∑
i =1
n
QL = ∑
i =1
Pbi + Qbi
2
31
2
2
Vi
Pbi + Qbi
2
Ri
(4.18)
Xi
(4.19)
2
2
Vi
where Pbi and Qbi are respectively the active and reactive power flow through branch i.
When the active and reactive power of a DG unit (i.e., PDGk and QDGk ) is injected at
bus k, Equations (4.18) and (4.19) can be respectively rewritten as follows:
k
PLDG = ∑
( Pbi + PDGk )2 R
k
QLDG = ∑
i =1
2
Vi
i =1
i +
∑
i = k +1
( Pbi + PDGk )2 X
2
Vi
Pbi2
n
i +
2
Vi
Pbi2
n
∑
k
i = k +1
Vi
i =1
k
2
Vi
Ri + ∑
( Qbi + QDGk )2 R
Xi + ∑
2
( Qbi + QDGk )2
i =1
Vi
2
Qbi2
n
i +
∑
i = k +1
Vi
n
Xi +
∑
i = k +1
Qbi2
Vi
(4.20)
Ri
2
Xi
2
(4.21)
The relationship between PDGk and QDGk can be expressed as:
QDGk = ak PDGk
(4.22)
where ak is defined in (4.15).
Substituting Equation (4.22) into Equations (4.20) and (4.21), we obtain:
k
PLDG = ∑
i =1
k
QLDG = ∑
i =1
(Pbi + PDGk )2 R
Vi
2
(Pbi + PDGk )2 X
Vi
2
i
+
n
2
∑
Pbi
n
Pbi
2
i =k +1 Vi
i
+
∑
i =k +1 Vi
2
2
k
Ri + ∑
i =1
k
Xi + ∑
i =1
(Qbi + ak PDGk )2 R
Vi
2
(Qbi + ak PDGk )2
Vi
2
i
n
+
∑
2
Qbi
i = k +1 Vi
Xi +
n
∑
2
(4.23)
2
Qbi
i = k +1 Vi
Ri
2
X i (4.24)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
32
4.3.2 Impact of the Size and Power Factor of DG on Power Losses*
It is revealed from either Equations (4.7) and (4.8) or Equations (4.16) and (4.17) or
Equations (4.23) and (4.24) that the active and reactive power losses are functions of
variables PDG and a (or pf DG ). Both variables have a significant impact on the power
losses. Based on either Equation (4.7) or Equation (4.16) or Equation (4.23), Figure 4.3
plots a valley-shaped curve of the active power loss with respect to the size and power
factor of a DG unit in a distribution system.
Active power loss (MW)
0.18
0.14
0.1
0.06
0.02
1
0.95
0.8
0.9
1.3
0.85
1.8
0.8
2.3
0.75
DG power factor
2.8
0.7
3.3
DG size (MW)
Figure 4.3. Impact of the size and power factor of a DG unit on system active power loss.
It is observed from Figure 4.3 that for a particular power factor, the loss commences to
reduce when the size of the DG unit is increased until the loss reaches the lowest level at
which the optimal size is specified. If the size is further increased, the loss starts to increase
and it is likely that it may overshoot the loss of the base case as a result of reverse power
flow. Similarly, given a DG size, the optimal power factor at which the loss is minimum is
identified. A similar trend can be observed for the variation of reactive power loss with
*
The work presented in this subsection has been published in D.Q. Hung, and N. Mithulananthan “Loss reduction and loadability
enhancement with DG: A dual-index analytical approach”, Applied Energy, vol. 115, pp. 233-241, Feb. 2014. The rest of this chapter has
been published in D.Q. Hung, N. Mithulananthan and R. C. Bansal, “Analytical strategies for renewable distributed generation
integration considering energy loss minimization,” Applied Energy, vol. 105, pp. 75-85, May 2013.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
33
respect to variables PDG and a (or pf DG ), as defined by either Equation (4.8) or Equation
(4.17) or Equation (4.24). In general, it is useful to operate a DG unit at its optimal size and
power factor to minimize the active and reactive power losses.
4.3.3 Energy Loss
The above alternative expressions for calculating the total active power loss can be utilized
depending on the availability of required data. The total annual energy loss in a distribution
system with a time duration ( ∆t ) of 1 hour can be expressed as follows:
24
24
0
t =1
Eloss = 365 ∫ Ploss (t )dt = 365∑ Ploss (t )∆t
4.4
(4.25)
Proposed Methodology
4.4.1 Approach 1 (A1)
This analytical approach 1 (A1) is developed based on “Elgerd’s loss formula” as
expressed by Equation (4.3) to determine the optimal size and power factor of a single DG
unit for minimising power losses. This is obtained by improving the previous work [24],
where the analytical expression was developed to calculate different types of a single DG
unit when the power factor is pre-specified. Approach A1 is then adapted to accommodate
different types of renewable DG units for minimising energy losses while considering the
time-varying characteristics of demand and generation. The study in [24] was also limited
to DG allocation for reducing power losses.
Sizing DG at Various Locations
The optimal size at each bus i for minimising the power loss can be expressed as [24]:
PDGi =
α ii (PDi + ai QDi ) − Ai − ai Bi
; QDGi = ai PDGi
2
α ii (ai + 1)
N
N
j =1
j ≠i
j =1
j ≠i
(4.26)
where Ai = ∑ (α ij Pj − β ij Q j ) , Bi = ∑ (α ij Q j + β ij Pj ) and ai is defined in Equation (4.6).
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
34
Equation (4.26) which is used to calculate the optimal size of different types of a single
DG unit at bus i for minimising power losses when pf DGi or value ai is known. The power
factor of the DG unit depends on the operating conditions and DG types adopted. The
optimal size of each DG type at each bus i for minimising the power loss can be
determined from Equation (4.26) by setting the value of pf DG in the following different
manners. DG technologies such as synchronous machine-based biomass DG, DFIG-based
wind DG, and inverters-based PV DG can fall under the following types depending on
their control strategy and active and reactive power capability.
•
Type 1 DG unit ( pf DG = 1) is capable of injecting active power only;
•
Type 2 DG unit ( pf DG = 0) is capable of injecting reactive power only;
•
Type 3 DG unit (0 < pf DG < 1 and sign = +1) is capable of injecting both active and
reactive power;
•
Type 4 DG unit (0 < pf DG < 1 and sign = −1) is capable of injecting active power
and absorbing reactive power.
The optimal active and reactive power sizes of a DG unit at bus i can be obtained from
Equation (4.26) by setting pf DGi = 1 or ai = 0 and pf DGi = 0 or ai = ∞ , respectively [24].
PDGi = PDi −
Ai
α ii
; QDGi = QDi −
Bi
α ii
(4.27)
Optimal Power Factor at Various Locations
Depending on the characteristic of loads, the load power factor of a distribution system
without reactive power compensation is normally in the range from 0.7 to 0.95 lagging
(inductive load). Hence, the optimal power factor of the DG unit could be lagging [24]. It
is assumed that the load power factor of the system considered in this work is lagging.
Equation (4.27) represents the optimum active power of Type 1 DG unit ( PDGi ) and the
optimal reactive power of Type 2 DG unit ( QDGi ). A combination of both PDGi and QDGi
injected simultaneously at bus i can produce the optimal size of Type 3 DG,
S DGi = PDGi + QDGi with lagging power factor. That means the DG unit is capable of
2
2
delivering both active and reactive power at bus i where the total system loss is minimum.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
35
Hence, in this concept, the optimal power factor of Type 3 DG at bus i ( opf DGi ) can be
lagging and calculated as follows:
PDGi
opf DGi =
(4.28)
PDGi + QDGi
2
2
4.4.2 Approach 2 (A2)
This analytical approach 2 (A2) is developed based on the “branch current loss formula” as
given by Equation (4.9) to specify the optimal size and power factor of a single DG unit for
reducing power losses. Similar to approach A1, approach A2 is then adapted to
accommodate different types of renewable DG units for minimising energy losses while
considering the time-varying characteristics of demand and generation. The application of
Equation (4.9) was presented for capacitor allocation and DG placement with unity power
factor at the peak load to reduce power losses [116, 118].
Sizing DG at Various Locations
The system loss reduction, which is obtained by subtracting Equations (4.16) from
Equation (4.11) (i.e. with and without a DG unit, respectively), can be expressed as
follows:
k
k
k
k
∆Ploss = −2 I ak ∑ I ai Ri − I ak ∑ Ri − 2ak I ak ∑ I ri Ri − ak I ak ∑ Ri
i =1
2
i =1
i =1
2 2
(4.29)
i =1
The system loss reduction is maximum if the partial derivative of Equation (4.29) with
respect to the active current injection from a DG unit at bus k is zero. This can be
described as follows:
k
k
k
k
∂∆Ploss
2
= −2∑ I ai Ri − 2ak ∑ I ri Ri − 2I ak ∑ Ri − 2ak I ak ∑ Ri = 0
∂I ak
i =1
i =1
i =1
i =1
(4.30)
The active current of the DG unit at bus k for maximizing loss reduction can be obtained
from Equation (4.30) as follows:
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
k
36
k
∑ I ai Ri + ak ∑ I ri Ri
I ak = − i =1
i =1
(
2
1 + ak
(4.31)
)∑ R
k
i
i =1
It is assumed that there is no significant change in the bus voltage after DG insertion.
From Equation (4.31) with PDGk = Vk I ak and QDGk = ak PDGk , where Vk is the voltage
magnitude of the DG unit at bus k, the optimal size of the DG unit at bus k and its
corresponding maximum loss reduction can be calculated as follows:
k
k
∑ I ai Ri + ak ∑ I ri Ri
PDGk = − Vk
i =1
(
2
1 + ak
∆Ploss
i =1
)∑ R
k
; QDGk = ak PDGk
(4.32)
i
i =1
k
 k

 ∑ I ai Ri + ak ∑ I ri Ri 
i =1

=  i =1
2
(4.33)
(1 + )∑ R
2
ak
k
i
i =1
Equation (4.32) can be used to calculate the optimal active and reactive power sizes of
the DG unit at various power factors in the range of 0 to 1 (leading/lagging). When the
values of pf DG are set at unity and zero, the optimal active and reactive power sizes of the
DG unit, respectively can be obtained from Equation (4.32) as follows:
k
k
∑ I ai Ri
PDGk =
− Vk i =1k
∑ Ri
∑ I ri Ri
; QDGk = − Vk
i =1
i =1
k
(4.34)
∑ Ri
i =1
Optimal Power Factor at Various Locations
The optimal power factor of the DG unit at each bus ( opf DG ) for minimising power losses
can be calculated by substituting Equation (4.34) into Equation (4.28).
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
37
Minimum Power Loss
When the value of pf DG is set at unity in Equation (4.33), the maximum loss reduction due
to the active power of the DG unit injected at bus k can be obtained. Similarly, when the
value of pf DG is set at zero in Equation (4.33), the maximum loss reduction due to the
reactive power of the DG unit injected at bus k can also be achieved. Hence, the total
maximum loss reduction due to both active and reactive power sizes of the DG unit
injected at bus k can be calculated as follows:
2
∆Ploss
 k

 k

 ∑ I ai Ri 
 ∑ I ri Ri 
 +  i =1

=  i =1 k
k
∑ Ri
∑ Ri
i =1
2
(4.35)
i =1
Hence, the total active power loss with the DG unit injected at bus k can be calculated
by subtracting Equation (4.35) from Equation (4.11) as follows:
PLDG = PL − ∆Ploss
(4.36)
4.4.3 Approach 3 (A3)
This novel analytical approach 3 (A3) is developed based on the “branch power flow loss
formula” as given in Equation (4.18) to identify the optimal size and power factor of a
single DG unit for minimising power losses. Similar to approaches A1 and A2, approach
A3 is then adapted to accommodate different types of renewable DG units for minimising
energy losses while considering the time-varying characteristics of demand and generation.
Sizing DG at Various Locations
The system loss reduction, which is obtained from subtracting Equation (4.23) from
Equation (4.18), can be expressed as follows:
k
∆Ploss = −2 PDGk ∑
i =1
Ri Pbi
Vi
2
k
− PDGk ∑
2
i =1
k
Ri
Vi
2
− 2ak PDGk ∑
i =1
Ri Qbi
Vi
2
k
− ak PDGk ∑
2
2
i =1
Ri
Vi
2
(4.37)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
38
The system loss reduction is maximum if the partial derivative of Equation (4.37) with
respect to the active power injection from a DG unit at bus k becomes zero. This can be
expressed as follows:
k
k
k
k
∂∆Ploss
RP
R
RQ
R
2
= −2∑ i 2bi − 2 PDGk ∑ i 2 − 2ak ∑ i 2bi − 2ak PDGk ∑ i2 = 0
∂PDGk
i =1 Vi
i =1 Vi
i =1 Vi
i =1 Vi
(4.38)
It is assumed that there is no significant change in the bus voltage after DG insertion.
From Equation (4.38), the active and reactive power sizes of the DG unit at bus k for
maximizing loss reduction can be given by Equation (4.39) and its corresponding
maximum loss reduction can be found by Equation (4.40) as follows:
k
∑
PDGk = −
i =1
Ri Pbi
Vi
2
k
+ ak ∑
Vi
i =1
(1 + )∑ V
2
ak
∆Ploss
RiQbi
k
Ri
i =1
i
2
; QDGk = ak PDGk
2
k
 k Ri Pbi
RiQbi 

a
+
k
∑
∑
2 
 i =1 Vi 2
i =1 Vi


=−
k
R
2
1 + ak ∑ i2
i =1 Vi
(
(4.39)
2
(4.40)
)
Equation (4.39) can be used to calculate the optimal active and reactive power sizes of
the DG unit at various power factors in the range of 0 to 1 (leading/lagging). Similar to
approach A2, when the values of pf DG are set at 1 and 0, the optimal active and reactive
power sizes of the DG unit, respectively can be obtained from Equation (4.39) as follows:
k
∑
PDGk = −
i =1
k
Ri Pbi
2
∑
RiQbi
2
Vi
i =1 Vi
; QDGk = − k
Ri
Ri
∑V 2
i =1
k
i
(4.41)
∑V 2
i =1
i
Optimal Power Factor at Various Locations
The optimal power factor of the DG unit at each bus ( opf DG ) for minimising power losses
can be calculated by substituting Equation (4.41) into Equation (4.28).
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
39
Minimum Power Loss
Similar to approach A2, the total maximum loss reduction due to both active and reactive
power sizes of the DG unit injected at bus k can be rewritten as:
2
∆Ploss
 k Ri Pbi 
 k RiQbi 




∑
2 
2 
∑

i =1 Vi
 +  i =1 Vi 
= k
k
Ri
Ri
∑V 2
i =1
i
2
(4.42)
∑V 2
i =1
i
Hence, the total active power loss with the DG unit injected at bus k can be calculated
by subtracting Equation (4.42) from Equation (4.18) as defined by (4.36).
4.4.4 Computational Procedure
This section presents a computational procedure for approaches A1, A2 and A3 using the
expressions developed earlier. These approaches are to accommodate different types of
renewable DG units to reduce energy losses while considering the time-varying demand
and the possible operating conditions of DG units. In this procedure, the power loss is
minimised first at the peak and average loads for dispatchable and nondispatchable DG
units, respectively to determine the size, location and power factor. The output of
dispatchable DG units is then adjusted based on the demand curve so that the energy loss is
minimum. For nondispatchable DG units, after finding the size at the average load, the
maximum size or the optimal size is identified using the DG output curve. The energy loss
is subsequently calculated based on the DG output curve. In order to demonstrate the
effectiveness of the proposed methodologies and algorithms developed, the following
scenarios are considered.
•
Scenario 1: No DG unit (Base case);
•
Scenario 2: Dispatchable biomass DG unit;
•
Scenario 3: Nondispatchable biomass DG unit;
•
Scenario 4: Nondispatchable wind DG unit;
•
Scenario 5: Nondispatchable PV DG unit.
Scenario 1: Run load flow for each period of the day and calculate the total annual
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
40
energy loss using Equation (4.25). In order to find the power loss, either Equation (4.3),
(4.9) or (4.18) could be used depending on availability of required data.
Scenario 2: The computational procedure is explained as follows:
Step 1: Run base case load flow at the peak load level and calculate the total power loss
using Equations (4.3), (4.9) or (4.18) for approaches A1, A2 and A3, respectively.
Step 2: Identify the optimal location, size and power factor of a DG unit at the peak load
level only.
peak
a) Find the optimal size for each bus ( S DGi ) using Equations (4.27), (4.34) and
(4.41) for approaches A1, A2 and A3, respectively and calculate the optimal
power factor for each bus using Equation (4.28).
b) Place the DG unit obtained earlier at each bus, one at a time and calculate the
approximate power loss for each case using Equation (4.3) for approach A1.
For approaches A2 and A3, calculate the approximate power loss using
Equations (4.36).
c) Locate the optimal bus at which the power loss is minimum with the
max
corresponding optimal size of the DG unit or its maximum output ( S DG ) at
that bus.
Step 3: Find the optimal output of the DG unit at the optimal location only for period t as
follows, where p.u. demand(t) is the load demand in p.u. at period t.
S DG = p.u. demand (t ) S DG
t
max
(4.43)
Step 4: Run load flow with each DG output obtained in Step 3 for each period and
calculate the total annual energy loss using Equation (4.25).
Scenarios 3-5: The computational procedure is explained as follows:
Step 1: Run load flow for the system without a DG unit at the average load level or at the
system load factor (LF) using Equation (4.1) and calculate the total power loss
using Equations (4.3), (4.9) or (4.18) for approaches A1, A2 and A3, respectively.
Step 2: Specify the optimal location, size and power factor of a DG unit at the average
load level only.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
a)
41
avg
Find the optimal size for each bus ( S DGi ) using Equations (4.27), (4.34) and
(4.41) for approaches A1, A2 and A3, respectively and calculate the optimal
power factor for bus i using Equation (4.28).
b) Place the DG unit obtained earlier at each bus, one at a time and calculate the
approximate power loss for each case using Equation (4.3) for approach A1.
For approaches A2 and A3, calculate the approximate power loss using
Equations (4.36).
c)
Locate the optimal bus at which the power loss is minimum with the
avg
corresponding optimal size of the DG unit at the average load level ( S DG ) at
that bus.
Step 3: Find the CF based on its daily output curve using Equation (4.2).
max
Step 4: Find the optimal size of the DG unit or its maximum output ( S DG ) at the optimal
location only as follows:
avg
max
S DG
=
S DG
(4.44)
CF
Step 5: Find the optimal DG output at the optimal location for period t as follows:
S DG = p.u. DG output (t ) S DG
t
max
(4.45)
Step 6: Run load flow with each DG output obtained in Step 5 for each period and
calculate the total annual energy loss using Equation (4.25).
The above procedures are developed to accommodate different types of renewable DG
units with optimal power factor. These procedures can be modified to allocate a DG unit
with a pre-specified power factor. When the power factor is pre-specified, the procedures
are similar to the above with exception that in Step 2.a in scenarios 2-5, the size is
calculated using Equation (4.26) rather than (4.27) for approach A1, Equation (4.32) rather
than (4.34) for A2, and Equation (4.39) rather than (4.41) for A3.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
4.5
42
Exhaustive Load Flow Solution
To validate the effectiveness of the proposed approaches A1, A2 and A3, the Exhaustive
Load Flow (ELF) solution [119] is employed. For each load level, a DG unit is placed at
each bus. Its size is changed from 0% to 100% of the sum of the total demand and the total
loss of the system in a step of 0.25%. The power factor of the DG unit is also varied for
each case from 0 (lagging) to unity in a step of 0.001. The total system power loss is
calculated for each case by load flow analyses. The total energy loss is estimated as a sum
of the power losses of all load levels over 24 hours a day times 365 days a year using
Equation (4.25). The best location, size and power factor are obtained in the case to which
the total energy loss is minimum without any violations of the voltages.
4.6
Case Study
4.6.1 Test System
The case study considered is the 69-bus one feeder radial distribution system as illustrated
in Figure 3.2. The lower and upper voltage thresholds are set at 0.95 p.u. and 1.05 p.u.,
respectively. The system load power factor is assumed to remain unchanged for each load
level (period). The distribution system considered in this work has the 24-hour load profile
as depicted in Figure 4.1 [36].
It is assumed that biomass DG units can be allocated at all buses in the system. The
location of PV and wind sources may be identified by resource and geographic factors. As
their sites are unspecified in the test system, these sources are assumed to be available at
all buses. However, when the location is pre-specified, the optimal size and power factor
corresponding to the lowest power loss can be quickly determined based on the proposed
approaches.
4.6.2 Numerical Results
Scenario 1: Figure 4.4a shows the 24-hour load curve in MVA for the system without DG
unit. This curve was developed based on the 24-hour load curve in p.u. as given in Figure
4.1. Figure 4.4b presents its corresponding 24-hour power loss curve. In this case, the total
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
43
annual energy loss is 1381.53 MWh which can be calculated as tracing the area under
Figure 4.4b times 365 days as defined in Equation (4.25).
Load demand (MVA)
5.0
4.5
4.0
3.5
3.0
2.5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
Power loss (KW)
250
200
150
100
50
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
Figure 4.4. Daily curves for (a) demand and (b) system power losses without a DG unit.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
44
Scenario 2: Figures 4.5a-b show the optimal output of a dispatchable biomass DG unit
and its corresponding minimum power loss, respectively for each hour of the day at
optimal bus 61. It is interesting to note that the DG output patterns which are determined
by approaches A1 and ELF are almost the same and follow the load pattern as illustrated in
Figure 4.4a. The daily power loss pattern with the DG unit also follows that of the base
case as shown in Figure 4.4b. Hence, approach A1 based on the peak load solution
combined with the load demand curve could be sufficient to specify the 24-hour optimal
DG output curve in MVA. In contrast, as a multiple-load level solution, the ELF repeats
the same computation for each load level. Similar results have been obtained using
proposed approaches A2 and A3 as shown in Figures 4.5a-b.
Table 4.1 summaries the results obtained by all the approaches. The outcomes achieved
using the proposed approaches (A1, A2 and A3) are in close agreement with the ELF. The
optimal location is found at bus 61. The difference in the optimal size and power factor due
to numerical errors is negligible. More importantly, the computational time by the
proposed approaches is significantly shorter than the ELF. Hence, the proposed approaches
could be feasible for use in large-scale systems. In addition, it is observed from Table 4.1
that the computational time of A2 and A3 is the same since both approaches are originally
derived from the same power loss formula. However, the error in the simulation results of
the size and location of the DG unit exists between A2 and A3. This error happens due to
the linearization of the original nonlinear equations (4.9) and (4.18). Another observation
is that Approach A3 is more complex than Approach A2. Approach A2 is derived from the
branch current loss formula (4.9), where the data inputs are the resistance and current of
branches. Approach A3 is derived from the branch power loss formula (4.18), where the
data inputs are the resistance of branches, the active and reactive power flowing through
these branches, and bus voltages.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
2.4
45
A1
DG size (MVA)
A2
2.1
A3
ELF
1.8
1.5
1.2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
25
A1
Power loss (kW)
A2
20
A3
ELF
15
10
5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
Figure 4.5. Daily curves at bus 61: (a) dispatchable biomass DG output and (b) system
power losses with a dispatchable biomass DG unit.
Table 4.1. Dispatchable biomass DG placement
Approach
A1
A2
A3
ELF
0.82
0.83
0.83
0.82
61
61
61
61
Optimal size (MVA)
2.222
2.222
2.298
2.241
Annual loss (MWh)
144.35
144.68
144.56
144.27
0.77
0.10
0.10
> 1625.67
Optimal power factor (lagging)
Optimal bus
CPU time (s)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
46
Scenario 3: Figures 4.6a-b present the optimal output of a nondispatchable biomass DG
unit and its corresponding minimum power loss, respectively for each hour of the day at
optimal bus 61. The DG output pattern by the A1 is just under that by the ELF.
Accordingly, the hourly power losses of both approaches are almost similar. The difference
is that the size of the DG unit obtained by approach A1 is 1.844 MVA which is 0.024
MVA slightly smaller than the ELF, as shown in Table 4.2. Consequently, the total annual
energy loss with the DG unit by the A1 and ELF are respectively almost the same at
184.68 MWh and 184.45 MWh, with a negligible difference of 0.12%. It is noted that only
one single solution at the average load level combined with the biomass output curve was
considered by the A1. Similar results have been found using the A2 and A3, as shown in
Figure 4.6a-b and Table 4.2.
Scenario 4: Figures 4.7a-b show the nondispatchable wind output curve following the
wind output curve in Figure 4.3 for every hour of the day and its corresponding power loss
at optimal bus 61. Similar to scenario 3, the wind DG output patterns specified by both A1
and ELF are nearly the same. The optimal sizes are found to be 3.684 MVA by the A1 and
3.316 MVA by the ELF. Hence, the annual total energy loss with the DG unit by the A1 is
307.52 MWh, whereas this value by the ELF is 294.24 MWh, as shown in Table 4.3. It is
noted that a single solution at the average load level associated with the wind output curve
in Figure 4.3 was considered by the A1. Similar results have been identified using the A2
and A3 as shown in Figure 4.7a-b and Table 4.3.
Scenario 5: Figures 4.8a-b show the result of a PV DG unit at optimal bus 61 by the A1
and ELF on the assumption that its output follows the nondispatchable PV output curve
(Figure 4.3). The output patterns achieved by both approaches are the same. However, the
optimal size is 3.618 MVA by the A1 and is 2.985 MVA by the ELF, with a difference of
0.63 MVA, as shown in Table 4.4. Hence, the total annual energy loss by the A1 is 648.06
MWh, which is 6.06% higher than the ELF. Similar to scenario 4, one single solution at the
average load level combined with the PV output curve (Figure 4.3) was considered by the
A1. Similar results have been specified using approaches A2 and A3 as shown in Figure
4.8 and Table 4.4.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
4.0
A1
A2
A3
ELF
3.0
DG size (MVA)
47
2.0
1.0
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
Power loss (kW)
30
A1
A2
A3
ELF
25
20
15
10
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
Figure 4.6. Daily curves at bus 61: (a) nondispatchable biomass DG output and (b) system
power losses with a nondispatchable biomass DG unit.
Table 4.2. Nondispatchable biomass DG placement
Approach
A1
A2
A3
ELF
0.82
0.83
0.83
0.82
61
61
61
61
Optimal size (MVA)
1.844
1.844
1.891
1.868
Annual loss (MWh)
184.68
184.99
185.26
184.45
0.77
0.10
0.10
> 1625.67
Optimal power factor (lagging)
Optimal bus
CPU time (s)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
4.0
48
A1
DG size (MVA)
A2
A3
3.0
ELF
2.0
1.0
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
Power loss (kW)
100
A1
A2
A3
ELF
75
50
25
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
Hour
(b)
Figure 4.7. Daily curves at bus 61: (a) wind DG output and (b) system power losses with a
wind DG unit.
Table 4.3. Nondispatchable wind DG placement
Approach
A1
A2
A3
ELF
0.82
0.83
0.83
0.82
61
61
61
61
Optimal size (MVA)
3.684
3.684
3.777
3.316
Annual loss (MWh)
307.52
305.00
309.24
294.24
0.77
0.10
0.10
> 1625.67
Optimal power factor (lagging)
Optimal bus
CPU time (s)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
DG size (MVA)
4.0
49
A1
A2
A3
ELF
3.0
2.0
1.0
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
Power loss (kW)
210
A1
A2
A3
ELF
160
110
60
10
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
Figure 4.8. Daily curves at bus 61: (a) PV DG output and (b) system power losses with a
PV DG unit.
Table 4.4. Nondispatchable PV DG placement
Approach
A1
A2
A3
ELF
0.82
0.83
0.83
0.82
61
61
61
61
Optimal size (MVA)
3.618
3.618
3.719
2.985
Annual loss (MWh)
648.06
657.72
668.14
608.81
0.77
0.10
0.10
> 1625.67
Optimal power factor (lagging)
Optimal bus
CPU time (s)
Figure 4.9 shows a comparison of the maximum and actual penetration levels of DG
units for scenarios 2-5. The actual penetration is calculated as the maximum DG
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
50
penetration times its CF. It is observed from Figure 4.9 that the maximum penetration
levels of nondispatchable DG units (i.e., the wind and PV units in scenarios 4 and 5,
respectively) are considerably higher than dispatchable DG units (i.e., the biomass unit in
scenarios 2). However, the actual penetration levels of the nondispatchable DG units are
significantly lower than the dispatchable DG units. This is because the dispatchable DG
generation pattern (Figure 4.5a) matches better with the load demand (Figure 4.4a) than the
nondispatchable DG output curves (Figures 4.7a and 4.8a for the wind and PV units,
respectively). However, this is not the case for the nondispatchable biomass unit in
scenario 3, which has the ability to operate at its continuous rated output for every hour of
the day (Figure 4.6a). As shown in Figure 4.9, the actual and maximum penetration levels
of the nondispatchable biomass unit are the same and are closer to the actual penetration of
the dispatchable biomass unit in scenario 2.
Figure 4.10 shows the energy loss reductions for scenarios 2-5. It is observed from the
figure that the energy loss reduction for the dispatchable DG unit (scenario 2) is higher
than the nondispatchable DG units (scenarios 3-5). This is due the fact that the
dispatchable DG generation pattern matches better with the load demand than the
nondispatchable DG output curves, as previously mentioned.
Figure 4.11 shows the voltage profiles for scenarios 1-5 at the extreme periods where
the voltage profiles are worst. In the absence of the DG units, the extreme period is
specified at peak period 12 at which the voltages at buses 57-66 are under the lower limit
of 0.94 p.u. In the presence of the DG units, by considering the combination of the demand
and DG output curves, the extreme periods are determined as follows: period 12 for
scenarios 2-3, period 16 for scenario 4 and period 13 for scenario 5. It is observed from the
figure that after DG insertion, the voltage profiles at the extreme periods are improved
significantly within the acceptable limit as expected. It is interesting to note that the
voltage profiles in dispatchable DG scenario 2 are better than those in nondispatchable DG
scenarios 3-5.
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
100
Max penetration
93.65
95.36
30.93
45.69
47.74
47.69
25
47.74
50
57.51
Penetration (%)
Actual penetration
75
0
2
3
4
5
Scenario No.
Figure 4.9. Maximum and actual penetration for scenarios 2-5.
3
25
53.09
2
77.74
50
86.63
75
89.55
Energy loss reduction (%)
100
0
4
5
Scenario No.
Figure 4.10. Annual energy loss reduction for scenarios 2-5.
Voltage (p.u.)
1.06
1.02
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
0.98
0.94
0.90
1
5
9
13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
Bus
Figure 4.11. Voltage profiles at extreme periods for scenarios 1-5.
51
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
52
It is noted that optimal sizes and locations obtained for power loss minimization using
the above analytical expressions are in close agreement with the results reported in [120]
and [32] using heuristic and ABC algorithms, respectively.
It is worth mentioning that the power factor of DG units as well as DG types adopted
can play a significant role in minimising energy losses. Based on the A1, Figures 4.12 and
4.13 depict the trends of energy loss reduction, at various DG power factors that represent
different DG types at bus 61 for scenarios 2-5. The energy loss reduction commences to
increase when the power factor is varied in order of leading, unity and lagging values and
until it reaches the maximum value when the DG unit operates at 0.82 optimal lagging
power factor. It is observed that Type 3 DG unit has the most positive impact on energy
loss reduction, while the lowest impact is determined in Type 4 DG unit. However, as
reported in [118], the grid codes of many countries require that grid-connected wind DG
units should provide the capabilities of reactive power control or power factor control in a
specific range. For instance, in the Ireland, the power factor of wind turbines is required to
be from 0.835 leading to 0.835 lagging. It should be from 0.95 leading to 0.95 lagging in
Italy and the United Kingdom. Hence, to assess the impact of the DG power factor on
energy losses, in this study, the power factor is limited in the range of 0.9 leading to 0.9
lagging. In this case, as shown in Figures 4.12 and 4.13, the best power factor for all
scenarios to achieve the highest energy loss reduction is determined at 0.9 lagging. The
optimal location for all scenarios is at bus 61. The optimal size of each DG unit and its
corresponding annual energy loss reduction for each scenario are presented in Figures 4.12
and 4.13.
Optimal DG size (MVA)
5
4
87.38
DG size
Loss
100
89.55
80
62.45
3
2
1
60
23.78
2.19
40
2.22
1.81
20
1.06
0
Energy loss reduction (%)
0.9 lag
Unity
0.9 lead
DG power factor
53
0.814 lag
(optimal)
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
0
4
1
3
3
Type of DG
Optimal DG size (MVA)
5
4
84.54
DG size
Loss
86.63
100
80
60.34
3
60
2
40
22.91
1.82
1.50
1
1.84
20
0.88
0
0
4
1
3
3
Type of DG
Scenario 3
Figure 4.12. DG placement with different power factors for scenarios 2-3.
Energy loss reduction (%)
0.9 lag
Unity
0.9 lead
DG power factor
0.814 lag
(optimal)
Scenario 2
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
Optimal DG size (MVA)
6
100
DG size
Loss
5
75.93
77.74
3.63
3.68
80
54.33
4
60
3
20.77
40
3.00
2
20
Energy loss reduction (%)
0.814 lag
(optimal)
0.9 lag
Unity
0.9 lead
DG power factor
54
1.76
1
0
4
1
3
3
Type of DG
0.9 lag
Unity
0.9 lead
DG power factor
0.814 lag
(optimal)
Scenario 4
5
75
DG size
Loss
4
48.54
53.09
45
35.50
3.57
3
13.54
60
3.62
30
2.94
2
15
1.73
1
Energy loss reduction (%)
Optimal DG size (MVA)
6
0
4
1
3
3
Type of DG
Scenario 5
Figure 4.13. DG placement with different power factors for scenarios 4-5.
4.7
Summary
This chapter presented three analytical approaches using three different power loss
formulas to identify the optimal size and power factor of a single DG unit at various
locations for minimising power losses and a methodology to identify the best location in
distribution systems. These approaches were easily adapted to accommodate different
CHAPTER 4. ANALYTICAL EXPRESSIONS FOR RENEWABLE DG INTEGRATION
55
types of renewable DG units (i.e., biomass, wind and solar PV) for minimising energy
losses while considering a combination of time-varying demand and different DG output
curves. The results demonstrated that the proposed approaches can be adequate to identify
the location, size and power factor of a single DG unit for minimising energy losses. The
three approaches can be utilized depending on availability of required data and produce
similar outcomes. They can lead to an optimal or near-optimal result as verified by the ELF
solution and other methods found in the literature. It is worth mentioning that dispatchable
DG units have a more positive impact on energy loss reduction and voltage profile
enhancement than nondispatchable DG units. The strategically optimized power factor of a
single DG unit based on the proposed expression can make a significant contribution to
energy loss reduction.
CHAPTER 5
WIND AND BIOMASS INTEGRATION FOR
ENERGY LOSS REDUCTION
5.1
Introduction
The proposed approaches in Chapter 4 are well-suited to accommodate different types of
single renewable DG units in distribution systems while considering the time-varying
characteristics of demand and generation. However, these approaches are unable to address
either multiple renewable DG units or a mix of different types of renewable DG units. As
reported in Chapter 2, a combination of dispatchable and nondispatchable DG placement
that considers the time-varying demand and generation for minimising energy losses has
not been reported in the literature so far.
This chapter presents a new methodology for the integration of dispatchable and
nondispatchable renewable DG units for minimising annual energy losses. In this
methodology, each nondispatchable wind unit is converted into a dispatchable source by
adding a biomass unit. Here, analytical expressions are first proposed to identify the
optimal size and power factor of a single DG unit simultaneously for each location for
minimising power losses. These expressions are then adapted to place multiple renewable
DG units for minimising annual energy losses while considering the time-varying
characteristics of demand and generation. A combination of dispatchable and
nondispatchable DG units is also proposed in this chapter. The proposed methodology is
tested in the 69-bus four feeder test distribution system (Figure 3.3) with different
scenarios of renewable DG.
56
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
5.2
57
Load and Renewable DG Modelling
5.2.1 Load Modelling
The system considered in this work is assumed to follow the normalized load curve of the
IEEE-RTS system plotted in Figure 5.1 [36]. As shown in this figure, each year is divided
into four seasons (winter, spring, summer and fall). For reasons of simplicity, an hourly
load curve of a day is representing each season. However, two hourly load curves of two
days (one for weekdays and one for weekends) which are representing each season could
be incorporated in the proposed methodology. The load curve of four 24-hour days
(24x4=96 hours) is subsequently representing the four seasons in a year (8760 hours). The
seasonal maximum and minimum in load demand occurred during summer and fall,
respectively. With a peak demand of 1 p.u., the LF or average load level of the system can
be estimated as the ratio of the area under the load curve in p.u. to the total duration.
96
LF = ∑
t =1
p.u. load (t )
96
(5.1)
1.2
Load demand in p.u.
Summer
1.0
Fall
Spring
0.8
Winter
0.6
0.4
0.2
0
12
24
36
48
60
72
84
96
Hour
Figure 5.1. Normalized hourly load demand curve.
5.2.2 Renewable DG Modelling
Two renewable resources, namely biomass and wind found in Section 3.3 are considered in
this chapter. The biomass DG unit is modeled as a synchronous machine and the wind DG
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
58
unit uses DFIGs or full converter synchronous machines. The biomass DG unit is assumed
to be a dispatchable source which can be dispatched according to the load curve as shown
in Figure 5.1. In this case, the CF of the biomass DG unit is equal to the LF as given in
Equation (5.1). The wind DG unit is assumed to be a nondispatchable source following the
output curve for each season per year [121], as depicted in Figure 5.2. It is noted that
different wind patterns could be easily incorporated in the proposed methodology below.
As shown in Figure 5.2, a year is divided into four seasons. An hourly generation output
pattern for a day is representing each season. The generation output curve of four 24-hour
days (24x4=96 hours) is then representing the four seasons in a year (8760 hours). The
seasonal maximum and minimum in wind power availability occurred during winter and
summer, respectively. With a peak of 1 p.u., the CF of the wind DG unit is defined as the
ratio of the area under the output curve in p.u. to the total duration.
96
CF = ∑
t =1
p.u. DG output (t )
96
(5.2)
1.2
Winter
Spring
Fall
Wind output in p.u.
1.0
Summer
0.8
0.6
0.4
0.2
0
12
24
36
48
60
72
84
96
Hour
Figure 5.2. Normalized hourly wind output curve.
5.3
Problem Formulation
As shown in Figure 5.1, each year has four seasons. A load curve for a 24-hour day is
representing each season. The load curve of four 24-hour days (24x4=96 hours) is
subsequently representing the four seasons in a year. The total number of hours per year is
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
59
365x24 (8760) hours. Therefore, the 96-hour load curve is repeated 91.25 times to
represent one year (91.25x96=8760). Here, 96 hours in four seasons a year are
t
corresponding to 96 periods (load levels). The active power loss, Ploss
, at each period t is
obtained from Equation (4.3) without a DG unit or Equation (4.7) with a DG unit. Hence,
the total annual energy loss in a distribution system with a time duration ( ∆t = 1 hour) can
be expressed as follows:
96
Eloss = 91.25∑ Ploss ∆t
t
(5.3)
t =1
5.4
Proposed Methodology
5.4.1 Expression for Sizing DG at Predefined Power Factor
This section briefly describes an analytical expression developed in [24] to calculate
different types of DG units for minimising power losses when the DG power factor is prespecified. The total active power loss can reach a minimum value if the partial derivative
of Equation (4.7) with respect to the active power injection from a DG unit at bus i ( PDGi )
becomes zero. This can be expressed as follows:
N
∂PLDG
= 2∑ [α ij (Pj + ai Q j ) + β ij (ai Pj − Q j )] = 0
∂PDGi
j =1
(5.4)
where ai is defined in Equation (4.6).
Equation (5.4) can be rearranged as follows:
α ii ( Pi + ai Qi ) + Ai + ai Bi = 0
where
N
N
j =1
j ≠i
j =1
j ≠i
(5.5)
Ai = ∑ (α ij Pj − β ij Q j ) , Bi = ∑ (α ij Q j + β ij Pj )
Substituting Equations (4.5) and (4.6) into Equation (5.5), we obtain [24]:
PDGi =
α ii (PDi + ai QDi ) − Ai − ai Bi
2
α ii (ai + 1)
(5.6)
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
60
Equation (5.6) is used to calculate the optimal size of different types of a single DG unit
at bus i for minimising power losses when ai (or pf DGi ) is known.
5.4.2 Proposed Expressions for Sizing DG at Optimal Power Factor
In this section, an analytical expressions is proposed by improving the previous work [24]
to determine the optimal size and power factor of each DG unit simultaneously for each
location. Here, the total active power loss is minimum if the partial derivative of Equation
(4.7) with respect to variable ai (or pf DGi ) becomes zero. This can be described as follows:
N
∂PLDG
= 2∑ [α ij Q j + β ij Pj ] = 0
∂ai
j =1
(5.7)
Equation (5.7) can be rearranged as follows:
α ii Qi + Bi = 0
(5.8)
Substituting Equation (4.6) into Equation (5.8), we get:
ai =
1 
Bi 
 QDi −

PDGi 
α ii 
(5.9)
The relationship between the pf DGi and variable ai can be expressed as follows:
(
)
pf DGi = cos tan −1 (ai ) .
(5.10)
Finally, the optimal PDGi and its pf DGi for the total system loss to be minimum can be
obtained from Equations (4.26), (5.9) and (5.10) as follows:
PDGi = PDi −
Ai
α ii
 −1  α Q − Bi  
 
pf DGi = cos tan  ii Di
α
P
A
−
ii
Di
i



(5.11)
(5.12)
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
61
5.4.3 Computational Procedure
In order to demonstrate the effectiveness of the proposed approach, the following four
scenarios are considered:
•
Scenario 1: No DG unit (Base case).
•
Scenario 2: Dispatchable biomass DG units.
•
Scenario 3: Nondispatchable wind DG units.
•
Scenario 4: A combination of dispatchable biomass and nondispatchable wind DG
units as a dispatchable source.
Here, the assumption is that the wind DG unit is nondispatchable, and owned by DG
developers and controlled by utilities. The biomass DG unit is dispatchable, and owned
and operated by utilities. For a long-term planning purpose, this study considers that the
load of all buses changes uniformly according to a load demand curve. In this method, the
power loss is minimised first at the peak and average loads for dispatchable and
nondispatchable DG units, respectively to determine the location, size and power factor.
This method requires less computation. However, in a real system, the load of all buses
does not change uniformly. In this case, the determination the location and power factor
should be evaluated at all load levels to achieve a more accurate outcome. The proposed
methodology can address this issue, but it requires a computational burden due to a large
number of load flow analyses.
Scenario 1: Run load flow for each period (or load level) of the day and estimated the
total annual energy loss using Equation (5.3).
Scenario 2: Figure 5.3 shows an example of the output curve of a single dispatchable
biomass DG unit for the 69-bus four-feeder test system (Figure 3.3), in four seasons. This
curve follows the load demand pattern in Figure 5.1 and was obtained using a
computational procedure as follows:
Step 1: Run base case load flow at the peak load level for the year and find the total
power loss using Equation (4.3).
Step 2: Find the optimal location, size and power factor of a DG unit at the peak load
level for the year.
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
62
peak
a) Find the optimal size ( PDGi ) and the optimal power factor using Equations
(5.11) and (5.12), respectively.
b) Place the DG unit obtained earlier at each bus, one at a time. Calculate the
power loss for each case using Equation (4.7).
c) Locate the optimal bus at which the power loss is minimum with the
max
corresponding optimal size or maximum output ( PDG ) at that bus.
Step 3: Find the optimal DG output at the optimal location for period t as follows, where
p.u. load(t) is the load demand in p.u. at period t.
PDG = p.u. load (t ) PDG
t
max
(5.13)
Step 4: Run load flow with each DG output obtained in Step 3 for each period, find the
total energy loss using Equation (5.3), and repeat Steps 2-4. Stop if any of the
following occurs and the previous iteration solution is obtained.
a) the bus voltage at any bus is over the upper limit;
b) the branch current is over the upper limit;
c) the total DG size is larger than the system demand plus loss†;
d) the maximum number of DG units are unavailable.
1.0
Summer
Generation (MW)
0.8
Spring
Fall
Winter
0.6
0.4
0.2
Dispatchable biomass DG
0.0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.3. Hourly optimal generation curve of a biomass DG unit.
†
In the absence of DG units, a distribution network is known as a passive network, which has a unidirectional power flow from the
source to loads. In the presence of DG units, the passive network becomes an active one that has a bidirectional power flow, which
exchanges between the source and loads. The problems associated with the active network is that as discussed in Section 4.3.2, an
appropriately sized DG unit can help reduce system losses significantly. However, an excessively oversized DG unit in the active
network may lead to feeder overloads, high losses, voltage rises and low system stability as a result of reverse power flow [5, 16, 102].
To avoid the reverse power flow, the constraint 4(c) is used.
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
63
Scenario 3: Figure 5.4 shows an example of the output curve of a single
nondispatchable wind DG unit for the 69-bus four-feeder test system (Figure 3.3), in four
seasons. This curve follows the wind output pattern in Figure 5.2 and was obtained using a
computational procedure as follows:
Step 1: Run load flow for the system without DG unit at the average load level for the
year or at the load factor as given in Equation (5.1) and find the total power loss
using Equation (4.3).
Step 2: Find the optimal location, size and power factor of a DG unit at the average load
level for the year.
avg
a) Find the optimal size ( PDGi ) and the optimal power factor using Equations
(5.11) and (5.12), respectively.
b) Place the DG unit obtained earlier at each bus, one at a time. Calculate the
power loss for each case using Equation (4.7).
c) Locate the optimal bus at which the power loss is minimum with the
corresponding optimal size at the average load level or the average output
avg
( PDG ) at that bus.
Step 3: Find the CF of the wind DG unit based on its daily output curve using Equation
(5.2).
Step 4: Find the optimal DG size or maximum DG output at the optimal location as
follows:
avg
max
PDG
=
PDG
(5.14)
CF
Step 5: Find the optimal DG output at the optimal location for period t as follows, where
p.u. DGoutput(t) is the DG output in p.u. at period t.
PDG = p.u. DG output (t ) PDG
t
max
(5.15)
Step 6: Run load flow with each DG output obtained in Step 5 for each period, find the
total energy loss using Equation (5.3), and repeat Steps 2-6. Stop if any of the
following occurs and the previous iteration solution is obtained.
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
a)
the bus voltage at any bus is over the upper limit;
b)
the branch current is over the upper limit;
c)
the total DG size is larger than the system demand plus loss;
d)
the maximum number of DG units are unavailable.
64
The above computational procedures are developed to accommodate DG units with
optimal power factor. These procedures can be modified to allocate DG units with a prespecified power factor. When the power factor of DG units is pre-specified, the
computational procedure is similar to the above with exception that the optimal DG size
for each bus is determined using Equation (5.6) rather than Equation (5.11).
1.0
Spring
Winter
Fall
Summer
Generation (MW)
0.8
0.6
0.4
0.2
Nondispatchable wind DG
0.0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.4. Hourly optimal generation curve of a nondispatchable wind DG unit.
Scenario 4: Figure 5.5 shows an example of the output curve of a dispatchable and
nondispatchable DG mix for the 69-bus four-feeder test system (Figure 3.3), in four
seasons. This curve follows the demand profile in Figure 5.1 and was obtained using the
computational procedure as explained below. Here, the wind output pattern in Figure 5.5
follows the wind output curve in Figure 5.2 on the condition that wind penetration is in its
maximum. The biomass DG units are utilized as an additional dispatchable source to fill up
the supply energy portion that the wind DG units cannot. Notice that the total DG output in
MW for each period in scenario 4 (a mix of one dispatchable DG unit and one
nondispatchable DG unit) is the same as that in scenario 2 (one dispatchable DG unit) on
the condition that nondispatchable DG penetration is in its maximum.
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
65
Step 1: Find the optimal location, size and power factor of a DG unit and the
corresponding total energy loss using the computational procedure in scenario 2.
Step 2: Select the optimal location and power factor of dispatchable and nondispatchable
DG units as calculated in Step 1.
max
Step 3: Find the optimal size or maximum output of the nondispatchable DG unit ( PDG )
over all periods on the condition that its output is no more than that of DG unit as
specified in Step 1, at each period.
Step 4: Find the optimal output of the nondispatchable DG unit for period t as given in
Equation (5.15).
Step 5: Calculate the output of the dispatchable DG unit that is equal to the output of the
DG unit in Step 1 minus the output of the nondispatchable DG unit in Step 4, for
each period; then find the optimal size or maximum output of the dispatchable DG
unit over all periods.
1.0
Summer
Generation (MW)
0.8
Fall
Spring
Winter
0.6
0.4
Dispatchable
biomass DG
0.2
Nondispatchable wind DG
0.0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.5. Hourly optimal generation curve of a wind-biomass DG mix.
5.5
Case Study
5.5.1 Test System
The proposed methodology was applied to the 69-bus four-feeder radial distribution
system as shown in Figure 3.3. The lower and upper voltage thresholds should be 0.95 p.u.
and 1.05 p.u., respectively. The feeder thermal limits are 5.1 MVA (270 A) [68].
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
66
The demand of the system is assumed to follow the normalized load curve in Figure 5.1
[36]. Wind DG units are assumed to be nondispatchable and follow the normalized wind
output curve in Figure 5.2. Biomass DG units are assumed to be allocated at any bus in the
system. The locations of wind DG units may be identified by resources and geographic
factors. As their sites are unspecified in the test system, they are assumed to be installed at
any bus. However, when the locations are pre-specified, the optimal sizes and power
factors with the lowest corresponding power loss can be quickly determined based on the
proposed methodology. The power factor of DG units remains unchanged over all periods.
The number of DG units is predefined at two for scenarios 2 and 3, and at four for scenario
4. However, the proposed methodology can consider the different number of DG units.
5.5.2 DG Placement without Considering Power Factor Limit
Figure 5.6 shows the hourly load demand and power loss curves of the system in four
seasons a year in scenario 1. The load demand curve shown in Figure 5.6 follows the
hourly load demand curve in Figure 5.1. The peak demand occurred at period 59 in
summer, whereas the lowest demand was at period 77 in fall. The significant power losses
were observed at periods in summer. The total annual energy import from the grid without
DG units is estimated as tracing the area under Figure 5.6 times 91.25 days. In this case,
the total annual energy import is found at 24.556 GWh, which is a sum of the total system
load demand (23.787 GWh) and the total system energy loss (0.769 GWh).
Without considering the power factor limit (i.e., the optimal power factor for each DG
unit is considered), Figures 5.7, 5.8 and 5.9 show the optimal output curves of DG units in
four seasons in scenarios 2, 3 and 4, respectively, and the power import from the grid. For
scenario 2, the total output of biomass DG units at each period (Figure 5.7) is dispatched
following the demand curve (Figure 5.6). Similarly, for scenario 4, the total output of
biomass-wind DG units at each period in Figure 5.9 is also dispatched according to the
demand curve in Figure 5.6. Here, the wind output pattern in Figure 5.9 follows the wind
output curve in Figure 5.2 on the condition that the wind penetration is in its maximum.
The biomass DG units are utilized as an additional dispatchable source to fill up the supply
energy portion that the wind DG units cannot. As the total DG output patterns of scenarios
2 and 4 are the same and are dispatched following the load demand in Figure 5.6, the
power loss at each period in scenario 2 is identical to that in scenario 4 as depicted in
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
67
Figure 5.10. On the other hand, as the wind DG units in scenario 3 (Figure 5.8) cannot
dispatch following the demand pattern in Figure 5.6, the power loss at each period in
scenario 3 is higher than that in scenarios 2 and 4 as shown in Figure 5.10. In addition, it
can be revealed from Figures 5.8-5.10 that the integration of DG units amounts to the
reduction in the total energy import from the grid in all scenarios, resulting from the DG
energy production and system energy loss reduction.
6
Summer
Load demand (MW)
5
Spring
4
Fall
Loss
Winter
3
2
1
Demand
0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.6. Hourly load demand and power loss curves (scenario 1).
6
Summer
Generation (MW)
5
Fall
Spring
4
Winter
3
Grid import
2
Biomass 2
1
Biomass 1
0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.7. Hourly optimal generation curve of biomass DG units (scenario 2).
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
6
Summer
5
Generation (MW)
68
Fall
Spring
4
Winter
3
Grid import
2
1
Wind 2
Wind 1
0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.8. Hourly optimal generation curve of wind DG units (scenario 3).
6
Summer
Generation (MW)
5
Fall
Spring
4
Winter
3
Grid import
2
Biomass 2
1
Wind 2
Biomass 1
Wind 1
0
0
12
24
36
48
60
72
84
96
Hour
Figure 5.9. Hourly optimal generation curve of a wind-biomass DG mix (scenario 4).
300
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Power loss (kW)
250
Summer
Spring
200
Fall
Winter
150
100
50
0
0
12
24
36
48
Hour
Figure 5.10. Hourly power loss curve in scenarios 1-4.
60
72
84
96
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
69
Tables 5.1 and 5.2 show a summary and comparison of the simulation results obtained
for four scenarios with and without DG units in the 69-bus system. For scenarios 2-4 with
DG units, the results include the type of DG units and the location, size and power factor
for each type. The annual energy loss and its loss reduction for each scenario are also
presented in these tables. The optimal locations of DG units for each scenario are identified
at buses 62 and 35 with the corresponding sizes and power factors as shown in the tables.
A significant energy loss reduction is observed in scenarios 2-4 (with DG units) when
compared to scenario 1 (without DG units). In scenarios with DG units, the highest loss
reduction is found in scenarios 2 and 4, while the lowest loss reduction is obtained in
scenario 3. The combination of dispatchable and nondispatchable DG units in scenario 4
can yield the same loss reduction as dispatchable biomass DG units in scenario 2. It is
noted that the optimal DG power factors at buses 62 and 35 are different at 0.79 and 0.83
(lagging), respectively.
Table 5.1 Optimal DG placement without considering power factor limit
Scenarios
1 (Base case)
DG type
2 (Biomass)
No DG
Biomass 1
Biomass 2
62
35
Size (MVA)
0.94
0.99
Power factor (lag.)
0.79
0.83
Bus
Annual loss (MWh)
768.50
365.38
Loss reduction (%)
52.46
Table 5.2 Optimal DG placement without considering power factor limit
Scenarios
DG type
3 (Wind)
4 (Wind-Biomass mix)
Wind 1
Wind 2
Wind 1
Bio 1
Wind 2
Bio 2
62
35
62
62
35
35
Size (MVA)
0.86
0.99
0.49
0.71
0.56
0.82
Power factor (lag.)
0.79
0.83
0.79
0.79
0.83
0.83
Bus
Annual loss (MWh)
426.92
365.38
Loss reduction (%)
44.45
52.46
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
70
5.5.3 Biomass versus Wind
Figure 5.11 shows the power loss reduction over 96 periods in four seasons in scenarios 24. It is obvious that scenario 2 can produce a maximum loss reduction over each period
because the biomass output was dispatched according to the varying demand curve. On the
other hand, the maximum loss reduction is found at a few periods in scenario 3 because the
wind DG output cannot be dispatched according to the varying demand curve. Scenario 4
can yield the same loss reduction as scenario 2. The advantage is that the biomass DG units
have capability to dispatch according to the load demand. Consequently, scenarios 2 and 4
that include the dispatchable biomass DG units are superior to scenario 3 from the
perspective of total annual energy loss reduction as shown in Figure 5.11.
Loss reduction (%)
100
Scenario 2
Scenario 3
Scenario 4
80
Fall
Summer
Spring
Winter
60
40
20
0
0
12
24
36
48
Hour
60
72
84
96
Figure 5.11. Hourly percentage power loss reduction in scenarios 2-4.
5.5.4 Voltage Profiles
Figure 5.12 shows the voltage profiles for scenarios 1-4 at the extreme periods (load
levels) where the voltage profiles are worst. In the absence of DG units, the extreme period
is at the peak period 59 as depicted in Figure 5.6, at which the voltages at some buses are
under 0.94 p.u. In the presence of DG units, by considering the combination of the demand
and DG output curves, the extreme periods are also at the peak period 59 for scenarios 2-4,
as shown in Figures 5.8-5.10.
It is observed from the figure that after DG units are integrated at the extreme periods,
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
71
the voltage profiles are improved significantly. It is interesting to note that the voltage
profiles in scenario 2 (dispatchable DG units) or scenario 4 (a mix of dispatchable and
nondispatchable DG units) are better than those in scenario 3 (nondispatchable DG units).
It is worth noting that the optimal size and location of DG units obtained for power loss
minimization using the proposed method are in close agreement with the results of recently
published methods such as heuristic [120], PSO [30, 122], SA [28], ABC [32], MTLBO
[33], HSA [34].
Voltage (p.u.)
1.06
Scenario 1
Scenario 2
Scenario 3
Scenario 4
1.02
0.98
0.94
0.90
1
5
9
13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
Bus
Figure 5.12. Voltage profile at extreme periods (period 59) for scenarios 1-4.
5.5.5 Power Factor Impact on Energy Loss
As reported in [123], the grid codes of many countries require that grid-connected wind
turbines should provide the capability of reactive power control or power factor control in
a specific range. For instance, in the Ireland, the power factor of wind turbines is required
to be from 0.835 leading to 0.835 lagging. It should be from 0.95 leading to 0.95 lagging in
Italy and the United Kingdom. Hence, in this study, the power factor is limited in the range
of 0.95 leading and 0.95 lagging to assess the impact of the power factor of DG units on
energy losses. Tables 5.3 and 5.4 summarize and compare the results of DG placement for
four different scenarios with and without DG units in the 69-bus system considering the
power factor limit from 0.95 leading to 0.95 lagging. For each scenario with DG units, the
results include the type, location, size, power factor and corresponding energy loss. The
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
72
optimal locations of DG units for each scenario are identified at buses 62 and 35 with the
corresponding sizes as shown in Tables 5.3 and 5.4. In this case, the best power factor of
all DG units is found to be at 0.95 lagging. However, the optimal power factor of DG units
are 0.79 and 0.83 (lagging), at buses 62 and 35, respectively, when the power factor limit
was not considered as shown in Tables 5.1 and 5.2. It is revealed that imposing the power
factor limit has a negative impact on the energy loss reduction at a maximum difference of
nearly 5% when compared to the case without considering the power factor limit, as
presented in Figure 5.13. However, this value may depend on the characteristics of the
system and DG output.
Table 5.3 Optimal DG placement considering power factor limit
Scenarios
1 (Base case)
DG type
No DG
2 (Biomass)
Biomass 1
Biomass 2
62
35
Size (MVA)
0.89
1.05
Power factor (lag.)
0.95
0.95
Bus
Annual loss (MWh)
768.50
401.41
Table 5.4 Optimal DG placement considering power factor limit
Scenarios
DG type
3 (Wind)
4 (Wind-Biomass mix)
Wind 1
Wind 2
Wind 1
Bio 1
Wind 2
Bio 2
62
35
62
62
35
35
Size (MVA)
0.81
0.96
0.44
0.67
0.52
0.79
Power factor (lag.)
0.95
0.95
0.95
0.95
0.95
0.95
Bus
Annual loss (MWh)
458.04
401.41
CHAPTER 5. WIND AND BIOMASS INTEGRATION FOR ENERGY LOSS REDUCTION
Energy loss reduction (%)
100
73
Without power factor limit
With power factor limit
75
52.46
50
47.77
52.46
44.45
47.77
40.40
25
0
Scenario 2
Scenario 3
Scenario 4
Figure 5.13. Impact of the power factor of DG units on energy loss reduction.
5.6
Summary
This chapter presented a methodology to determine the optimal location, size and power
factor of dispatchable and nondispatchable renewable DG units for minimising annual
energy losses in distribution systems. In this methodology, analytical expressions were first
proposed to determine the optimal size and power factor of a single DG unit
simultaneously for each location to minimize power losses. These expressions were then
adapted to locate and size different types of renewable DG units and calculate the optimal
power factor for each unit to minimize energy losses while considering the time-varying
characteristics of demand and generation. Moreover, a combination of dispatchable and
nondispatchable renewable DG units was proposed in this chapter. The proposed
methodology was applied to the 69-bus four-feeder test distribution system with different
renewable DG scenarios. The results showed that dispatchable DG units or a combination
of dispatchable and nondispatchable DG units can minimize annual energy losses
significantly when compared to nondispatchable DG units alone. The results also indicated
that a maximum annual energy loss reduction is obtained for all the scenarios proposed
with DG operation at optimal power factor.
CHAPTER 6
MULTI-OBJECTIVE PV INTEGRATION
6.1
Introduction
Depending on the location and technology of PV adopted, a power system would
accommodate up to an estimated 50% of the PV penetration [16], [124]. However, the
time-varying load model (i.e., time-varying voltage-dependent load model) may diversely
affect the estimated PV penetration. Moreover, Chapter 2 showed that multiobjective
planning for renewable DG in distribution systems that considers probabilistic generation
and time-varying load models has not been reported in the literature. In addition, Chapters
4-5 reported DG allocation for minimising energy loss as a single-objective function.
This chapter studies the penetration of PV units in a distribution system with several
different types of time-varying load models. Here, a new multiobjective index (IMO)based analytical expression is proposed to identify the size of a single PV-based DG unit
with objectives of simultaneously reducing active and reactive power losses and voltage
deviation. This expression is then adapted to place PV units while considering the
characteristics of varying-time load models and probabilistic generation. Three different
types of customers with dissimilar load patterns (i.e., industrial, residential and
commercial) and a mix of all these customers are defined by time-varying voltagedependent load models. The 33- and 69-bus test distribution systems shown in Figures 3.1
and 3.2, respectively are employed to validate the proposed methodology.
74
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
6.2
75
Load and Solar PV Modelling
6.2.1 Load Modelling
The demand of the system under the study is assumed to follow different normalized daily
load patterns (i.e., industrial, residential and commercial) with a peak of 1 p.u., as shown in
Figure 6.1 [125]. The time-varying voltage-dependent load model or the time-varying load
model defined in Section 3.2 is also considered in this work. For each load model, the load
factor (LF) or the average load level of the system can be defined as the area under the load
curve in p.u. divided by the total duration:
24
LF = ∑
t =1
Demand (p.u.)
1.0
0.8
p.u. demand (t )
24
(6.1)
Industrial
Residential
Commercial
0.6
0.4
0.2
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 6.1. Normalized daily demand curve for various customers.
6.2.2 Solar PV Modelling
The solar irradiance for each hour of the day is modeled by the Beta Probability Density
Function (PDF) based on historical data which have been collected for three years from the
site (lat: 39.45, long: -104.65, California, USA) [126]. To obtain this PDF, a day is split
into 24-h periods (time segments), each of which is one hour and has its own solar
irradiance PDF. From the collected historical data, the mean and standard deviation of the
hourly solar irradiance of the day is calculated. It is assumed that each hour has 20 states
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
76
for solar irradiance with a step of 0.05 kW/m2‡. From the calculated mean and standard
deviation, the PDF with 20 states for solar irradiance is generated for each hour of the day
and the probability of each solar irradiance state is determined. Accordingly, the PV output
power is obtained for that hour. The model is explained below.
The probability of the solar irradiance state s during any specific hour can be calculated
as follows [27]:
ρ ( s) =
s2
∫ f b (s)ds
(6.2)
s1
where s1 and s2 is solar irradiance limits of state s; f b (s ) is the Beta distribution function
of s, which is calculated using Equation (3.2).
The total expected output power (average output power) of a PV module across any
specific period t, PPV (t ) (t = 1 hour), can be obtained as a combination of Equation (6.2)
and Equation (3.3) [27]. This can be expressed as follows:
1
PPV (t ) = ∫ PPVo ( s ) ρ ( s )ds
(6.3)
0
For example, given the mean ( µ ) and standard deviation ( σ ) of the hourly solar
irradiance found in Table B.1 (Appendix B), the PDF for 20 solar irradiance states with an
interval of 0.05 kW/m2 for periods 8, 12 and 16 are generated using Equations (3.2) and
(6.2), and plotted in Figure 6.2. Obviously, as the solar irradiance is time and weatherdependent, different periods have different PDFs. The area under the curve of each hour is
unity. Another example is that given the parameters of a PV module found in Table B.2
(Appendix B), the expected output of the PV module with respect to 20 solar irradiance
states (Figure 6.2) is calculated using Equation (6.3) and plotted in Figure 6.3. For period
8, the total expected output power, which is calculated as the area under the curve of that
period (Figure 6.3), is 53.08 W. As the period is assumed at one hour, the PV module is
expected to output at 53.08 Wh. Similarly, the expected PV outputs for periods 12 and 16
are found to be 129.96 and 73.42 Wh, respectively. It is observed from Figure 6.3 that a
‡
This study considers the solar irradiance in the range of 0-1 kW/m2. However, a larger range (e.g., 0-1.5 kW/m2) can be used,
providing that the maximum solar irradiance is included in this range. In such a case, the number of steps or the size of each step is
changed to suit the range.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
77
difference in the expected PV output patterns exists among hours 8, 12 and 16.
0.25
0.20
Hour 8
Hour 12
Probability
Hour 16
0.15
0.10
0.05
0.00
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
0.75
0.85
0.95
Solar irradiance (kW/m2)
Figure 6.2. PDF for solar irradiance at hours 8, 12 and 16.
Expected PV output (W)
25
Hour 8
Hour 12
20
Hour 16
15
10
5
0
0.05
0.15
0.25
0.35
0.45
0.55
0.65
Solar irradiance (kW/m2)
Figure 6.3. Expected output of a PV module at hours 8, 12 and 16.
The capacity factor of a PV module ( CFPV ) can be defined as the average output power
avg
max
( PPV ) divided by the rated power or maximum output ( PPV ) [27]:
avg
CFPV =
PPV
max
(6.4)
PPV
Once the average output power is calculated using (6.3) for each hour based on three
years of the collected historical data as previously mentioned, the average and maximum
output powers are obtained for the day. The CFPV is then obtained using (6.4).
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
78
As described in Section 3.3.4, the inverter-based PV technology [101, 104], which is
capable of delivering active power and exporting or consuming reactive power, is adopted
in this study. The relationship between the active and reactive power of a PV unit at bus k
( PPVk and QPVk ) can be expressed as follows [24]:
Q PVk = a k PPVk
(
where, a k = ± tan cos
−1
( pf PVk ));
(6.5)
a k is positive for the PV unit supplying reactive power
and negative for the PV unit consuming reactive power; and pf PVk is the operating power
factor of the PV unit at bus k.
6.2.3 Combined Generation-Load Model
To incorporate the PV output powers as multistate variables in the problem formulation,
the combined generation-load model reported in [27] is adopted in this study. The
continuous PDF has been split into different states. As previously mentioned, each day has
24-h periods (time segments), each of which has 20 states for solar irradiance with a step of
0.05 kW/m2 for calculating the PV output powers. As the load demand is constant during
each hour, its probability is unity. Therefore, the probability of any combination of the
generation and load is the probability of the generation itself.
6.3
Problem Formulation
6.3.1 Impact Indices
In this study, three indices: active power loss, reactive power loss and voltage deviation are
employed to describe the PV impacts on the distribution system. These indices play a
critical role in PV planning and operations due to their significant impacts on utilities’
revenue, power quality, and system stability and security. They are explained below.
Active Power Loss Index
Figure 6.4a shows a n-branch radial distribution system without a PV unit, where Pi and
Qi are respectively the active and reactive power flow through branch i; PDi and QDi are
respectively the active and reactive load powers at bus i. The total power loss in n-branch
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
79
system without a PV unit (PL) can be calculated using Equation (4.18). Figure 6.4b
presents this system with a PV unit located at any bus, say bus k, where PPVk and QPVk are
respectively the active and reactive powers of the PV unit at bus k. In this case, bus k is
identical to bus i+1 (k = 2, 3, … n+1). As illustrated in Figure 6.4b, due to the active and
reactive powers of the PV unit injected at bus k, the active and reactive powers flowing
from the source to bus k is reduced, whereas the power flows in the remaining branches are
unchanged. Accordingly, the power loss defined by Equation (4.18) can be rewritten as:
k
PLPV = ∑
i =1
k
+∑
i =1
(Pi − PPVk )2 R
Vi
2
i
(Qi − QPVk )2 R
Vi
i
2
+
+
n
Pi
i = k +1
Vi
∑
2
2
(6.6)
2
n
Qi
i = k +1
Vi
∑
Ri
2
Ri
(a)
(b)
Figure 6.4. A radial distribution system: (a) without a PV unit and (b) with a PV unit.
Substituting Equations (6.5) and (4.18) into Equation (6.6), we obtain:
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
k
PLPV = ∑
80
PPVk − 2 Pbi PPVk
2
Vi
i =1
k
+∑
2
Ri
ak PPVk − 2Qbi ak PPVk
2
(6.7)
2
Vi
i =1
2
Ri + PL
The active power loss index (ILP) can be defined as the ratio of Equations (6.7) and
(4.18) as follows:
ILP =
PLPV
(6.8)
PL
Reactive Power Loss Index
The total reactive power loss (QL) in a radial distribution system with n branches can be
using Equation (4.19). Similar to Equation (6.7), when both PPVk and Q PVk = a k PPVk are
injected at bus k, Equation (4.19) can be rewritten as:
k
QLPV = ∑
PPVk − 2 Pbi PPVk
2
Vi
i =1
k
+∑
2
Xi
ak PPVk − 2Qbi ak PPVk
2
(6.9)
2
Vi
i =1
2
X i + QL
The reactive power loss index (ILQ) can be defined as the ratio of Equations (6.9) and
(4.19) as follows:
ILQ =
QLPV
QL
(6.10)
Voltage Deviation Index
As shown in Figure 6.4a, the voltage deviation (VD) along the branch from bus i to bus
i+1, ( Ri + jX i ), can be expressed as [127]:
VDi =
Ri Pbi + X i Qbi
Vi +1
(6.11)
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
81
2
From Equation (6.11), the total voltage deviation squared ( VD ) in the whole system
with n branches can be written as:
n
VD = ∑
2
(Ri Pbi + X i Qbi )2
(6.12)
2
Vi +1
i =1
When both PPVk and QPVk are injected at bus k (Figure 6.4b), Equation (6.12) can be
rewritten as:
k
Ri (Pbi − PPVk )
i =1
Vi +1
VDPV = ∑
2
2
2
2
X i (Qbi − QPVk )
i =1
Vi +1
2
k
+ 2∑
∑
2
Vi +1
2
2
n
2
X i Qbi
∑
+
2
2
Ri Pbi
i = k +1
k
+∑
2
n
+
i = k +1
Vi +1
Ri X i (Pbi − PPVk )(Qbi − QPVk )
Vi +1
i =1
2
(6.13)
2
+2
n
∑
Ri X i Pbi Qbi
i = k +1
Vi +1
2
Substituting Equations (6.5) and (6.12) into Equation (6.13), we obtain:
2
VDPV
k
=∑
(
Ri PPVk − 2 Pbi PPVk
2
i =1
k
+∑
2
(
Vi +1
2
)
X i ak PPVk − 2Qbi ak PPVk
2
i =1
k
− 2∑
2
(
2
Vi +1
2
)
(6.14)
Ri X i Pbi ak PPVk + Qbi PPVk − ak PPVk
2
Vi +1
i =1
2
) +VD
2
Finally, the voltage deviation index (IVD) of a distribution system can be defined as the
ratio of Equations (6.14) and (6.12) as follows:
2
IVD =
VDPV
VD
2
(6.15)
6.3.2 Multiobjective Index
On the one hand, when the PV unit is allocated for minimising either the active or reactive
power loss (i.e., ILP or ILQ, respectively), this would potentially limit the PV penetration
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
82
with a high voltage deviation. On the other hand, a high penetration level could be
achieved when the PV unit is considered for reducing the voltage deviation (IVD) alone,
but the system losses could be high. To include all the indices in the analysis, a
multiobjective index (IMO) can be defined as a combination of the ILP, ILQ and IVD
indices with proper weights:
IMO = σ 1 ILP + σ 2 ILQ + σ 3 IVD
where
∑i=1σ i = 1.0 ∧ σ i ∈ [0, 1.0] .
3
(6.16)
This can be performed as all impact indices are
normalized with values between zero and one [29]. When a PV unit is not connected to the
system (i.e., base case system), the IMO is the highest at one.
The weights are intended to give the relative importance to each impact index for PV
allocation and depend on the analysis purpose (e.g., planning or operation) [29, 54, 55, 58].
The determination of the proper weighting factors will also depend on the experience and
concerns of the system planner. The PV installation has a significant impact on the active
and reactive power losses and voltage profiles. The active power loss is currently one of
the major concerns due to its impact on the distribution utilities’ profit, while the reactive
power loss and voltage profile are less important than the active power loss. Considering
these concerns and referring to previous reports in [29, 54, 55, 58], this study assumes that
the active power loss receives a significant weight of 0.5, leaving the reactive power loss
and the voltage deviation of 0.25 each. However, the above weights can be adjusted based
on the distribution utility priority.
As the solar irradiance is a random variable, the PV output power and its corresponding
IMO are stochastic during each hour. The IMO can be formulated in the expected value. To
calculate the IMO, the power load flow is analyzed for each combined generation-load
state. It is assumed that IMO (s ) is the expected IMO at solar irradiance s, the total
expected IMO over any specific period t, IMO (t ) (t = 1 hour) can be formulated as a
combination of Equations (6.2) and (6.16) as follows:
1
IMO(t ) = ∫ IMO( s ) ρ ( s )ds
0
(6.17)
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
83
The average IMO (AIMO) over the total period (T = 24) in a system with a PV unit can
be obtained from Equation (6.17). This can be expressed as follows:
T
AIMO =
1
1 T
IMO
(
t
)
dt
=
∑ IMO(t ) × ∆t
T ∫0
T t =1
(6.18)
where ∆t is the time duration or time segment of period t (1 hour in this study). The lowest
AIMO implies the best PV allocation for reducing active and reactive power losses and
enhancing voltage profiles.
6.4
Proposed Analytical Approach
6.4.1 Sizing PV
Most of the existing analytical methods have addressed DG allocation in distribution
systems for reducing the active power loss as a single-objective index [21-24]. This work
proposes a new analytical expression based on the multiobjective index (IMO) as given by
Equation (6.16) for sizing a PV-based DG unit at a pre-defined power factor. Substituting
Equations (6.8), (6.10) and (6.15) into Equation (6.16), we get:
IMO =
σ1
PL
PLPV +
σ2
QL
Q LPV +
σ3
VD
2
2
VD PV
(6.19)
To find the minimum IMO value, the partial derivative of Equation (6.19) with respect
to PPVk becomes zero:
∂IMO σ 1 ∂PLPV σ 2 ∂QLPV
σ ∂VD PV
=
+
+ 32
=0
PL ∂PPVk Q L ∂PPVk VD ∂PPVk
∂P PVk
2
(6.20)
The partial derivatives of Equations (6.7), (6.9) and (6.14) with respect to PPVk can be
written as:
∂PLPV
2
= −2 Ak + 2C k PPVk − 2 Bk a k + 2C k a k PPVk
∂PPVk
(6.21)
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
84
∂Q LPV
2
= −2 Dk + 2 Fk PPVk − 2 E k a k + 2 Fk a k PPVk
∂PPVk
(6.22)
∂VD PV
2
= 2Gk PPVk − 2 H k + 2 I k a k PPVk − 2 J k a k
∂PPVk
2
(6.23)
− 2 K k a k − 2 Lk + 4M k a k PPVk
k
Ak = ∑
where
i =1
k
Dk = ∑
i =1
2
k
Ri
i =1
Vi +1
Gk = ∑
k
Ri Pbi
Vi
2
X i Pbi
Vi
; Bk = ∑
2
i =1
k
; Ek = ∑
k
Kk = ∑
i =1
; Hk = ∑
i =1
Ri X i Pbi
Vi +1
2
Vi
2
Ri Pbi
Vi +1
2
2
Vi
k
i =1
Vi
2
k
; Fk = ∑
i =1
2
k
i =1
Ri X i Qbi
Vi +1
Ri
i =1
; Ik = ∑
; Lk = ∑
k
; Ck = ∑
X i Qbi
i =1
k
2
Ri Qbi
2
Xi
Vi
2
k
Xi
Vi +1
2
2
; Jk = ∑
i =1
k
; Mk = ∑
i =1
2
X i Qbi
Vi +1
2
Ri X i
Vi +1
2
Substituting Equations (6.21), (6.22), (6.23) into Equation (6.20), we get:
PPVk
σ2
σ 1

 P ( Ak + a k Bk ) + Q (Dk + a k E k )
L
 L

 σ3
(H k + a k J k + a k K k + Lk ) 
+
2
VD

=
σ2
σ 1

2
2
 P C k + a k C k + Q Fk + a k Fk 
L
 L


 σ3
2
Gk + a k I k + 2a k M k
+

2
 VD

(
)
(
(
)
(6.24)
)
The power factor of a PV unit depends on the operating conditions and technology
adopted. Given a pf PVk or ak value, the active power size of a PV unit for the minimum
IMO can be obtained from Equation (6.24). The reactive power size is then obtained using
Equation (6.5).
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
85
6.4.2 Computational Procedure
In this section, a computational procedure is developed to allocate PV units for reducing
the AIMO while considering the time-varying load models and probabilistic generation. To
reduce the computational burden, the IMO is first minimised at the average load level as
defined by Equation (6.1) to specify the location of a PV unit. This average load level has a
significantly larger duration than other loading levels (e.g., peak or low load levels). The
size is then calculated at that location based on the probabilistic PV output curve by
minimising the AIMO over all periods. The computational procedure is summarized in the
following steps:
Step 1: Run load flow for the system without a PV unit at the average load level or at the
system load factor (LF) using (6.1) and calculate the IMO using (6.16).
Step 2: Specify the location and size at a pre-defined power factor of a PV unit at the
average load level only.
avg
a) Find the PV size at each bus ( PPV ) using (6.24).
k
b) Place the PV unit obtained earlier at each bus and calculate the IMO for each
case using (6.16).
c) Locate the optimal bus at which the IMO is minimum with the corresponding
avg
size of the PV unit at the average load level ( PPV ) at that bus.
k
Step 3: Find the capacity factor of the PV unit ( CFPVk ) using (6.4).
max
Step 4: Find the optimal size of the PV unit or its maximum output ( PPVk ) at the optimal
location obtained in Step 2 as follows, where depending on the patterns of demand
and generation, an adjusted factor, k PV (e.g., 0.8, 0.9 or 1.1) could be used to
achieve a better outcome:
avg
max
PPVk
= k PV ×
PPV
k
CFPVk
(6.25)
Step 5: Find the PV output at the optimal location for period t as follows, where
p.u. PV output (t ) is the PV output in p.u. at period t, which is calculated using
equations (3.2), (3.3), (6.2) and (6.3), and normalized:
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
86
PPVk (t ) = p.u. PV output (t ) × PPVk
max
(6.26)
Step 6: Run load flow with each PV output obtained in Step 5 for each state over all the
periods of the day and calculate the AIMO using (6.18).
Step 7:
Repeat Steps 4-6 by adjusting k PV in (6.25) until the minimum AIMO is
obtained.
6.5
Case Study
6.5.1 Test Systems
The proposed approach was applied to two radial test distribution systems. The first system
illustrated in Figure 3.2 has one feeder, 69 buses and a peak demand of 3800 kW and 2690
kVAr [112]. The second system shown in Figure 3.1 has one feeder, 33 buses and a peak
demand of 3715 kW and 2300 kVAr [111]. Figures 6.5 and 6.6 present the 69- and 33-bus
systems, respectively, which are incorporated with different load types (i.e., industrial,
residential and commercial). The constraint of operating voltages is assumed from 0.95 to
1.05 p.u. [99].
Load Modelling
Five types of time-varying load models are considered in this study:
1. Time-varying industrial load model
2. Time-varying residential load model
3. Time-varying commercial load model
4. Time-varying mixed load model
5. Time-varying constant load model
For both 69- and 33-bus systems, the loads are modeled by Equation (3.1) by combining
the time-varying demand patterns for industrial, residential and commercial loads. These
loads are shown in Figure 6.1 with the voltage-dependent load type with appropriate
voltage exponents defined in Table 3.1.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
87
Figure 6.5. The 69-bus test distribution system.
Figure 6.6. The 33-bus test distribution system.
Solar PV Modelling
The presented method can be applied to either solar farm or roof-top PV. However, the
roof-top PV has been considered as an example to validate the proposed methodology in
this work. It is assumed that a PV unit provides active and reactive power at a lagging
power factor of 0.9 which is compliant with the new German grid code [103]. The mean
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
88
and standard deviation (i.e., µ and σ, respectively) for each hour of a day are calculated
using the hourly historical solar irradiance data collected for three years, as provided in
Table B.1 (Appendix B) [126]. The characteristics of a PV module [91] employed for the
PV model (3.3) can be found in Table B.2 (Appendix B). The solar irradiance s is
considered at an interval of 0.05 kW/m2. Using Equations (3.2), (3.3), (6.2) and (6.3), the
hourly expected output of the PV module is calculated and plotted in Figures 6.7a-c. It is
observed from these figures that a difference in the PV output patterns exists among hours
6-19. Actually, this is due to dependence of the PV output on the solar irradiance, ambient
temperature and the characteristics of the PV module itself. The total expected output
power for each hour can be calculated as a summation of all the expected output powers at
that hour. Accordingly, the normalized expected PV output for the 24-h period day is
plotted in Figure 6.8.
6.5.2 Location Selection
As previously mentioned, to select the best location, after one load flow analysis for the
base case system at average load level, a PV unit is sized at various buses using Equation
(6.24) and the corresponding multiobjective (IMO) for each bus is calculated. The best
location at which the IMO is lowest is subsequently determined. Figure 6.9a shows the
optimal sizes of a PV unit at various buses with the corresponding IMO values in the 69bus system with the industrial load model. The sizes are significantly different in the range
of 0.39 to 2.34 MW. It is observed from the figure that the best location is bus 61 where
the IMO is lowest. Similarly, the best location is specified at bus 6 in the 33-bus system
with the industrial load model, as depicted in Figure 6.9b. It is noticed that given a fixed
location due to resource availability and geographic limitations, the optimal size to which
the IMO is lowest can be identified from the respective figures. For the other load models
(i.e., constant, residential, commercial and mixed), the best locations are at buses 61 and 6
in the 69- and 33-bus systems, respectively. However, depending on the daily demand
patterns and characteristic of systems, the locations may be different among load models.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
Expected PV output (W)
25
89
Hour 6
Hour 7
Hour 8
Hour 9
Hour 10
20
15
10
5
0
0.05
0.15
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
0.75
0.85
0.95
0.75
0.85
0.95
Solar irradiance (kW/m2)
(a)
Expected PV output (W)
25
Hour 11
Hour 12
Hour 13
Hour 14
Hour 15
20
15
10
5
0
0.05
0.15
0.25
0.35
0.45
0.55
0.65
Solar irradiance (kW/m2)
(b)
Expected PV output (W)
25
Hour 16
Hour 17
Hour 18
Hour 19
20
15
10
5
0
0.05
0.15
0.25
0.35
0.45
0.55
0.65
Solar irradiance (kW/m2)
(c)
Figure 6.7. Expected PV output for hours: (a) 6-10, (b) 11-15 and (c) 16-19.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
90
PV output (p.u.)
1.0
0.8
0.6
0.4
0.2
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 6.8. Normalized daily expected PV output.
PV size
IMO
1.0
8
0.8
6
0.6
4
0.4
2
0.2
0
IMO
Optimal PV size (MW)
10
0.0
1
5
9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69
Bus
(a)
PV size
IMO
1.0
8
0.8
6
0.6
4
0.4
2
0.2
0
IMO
Optimal PV size (MW)
10
0.0
1
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33
Bus
(b)
Figure 6.9 PV size with respect to IMO at various locations at average load level for the
industrial load model: (a) 69-bus system and (b) 33-bus system.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
91
6.5.3 Sizing with Respect to Indices
For the 69-bus system, Figure 6.10 shows the hourly expected outputs of a PV unit at bus
61 over one day (06:00 to 19:00) with different time-varying load models. These PV
output patterns exactly follow the expected PV output curve depicted in Figure 6.8. The
maximum output of the PV unit for each load models, which is indentified at hour 11,
shows its optimum size. Figure 6.11 presents the expected IMO values which are
respectively obtained for the 69-bus system with the PV unit. At each period of the day, the
IMO values in the system with the PV unit are substantially declined when compared to the
system without the PV unit (IMO = 1 p.u.). This indicates that the PV installation
positively affects the IMO. Figure 6.12 shows a comparison of the optimal PV size, and the
averages of IMO and its components (ILP, ILQ and IVD) in the 69-bus system for different
time-varying load models. As shown in Figure 6.12, a significant difference in the optimal
size of the PV unit is observed when different time-varying load models are considered.
The PV size for the commercial load is remarkably larger than the industrial and residential
loads. This is due to the fact that the commercial consumption and PV output availability
(Figures 6.1 and 6.11) almost occurred simultaneously during the day, while the industrial
and residential customers had most of the consumption during the night. It is revealed from
Figure 6.12 that the maximum PV size is determined for the commercial load, whereas the
minimum PV size is indentified for the residential load. In addition, the size of the PV unit
for the time-varying constant load model is roughly 9.09% bigger than the time-varying
mixed load model. A similar trend has been observed for the 33-bus system.
2.0
PV output (MW)
1.6
1.2
Constant
Industrial
Residential
Commercial
Mixed
0.8
0.4
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 6.10. Hourly expected PV outputs at bus 61 for the 69-bus system for different
time-varying load models.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
92
1.0
IMO (p.u.)
0.8
0.6
Constant
Industrial
Residential
Commercial
Mixed
0.4
0.2
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 6.11. Hourly expected IMO curves for the 69-bus system with a PV unit at bus 61
for different time-varying load models.
PV size and indices
2.0
1.6
1.2
0.8
0.4
0.0
Const
Ind
Res
Com
Mixed
Load model
Size (MW)
AILP
AILQ
AIVD
AIMO
Figure 6.12. PV size and indices for the 69-bus system with a PV unit at bus 61 for
different time-varying load models.
Table 6.1 shows a summary and comparison of the results of PV allocation obtained in
the 69- and 33-bus systems with different time-varying load models. The results include
the optimum bus, size and penetration of the PV unit and corresponding AIMO for each
load model. Differences in the location, size and penetration exist among the load models.
For the 69-bus system, the minimum and maximum AIMO values are respectively 0.573
(p.u.) for the commercial load model and 0.660 (p.u.) for the residential load model. A
similar trend is observed for the 33-bus system. The lowest AIMO is 0.716 (p.u.) for the
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
93
commercial load model, whereas the highest AIMO is 0.770 (p.u.) for the residential load
model.
Table 6.1. PV allocation in the 69- and 33-Bus Systems
69-bus System
33-bus system
Load
models
Bus
Size
(MW)
AIMO
Bus
Size
(MW)
AIMO
Constant
61
1.20
0.609
6
1.80
0.737
Industrial
61
1.05
0.590
6
1.55
0.722
Residential
61
0.90
0.660
6
1.15
0.770
Commercial
61
1.85
0.573
6
2.50
0.716
Mixed
61
1.10
0.622
6
1.65
0.754
6.5.4 PV Penetration and Energy Losses
Figure 6.13 shows the PV penetration levels in the 69- and 33-bus systems with different
time-varying load models. First, it is observed that the time-varying load models adopted
have a diverse impact on the penetration level. In the 69-bus system, the penetration levels
are 32.59% for the commercial load model and 19.55% and 17.38% for the industrial and
residential load models, respectively. This is because the PV generation pattern (Figure
6.7) matches better with the commercial demand than the industrial and residential demand
curves (Figure 6.1). Similarly, in the 33-bus system, the penetration levels are 45.23% for
the commercial load model and 29.64% and 22.80% for the industrial and residential load
models, respectively. Secondly, it is shown from Figure 6.13 that there is a difference in
the PV penetration between the time-varying constant and mixed load models in both test
systems. In the 69-bus system, the PV penetration is 22.18% for the time-varying constant
load model, whereas this value is 20.34% for the time-varying mixed load model.
Similarly, in the 33-bus system, the PV penetration levels are 34.18% and 31.33% for the
time-varying constant and mixed load models, respectively. Finally, it is also revealed that
the system load characteristics play a crucial role in determining the PV penetration. For
each load model, the PV penetration in the 69-bus system is lower than the 33-bus system,
as shown in Figure 6.13.
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
40
69-bus system
33-bus system
31.33
20.34
45.23
32.59
22.80
17.38
29.64
10
19.55
20
34.18
30
22.18
PV penetration (%)
50
94
0
Const
Ind
Res
Com
Mixed
Load models
Figure 6.13. PV penetration levels in the 69- and 33-bus systems.
Table 6.2 shows a summary and comparison of the energy loss of the system without
and with the PV unit over a day (EL and ELPV, respectively) for different time-varying load
models. The daily energy loss is calculated as a sum of all hourly power losses over the
day. For each load model, it is observed that the energy loss of the system with the PV unit
is significantly reduced when compared to that of the system without the PV unit. In
addition, due to inclusion of the active and reactive load voltage exponents in the mixed
load model, the energy losses with and without the PV unit for this model are respectively
lower than the constant load model. Table 6.2 also shows the results of the energy loss
reduction of the two systems (∆E) for all load models. In both systems, the maximum loss
reduction is observed in the commercial load, whereas the minimum value is obtained in
the industrial customer. This is due to the fact that the PV generation matches better with
the commercial load than the industrial customer, as previously mentioned.
Table 6.2. Energy loss reduction over a day for 69 and 33-Bus Systems
69-bus System
Load
models
33-bus system
EL
(MWh)
ELPV
(MWh)
∆E
(%)
EL
(MWh)
ELPV
(MWh)
∆E
(%)
Constant
1.87
1.32
29.54
1.73
1.25
28.13
Industrial
1.56
1.11
28.50
1.51
1.18
21.32
Residential
1.49
1.01
32.28
1.45
1.11
23.33
Commercial
1.68
0.52
68.90
1.63
0.81
50.20
Mixed
1.54
1.08
29.79
1.43
1.04
27.58
CHAPTER 6. MULTI-OBJECTIVE PV INTEGRATION
6.6
95
Summary
This chapter proposed an analytical approach to determine the penetration of PV units in a
distribution system with different types of time-varying load models. In this approach, an
IMO-based analytical expression was proposed to identify the size of PV units, which is
capable of supplying active and reactive power, with objectives of simultaneously reducing
active and reactive power losses and voltage deviation. The analytical expression was then
adapted to accommodate PV units while considering the characteristics of time-varying
voltage-dependent load models and probabilistic generation. The Beta PDF model was
used to describe the probabilistic nature of solar irradiance. The results indicated that the
time-varying load models play a critical role in determining the PV penetration in any
distribution system. For the residential load model, a poor match between the generation
and demand leads to relatively low PV penetration levels, roughly 17% and 23% in the 69and 33-bus systems, respectively. Similarly, for the industrial load, due to a mismatch
between the generation and demand, the 69- and 33-bus systems can accommodate PV
penetration levels of approximately 20% and 30%, respectively. In contrast, for the
commercial load model, a good match between the demand and generation results in
higher penetration levels at around 33% and 45% in the respective 69- and 33-bus systems.
In addition, a practical load model which is defined as a time-varying mixed load model of
residential, industrial and commercial types was examined. It was observed that the PV
penetration in the time-varying mixed load model is lower than the time-varying constant
load model. This study recommends that the time-varying mixed load model should be
used for determining PV penetration for a distribution network.
CHAPTER 7
PV AND BES INTEGRATION FOR ENERGY
LOSS AND VOLTAGE STABILITY
7.1
Introduction
As discussed in Chapters 4-6, PV units can be allocated to minimize energy losses and
enhance voltage profiles in distribution systems. However, the high penetration of this
intermittent renewable source together with demand variations has introduced many
challenges to distribution systems such as power fluctuations, voltage rise, high losses and
low voltage stability [5]. Consequently, generated power curtailment, dump loads and
dispatchable BES systems have been utilized together with intermittent renewable DG
units (i.e., wind and solar) to eliminate the intermittency, reduce power fluctuations and
avoid any violation of the system constraints [128].
As discussed in Chapter 2, renewable DG integration in distribution systems that
considers energy loss and voltage stability has attracted attention in recent years, but both
issues have been addressed separately. Few studies on renewable DG allocation (e.g.,
biomass, wind and solar) have been presented for minimising energy losses considering
demand and generation variations. Similarly, few works on renewable DG placement have
been reported for voltage stability enhancement. Furthermore, depending on the
characteristics of loads served, optimal DG power factor dispatch for each load level would
be a crucial part for minimising energy losses. However, most of the current studies have
assumed that DG units operate at pre-specified power factors.
96
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
97
This chapter studies the integration of PV and BES units in a commercial distribution
system for reducing energy loss and enhancing voltage stability. Here, each
nondispatchable PV unit is converted into a dispatchable source with a combination of PV
and BES units. New multiobjective index (IMO)-based analytical expressions are proposed
to capture the size and power factor of the combination of PV and BES units. A SelfCorrection Algorithm (SCA) is also developed for sizing multiple PV and BES units while
considering the time-varying demand and probabilistic generation. The proposed
methodology is tested in the 33-bus test distribution system (Figure 3.1).
7.2
Load and Generation Modelling
7.2.1 Load Modelling
The demand of the system under the study is assumed to follow a 24-h daily commercial
load curve [125] as shown in Figure 6.1. The time-varying commercial load model as
defined in Section 3.2 is also considered in this work.
7.2.2 Nondispatchable PV Modelling
The PV unit considered is a nondispatchable and probabilistic source and its modelling is
described in Section 6.2.2. Given the fact that capacitors have been traditionally utilized to
deliver reactive power or correct power factors for loss reduction and voltage stability
enhancement. However, they are not smooth in controlling voltages and not flexible to
compensate for transient events due to the impact of intermittent renewable energy
resources [100, 101]. As a fast response device, the inverter-based PV unit has the
capability to control reactive power or power factors for loss minimization and voltage
regulation while supplying energy as a primary purpose [100, 101]. This study considers
that a PV unit is associated with two types of converters (type 1 and type 2) for
comparison.
•
Type 1 is capable of operating at any desired power factor (lagging/leading) to
deliver active power and inject or absorb reactive power over all periods [100, 101,
104].
•
Type 2 can deliver active power only (i.e., unity power factor) as per the standard
IEEE 1547 [99].
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
98
7.2.3 Dispatchable BES Modelling
The Battery Energy Storage (BES) unit is modelled as a dispatchable source described in
Section 3.3.1.2. The BES energy variation at bus k in period t can be expressed as [129]:
DISCH
E BESk (t ) = E BESk (t − 1) −
PBESk (t )
ηd
∆t , for PBESk (t ) > 0
(7.1)
E BESk (t ) = E BESk (t − 1) − η c PBESk (t )∆t , for PBESk (t ) ≤ 0
CH
CH
DISCH
where E BESk is the total energy stored in the BES unit; PBESk
and PBESk
are respectively
the charge and discharge power of the BES unit; η c and η d are respectively the charge
and discharge efficiencies of the BES unit; ∆t is the time duration of period t.
The lower and upper bounds of the BES unit should be satisfied as follows [107]:
E BESk ≤ E BESk (t ) ≤ E BESk
min
min
max
(7.2)
max
where E BESk and E BESk are respectively the lower and upper bounds of the energy in the
BES unit. In this research, the lower and upper bounds are assumed to be 20% and 90% of
the installed capacity of the BES unit, respectively [107, 130].
7.3
Problem Formulation
7.3.1 Conceptual Design
Figure 7.1a-b shows the proposed conceptual model of a grid-connected PV and BES
system (PV-BES). This system is intended to be installed on the rooftop areas of
commercial buildings. The idea is to convert each nondispatchable to dispatchable PV unit
with a combination of PV and BES units to retain the system active and reactive power
losses for each load level at the lowest levels. This combination can produce a daily
amount of dispatchable energy, E( PV + BES ) . Here, in a 24-h day cycle, the PV unit is
generating an amount of energy, E PV . A portion of this energy is delivered to the grid,
GRID
E PV
CH
. The redundant energy of the PV unit is used to charge the BES unit, E BES rather
than curtailing it when the PV output is high during the day. This stored energy is then
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
DISCH
discharged to the grid, E BES
99
when the PV output is small or zero during the night. The
PV and BES units are placed in the same bus to avoid network energy losses during the
charge of the BES unit. The daily energy amount of a combination of PV and BES units
over the total period (T = 24 hours) at bus k can be written as:
(a)
2
Output (MW)
E PV
BES charging
from PV ( E CH )
BES
2
1
E ( PV + BES )
1
DG generating to grid
( GRID )
EPV
BES discharging
DISCH )
to grid (E BES
0
1
2
3
4
5
6
7
8
BES discharging
to grid ( E DISCH )
BES
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
Figure 7.1. Conceptual model of grid-connected PV-BES system: (a) Connection diagram
and (b) Charging and discharging characteristics of BES and PV outputs.
T
24
0
t =1
E ( PV + BES )k = ∫ Pk (t )dt = ∑ Pk (t )∆t
(7.3)
where Pk (t ) is the active power output of the combination of PV and BES units at bus k at
period t across a given day. The power factor of PV and BES units are optimally
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
100
dispatched for each 1-h period. From the utility perspective, this model can reduce energy
loss and enhance voltage stability, which are respectively related to active and reactive
power loss indices as explained below.
7.3.2 Impact Indices
Active Power Loss Index
When a mix of PV and BES units, ( PV + BES ) is injected both active power ( Pk ) and
reactive power ( Qk ) at bus k, Equation (4.18) can be rewritten as:
k
PL ( PV + BES ) = ∑
(Pbi − Pk )2 R
i =1
(
Let ak = ± tan cos
Vi
−1
i
2
+
2
n
Pbi
∑
i = k +1 Vi
( pf k )) ;
2
k
Ri + ∑
(Qbi − Qk )2 R
Vi
i =1
i
2
+
n
∑
2
Qbi
i =k +1 Vi
2
Ri
(7.4)
ak is positive for the PV-BES mix injecting reactive power
and ak is negative for the PV-BES mix consuming reactive power; pf k is the operating
power factor of the PV-BES mix at bus k, the relationship between Pk and Qk at bus k can
be expressed as:
Qk = ak Pk
(7.5)
From Equations (4.18), (7.4) and (7.5), we obtain:
k
PL ( PV + BES ) = ∑
i =1
Pk − 2 Pbi Pk
2
Vi
2
k
Ri + ∑
ak Pk − 2Qbi ak Pk
2
i =1
2
Vi
2
Ri + PL
(7.6)
Finally, the active power loss index (ILP) is defined as the ratio of Equations (7.6) and
(4.18) as follows:
ILP =
PL ( PV + BES )
PL
(7.7)
where the total active power loss (PL) in a radial distribution system with n branches can be
calculated as Equation (4.18).
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
101
Reactive Power Loss Index
Similar to Equation (7.6), when a mix of PV and BES units, ( PV + BES ) is injected both
Pk and Qk = ak Pk at bus k, Equation (4.19) can be rewritten as follows:
k
QL ( PV + BES ) = ∑
Pk − 2 Pi Pk
2
Vi
i =1
2
k
Xi + ∑
ak Pk − 2Qi ak Pk
2
2
i =1
Vi
2
X i + QL
(7.8)
Finally, the reactive power loss index (ILQ) is defined as the ratio of Equations (7.8)
and (4.19) as follows:
ILQ =
QL ( PV + BES )
QL
(7.9)
where the total reactive power loss (QL) in a radial distribution system with n branches can
be calculated as Equation (4.19).
7.3.3 Multiobjective Index
The multiobjective index (IMO) is a combination of the ILP and ILQ indices, respectively
related to energy loss and voltage stability by assigning a weight to each index. The IMO
index that can be utilized to assess the performance of a distribution system with PV and
BES inclusion can be expressed as follows:
IMO = σ 1ILP + σ 2 ILQ
where
∑i=1σ i = 1.0 ∧ σ i ∈ [0, 1.0] .
2
(7.10)
This can be performed since all impact indices are
normalized (values between zero and one) [29]. When hybrid PV and BES systems are not
connected to the system (i.e., base case system), the IMO is the highest at one.
These weights are intended to give the corresponding importance to each impact index
for the connection of hybrid PV-BES systems and depend on the required analysis (e.g.,
planning and operation) [29, 54, 55, 58]. The determination of suitable values for the
weights will also rely on the experience and concerns of engineers. The integration of
hybrid PV-BES systems has a significant impact on the energy loss and voltage stability of
distribution networks. Currently, the energy loss is one of the major concerns at the
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
102
distribution system scale due to its impact on the utilities’ profit, while the voltage stability
is less important than the energy loss. Therefore, the weight for the energy loss should be
higher than that for the voltage stability. In future, if the importance of voltage stability is
increased due to high intermittent renewable penetration and an increase in loads and
system security, the weights can be adjusted based on the priority. Considering the above
current concerns and referring to previous research papers [29, 54, 55, 58], this study
assumes that the active power loss related to energy loss receives a significant weight of
0.7, leaving the reactive power loss related to voltage stability at a weight of 0.3.
The IMO at period t, IMO (t ) is obtained from Equation (7.10). Hence, the average
multiobjective index (AIMO) over the total period (T = 24 hours) in a distribution system
with an interval ( ∆t ) of 1 hour can be expressed as follows:
T
AIMO =
1
1 24
IMO
(
t
)
dt
=
∑ IMO(t )∆t
T ∫0
24 t =1
(7.11)
The lowest AIMO implies the best PV and BES allocation for energy loss reduction and
voltage stability enhancement. The objective function defined by the AIMO in Equation
(7.11) is subject to technical constraints as follows. The bus voltages ( Vk ) must remain
within acceptable limits in all periods
Vmin ≤ Vk (t ) ≤ Vmax
(7.12)
7.3.4 Energy Loss and Voltage Stability
Energy Loss
The active power loss at each period t, Ploss (t ) can be obtained from Equation (4.18)
without a PV-BES unit or Equation (7.6) with a PV-BES unit. Hence, the total annual
energy loss ( Eloss ) over the total period (T = 24 hours) in a distribution system with a time
duration ( ∆t ) of 1-h can be expressed as:
T
24
0
t =1
Eloss = 365∫ Ploss (t )dt = 365∑ Ploss (t )∆t
(7.13)
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
103
Voltage Stability
The static voltage stability can be analyzed using the relationship between the receiving
Power (P) and the Voltage (V) at a certain bus in a distribution power system, as illustrated
in Figure 7.2. This curve is known as a P-V curve and obtained using the CPF technique
[131]. The Critical Point (CP) or the voltage collapse point in the curve represents the
maximum loading (λmax) of the system. The Voltage Stability Margin (VSM) is defined as
the distance from an operating point to the critical point. As shown in Figure 7.2, the
scaling factor of the load demand at a certain operating point (λ) varies from zero to λmax.
When a hybrid PV-BES system is properly injected in the system, the loss reduces.
Accordingly, the V1 and CP1 enhance to V2 and CP 2 , respectively. Hence, the maximum
loadability increases from λmax1 to λmax2 as defined as follows [45, 51]. The voltage
stability margin subsequently improves from VSM1 to VSM2.
PD = λPDo ; QD = λQDo
(7.14)
where PDo and QDo correspond to the initial active and reactive power demands,
respectively.
1.1
Without DG unit
1.0
With DG unit
V2
V1
0.9
Voltage (p.u.)
0.8
0.7
VSM2
0.6
VSM1
0.5
CP1
0.4
0.3
00
1
2
(λ)
Loading parameter
3
CP2
λmax1 4λmax2
Figure 7.2. Hybrid PV-BES system impact on maximum loadability and voltage stability
margin [45, 51].
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
7.4
104
Proposed Methodology
7.4.1 Proposed Analytical Expressions
Most of the current analytical approaches have addressed PV placement in distribution
systems for active power loss minimization as a single-objective index [21-25]. Chapter 4
also presented the analytical approaches to accommodate renewable DG units for energy
loss reduction only. In addition, a multiobjective index (IMO)-based analytical approach
was reported in Chapter 6, but it can be used for the PV allocation only. This section
presents new analytical expressions based on the multiobjective index (IMO) defined by
Equation (7.10) to calculate the size and power factor of a mix of PV and BES units.
Substituting Equations (7.7) and (7.9) into Equation (7.10), we obtain:
IMO( Pk , ak ) =
σ1
PL
PL ( PV + BES ) +
σ2
QL
QL ( PV + BES )
(7.15)
As given in Equation (7.15), the IMO variation is a function of the PV-BES penetration
level related to variables Pk and ak (or pf k : the power factor of the PV-BES mix at bus k).
At the minimum IMO, the partial derivative of Equation (7.15) with respect to both
variables at bus k becomes zero.
∂IMO σ 1 ∂PL ( PV + BES ) σ 2 ∂QL ( PV + BES )
=
+
=0
∂P k
PL
∂Pk
QL
∂Pk
(7.16)
∂IMO σ 1 ∂PL ( PV + BES ) σ 2 ∂QL ( PV + BES )
=
+
=0
∂a k
∂ak
∂ak
PL
QL
(7.17)
The derivative of Equations (7.6) and (7.8) with respect to Pk can be expressed as
follows:
∂PL ( PV + BES )
2
= −2 Ak + 2 Bk Pk − 2Ck ak + 2 Bk ak Pk
∂Pk
(7.18)
∂QL ( PV + BES )
2
= −2 Dk + 2 Ek Pk − 2ak Fk + 2ak Ek Pk
∂Pk
(7.19)
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
k
where
Ak = ∑
i =1
k
Dk = ∑
i =1
k
Ri Pbi
Vi
2
i =1
X i Pbi
Vi
; Bk = ∑
2
k
; Ek = ∑
i =1
k
Ri
Vi
2
Vi
2
Ri Qbi
; Ck = ∑
Vi
i =1
k
Xi
; Fk = ∑
105
2
X i Qbi
i =1
Vi
2
Substituting Equations (7.18) and (7.19) into Equation (7.16), we get:
Pk =
σ 1 ( Ak + Ck ak )QL + σ 2 ( Dk + ak Fk ) PL
2
2
σ 1 ( Bk + Bk ak )QL + σ 2 ( Ek + Ek ak ) PL
(7.20)
The derivative of Equations (7.6) and (7.8) with respect to ak can be expressed as
follows:
∂PL ( PV + BES )
2
= −2Ck Pk + 2 Bk ak Pk
∂ak
(7.21)
∂QL ( PV + BES )
2
= −2 Fk Pk + 2ak Ek Pk
∂ak
(7.22)
Substituting Equations (7.21) and (7.22) into Equation (7.17), we obtain:
ak =
σ 1Ck QL + σ 2 Fk PL
Pk (σ 1Bk QL + σ 2 Ek PL )
(7.23)
The relationship between the power factor of a PV-BES unit ( pf k ) and variable ak at
bus k can be expressed as follows:
(
pf k = cos tan
−1
(ak ))
(7.24)
At the minimum IMO, the optimal size and power factor at bus k, period t (i.e., Pk (t )
and pf k (t ) , respectively) can be obtained from Equations (7.20), (7.23) and (7.24) as:
Pk (t ) =
σ 1 Ak (t )QL (t ) + σ 2 Dk (t ) PL (t )
σ 1Bk (t )QL (t ) + σ 2 Ek (t ) PL (t )
(7.25)
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
 −1  σ C (t )QL (t ) + σ 2 Fk (t ) PL (t )  
 
pf k (t ) = cos tan  1 k
σ
A
(
t
)
Q
(
t
)
σ
D
(
t
)
P
(
t
)
+
1
k
L
2
k
L



106
(7.26)
The optimal size and power factor of a single PV-BES unit for each period can be
calculated using Equations (7.25) and (7.26), respectively. When multiple PV-BES units
are considered, the SCA developed below is employed.
7.4.2 Self-Correction Algorithm
Sizing PV-BES
This section presents a new algorithm to size multiple PV-BES units, which are known as a
combination of PV and BES units, at a number of pre-specified buses to minimize the
active and reactive power losses at each load level. As proposed in Section 7.2.1, each PVBES unit is placed at the same bus. Here, the PV-BES unit is modelled as a dispatchable
source. The algorithm includes two tasks. The first task is to calculate the approximate size
and power factor of the PV-BES unit using Equations (7.25) and (7.26) at pre-specified
buses, respectively. The second task is to re-calculate the size and power factor of each
PV-BES unit obtained previously using Equations (7.25) and (7.26), respectively. The
second task is repeated until the difference between the last and previous IMO values is
reached to a pre-defined tolerance (zero in this study). The algorithm involves the
following steps:
Step 1: Set buses to install PV-BES units.
Step 2: Run load flow for the first period and calculate the size and power factor of each
PV-BES unit for each bus using Equations (7.25) and (7.26), respectively. Find the
IMO for each case using Equation (7.10). Locate the bus where the IMO is the
lowest with the corresponding size and power factor. Update the load data with the
PV-BES unit obtained at this bus. Repeat Step 2 for the rest of the selected buses.
Step 3: Re-calculate the size and power factor by repeating Step 2 until the difference
between the last and previous IMO values is reached to zero.
Step 4: Repeat Steps 2 to 3 for the rest periods. Calculate the AIMO using Equation (7.11).
The above algorithm is developed to place PV-BES units considering the optimal power
factor. This algorithm can be modified to allocate PV-BES units with a pre-specified
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
107
power factor. When the power factor is pre-specified, the algorithm is similar to the above
with exception that in Step 2, the size of the PV-BES unit for each bus is determined using
Equation (7.20) rather than Equation (7.25). After the size of the combination of the PVBES unit is found for each bus, two additional analyses explained below are implemented
to capture the individual size of the PV and BES units for each selected bus.
Sizing PV
As shown in Figure 7.1a-b, the daily charging and discharging energies at bus k is obtained
from the hourly input and output power of the BES unit.
T
CH
EBES k
=∫
CH
PBES k
24
(t )dt = ∑ PBES k (t )∆t
CH
T
24
E BES k = ∫ PBES k (t )dt = ∑ PBES k (t )∆t
DISCH
(7.27)
t =1
0
DISCH
DISCH
(7.28)
t =1
0
The total output energies of the PV-BES mix and PV unit at bus k is respectively
calculated as follows:
E( PV + BES ) k = EPVk + EBES k
(7.29)
E PVk = E PVk + E BES k
(7.30)
GRID
GRID
GRID
where E PVk
DISCH
CH
is the amount of PV energy delivering to the grid at bus k. The charging and
discharging energy of the BES unit at bus k with a round trip efficiency ( η BES = ηc ×ηd ) is
expressed as:
DISCH
E BES k
= η BES E BES k
CH
(7.31)
The total output energy of the PV unit at bus k can be obtained from Equations (7.29),
(7.30) and (7.31) as follows:
E( PV + BES ) k − (1 − η BES )E PVk
GRID
E PVk =
η BES
(7.32)
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
108
The maximum power generation of the PV unit during a specific period over a 24-h day
cycle is utilized to specify the power rating or optimal size of the PV unit at bus k.
PPVk = k PV EPVk
unit
(7.33)
unit
where k PV =
unit
amount of
PPV
unit
EPV
unit
unit
, PPV is the maximum output of a PV module unit, and E PV is the
PV generated energy over a 24-h day. Assuming η BES =1, i.e.,
E PVk = E( PV + BES ) k , the initial PV size is calculated from Equation (7.33) as
PPVk = k PV E( PV + BES ) k , and E PVk
'
unit
GRID '
is then obtained from Figure 7.1a-b, for example.
When ηBES is less than unity, PPVk increases. However, as demonstrated in the simulation
GRID
GRID '
results, E PVk rises insignificantly compared to E PVk . Hence, the optimal PV size is
obtained from Equations (7.32) and (7.33) as follows:
PPVk =
E
unit
k PV 


( PV + BES ) k
GRID '
− (1 − η BES )EPVk 

η BES

(7.34)
Sizing BES
The optimal size of the BES unit at bus k is calculated with respect to the power rating
( PBES k ) and energy capacity ( E BES k ) such that it can accommodate all redundant energy of
the PV unit that needs to be curtailed to maintain the system loss for each period at the
lowest level. The maximum charging and discharging power during a specific period
across a 24-h day cycle is utilized to specify the power rating of the BES unit. The
maximum charging energy during this cycle is used to determine the energy capacity of the
BES unit.
7.5
Case Study
7.5.1 Test System
The proposed methodology was applied to the 33-bus distribution system depicted in
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
109
Figure 3.1. The system demand follows a commercial load curve illustrated in Figure 6.1.
It is assumed that operating voltages are from 0.95 to 1.05 p.u. The hourly expected output
of the PV module is plotted in Figure 6.8. Three PV units are assumed to be allocated at
buses 12, 20 and 24. Sodium-sulfur BES unit considered has a roundtrip efficiency of 77%.
To demonstrate the effectiveness of the methodology, the following scenarios are
considered.
•
Scenario 1: Three PV-BES units that can generate both active and reactive power at
optimal power factor for each period, as proposed in this chapter.
•
Scenario 2: Three PV-BES units that can deliver active power only (i.e., unity power
factor) for all periods as per the standard IEEE 1547 [99].
7.5.2 Numerical Results
Sizing PV and BES Units
Figure 7.3a-c shows the results of PV-BES placement with optimal power factor dispatch
at buses 12, 20 and 24 for scenario 1. The number of PV-BES units can be limited due to
the availability of PV resources and geographic limitations. The output and power factor of
PV-BES units are optimally dispatched for each 1-h period across a 24-h day cycle such
that the system can achieve the lowest IMO for each period. As shown in Figure 7.3a, PVBES units 1, 2 and 3 correspond to the PV-BES units located at buses 12, 20 and 24
respectively. The output curves of these PV-BES units follow the load demand pattern in
Figure 3.1 as the PV-BES units are dispatchable sources. It can be seen from Figure 7.3b
that the power factor of PV-BES unit 1 at bus 12 is dispatched for each period across a 24h day in the range of 0.860 and 0.867 (lagging). For PV-BES unit 2 at bus 20, the power
factor varies from 0.899 to 0.901 (lagging). Similarly, the power factor of PV-BES unit 3
at bus 24 varies between 0.872 and 0.876 (lagging). Figure 7.3c shows the ILP, ILQ and
IMO values for each period related to the active power loss, reactive power loss and
multiobjective indices respectively after the three PV-BES units are installed in the system.
Significant reductions in the indices ILP, ILQ and IMO show the positive effect of three
PV-BES units placement on the system. At each period, the ILP is lower than the ILQ,
indicating that the system can benefit more from reducing the active power loss than the
reactive power loss. Similar results have been obtained for scenario 2 (i.e., the PV-BES
unit is capable of delivering active power only).
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
1.5
110
PV-BES 1
Ouput (MW)
PV-BES 2
1.0
PV-BES 3
0.5
0.0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(a)
0.910
PV-BES 1
PV-BES 2
PV-BES 3
Power factor
0.900
0.890
0.880
0.870
0.860
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(b)
ILP/ILQ/IMO
0.38
ILQ
ILP
IMO
0.37
0.36
0.35
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
(c)
Figure 7.3. Daily PV-BES outputs, power factor and index curves for scenario 1: (a) PVBES outputs, (b) Power factor of PV-BES units, (c) Indices with three PV-BES units.
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
111
Table 7.1 summaries the results of PV-BES placement for scenarios 1 and 2, including
the optimal size and power factor for each location. The optimal size of each PV-BES unit
which corresponds to its maximum output at hour 11 is obtained from Figure 7.3a. Table
7.1 also shows the AILP, AILQ and AIMO values which correspond to the average active
power loss, average reactive power loss and average multiobjective indices over 24 hours
across the day, respectively. It can be seen from Table 7.1 that in scenario 1, the power
factors of the PV-BES units at buses 12, 20 and 24 are different at 0.867, 0.901 and 0.876
(lagging), respectively. It is also observed from the table that operation of the PV-BES
units with power factor dispatch for each period in scenario 1 can make a significant
contribution to minimising the AIMO when compared to that with unity power factor in
scenario 2.
Table 7.1. PV-BES placement with optimal lagging and unity power factors
Scenario
Bus
Size (MW)
Power
factor
AILP
AILQ
AIMO
1
12
1.160
0.867
0.3484
0.3691
0.3546
20
0.326
0.901
24
1.164
0.876
12
1.155
1.000
0.5150
0.5255
0.5181
20
0.327
1.000
24
1.167
1.000
2
Figure 7.4 presents the hourly expected PV output at bus 12 for scenario 1 with optimal
power factor dispatch. This curve exactly follows the expected PV output curve in Figure
3.2. The maximum output of each PV unit that is indentified at hour 12 indicates its
optimum size. The figure also shows the amount of energy that the PV unit can generate
versus the amount of PV-BES energy accommodated by the network to retain the loss for
each period at the lowest level. The sum of the hourly differences between these two
patterns identifies the amounts of energy charged and discharged by the BES unit. The
amount of PV energy that needs to be curtailed to remain the minimum energy loss is
stored into the BES unit. This stored energy portion is then discharged to the grid
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
112
following the PV-BES output curve to keep the lowest energy loss as well. The maximum
difference found at hour 13 gives the maximum power of the charging energy or the power
rating of the BES unit ( PBES ). The maximum charging energy over a 24-h day cycle is
used to calculate the capacity of the BES unit ( E BES ). The charging and discharging time
of the BES unit can be identified from Figure 7.4. Similar results have been found for the
PV-BES units at buses 20 and 24 in scenario 1 (optimal power factor) and buses 12, 20 and
24 in scenario 2 (unity power factor) as well.
PV-BES output
1.0
PPV
Output (MW)
1.5
PBES
PV output
BES
charging
from PV
2.0
0.5
0.0
BES discharging
to grid
PV generating to grid
BES discharging
to grid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Hour
Figure 7.4. Daily charging and discharging curves of BES unit at bus 12 for scenario 1.
Tables 7.2 and 7.3 summarize the results of the size of PV units and the power rating
and energy capacity of BES units for each location in scenarios 1 and 2, respectively. It is
observed from the tables that the similarity in the size of the PV units in MW, the power
rating of the BES units in MW and the energy capacity of the BES units in MWh exist
between scenarios 1 and 2. However, as previously mentioned, the PV-BES units in
scenario 1 deliver both active and reactive power at optimal lagging power factor for each
period across a 24-h day (see Figure 7.3b), as proposed in this chapter, whereas the PVBES units in scenario 2 only supply active power over all periods as per the standard IEEE
1547 [99]. Particularly, as shown in Table 7.2, the total size of the PV units is 4.336 MW
of the active power and 2.396 MVAr of the reactive power. The total active and reactive
power ratings of the BES units are 1.804 MW and 0.997 MVAr, respectively and the total
energy capacity of the BES units over the day is 13.544 MWh. In this scenario, the BES
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
113
units also either absorb or inject the amount of reactive power for each hour of the day. For
scenario 2, as shown in Table 7.3, the total active power size of the PV units is 4.336 MW.
The total active power rating of the BES units is 1.803 MW and the total energy capacity
of the BES units over the day is 13.549 MWh. Unlike scenario 1, in this scenario, as the
BES units operate at unity power factor, there is no reactive power delivered or absorbed
by these units.
Table 7.2. Sizing PV and BES units at optimal lagging power factor (Scenario 1)
Bus
12
20
24
Total
PV size (MW)
1.858
0.526
1.952
4.336
PV size (MVAr)
1.068
0.253
1.075
2.396
BES power rating (MW)
0.770
0.221
0.813
1.804
BES power rating (MVAr)
0.443
0.106
0.448
0.997
BES energy capacity (MWh)
5.750
1.655
6.139
13.544
Table 7.3. Sizing PV and BES units at unity power factor (Scenario 2)
Bus
12
20
24
Total
PV size (MW)
1.858
0.526
1.952
4.336
BES power rating (MW)
0.773
0.220
0.810
1.803
BES energy capacity (MWh)
5.786
1.648
6.115
13.549
Energy Loss and Voltage Stability
Figures 7.5 and 7.6 show the results of energy loss and PV curve-based voltage stability
margin of the system with and without the PV-BES units, respectively. The power factors
of the PV-BES units is set at unity in compliance with the current standard IEEE 1547 [99]
and optimally dispatched for each period as proposed in this chapter. It is observed from
the figures that operation of the PV-BES units with optimal power factor dispatch
(scenario 1) can significantly reduce energy loss and better enhance voltage stability when
compared to that with unity power factor (scenario 2).
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
114
As illustrated in Figure 7.5, the system power loss for scenario 1 with optimal power
factor dispatch for each period is rather lower than that for scenario 2 with unity power
factor. Table 7.4 summarizes the results of the annual energy losses of the system for all
scenarios. Before PV-BES insertion (i.e., for the base case scenario), the annual energy
loss is 701.33 MWh. After PV-BES installation, scenario 1 obtains a maximum energy loss
reduction of 70.44%, whereas scenario 2 achieves an energy loss reduction of 56.55%
only.
As shown in Figure 7.6, V is the normal operating point voltages (λ = 1), λmax is the
maximum loading, VSM is the voltage stability margin that is defined as the distance from
the operating point to a voltage collapse point or a critical point (CP), ∆VSM is an increase
in the voltage stability margin. In scenario 1, when three PV-BES units generate an amount
of 2.65 MW at their optimal power factors found in Table 7.1, the normal operating point
voltage at the weakest point (bus 18) improves from V0 (without PV-BES units) to V1 (with
PV-BES units). The maximum loading increases from λmax0 (without PV-BES units) to
λmax1 (with PV-BES units). Hence, the voltage stability margin in scenario 1 (∆VSM1) is
enhanced by roughly 0.29. Similarly, the ∆VSM2 in scenario 2 is increased by
approximately 0.25. These results are summarized in Table 7.4. It is obvious that the
combination of the PV and BES units with optimal power factor dispatch for each period
(scenario 1) achieves a larger VSM value than that with unity power factor (scenario 2).
Figure 7.7 presents the voltage profiles for scenarios: without the PV-BES units (base
case scenario) and with the PV-BES units at the optimal and unity power factors (i.e.,
scenarios 1 and 2, respectively) at the extreme periods where the voltage profiles are worst.
Without the PV-BES units, the extreme period is specified at the peak period 11 as
depicted in Figure 7.7, at which the voltages at several buses are under the lower limit of
0.95 p.u. With the PV-BES units, by considering the combination of the demand and PVBES output curves, the extreme period is identified at the peak period 11. It is observed
from Figure 7.7 that after the PV-BES units are integrated at the extreme periods, the
voltage profiles improve significantly. The voltage profile in scenario 1 is better than that
in scenario 2.
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
160
No PV-BES
Power loss (kW)
PV-BES, unity PF
120
PV-BES, optimal PF
80
40
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
Hour
Figure 7.5. PV-BES impact on energy loss.
1.2
No PV-BES
PV-BES, optimal PF
V2
V1
V0
1.0
Voltage (p.u.)
PV-BES, unity PF
0.8
VSM 2
0.6
VSM 1
CP 1 CP 2
0.4
CP 0
VSM 0
∆ VSM 2
∆VSM 1
λ max0
λ max1λ max2
0.2
0
1
2
3
Loading parameter (λ )
4
5
Figure 7.6. PV-BES impact on maximum loadability and voltage stability margin.
Voltage (p.u.)
1.02
No PV-BES
PV-BES, unity PF
PV-BES, optimal PF
0.98
0.94
0.90
1
3
5
7
9
11
13
15 17 19 21
23
25 27
Bus
Figure 7.7. Voltage profiles at extreme periods for all scenarios.
29
31
33
115
CHAPTER 7. PV AND BES INTEGRATION FOR ENERGY LOSS AND VOLTAGE STABILITY
116
Table 7.4. Energy loss and voltage stability
Scenario
7.6
Annual
energy loss
Annual loss
reduction
(MWh)
(%)
Voltage stability
V (p.u.)
λmax
0.9175
4.1217
∆VSM
Base case
701.33
1
207.31
70.44
0.9878
4.4120
0.2903
2
304.72
56.55
0.9663
4.3673
0.2456
Summary
This chapter presented a new methodology to accommodate a combination of PV and BES
units for reducing energy loss and enhancing voltage stability in distribution systems. Here,
each nondispatchable PV unit is converted into a dispatchable source with a combination
of PV and BES units. New IMO-based analytical expressions were proposed to calculate
the size and power factor of the PV-BES combination. A self-correction algorithm was
developed as well to size multiple PV and BES units while considering the time-varying
demand and probabilistic generation. The power factors are optimally dispatched at each
load level. The Beta PDF model was employed to describe the probabilistic nature of solar
irradiance. The results indicated that the model can support high PV penetration associated
with an efficient usage of BES sources. Operation of PV and BES units with optimal
power factor dispatch for each load level can significantly reduce energy losses and better
enhance voltage stability when compared to that with unity power factor which currently
follows the standard IEEE 1547. This result implies that the standards and regulatory
frameworks regarding PV planning and operations need to be revised.
CHAPTER 8
BENEFIT AND COST ANALYSES FOR BIOMASS
INTEGRATION
8.1
Introduction
Chapters 4-7 presented approaches to integrate renewable DG and its operating strategies
for energy loss reduction and voltage stability enhancement in distribution systems.
However, the size of DG units obtained from the existing studies may not match the
standard sizes available in the market. Furthermore, a comprehensive benefit-cost study on
multiple DG planning with optimal power factor that considers the issues of energy losses
and voltage stability has not been reported in the literature.
In this chapter, analytical expressions are presented based on a multi-objective index
(IMO) to determine the optimal power factor for reducing energy losses and enhancing
voltage stability in industrial distribution systems over a given planning horizon. Here,
new analytical expressions are developed to efficiently capture the optimal power factor of
each DG unit with a commercial standard size to ease the computational burden. In this
study, it is assumed that DG units are owned and operated by distribution utilities. To
make the work comprehensive, in addition to the analytical expressions presented to
specify the optimal power factor, a benefit-cost analysis is carried out in this work to
determine the optimal location, size and number of DG units. The total benefit as a sum of
energy sales, energy loss reduction, network upgrade deferral and emission reduction is
117
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
118
compared to the total cost including capital, operation and maintenance costs. The
methodology is applied to a 69-bus industrial distribution system.
8.2
Load and DG Modelling
8.2.1 Load Modelling
The system considered under the study is assumed to follow the industrial load duration
curve as shown in Figure 8.1, including four discrete load bands (maximum, normal,
medium and minimum) that change as the load grows over a planning horizon. The load
factor or average load level of the system over the base year, LFbase can be defined as the
ratio of the area under load curve to the total duration (four load bands: 8760 hours). That
means LFbase =
8760
∑
t =1
p.u. load (t )
, where p.u. load (t) is the demand in p.u. at period t.
8760
Assuming the growth rate of demand a year (δ), the load factor or average load level of the
system over a given planning horizon (Ny), LF can be calculated as:
1 Ny 8760 p.u. load (t )
y
LF =
× (1 + δ )
∑
∑
Ny y =1 t =1
8760
(8.1)
The time-varying industrial load model defined in Section 3.2 is considered in this
work.
Figure 8.1. Nominalised Load duration curve.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
119
8.2.2 DG Modelling
As described in Section 3.3.1, gas turbine engines fuelled by biogas produced from
biomass materials are adopted in this work. The biogas can be considered as natural gas
standards. As a synchronous generator, the biomass gas turbine-based DG unit is capable
of delivering active power and injecting or absorbing reactive power. It is assumed that the
DG units offer constant output powers at their rated capacities. Given PDGi and QDGi
values which correspond to the active and reactive power of a DG unit injected at bus i, the
power factor of the DG unit at bus i ( pf DGi ) can be expressed as follows:
opf DGi =
8.3
PDGi
2
PDGi
+ QDGi
2
(8.2)
Problem Formulation
8.3.1 Impact Indices
Active and reactive power loss indices have been used to evaluate the impact of DG
inclusion in a distribution system [29, 54, 55, 57]. These indices play a critical role in DG
planning and operations due to their significant impacts on utilities’ revenue, power
quality, system stability and security, and environmental efficiency. In this study, the
active and reactive power loss indices are utilized for reducing power losses and enhancing
voltage stability.
Active Power Loss Index
Substituting Equations (4.5) and (4.6) into Equation (4.3), we obtain the total active power
loss with a DG unit (PLDG) as follows:
N N α
ij ( ( PDGi − PDi ) Pj + ( QDGi − QDi ) Q j ) 
PLDG = ∑∑ 

i =1 j =1 
 + βij ( ( QDGi − QDi ) Pj − ( PDGi − PDi ) Q j ) 
(8.3)
The active power loss index (ILP) is defined as the ratio of Equations (8.3) and (4.3) as
follows:
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
ILP =
PLDG
PL
120
(8.4)
where PL is calculated using Equations (4.3).
Reactive Power Loss Index
Substituting Equation (4.5) and (4.6) into Equation (4.4), we obtain the total reactive
power loss with DG unit (QLDG) as follows:
N N γ
ij ( ( PDGi − PDi ) Pj + ( QDGi − QDi ) Q j ) 
QLDG = ∑∑ 

ξ
+
Q
−
Q
P
−
P
−
P
Q
(
)
(
)
(
)
ij
DGi
Di
j
DGi
Di
j

i =1 j =1 

(8.5)
The reactive power loss index (ILQ) is defined as the ratio of Equations (8.5) and (4.4)
as follows:
ILQ =
QLDG
QL
(8.6)
where QL is calculated using Equations (4.4).
8.3.2 Multiobjective Index
The multiobjective index (IMO) is a combination of the ILP and ILQ impact indices, which
are respectively related to energy loss and voltage stability by giving a weight to each
impact index. This IMO index can be expressed by Equation (8.7) which is subject to the
constraint on the pre-specified apparent power of DG capacity ( S DGi ) through a
relationship between PDGi and QDGi . That means:
IMO = σ 1ILP + σ 2 ILQ
S DGi = PDGi + QDGi
2
subject to
where
(8.7)
∑i=1σ i = 1.0 ∧ σ i ∈ [0, 1.0] .
2
2
2
This can be performed as all impact indices are
normalized with values between zero and one [29]. When DG units are not connected to
the system (i.e., base case system), the IMO is the highest at one. As described in Section
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
121
7.3.3, this study assumes that the active power loss related to energy loss receives a
significant weight of 0.7, leaving the reactive power loss related to voltage stability at a
weight of 0.3.
The lowest IMO implies the best DG allocation for energy loss reduction and voltage
stability enhancement. The objective function defined by the IMO in Equation (8.7) is
subject to technical constraints described below.
8.3.3 Technical Constraints
The maximum DG penetration, which is calculated as the total capacity of DG units, is
limited to less than or equal to a sum of the total system demand and the total system loss.
N
N
N
N
i=2
i =2
i=2
i=2
∑ PDGi ≤ ∑ PDi + PL ; ∑ QDGi ≤ ∑ QDi + QL
(8.8)
where PL and QL are respectively calculated using Equations (4.3) and (4.4).
The voltage at each bus is maintained close to the nominal voltage.
Vi min ≤ Vi ≤ Vi max
(8.9)
where Vi min and Vi max are respectively the lower and upper bounds of the voltage at bus i,
Vi = 1 p.u. (substation nominal voltage).
max
The thermal capacity of circuit n ( S n
) is less than the maximum apparent power
transfer ( S n ).
Sn ≤ S n
max
(8.10)
8.3.4 Energy Loss and Voltage Stability
Energy Loss
The total active power loss of a system with a DG unit at each period t, Ploss (t ) can be
obtained from Equation (4.7). Here, the total period duration of a year is 8760 hours, which
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
122
are calculated as a sum of all the total period durations of all the load levels throughout a
year as shown in Figure 8.1. The total annual energy loss in a distribution system can be
calculated as ALoss y =
8760
∑ Ploss (t ) .
Hence, the total energy loss over a given planning
t =1
horizon (Ny), E Loss can be expressed as:
Ny 8760
E Loss = ∑ ∑ Ploss ( y, t ) × ∆t
(8.11)
y =1 t =1
where ∆t is 1 hour, which is the time duration of period t.
Voltage Stability
As described in Section 6.2, static voltage stability in a power system can be analyzed
using a P–V curve, which is obtained using the continuous power flow method [131]. As
DG units are injected appropriately in the system, the VSM increases. The power of the
load demands increases by a scaling factor ( λ ) as defined by Equation (7.14).
8.3.5 Benefit and Cost Analysis
Utility’s Benefit
The present value benefit (B) in $ given to a utility to encourage DG connection over a
planning horizon from owning and sitting its own DG units can be expressed as follows:
Ny
B=∑
y =1
R y + LI y + EI y
(1 + d ) y
N
+ ND ∑ PDGi
(8.12)
i =2
where all annual values are discounted at the rate d; Ry is the annual energy sales ($/year);
LIy is the loss incentive ($/year); EI y is the emission incentive ($/year); ND is the network
deferral benefit ($/kW); PDGi is the total DG capacity connected at bus i (kW); and Ny is
the planning horizon (years). The LIy can be written as [68, 69]:
LI y = CLoss y (TLoss y − ALoss y )
where CLossy is the loss value ($/MWh), ALossy is the actual annual energy loss of the
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
123
system with DG units (MWh), and TLossy is the target level of the annual energy loss of
the system without DG units (MWh).
When DG units are integrated into the grid for primary energy supply purposes, the
environmental benefit as a result of reducing the usage of fossil fuel energy resources
could be obtained. The EIy including the emission produced by the electricity purchased
from the grid and DG units can be formulated as [74]:
EI y = CE y (TE y − AE y )
where CEy is the cost of each ton of generated CO2 ($/TonCO2); AEy is the actual annual
emission of a system with DG units (TonCO2); TEy is the target level of the annual
emission of the system without DG unit (TonCO2).
Utility’s Cost
The present value cost (C) in $ incurred by a distribution utility over a planning horizon
can be expressed as [68, 69]:
Ny
C=∑
y =1
OM y
(1 + d ) y
N
+ C DG ∑ PDGi
(8.13)
i=2
where OMy is the annual operation, maintenance and fuel costs ($/year) in year y; CDG is
the capital cost of a DG unit ($/kW).
Benefit-Cost Ratio Analysis
The benefit to cost ratio (BCR) can be expressed as follows:
BCR =
B
C
(8.14)
where the B and C are calculated using Equations (8.12) and (8.13), respectively. The
decision for the optimal location, size and number of DG units is obtained when the BCR
as given by Equation (8.14) is highest.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
8.4
124
Proposed Methodology
As discussed in Chapter 4, it becomes necessary to study the optimal power factor of DG
units for minimising power losses to which the active and reactive power injections of each
DG unit are optimized simultaneously.
8.4.1 Optimal Power Factor
In practice, the choice of the best DG capacity may follow commercial standard sizes
available in the market or be limited by energy resource availability. Given such a prespecified DG capacity, the DG power factor can be optimally calculated by adjusting the
active and reactive power sizes at which the IMO as defined by Equation (8.7) can reach a
minimum level. Using the Lagrange multiplier method, we can mathematically convert the
constrained problem defined by Equation (8.7) into an unconstrained one as follows:
(
L(PDGi , QDGi , λi ) = σ 1ILP + σ 2 ILQ + λi S DGi − PDGi − QDGi
2
2
2
)
(8.15)
where λi is the Lagrangian multiplier.
Substituting Equations (8.4) and (8.6) into Equation (8.15), we obtain:
L=
σ1
PL
PLDG +
σ2
QL
(
QLDG + λi S DGi − PDGi − QDGi
2
2
2
)
(8.16)
The necessary conditions for the optimization problem, given by Equation (8.16), state
that the derivatives with respect to control variables PDGi , QDGi and λi become zero.
∂L
σ ∂P
σ Q
= 1 LDG + 2 LDG − 2λi PDGi = 0
∂PDGi P L ∂PDGi QL ∂PDGi
(8.17)
∂L
σ ∂P
σ Q
= 1 LDG + 2 LDG − 2λi QDGi = 0
∂QDGi P L ∂QDGi QL ∂QDGi
(8.18)
∂L
2
2
2
= PDGi + QDGi − S DGi = 0
∂λi
(8.19)
The derivative of Equations (8.3) and (8.5) with respect to PDGi and QDGi are given as:
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
125
N
∂PLDG
= 2∑ [α ij Pj − β ij Q j ] = 2α ii Pi + 2 Ai
∂PDGi
j =1
(8.20)
N
∂QLDG
= 2∑ [γ ij Pj − ξ ij Q j ] = 2γ ii Pi + 2Ci
∂PDGi
j =1
(8.21)
N
∂PLDG
= 2∑ [α ij Q j + β ij Pj ] = 2α ii Qi + 2 Bi
∂QDGi
j =1
(8.22)
N
∂QLDG
= 2∑ [γ ij Q j + ξij Pj ] = 2γ ii Qi + 2 Di
∂QDGi
j =1
(8.23)
where
N
N
j =1
j ≠i
j =1
j ≠i
N
N
j =1
j ≠i
j =1
j ≠i
Ai = ∑ (α ij Pj − β ij Q j ) ; Bi = ∑ (α ij Q j + β ij Pj ) ;
Ci = ∑ (γ ij Pj − ξij Q j ) ; Di = ∑ (γ ij Q j + ξij Pj )
Substituting Equations (8.20) and (8.21) into Equation (8.17), we obtain:
2σ 1
[α ii Pi + Ai ] + 2σ 2 [γ ii Pi + Ci ] − 2λi PDGi = 0
PL
QL
(8.24)
Substituting Equation (4.5) into Equation (8.24), we obtain:
PDiYi −
PDGi =
where
Yi =
σ 1 Ai
−
σ 2Ci
PL
Yi − λi
σ 1α ii
PL
+
QL
(8.25)
σ 2γ ii
QL
Similarly, substituting Equations (8.22) and (8.23) into Equation (8.18), we obtain:
2σ 1
[α ii Qi + Bi ] + 2σ 2 [γ iiQi + Di ] − 2λi QDGi = 0
PL
QL
(8.26)
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
126
Substituting Equation (4.6) into Equation (8.26), we obtain Equation (8.27), where Yi is
given in Equation (8.25).
QDiYi −
QDGi =
σ 1Bi
PL
Yi − λi
−
σ 2 Di
QL
(8.27)
Substituting Equations (8.25) and (8.27) into Equation (8.19), we obtain:
Yi − λi = ±
2
1
S DGi

σ A σ C  
σB σ D 
 PDiYi − 1 i − 2 i  +  QDiYi − 1 i − 2 i 
PL
QL  
PL
QL 

2
(8.28)
Substituting Equation (8.28) into Equations (8.25) and (8.27), we obtain:
PDGi = ±
QDGi = ±

σ A σ C 
 PDiYi − 1 i − 2 i  S DGi
PL
QL 

2

σ A σ C  
σB σ D 
 PDiYi − 1 i − 2 i  +  QDiYi − 1 i − 2 i 
PL
QL  
PL
QL 

2

σB σ D 
 QDiYi − 1 i − 2 i  S DGi
PL
QL 

2

σ A σ C  
σB σ D 
 PDiYi − 1 i − 2 i  +  QDiYi − 1 i − 2 i 
PL
QL  
PL
QL 

2
(8.29)
(8.30)
It is observed from Equation (8.29) that PDGi can be positive or negative, depending on
the characteristic of system loads. However, the load power factor of a distribution system
without reactive power compensation is normally in the range from 0.7 to 0.95 lagging
(inductive load). PDGi is assumed to be positive in this study, i.e., the DG unit delivers
active power. QDGi can be positive or negative, as given by Equation (8.30). QDGi can be
positive with inductive loads or negative with capacitive loads (i.e., the DG unit injects or
absorbs reactive power).
Given a S DGi value is pre-defined, the optimal PDGi and QDGi values are respectively
calculated using Equations (8.29) and (8.30) to minimize the IMO as defined by Equation
(8.7), after running only one load flow for the base case system. Accordingly, the optimal
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
127
power factor ( pf DGi ) value is specified using Equation (8.2). Any power factors rather
than the optimal pf DGi value will lead to a higher IMO.
8.4.2 Computational Procedure
DG units are considered to be placed at an average load level (LF), defined by Equation
(8.1), over a given planning horizon, which has the most positive impact on the IMO. This
also reduces the computational burden and the search space. The energy loss given by
Equation (8.11) is calculated by a multiyear multiperiod power flow analysis over the
planning horizon. The computational procedure is explained for each step as follows:
Step 1: Set the apparent power of DG units ( S DGi ) and the maximum number of buses to
connect DG units.
Step 2: Run load flow for the system without DG units at the average load level over the
planning horizon (LF) using Equation (8.1).
Step 3: Find the optimal power factor of each DG unit for each bus using Equation (8.2).
Place this DG unit at each bus and find the IMO for each case using Equation
(8.7).
Step 4: Locate the optimal bus for DG installation at which the IMO is the lowest with the
corresponding optimal size and power factor at that bus.
Step 5: Run multiyear multiperiod load flow with the DG size obtained in Step 4 over the
planning horizon. Calculate the energy loss and its corresponding BCR using
Equations (8.11) and (8.14), respectively.
Step 6: Repeat Steps 3-5 until “the maximum number of buses is reached”. These buses
are defined as “a set of candidate buses”. Continue to connect DG units to “these
candidate buses” by repeating Steps 3-5.
Step 7: Stop if any of the violations of the constraints (Section 8.3.3) occurs or the last
iteration BCR is smaller than the previous iteration one. Obtain the results of the
previous iteration.
8.5
Case Study
8.5.1 Test System
The proposed methodology was applied to an 11 kV 69-bus radial distribution system that
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
128
is fed by a 6 MVA 33/11 kV transformer, as depicted in Figure 3.3 [113]. The total active
and reactive power of the system at the average load level defined by Equation (8.1) is 3.35
MW and 2.30 MVAr, respectively.
8.5.2 Assumptions and Constraints
The operating voltages at all buses are limited in the range of 0.95 to 1.05 p.u. The feeder
thermal limits are 5.1 MVA (270 A) [68]. It is assumed that the time-varying voltage
dependent industrial load as defined in Equation (3.1) is considered in this simulation. The
loading at each bus follows the industrial load duration curve across a year shown in
Figure 8.1 over a planning horizon of 15 years with a yearly demand growth of 3%. As
given by Equation (8.1), the load factor or average load level over the planning horizon
(LF) is 0.75. All buses are candidate for DG investment and more than one DG unit can be
installed at the same bus. The substation transformers are close to their thermal rating and
would need replacing in the near future while the conductors exhibit considerable extra
headroom for further demand. For reasons of simplicity, DG units are connected at the start
of the planning horizon and operating for the whole time a year (8760 hours) at rated
capacity throughout the planning horizon. That means the average utilization factor of DG
units is 100%. Gas turbine-based DG technology is used. Its size (SDG) is pre-specified at
0.8 MVA. The input data given in Table 8.1, are employed for benefit and cost analyses.
Table 8.1. Economic input data
Gas turbine-based DG capacity [68]
Investment cost [68]
0.8 MVA
$976 / kW
Operation and maintenance and fuel costs [68]
$46 / MWh
Electricity sales [68]
$76 / MWh
Loss incentive [68]
$78 / MWh
Network upgrade deferral benefit for deferral of transformer upgrades [68]
$407 / kW of DG
Emission factor of grid [74]
0.910 TonCO2 / MWh
Emission factor of 1 MVA gas engine [74]
0.773 TonCO2 / MWh
Emission cost [74]
$10 / TonCO2
Discount rate [68]
9%
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
129
8.5.3 Numerical Results
The total load of the system is 4.07 MVA. Given a pre-defined DG size of 0.8 MVA each
and the constraint of DG penetration as defined by Equation (8.8), the maximum number
of DG units is limited to be five with a total size of 4 MVA. To compare the benefits
brought to the utility, five following scenarios have been analysed.
•
Scenario 1: One biomass DG unit;
•
Scenario 2: Two biomass DG units;
•
Scenario 3: Three biomass DG units;
•
Scenario 4: Four biomass DG units;
•
Scenario 5: Five biomass DG units.
Location, Size and Power Factor with respect to Indices
Figure 8.2 presents the 69-bus system with DG units. The optimal locations are identified
at buses 62, 35, 25, 4 and 39 where five DG units (i.e., DGs 1, 2, 3, 4 and 5, respectively)
are optimally placed. Table 8.2 shows a summary of the results of the location, power
factor and size of DG units for the five scenarios as mentioned earlier over the planning
horizon of 15 years. As each DG unit is pre-defined at 0.8 MVA, its power factor is
adjusted such that the IMO index obtained for each scenario is lowest. The optimal power
factor for each location is quite different, in the range of 0.82-0.89 (lagging). The total size
is increased from 0.8 to 4 MVA with respect to the number of DG units increased from one
to five. It has been found from the simulation that three scenarios (i.e, 3, 4 and 5 DG units)
satisfy the technical constraints. When less than three DG units are considered, the
violation of the voltage constraint (i.e., the operating voltages are under 0.95 p.u) occurs at
several buses in the system.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
130
Figure 8.2. Single line diagram of the 69-bus test distribution system with DG units.
Table 8.2. Location, size and power factor of DG units
Scenarios
DG
location
DG size
(MVA)
DG power
factor (lag.)
Total DG size
(MVA)
Permissible
constraints?
1 DG
62
0.8
0.87
0.8
No
2 DGs
62
35
0.8
0.8
0.87
0.89
1.6
No
3 DGs
62
35
25
0.8
0.8
0.8
0.87
0.89
0.89
2.4
Yes
4 DGs
62
35
25
4
0.8
0.8
0.8
0.8
0.87
0.89
0.89
0.85
3.2
Yes
5 DGs
62
35
25
4
39
0.8
0.8
0.8
0.8
0.8
0.87
0.89
0.89
0.85
0.82
4.0
Yes
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
131
Figure 8.3 shows a comparison of the ILP, ILQ and IMO indices with different numbers
of DG units over the planning horizon, which are related to the active power loss index,
reactive power loss index and a multi-objective index. As shown in Figure 8.3, the indices
reduce when the number of DG units is increased from one to five. However, when the
number of DG units is further increased, the total penetration of DG units is higher than the
total demand as previously mentioned along with an increase in the values of indices.
Substantial reductions in the indices are observed in three scenarios (i.e., 3, 4 and 5 DG
units) when compared to one and two DG units. For each scenario, the ILP is lower than
the ILQ. This indicates that the system with DG units can benefit more from minimising
the active power loss than to the reactive power loss.
1.0
ILP
ILQ
IMO
Indices
0.8
0.6
0.4
0.2
0.0
1
2
3
4
5
Number of DGs
Figure 8.3. Indices (ILP, ILQ and IMO) for the system with various numbers of DG units
over planning horizon.
DG Impact on Energy Loss and Voltage Stability
Figure 8.4 presents the total energy loss of the system for different scenarios without and
with DG units over the planning horizon. For each scenario, the total energy loss for each
year is estimated as a sum of all the energy losses at the respective load levels of that year.
As shown in Figure 8.4, the system energy loss with no DG units increases over the
planning horizon due to the annual demand growth of 3%. A significant reduction in the
energy loss over the planning horizon is observed for the scenarios with DG units when
compared to the scenario without DG units. The lowest energy loss is achieved for the
scenario with five DG units. As the amount of the power generation from three DG units is
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
132
still not sufficient, the system energy loss for the scenario with three DG units reduce
insignificantly when compared to that with four or five DG units.
Energy loss (MWh)
1500
No DG
3 DGs
4 DGs
5 DGs
1200
900
600
300
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Year
Figure 8.4. Losses of the system with and without DG units over planning horizon.
Figure 8.5 shows the impact of DG allocation on the voltage stability of the system with
and without DG units over the planning horizon of 15 years. For each year, the simulation
has been implemented at the maximum demand, where the voltage stability margin (VSM)
is worst when compared to the other loading levels. In each year, as defined in Figure 7.2,
the VSM of the system with 3-5 DG units significantly enhances when compared to that of
the system without DG units. For example, when three DG units generate an amount of 2.4
MVA at buses 62, 35 and 25 in the first year, as found in Table 8.2, the VSM increases to
4.5918 from the base case value of 2.8681 (without DG units). A similar trend has been
found for years 2-15 as shown in Figure 8.5. Furthermore, it can be seen from Figure 8.5
that a significant increase in the voltage stability margin is found for the scenarios with
four or five DG units when compared to three DG units. This is due to the fact that the ILP,
which is related to the reactive power loss of the system, significantly reduces for the
scenario with four or five DG units when compared to three DG units, as shown in Figure
8.3. In addition, it can be observed from Figure 8.5 that the VSM values with and without
DG units reduce with respect to a yearly demand growth of 3%. Hence, the lowest VSM
values are found in the year 15.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
Voltage stability margin
6.0
No DG
4 DGs
133
3 DGs
5 DGs
4.5
3.0
1.5
0.0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Year
Figure 8.5. Voltage stability margin curves for all scenarios over planning horizon.
Table 8.3 shows a summary of the results of energy losses without and with DG units
for each scenario over the planning horizon of 15 years. The energy savings due to loss
reduction is beneficial. A maximum energy savings is achieved for the scenario with five
DG units when compared to three and four DG units. Table 8.3 also presents a summary of
the results of voltage stability with and without DG units over the planning horizon. The
average voltage stability margin of the system (AVSM) is calculated as a sum of the VSM
values of all years divided by the total planning horizon. An increase in the average voltage
stability margin (∆AVSM) is observed after 3-5 DG units are installed in the system. It is
observed from Table 8.3 that the VSM for each scenario increases with respect to an
increase in the number of DG units installed in the system as well as a reduction in the
overall energy loss of the system.
Table 8.3. Energy loss and voltage stability over planning horizon
Scenarios
Energy loss
Energy savings
(GWh / 15 years)
(GWh / 15 years)
Voltage stability
AVSM
∆AVSM
Base case
14.91
2.1667
3 DGs
5.97
8.94
3.5745
1.4078
4 DGs
4.46
10.45
3.5758
1.4091
5 DGs
4.35
10.56
3.6855
1.5188
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
134
Benefit and Cost Analysis
Table 8.4 presents the results of the total benefit and cost for three scenarios (i.e., 3, 4 and
5 DG units) without and with additional benefits over the planning horizon of 15 years.
The additional benefit includes the loss incentive (LI), emission incentive (EI) and network
upgrade deferral (ND). The total benefit (B) is a sum of all the additional benefits and the
energy sales (R). The total cost (C) is a sum of the operation, maintenance and fuel cost
(OM) and the DG capacity cost (CDG ∑PDGi). Table 8.5 shows a comparison of the results
for three different scenarios without and with additional benefits over the planning horizon.
The results include the benefit-cost ratio (BCR), net present value (NPV = B - C), payback
period, and internal rate of return (IRR).
For exclusion of the additional benefits, it is observed from Table 8.5 that the BCR is
the same for all the scenarios at 1.288. The best solution is five DG units as the NPV is
highest at k$4162. This solution generates an IRR of 16.48% and a payback period of 5.6
years. For inclusion of the additional benefits, it can be seen from Table 8.4 that the energy
sales (R) accounts for around 89-90% of the B, leaving the total additional benefit (LI, EI
and ND) at roughly 10-11%. It is obvious that the R has a significant impact on the BCR
when compared to the total additional benefit. However, the additional benefits,
particularly the LI play a critical role in decision-making about the total number of DG
units or the amount of DG capacity installed. This factor has an impact on the BCR. As
shown in Table 8.5, the BCR slightly drops from 1.450 to 1.438 when the number of DG
units is increased from three to five, respectively. The best solution is three DG units with
the highest BCR of 1.450. This solution generates an NPV of k$3993, an IRR of 32.65%
and a payback period of 2.80 years. In general, in the absence of the additional benefits, the
optimal number of DG units is five, while in the presence of the additional benefits, this
figure is three. Inclusion of the additional benefits in the study can lead to faster investment
recovery with a higher BCR, a higher IRR and a shorter payback period when compared to
exclusion of the additional benefits. In addition, it can be observed from Table 8.5 that the
NPV value will further increase with increasing DG units installed. However, the system
cannot accommodate more than five DG units due to the violation of the maximum DG
penetration constraint as defined by Equation (8.8).
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
135
Table 8.4. Analysis of the present value benefit and cost for different scenarios over
planning horizon
Without additional benefits
With additional benefits
Number of DGs
3 DGs
4 DGs
5 DGs
3 DGs
4 DGs
5 DGs
R (k$)
11421
15090
18624
11421
15090
18624
LI (k$)
--
--
--
336
392
387
EI (k$)
--
--
--
244
316
379
ND ∑PDGi (k$)
--
--
--
860
1137
1403
11421
15090
18624
12862
16934
20793
R / B (%)
88.80
89.11
89.57
(LI+EI+ ND ∑PDGi) / B (%)
11.20
10.89
10.43
Total benefit, B (k$)
OM (k$)
6804
8990
11095
6804
8990
11095
CDG ∑PDGi (k$)
2065
2728
3367
2065
2728
3367
Total cost, C (k$)
8869
11718
14462
8869
11718
14462
Table 8.5. Comparison of different scenarios over planning horizon
Without additional benefits
With additional benefits
Number of DGs
3 DGs
4 DGs
5 DGs
3 DGs
4 DGs
5 DGs
BCR = B/C
1.288
1.288
1.288
1.450
1.445
1.438
NPV = B – C (k$)
2552
3372
4162
3993
5216
6331
Payback period (years)
5.60
5.60
5.60
2.80
2.82
2.86
Internal rate of return, IRR (%)
16.48
16.48
16.48
32.65
32.38
31.93
Figure 8.6 shows an increase in the NPV with the corresponding average DG utilization
factors over the planning horizon of 15 years for three scenarios (i.e., 3, 4 and 5 units) with
the additional benefits. It is observed from the figure that given a certain average DG
utilization factor in the range of 0-100%, the NPV is highest for the scenario with five DG
units, whereas this figure is lowest for the scenario with three DG units. In addition, for
each scenario, the NPV is maximum when the utilization factor is 100% as estimated in
Table 8.5. However, in practice, this factor may be less than 100% due to interruption for
maintenance and others. Consequently, the respective NPV will be reduced as shown in
Figure 8.6.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
136
Figure 8.7 shows the percentage ratio of the total demand plus total loss to the thermal
limit (6 MVA) of the transformer over the planning horizon with a demand growth of 3%.
For the scenarios with DG units, the curves are plotted at the average DG utilization factor
of 100%. Obviously, without DG connection, an investment would be needed to add a new
transformer before year 4. However, the selected three-DG scenario can defer in upgrading
this current transformer (6 MVA) to 11 years. A higher deferral is achieved for the
scenarios with four or five DG units.
7.5
3 DGs
4 DGs
NPV (million $)
6.0
5 DGs
4.5
3.0
1.5
0.0
10
20
30
40
50
60
70
80
90
100
Average utilization of DG (%)
Figure 8.6. NPV at various average DG utilization factors for different scenerios over
planning horizon.
Percentage ratio (%)
200
No DGs
3 DGs
4 DGs
5 DGs
150
Transformer upgrade required
100
Trans. rating
50
Trans. upgrade deferred
0
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
Year
Figure 8.7. Percentage ratio of the total demand plus loss to the thermal transformer limit
over planning horizon.
CHAPTER 8. BENEFIT AND COST ANALYSES FOR BIOMASS INTEGRATION
8.6
137
Summary
This chapter developed an investment planning framework for integrating multiple DG
units in industrial distribution systems where the DG units are assumed to be owned and
operated by utilities. In this framework, analytical expressions were proposed to efficiently
identify the optimal power factor of DG units for minimising energy losses and enhancing
voltage stability. The decision for the optimal location, size and number of DG units is
achieved through a benefit-cost analysis. The total benefit includes energy sales and three
additional benefits including loss reduction, network upgrade deferral and emission
reduction. The total cost is a sum of capital, operation and maintenance costs. The results
obtained on a 69-bus test distribution system indicated that the additional benefits,
particularly the loss incentive have a significant impact on decision-making about the total
number of DG units or the amount of DG capacity installed. The additional benefits
together accounted for 10-11% of the total benefit when compared to the energy sales of
89-90%. Inclusion of these benefits in the study can lead to faster investment recovery with
a high benefit-cost ratio, a high internal rate of return and a short payback period.
When DG units are owned by DG developers, the additional benefits should be shared
between the distribution utility and DG developer to encourage DG connection. In this
situation, the proposed methodology could be used as guidance for the utility on how to
plan and operate DG units to obtain the additional benefits.
CHAPTER 9
CONCLUSIONS
9.1
Summary
Increasing interest in the deployment of renewable DG worldwide, especially intermittent
resources (i.e., wind and solar), together with demand variations is forcing modifications to
the planning and operations of renewable DG units. The smart grid has been introduced as
an important part of these modifications. As an integral part of the smart grid, a smart
integration approach was presented in this thesis, specifically focusing on high renewable
penetration along with an efficient usage of BES units in distribution systems. The thesis
also aimed to show how to accommodate and operate renewable DG and associated BES
units behind the concept of the optimal power factor to maximize technical, economical
and environmental benefits from the utilities’ perspective. The thesis can be summarized
along with main findings drawn from the individual chapter as below.
In Chapter 2, the background of DG integration and associated BES usage in
distribution systems was provided. This was followed by a literature review addressing DG
integration in distribution systems with different aspects such as loss reduction, voltage
stability, voltage profiles and benefit-cost analyses. It was observed that traditional DG
planning approaches are typically focused on locating and sizing where DG units are
assumed to be dispatchable and located at the peak demand. However, few studies
indicated that such approaches may not solve a practical case of intermittent renewable DG
units that considers the time-varying demand and variant/probabilistic generation.
Moreover, most existing approaches have assumed that DG units operate at pre-specified
138
CHAPTER 9. CONCLUSIONS
139
power factor under the recommendation of the current standard IEEE 1547, normally unity
power factor. The concept and application of hybrid PV and BES systems in distribution
systems was also reviewed. The hybrid system was found to be favoured in the literature to
eliminate the intermittency of PV sources and support high PV penetration. In addition, it
was shown that a constant or voltage-dependent load model is usually assumed in most
traditional DG planning approaches.
In contrast to the traditional approaches, Chapter 3 described the models of timevarying voltage-dependent load demand and the time-varying/probabilistic generation
which were adopted for renewable DG planning in this thesis. These models can make the
assessment of renewable integration more accurate when compared to the traditional
model. In addition, this chapter introduced three test distribution systems: 33-bus (one
feeder), 69-bus (one feeder) and 69-bus (four feeders), which were employed to validate
the effectiveness of the proposed methods in this thesis.
The contribution chapter started with Chapter 4 where three alternative analytical
approaches were presented to facilitate the determination of the size and operating strategy
of a single renewable DG unit to reduce power losses. A methodology to identify the best
location was also developed in this chapter. The three approaches were respectively
derived from three different power loss formulas. They were easily adapted to
accommodate different types of renewable DG units (i.e., biomass, wind and solar PV) for
minimising energy losses while considering the time-varying demand and possible
operating conditions of DG units. It was indicated that the three approaches can be utilized
depending on availability of required data and produce similar outcomes. It was also
shown that a maximum energy loss reduction is achieved for all the proposed scenarios
with optimal power factor operation when compared to pre-defined power factors,
especially unity power factor. Depending on the characteristics of demand and generation,
a distribution system would accommodate up to an estimated 48% of the nondispatchable
renewable DG penetration. A higher penetration level could be obtained for dispatchable
renewable DG units. However, the importance of hybrid dispatchable and nondispatchable
DG units also needs to be examined.
Chapter 5 presented a methodology to determine the optimal location, size and power
factor of hybrid dispatchable and nondispatchable renewable DG units for minimising
CHAPTER 9. CONCLUSIONS
140
annual energy losses. The concept behind this methodology is that each nondispatchable
wind unit is converted into a dispatchable source with a mix of wind and biomass units. In
this methodology, analytical expressions were first proposed to determine the optimal size
and power factor of each DG unit simultaneously for each location to minimise power
losses. These expressions were then adapted to locate and size different types of renewable
DG units and calculate the optimal power factor for each unit to minimise energy losses
while considering the time-varying characteristics of demand and generation. It was shown
that dispatchable DG units or hybrid dispatchable and nondispatchable DG units can
minimise annual energy losses significantly when compared to nondispatchable DG units
alone.
In addition to the methods using the constant load models presented in Chapters 4-5, an
analytical approach was introduced in Chapter 6 to determine the penetration of PV units
in a distribution system with different types of time-varying load models. In this approach,
an IMO-based analytical expression was proposed to identify the size of a PV unit, which
is capable of supplying active and reactive power, with a multi-objective of simultaneously
reducing active and reactive power losses and voltage deviation. The analytical expression
was then adapted to accommodate PV units while considering the characteristics of timevarying voltage-dependent load models and probabilistic generation. The Beta PDF model
was used to describe the probabilistic nature of solar irradiance. It was indicated that an
accurate modeling of the demand profile based on the time-varying voltage-dependent load
models together with probabilistic generation can help in determining the penetration of
PV units into a distribution system precisely.
Unlike Chapters 4-6, a new methodology to accommodate hybrid PV and BES systems
was proposed in Chapter 7 for reducing energy loss and enhancing voltage stability. Here,
each nondispatchable PV unit is converted into a dispatchable source with a combination
of PV and BES units. New IMO-based analytical expressions were proposed to calculate
the size and power factor of hybrid PV and BES units. A self-correction algorithm was
developed as well to size multiple PV and BES units while considering the time-varying
demand and probabilistic generation. It was shown that the model can support high PV
penetration associated with an efficient usage of BES sources. Optimal power factor
dispatch could be one of the aspects to be considered in the strategy of PV integration. A
significant energy loss reduction and voltage stability enhancement can be achieved for all
CHAPTER 9. CONCLUSIONS
141
the proposed scenarios with PV dispatch at optimal power factor for each load level when
compared to PV generation at unity power factor which follows the current standard IEEE
1547. Consequently, this result implies that the standards and regulatory frameworks
regarding PV planning and operations need to be revised.
Finally, in addition to the technical benefits thoroughly discussed in Chapters 4-7, it is
necessary to evaluate the costs and benefits of DG installation. Chapter 8 developed a
comprehensive multi-year framework for biomass DG investment planning in distribution
systems. In this framework, given a DG unit with a commercial standard size, the dualindex based expressions proposed can identify the optimal power factor for minimising
energy losses and enhance voltage stability. The decision for the optimal location, size and
number of DG units is achieved through a benefit-cost analysis. It was shown that
inclusion of energy loss reduction together with other benefits such as network investment
deferral and emission reduction in the analysis would recover DG investments faster.
9.2
Contributions
The main contributions of this thesis can be summarized as follows:
Chapter 4: A new concept behind the optimal power factor operation was introduced.
Three alternative analytical approaches were presented to determine the location, size and
power factor of different types of single renewable DG units for minimising energy losses
while considering the time-varying demand and generation.
Chapter 5: A new concept to covert each nondispatchable wind into a dispatchable
source with a combination of wind and biomass units was proposed. Analytical
expressions were developed to identify the optimal size and power factor of DG units
simultaneously. A methodology was presented to accommodate hybrid dispatchable
biomass and nondispatchable wind units for minimising energy losses.
Chapter 6: An IMO-based expression was developed to locate and size a PV unit with a
multiobjective of simultaneously reducing active and reactive power losses and voltage
deviation. A methodology was presented to determine the penetration of PV units for
distribution systems while considering the characteristics of time-varying load models and
probabilistic generation.
CHAPTER 9. CONCLUSIONS
142
Chapter 7: A new concept to covert each nondispatchable PV unit into a dispatchable
source with a combination of PV and BES units was introduced. IMO-based analytical
expressions were presented to calculate the size and power factor of hybrid PV-BES units
for reducing energy losses and enhancing voltage stability. A self-correction algorithm was
developed to size multiple PV and BES units.
Chapter 8: Dual index-based analytical expressions were proposed to efficiently capture
the optimal power factor of each DG with a standard size for minimising energy losses and
enhancing voltage stability. A comprehensive multi-year multi-period framework for
biomass DG investment planning was presented based on a benefit-cost analysis over a
given planning horizon.
9.3
Future Research
Future research should be focused on the following issues:
1. A cost-benefit analysis for integrating dispatchable and non-dispatchable sources
(biomass, PV and wind) as well as BES units into distribution systems.
2. A framework for DG planning that includes reliability to provide a more accurate
evaluation of DG benefits.
3. A policy or mechanism of power factor dispatch in the electricity market for
renewable DG and associated BES units.
4. A framework for distribution system planning with renewable DG and associated
BES units in a deregulated environment.
5. A framework for hybrid PV and Electric Vehicle (EV) planning.
6. An advanced framework for distribution system planning which simultaneously
considers reconfiguration, renewable DG, BES units and capacitors.
7. A strategy of coordination control considering the interaction of renewable DG and
EV units with voltage and reactive power control devices such as switchable
capacitors, voltage regulators and tap changers.
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APPENDIX A
Table A.1. System data of 33-bus test distribution system
Sending bus
no.
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 bus
no.
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
Resistance
(Ω)
0.0922
0.4930
0.3660
0.3811
0.8190
0.1872
1.7114
1.0300
1.0400
0.1966
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
Reactance
(Ω)
0.0477
0.2511
0.1864
0.1941
0.7070
0.6188
1.2351
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
Substation voltage = 12.66 kV, MVA base = 10 MVA
155
Load at receiving end bus
P (kW)
Q (kVAr)
100
60
90
40
120
80
60
30
60
20
200
100
200
100
60
20
60
20
45
30
60
35
60
35
120
80
60
10
60
20
60
20
90
40
90
40
90
40
90
40
90
40
90
50
420
200
420
200
60
25
60
25
60
20
120
70
200
600
150
70
210
100
60
40
APPENDIX A
156
Table A.2. System data of 69-bus one feeder test distribution system
Sending bus
no.
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
3
28
29
30
31
32
33
34
3
36
37
38
39
40
41
42
43
44
45
4
47
48
Receiving bus
no.
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
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
Resistance
(Ω)
0.0005
0.0005
0.0015
0.0251
0.3660
0.3811
0.0922
0.0493
0.8190
0.1872
0.7114
1.0300
1.0440
1.0580
0.1966
0.3744
0.0047
0.3276
0.2106
0.3416
0.0140
0.1591
0.3463
0.7488
0.3089
0.1732
0.0044
0.0640
0.3978
0.0702
0.3510
0.8390
1.7080
1.4740
0.0044
0.0640
0.1053
0.0304
0.0018
0.7283
0.3100
0.0410
0.0092
0.1089
0.0009
0.0034
0.0851
0.2898
Reactance
(Ω)
0.0012
0.0012
0.0036
0.0294
0.1864
0.1941
0.0470
0.0251
0.2707
0.0691
0.2351
0.3400
0.3450
0.3496
0.0650
0.1238
0.0016
0.1083
0.0690
0.1129
0.0046
0.0526
0.1145
0.2745
0.1021
0.0572
0.0108
0.1565
0.1315
0.0232
0.1160
0.2816
0.5646
0.4673
0.0108
0.1565
0.1230
0.0355
0.0021
0.8509
0.3623
0.0478
0.0116
0.1373
0.0012
0.0084
0.2083
0.7091
Load at receiving end bus
P (kW)
Q (kVAr)
0.00
0.00
0.00
0.00
0.00
0.00
0.00
0.00
2.60
2.20
40.40
30.00
75.00
54.00
30.00
22.00
28.00
19.00
145.00
104.00
145.00
104.00
8.00
5.50
8.00
5.50
0.00
0.00
45.50
30.00
60.00
35.00
60.00
35.00
0.00
0.00
1.00
0.60
114.00
81.00
5.30
3.50
0.00
0.00
28.00
20.00
0.00
0.00
14.00
10.00
14.00
10.00
26.00
18.60
26.00
18.60
0.00
0.00
0.00
0.00
0.00
0.00
14.00
10.00
19.50
14.00
6.00
4.00
26.00
18.55
26.00
18.55
0.00
0.00
24.00
17.00
24.00
17.00
1.20
1.00
0.00
0.00
6.00
4.30
0.00
0.00
39.22
26.30
39.22
26.30
0.00
0.00
79.00
56.40
384.70
274.50
APPENDIX A
Sending bus
no.
49
8
51
9
53
54
55
56
57
58
59
60
61
62
63
64
11
66
12
68
157
Receiving bus
no.
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
Resistance
(Ω)
0.0822
0.0928
0.3319
0.1740
0.2030
0.2842
0.2813
1.5900
0.7837
0.3042
0.3861
0.5075
0.0974
0.1450
0.7105
1.0410
0.2012
0.0047
0.7394
0.0047
Reactance
(Ω)
0.2011
0.0473
0.1114
0.0886
0.1034
0.1447
0.1433
0.5337
0.2630
0.1006
0.1172
0.2585
0.0496
0.0738
0.3619
0.5302
0.0611
0.0014
0.2444
0.0016
Substation voltage = 12.66 kV, MVA base = 10 MVA
Load at receiving end bus
P (kW)
Q (kVAr)
384.00
274.50
40.50
28.30
3.60
2.70
4.35
3.50
26.40
19.00
24.00
17.20
0.00
0.00
0.00
0.00
0.00
0.00
100.00
72.00
0.00
0.00
1244.00
888.00
32.00
23.00
0.00
0.00
227.00
162.00
59.00
42.00
18.00
13.00
18.00
13.00
28.00
20.00
28.00
20.00
APPENDIX A
158
Table A.3. System data of 69-bus four feeder test distribution system
Sending bus
no.
1
2
3
4
5
6
7
8
4
10
11
12
13
14
1
16
17
18
19
20
21
17
23
24
25
26
27
28
1
30
31
32
33
34
35
36
37
32
39
40
41
42
40
44
42
35
47
48
49
1
51
52
53
54
Receiving bus
no.
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
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
Resistance
(Ω)
1.097
1.463
0.731
0.366
1.828
1.097
0.731
0.731
1.080
1.620
1.080
1.350
0.810
1.944
1.080
1.620
1.097
0.366
1.463
0.914
0.804
1.133
0.475
2.214
1.620
1.080
0.540
0.540
1.080
1.080
0.366
0.731
0.731
0.804
1.170
0.768
0.731
1.097
1.463
1.080
0.540
1.080
1.836
1.296
1.188
0.540
1.080
0.540
1.080
1.080
1.080
0.366
1.463
1.463
Reactance
(Ω)
1.074
1.432
0.716
0.358
1.790
1.074
0.716
0.716
0.734
1.101
0.734
0.917
0.550
1.321
0.734
1.101
1.074
0.358
1.432
0.895
0.787
1.110
0.465
1.505
1.110
0.734
0.367
0.367
0.734
0.734
0.358
0.716
0.716
0.787
1.145
0.752
0.716
1.074
1.432
0.734
0.367
0.734
1.248
0.881
0.807
0.367
0.734
0.367
0.734
0.734
0.734
0.358
1.432
1.432
Load at receiving end bus
P (kW)
Q (kVAr)
100
90
60
40
150
130
75
50
15
9
18
14
13
10
16
11
20
10
16
9
50
40
105
90
25
15
40
25
60
30
40
25
15
9
13
7
30
20
90
50
50
30
60
40
100
80
80
65
100
60
100
55
120
70
105
70
80
50
60
40
13
8
16
9
50
30
40
28
60
40
40
30
30
25
150
100
60
35
120
70
90
60
18
10
16
10
100
50
60
40
90
70
85
55
100
70
140
90
60
40
20
11
40
30
36
24
30
20
APPENDIX A
Sending bus
no.
55
52
57
58
59
55
61
62
63
62
65
66
7
68
159
Receiving bus
no.
56
57
58
59
60
61
62
63
64
65
66
67
68
69
Resistance
(Ω)
0.914
1.097
1.097
0.270
0.270
0.810
1.296
1.188
1.188
0.810
1.620
1.080
0.540
1.080
Substation voltage = 11 kV, MVA base = 10 MVA
Reactance
(Ω)
0.895
1.074
1.074
0.183
0.183
0.550
0.881
0.807
0.807
0.550
1.101
0.734
0.367
0.734
Load at receiving end bus
P (kW)
Q (kVAr)
43
30
80
50
240
120
125
110
25
10
10
5
150
130
50
30
30
20
130
120
150
130
25
15
100
60
40
30
APPENDIX B
Table B.1. Mean and Standard Deviation of Solar Irradiance
Hour
µ
(kW/m2)
σ
(kW/m2)
Hour
µ
(kW/m2)
σ
(kW/m2)
6
0.019
0.035
13
0.648
0.282
7
0.096
0.110
14
0.590
0.265
8
0.222
0.182
15
0.477
0.237
9
0.381
0.217
16
0.338
0.204
10
0.511
0.253
17
0.190
0.163
11
0.610
0.273
18
0.080
0.098
12
0.657
0.284
19
0.017
0.032
Table B.2. Characteristics of the PV module
PV module characteristics
Value
0
43
Current at maximum power point, IMPP (A)
7.76
Voltage at maximum power point, VMPP (V)
28.36
Nominal cell operating temperature, NOT ( C)
Short circuit current, Isc (A)
8.38
Open circuit voltage, Voc (V)
36.96
o
Current temperature coefficients, Ki (A / C)
0.00545
o
Voltage temperature coefficients, Kv (V / C)
0.1278
160