128,99 €
Mehr erfahren.
- Herausgeber: John Wiley & Sons
- Kategorie: Wissenschaft und neue Technologien
- Sprache: Englisch
An original look from a microeconomic perspective for power system optimization and its application to electricity markets * Presents a new and systematic viewpoint for power system optimization inspired by microeconomics and game theory * A timely and important advanced reference with the fast growth of smart grids * Professor Chen is a pioneer of applying experimental economics to the electricity market trading mechanism, and this work brings together the latest research * A companion website is available Edit
Sie lesen das E-Book in den Legimi-Apps auf:
Seitenzahl: 629
Veröffentlichungsjahr: 2017
Ähnliche
Table of Contents
Title Page
Copyright
Dedication
Contributors
Foreword
Preface
Acknowledgments
List of Figures
List of Tables
Acronyms
Symbols
Chapter 1: Introduction
1.1 Power System Optimal Planning
1.2 Power System Optimal Operation
1.3 Power System Reactive Power Optimization
1.4 Optimization in Electricity Markets
Chapter 2: Theories and Approaches of Large-Scale Complex Systems Optimization
2.1 Basic Theories of Large-scale Complex Systems
2.2 Hierarchical Optimization Approaches
2.3 Lagrangian Relaxation Method
2.4 Cooperative Coevolutionary Approach for Large-scale Complex System Optimization
Chapter 3: Optimization Approaches in Microeconomics and Game Theory
3.1 General Equilibrium Theory
3.2 Noncooperative Game Theory
3.3 Mechanism Design
3.4 Duality Principle and Its Economic Implications
Chapter 4: Power System Planning
4.1 Generation Planning Based on Lagrangian Relaxation Method
4.2 Transmission Planning Based on Improved Genetic Algorithm
4.3 Transmission Planning Based on Ordinal Optimization
4.4 Integrated Planning of Distribution Systems Based on Hybrid Intelligent Algorithm
Chapter 5: Power System Operation
5.1 Unit Commitment Based on Cooperative Coevolutionary Algorithm
5.2 Security-Constrained Unit Commitment with Wind Power Integration Based on Mixed Integer Programming
5.3 Optimal Power Flow with Discrete Variables Based on Hybrid Intelligent Algorithm
5.4 Optimal Power Flow with Discrete Variables Based on Interior Point Cutting Plane Method
Chapter 6: Power System Reactive Power Optimization
6.1 Space Decoupling for Reactive Power Optimization
6.2 Time Decoupling for Reactive Power Optimization
6.3 Game Theory Model of Multi-agent Volt/VAR Control
6.4 Volt/VAR Control in Distribution Systems Using an Approach Based on Time Interval
Chapter 7: Modeling and Analysis of Electricity Markets
7.1 Oligopolistic Electricity Market Analysis Based on Coevolutionary Computation
7.2 Supply Function Equilibrium Analysis Based on Coevolutionary Computation
7.3 Searching for Electricity Market Equilibrium with Complex Constraints Using Coevolutionary Approach
7.4 Analyzing Two-Settlement Electricity Market Equilibrium by Coevolutionary Computation Approach
Chapter 8: Future Developments
8.1 New Factors in Power System Optimization
8.2 Challenges and Possible Solutions in Power System Optimization
Appendix
A.1 Header File
A.2 Species Class
A.3 Ecosystem Class
A.4 Main Function
References
Index
End User License Agreement
Pages
vii
xvii
xviii
xix
xx
xxi
xxii
xxiii
xxiv
xxv
xxxv
xxxvi
xxxvii
xxxix
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
Guide
Table of Contents
Begin Reading
List of Illustrations
Chapter 1: Introduction
Figure 1.1 Typical load duration curve.
Figure 1.2 Block bidding and continuous bidding curves.
Chapter 2: Theories and Approaches of Large-Scale Complex Systems Optimization
Figure 2.1 Multi-level hierarchical power systems.
Figure 2.3 Static hierarchy of large-scale systems.
Figure 2.4 A general subsystem representation of the large-scale systems.
Figure 2.5 The representation of the overall large-scale system.
Figure 2.6 Diagram of a two-level nonfeasible decomposition–coordination.
Figure 2.7 Diagram of a two-level feasible decomposition–coordination.
Figure 2.8 Framework of cooperative coevolutionary model.
Figure 2.9 Aggregated supply curve with capacity constraint.
Chapter 3: Optimization Approaches in Microeconomics and Game Theory
Figure 3.1 Existence of equilibrium.
Figure 3.2 The revelation principle.
Figure 3.3 Network of types.
Figure 3.4 Framework of Lagrangian relaxation algorithm.
Chapter 4: Power System Planning
Figure 4.1 The framework of JASP.
Source
: Chen 2004. Reproduced with permission from Elsevier.
Figure 4.2 The framework of the Lagrangian relaxation method.
Source
: Chen 2004. Reproduced with permission from Elsevier.
Figure 4.3 A single hydroelectric generator unit under peak load condition.
Source
: Chen 2004. Reproduced with permission from Elsevier.
Figure 4.4 Procedure to determine the loading position of a hydroelectric generating unit.
Source
: Chen 2004. Reproduced with permission from Elsevier.
Figure 4.5 Planning solutions of six-bus system, in case 1.
Source
: Wang 2001. Reproduced with permission from IEEE.
Figure 4.6 System structure of case 2.
Source
: Wang 2001. Reproduced with permission from IEEE.
Figure 4.7 Optimal expanding procedure of case 2.
Source
: Wang 2001. Reproduced with permission from IEEE.
Figure 4.8 Average convergence curve of case 2.
Source
: Wang 2001. Reproduced with permission from IEEE.
Figure 4.9 Five types of OPCs.
Source
: Xie 2007. Reproduced with permission from IEEE.
Figure 4.10 Original six-node Garver system.
Source
: Xie 2007. Reproduced with permission from IEEE.
Figure 4.11 Ordered performance curve for rough estimation.
Source
: Xie 2007. Reproduced with permission from IEEE.
Figure 4.12 Ordered performance curve for the Garver system.
Source
: Xie 2007. Reproduced with permission from IEEE.
Figure 4.13 Standardized error distribution for sample.
Source
: Xie 2007. Reproduced with permission from IEEE.
Figure 4.14 Flowchart of hybrid intelligent algorithm.
Figure 4.15 Diagram of the example distribution system.
Figure 4.16 SVM parameter optimization process.
Chapter 5: Power System Operation
Figure 5.1 Framework of the cooperative coevolutionary algorithm.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.2 Stochastic optimization method for solving dual problem.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.3 Generate the final solution of the original problem from the dual solution.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.4 Algorithm for feasible unit commitment scheme formation.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.5 Distribution of CCA final solutions.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.6 Influence of unit number on CPU time of CCA.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.7 Influence of time period number on CPU time of CCA.
Source
: Chen 2002. Reproduced with permission from IEEE.
Figure 5.8 Feasible solution under the adjustment time constraint.
Figure 5.9 The curve of the forecasted wind power output and its confidence interval compared with actual values.
Figure 5.10 The space of wind generation considering two wind farms.
Figure 5.11 Performance curves of the three methods.
Figure 5.12 Penetration levels of wind power with five wind farms in each hour.
Figure 5.13 The average convergence characteristics of AGA and SGA.
Figure 5.14 The statistics of ultimate solution for AGA and SGA.
Figure 5.15 The average convergence characteristic of the presented algorithm.
Figure 5.16 The complexity of the proposed algorithm.
Figure 5.17 Flowchart of solving OPF by IPCPM.
Source
: Liu 2009. Reproduced with permission from IEEE.
Figure 5.18 Schematic diagram of optimal solutions.
Source
: Liu 2009. Reproduced with permission from IEEE.
Figure 5.19 The optimizing trajectory comparison of the simplex method to the interior point method.
Source
: Liu 2009. Reproduced with permission from IEEE.
Figure 5.20 Relationship between objective function and transformer tap in five-bus system.
Source
: Liu 2009. Reproduced with permission from IEEE.
Figure 5.21 Flowchart of optimal base identification.
Source
: Liu 2009. Reproduced with permission from IEEE.
Chapter 6: Power System Reactive Power Optimization
Figure 6.1 Characterization of MAS.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.2 MAS architecture.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.3 Hierarchical model of ORPD.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.4 Network control structure of global ORPD.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.5 Layer control structure of subsystem of ORPD.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.6 Nodal voltages comparison of the 125-bus system.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.7 Comparison of 10 kV bus voltages of the 199-bus system.
Source
: Zhang 2004. Reproduced with permission from Elsevier.
Figure 6.8 Tested network.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.9 Hourly total load curves.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.10 Dispatch curves of tap 1.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.11 Dispatch curves of tap 2.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.12 Dispatch curves of capacitor 1.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.13 Dispatch curves of capacitor 2.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.14 Response curves of voltage at bus 1.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.15 Hourly active power losses of the network.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.16 Relationship of objective functions with the number of controls.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.17 Model for simulation.
Source
: Zhang 2005. Reproduced with permission from Elsevier.
Figure 6.18 Results for main grid.
Figure 6.19 Results for main subsystem.
Figure 6.20 Typical daily load curve (1).
Figure 6.21 Typical daily load curve (2).
Figure 6.22 Load level partition specification.
Figure 6.23 Flowchart of time-interval base volt/VAR control algorithm.
Figure 6.24 One-line diagram of test distribution system.
Figure 6.25 Four-load level partition results.
Figure 6.26 Six-load level partition results.
Figure 6.27 Voltage change of bus 14 over a day.
Figure 6.28 Comparison of real power losses.
Figure 6.29 OLTC schedule of the next day under five load levels.
Chapter 7: Modeling and Analysis of Electricity Markets
Figure 7.1 Illustration of electricity market models.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.2 Framework of cooperative coevolutionary model.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.3 Pseudo-code of CGA.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.4 Pseudo-code of fitness evaluation procedure.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.5 Market demand and price of CCEM for standard Cournot model.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.6 Variation of market price in coevolution process.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.7 Pareto improvement solutions.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.8 Firm 's piecewise affine supply function.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.9 Framework of cooperative coevolutionary model.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.10 Coding structure of chromosome for piecewise affine supply function model.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.11 Affine supply functions.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.13 Simulation results with competitive starting functions.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.14 Simulation results with Cournot starting functions.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.15 Simulation results with competitive starting functions and load duration characteristic (7.32).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.16 Simulation results with Cournot starting functions and load duration characteristic (7.32).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.18 Simulation results with affine starting functions and cost functions (7.33).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.19 Simulation results with competitive starting functions and cost functions (7.33).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.20 Simulation results with Cournot starting functions and cost functions (7.33).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.21 Simulation results with competitive starting functions and .
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.22 Simulation results with Cournot starting functions and .
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.21 Starting supply functions.
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.22 Marginal cost functions of cost functions (7.33).
Source
: Chen 2006. Reproduced with permission from IEEE.
Figure 7.23 Individual fitness evaluation methodology.
Figure 7.24 Two-bus example system.
Figure 7.25 Evolution of strategic variable corresponding to the representatives during the evolutionary process in case C.
Figure 7.26 Variation of each participant's expected profit with respect to its strategic variable, assuming the opponents hold the convergence bids in case C.
Figure 7.27 The three-bus example system.
Figure 7.28 Evolution of strategic variable corresponding to the representatives during the evolutionary process in Case .
Figure 7.29 Variation of each participant's expected profit with respect to its strategic variable, assuming the opponents hold the convergence bids in Case .
Figure 7.30 Variation of market clearing solution with respect to G2's strategic variable assuming the opponents hold the convergence bids in Case .
List of Tables
Chapter 3: Optimization Approaches in Microeconomics and Game Theory
Table 3.1 The prisoners' dilemma
Table 3.2 Payoffs from a simple game
Chapter 4: Power System Planning
Table 4.1 The main parameters of existing power plants
Table 4.2 The main parameters of candidate power plants
Table 4.3 The annual growth of system total load and energy
Table 4.4 System economic and reliability indices
Table 4.5 Construction scheme of the new plants
Table 4.6 Results of keeping excellent seeds changing
Table 4.7 Optimal and suboptimal schemes of case 2
Table 4.8 New lines for case 3
Table 4.9 Planning schemes in -year transmission expansion planning
Table 4.10 Size of selected subset for five OPC-based problems
Table 4.11 Basic data for the modified Garver system
Table 4.12 Quadratic generation cost function ($)
Table 4.13 Quadratic loss of load cost function ($)
Table 4.14 Original and maximum target number of lines
Table 4.15 Planning schemes in the selected subset and “good enough” subset (subset is top 1% of )
Table 4.17 Planning schemes in the selected subset and “good enough” subset (subset is top 5% of )
Table 4.16
Table 4.18 Error of scheme no. 75 ($10 000)
Table 4.19 Optimization results
Table 4.20 Costs (Yuan) of different planning schemes
Table 4.21 Reliability of different planning schemes
Chapter 5: Power System Operation
Table 5.1 System daily load
Table 5.2 Hourly forecasted output (MW) of wind power
Table 5.3 SCUC schedule with five wind farms solved by method 3
Table 5.4 Different settings of ratio percentage
Table 5.5 The type of optimal solutions
Table 5.6 Setting of discrete variables of test systems
Table 5.7 Comparison of results between former algorithm and improved algorithm in one iteration
Table 5.8 Comparison between results with and without perturbation
Table 5.9 Optimal solution type with perturbation vector
Chapter 6: Power System Reactive Power Optimization
Table 6.1 ORPD simulation results: comparison between CGA and MAS approaches for two bus systems
Table 6.2 Parameters of three tested schemes
Table 6.3 Total operating times of transformer taps
Table 6.4 Total operating times of capacitor banks
Table 6.5 Nodal voltage distributions for various schemes
Table 6.6 Nodal voltage distributions
Table 6.7 Costs and gains of the game
Table 6.8 Payoffs from noncooperative game of AVC in normal form
Table 6.9 The costs and gains of the game considering gateway voltage
Table 6.10 Payoffs from the cooperative game of AVC
Table 6.11 Detailed information of concerned items
Table 6.12 Detailed information of concerned items
Table 6.13 Control effects of AVC
Table 6.14 Payoffs of the game in mechanism 1 in normal form.
Table 6.15 Payoffs of the game in mechanism 2 in normal form.
Table 6.16 Capacitor data for distribution system
Table 6.17 Optimal dispatch schedule for day ahead (for capacitors: 0 = OFF; 1 = ON)
Table 6.18 Influence of maximum allowable switching operations for capacitors
Table 6.19 OLTC schedule under different to 7
Chapter 7: Modeling and Analysis of Electricity Markets
Table 7.1 Producers' cost data
Table 7.2 Demand function parameters
Table 7.3 Cournot–Nash equilibrium results
Table 7.4 Cournot–Nash equilibrium results
Table 7.5 Producers' cost data
Table 7.6 Cournot–Nash equilibrium results
Table 7.7 Pareto improvement results
Table 7.8 Collusion results
Table 7.9 Firms' cost data from Table 2 in Baldick and Hogan 280
Table 7.10 Simulation results of affine supply function model
Table 7.11 Cost coefficients of the GenCos
Table 7.12 Cost coefficients of the consumers
Table 7.13 Simulation results for three-bus example system
Table 7.14 CGA parameters
Table 7.15 Cost coefficients of the three GenCos
Table 7.16 Simulation results for three-GenCos example
Table 7.17 Market power for three-GenCos example
Table 7.18 Simulation results for the three-GenCos example with different slopes of the demand function
Table 7.19 Simulation results for the three-GenCos example with different cost coefficients
Table 7.20 Simulation results for the three-GenCos example with capacity constraints
Table 7.21 Cost coefficients of the five GenCos
Table 7.22 Simulation results for five-GenCos example
POWER SYSTEM OPTIMIZATION
LARGE-SCALE COMPLEX SYSTEMS APPROACHES
Haoyong Chen
South China University of Technology, P. R. China
Honwing Ngan
Asia-Pacific Research Institute of Smart Grid and Renewable Energy, Hong Kong
Yongjun Zhang
South China University of Technology, P. R. China
with contributions from
Xifan Wang and Xiuli Wang
Xi'an Jiaotong University, P. R. China
Tony C.Y. Chung
University of Saskatchewan, Canada
Fuqiang Zhang
Washington University, USA
Zechun Hu
Qinghua University, P. R. China
Min Xie
South China University of Technology, P. R. China
This edition first published 2016
© 2016 John Wiley & Sons Singapore Pte. Ltd.
Registered office
John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, \#07-01 Solaris South Tower, Singapore 138628.
For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.
All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without either the prior written permission of the Publisher, or authorization through payment of the appropriate photocopy fee to the Copyright Clearance Center. Requests for permission should be addressed to the Publisher, John Wiley & Sons Singapore Pte. Ltd., 1 Fusionopolis Walk, \#07-01 Solaris South Tower, Singapore 138628, tel: 65-66438000, fax: 65-66438008, email: [email protected].
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.
Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.
Library of Congress Cataloging-in-Publication Data applied for
ISBN: 9781118724743
To our parents
Contributors
Haoyong Chen Department of Electrical Engineering, South China University of Technology, Guangzhou, Guangdong, P. R. China
Tony C.Y. Chung University of Saskatchewan, Saskatoon, Canada
Zechun Hu Qinghua University, Beijing, P. R. China
Honwing Ngan Asia-Pacific Research Institute of Smart Grid and Renewable Energy, Kowloon, Hong Kong
Xifan Wang Xi'an Jiaotong University, Xi'an, Shaanxi, P. R. China
Xiuli Wang Department of Electric Power Engineering, Xi'an Jiaotong University, Xi'an, Shaanxi, P. R. China
Min Xie South China University of Technology, Guangzhou, P. R. China
Fuqiang Zhang Washington University in Saint Louis, Saint Louis, USA
Yongjun Zhang Department of Electrical Engineering, South China University of Technology, Guangzhou, Guangdong, P. R. China
Foreword
This book, in short, is a valuable assessment that presents profound knowledge and ideas about electric power systems and their functions. Having served our society for a long time, these infrastructures have now gained increased complexity. Further developments, such as smart grids and renewable energy technologies, have made new contributions to how power is gathered. Whether for knowledgeable students or accomplished researchers already in the field, the contents of this book are sure to contribute to a heightened viewpoint of the changing system.
During 2008, when I served as the President of the IEEE Power and Energy Society, I guided the IEEE Smart Grid New Initiatives Project involving many IEEE Societies through a successful year. In that time, I also made a decision to change the Society's name from its former title of IEEE Power Engineering Society in order to reflect the industry's continuing evolution.
This text is no exception in addressing the growth of the energy sector. Power System Optimization provides thought-provoking revelations into understanding and approaching these large-scale complex systems. The theories and interpretations in this book are presented in a detailed way and with clear meaning that make the realization of these concepts much easier to grasp.
Readers will find the explanations in this book useful in merging current applications to meet increasing advances in the field of energy and power. As the integration of unique systems becomes apparent, a broader understanding of theories and practices will serve useful in achieving optimal success.
Seeking to do just that, this book gathers approaches from different disciplines, such as systems engineering, operations research, and microeconomics. Presented in a unified manner are the vast topics of power system optimization, including: power system planning, operation, reactive power optimization, and electricity markets. The economic implication of the duality principle in mathematical programming is discussed first. In later chapters, the applications of their theories and methods to the components of the power system are explained in great detail. Theories of large-scale systems optimization are surveyed, and several theories used in microeconomics – such as general equilibrium theory, game theory, and mechanism design – are linked to provide contextual approaches. Decomposition–coordination approaches are also introduced, with an emphasis on the Lagrangian relaxation method and coevolutionary approach. The source code of the coevolutionary algorithm is given in the appendix and readers can further develop their own applications based on it.
In becoming familiar with this book, readers will gain an improved insight into the uses of the changing power designs such as electric power systems. They are characterized by large-scale engineering systems, coupled with market systems (electricity markets) and communication and control systems, along with other various systems. Developing advanced optimization approaches is crucial in ensuring that these structures remain intact.
This book is designed to be especially suitable for researchers and students in electric power engineering and related studies, as it can provide new understandings for electric power engineers. Through examples and models shown in the text, an observer can better their perspective on how to integrate existing knowledge with emerging ideas in this field. For those who seek to gain deeper insights into energy development, I am confident that this book proves to be a vital perspective on power system optimization.
Wanda RederIEEE Fellow
Preface
The approaches of large-scale system optimization have long been applied to power system planning and operation, and there is extensive literature on such optimization. On the other hand, optimization is also the basic tool for electricity markets, and is often used with microeconomic models. However, people seldom look at physical power systems and economic market systems in microeconomics from a unified system point of view. In fact, both are large-scale distributed systems, and there are intrinsic connections between optimization approaches of power systems and microeconomics (Figure 0.1). In general, a power system (an engineering system composed of generators, loads, and transmission lines) and a microeconomic system (a social system composed of producers, consumers, and markets) have many common characteristics, such as the following:
they both consist of subsystems interconnected together,
more than one controller or decision-maker is present, resulting in decentralized computations,
coordination between the operation of the different controllers is required, resulting in hierarchical structures, and
correlated but different information is available to the controllers.
Figure 0.1 Analogy between a power system and a market system.
Many optimization approaches have been developed for power system planning and operation, such as linear programming, nonlinear programming, integer programming, and mixed integer programming. Decomposition and coordinationtechniques such as Dantzig–Wolfe decomposition, Benders' decomposition, and Lagrangian relaxation are often used. On the other hand, mathematical optimization is essential to modern microeconomics, which is the theory about optimal resource allocation, defined as “the study of economics at the level of individual consumers, groups of consumers, or firms … The general concern of microeconomics is the efficient allocation of scarce resources between alternative uses but more specifically it involves the determination of price through the optimizing behavior of economic agents, with consumers maximizing utility and firms maximizing profit” (from the Economist's Dictionary of Economics). Because the market system can also be regarded as a large-scale system containing many subcomponents (buyers and sellers), the decomposition and coordination principle are also adopted. Then a unified view of optimization for power systems/electricity markets can be established from the large-scale complex systems perspective. This is the starting point of this book.
Here, as an example, we take the unit commitment (UC) problem, which is a classic optimization problem in power system operation. Consider a thermal power system with units. It is required to determine the start-up, shut-down, and generation levels of all units over a specified time horizon . The objective is to minimize the total cost subject to system demand and spinning reserve requirements, and other individual unit constraints. The notation to be used in the mathematical model is defined as follows:
time horizon studied, in hours (h);
number of thermal units;
power generated by unit
at time
, in megawatts (MW);
state of unit
at time
, denoting the number of hours that the unit has been ON (positive) or OFF (negative);
decision variable of unit
at time
, 1 for up, 0 for down;
fuel cost of unit
for generating power
at time
;
start-up cost of unit
at time
;
system demand at time
, in megawatts (MW).
The objective function of UC is to minimize the total generation and start-up cost:
The system power balance constraint is
The individual unit constraints include: unit generation limit, minimum up/down-time, ramp rate, unit spinning reserve limit, etc.
Here we only give a simplified model description, and the detailed formulation of UC will be given in the later chapters.
Different solution methods, such as priority list, dynamic programming, mixed integer programming, and Lagrangian relaxation, have been proposed by researchers. We take the Lagrangian relaxation method as an example. The basic idea of Lagrangian relaxation is to relax the systemwide constraints, such as the power balance constraint, by using Lagrange multipliers, and then to decompose the problem into individual unit commitment subproblems, which are much easier to solve. Lagrangian relaxation can overcome the dimensional obstacle and get quite good suboptimal solutions. By using the duality theory, the systemwide constraint (here referring to the power balance constraint) of the primal problem is relaxed by the Lagrangian function (3). Then the two-level maximum–minimum optimization framework shown in Figure 0.2 is formed. The low-level problems (4) solve the optimal commitment of each individual unit. The high-level problem (5) optimizes the vector of Lagrange multipliers, and a subgradient optimization method is often adopted. When is passed to the subproblems, each individual unit will optimize its own production , namely to minimize its cost or maximize its profit. In this procedure, serves as the function of market prices to coordinate the production of all units to reach the requirement of system demand. The optimization of Lagrange multipliers is in fact the price adjustment process in the market.
Figure 0.2 Illustration of Lagrangian relaxation.
The Lagrangian function is
where is the Lagrange multiplier associated with demand at time .
The individual unit subproblems are
subject to all individual unit constraints.
The high-level dual problem is
We can compare this optimization procedure with a market economy. Consider an economy with agents and commodities . A bundle of commodities is a vector . Each agent has an endowment and a utility function . These endowments and utilities are the primitives of the exchange economy, so we write . Agents are assumed to take as given the market prices for the goods. The vector of market prices is ; all prices are nonnegative.
Each agent chooses consumption to maximize his/her utility given his/her budget constraint. Therefore, agent solves
The consumer's “wealth” is , the amount he/she could get if he/she sold his/her entire endowment. We can write the budget set as
A key concept of a market system is equilibrium. Market equilibrium refers to a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. There are two kinds of equilibrium considered in microeconomics, namely, competitive equilibrium and Nash equilibrium.
A competitive (or Walrasian) equilibrium for the economy is a vector such that the following hold.
Agents maximize their utilities: for all
,
Markets clear: for all
,
The above model (6) and (9) is apparently a decentralized large-scale optimization model, which is similar in form to power system optimization problems such as the above-mentioned unit commitment. Clearly, we can see that the utility maximization problem (6) of each agent corresponds to the individual unit subproblem (4
Acknowledgments
From Professor Fuqiang Zhang, from Olin Business School, Washington University, St. Louis, USA, I got many valuable suggestions. The book was supported in part by the China National Funds for Excellent Young Scientists (51322702) and in part by the National Natural Science Foundation of China (51177049).
H.C.
Acronyms
AC
alternating current
ACCPM
analytic center cutting plane method
ACE
agent-based computational economics
AGA
annealing genetic algorithm
AGA
genetic algorithm with annealing selection
AGC
automatic generation control
AVC
automatic voltage control
BES
battery energy storage
CACD
cost of adjusting control device
CCA
coevolutionary computation approach
CCA
cooperative coevolutionary algorithm/approach
CCEM
coevolutionary computation applied to the electricity market
CCGA
cooperative coevolutionary genetic algorithm
CCHP
combined cooling, heat, and power
CEA
coevolutionary algorithm
CGA
cataclysmic genetic algorithm
CGA
coevolutionary genetic algorithm
CHP
combined heat and power
CRF
capital recovery factor
CSF
conjectured supply function
DAI
distributed artificial intelligence
DC
direct current
DG
distributed generation
DisCo
distribution company
DMS
distribution management system
DP
dynamic programming
DSR
demand-side response
EA
evolutionary algorithm
EEF
equivalent energy function
EENS
expected energy not served
EP
evolutionary programming
EPEC
equilibrium problem with equilibrium constraints
ES
energy storage
ES
evolution strategy
ESS
entirety selection scheme
GA
genetic algorithm
GenCo
generation company
GGDF
generalized generation distribution factor
IAEA
International Atomic Energy Agency
ICM
intelligent communication manager
IEEE
Institute of Electrical and Electronics Engineers
IMC
iterative Monte Carlo
IPCPM
interior point cutting plane method
IPD
iterated prisoners' dilemma
ISO
independent system operator
IWM
individual welfare maximization (algorithm)
JASP
Jiaotong Automatic System Planning Package
KDM
knowledge data manager
KKT
Karush–Kuhn–Tucker
KT
Kuhn–Tucker
LCS
layer control structure
LI
Lerner Index
LMP
locational marginal price
LOLC
loss of load cost
LOLP
loss of load probability
LR
Lagrangian relaxation
LSF
linear supply function
LSFE
linear supply function equilibrium
MAS
multi-agent system
MCP
mixed complementarity problem
MIOPF
mixed integer optimal power flow
MIP
mixed integer programming
MPEC
mathematical program with equilibrium constraints
MW
megawatts
NCP
nonlinear complementarity problem
NCS
network control structure
NGO
nongovernmental organization
NPV
net present value
OLTC
on-load tap changer
OO
ordinal optimization
OPC
ordered performance curve
OPF
optimal power flow
ORPC
optimal reactive power control
ORPD
optimal reactive power dispatch
ORPP
optimal reactive power planning
PD
prisoners' dilemma
PES
Power and Energy Society of IEEE
PHEV
plug-in hybrid electric vehicle
PHS
pumped hydro storage
PoolCo
(independent power) pooling company
PSO
particle swarm optimization
PV
(solar) photovoltaics
PX
Power Exchange
RES
renewable energy source
RMS
reason maintenance system
RO
robust optimization
RTO
regional transmission organization
RTOSE
real-time operating system extensions
SA
simulated annealing (algorithm)
SCADA
supervisory control and data acquisition
SCED
security-constrained economic dispatch
SCCP
stochastic chance constrained programming
SCPM
simplex cutting plane method
SCUC
security constrained unit commitment
SFE
supply function equilibrium
SGA
simple genetic algorithm
SGA
standard genetic algorithm
SP
stochastic programming
SVM
support vector machine
TEAM
transmission economic assessment methodology
TMM
time map manager
UAC
unit adjustment cost
UC
unit commitment
VAR
volt-ampere reactive
VCM
volt/VAR control mismatching
WASP
Wien Automatic System Planning Package
WECS
wind energy conversion system
Symbols
generalized generation distribution factor of unit
in branch
coefficients of the quadratic production cost function of unit
impedance of branch
flow capacity of branch
branch set
index of unit
set of thermal units
number of hours within the planning period
production cost function
start-up cost function
cost of the interval
of the piecewise start-up cost function of unit
upper output limit of unit
lower output limit of unit
spinning reserve provided by unit
in period
spinning reserve requirement of the system in time period
ramp-up rate limit of unit
ramp-down rate limit of unit
Chapter 1Introduction
Optimization theories and approaches have been extensively applied to power system planning and operation problems. This is a rather traditional and ongoing research area [1]. With the complication of power systems, the deregulation of the power industry, and the development of smart grids, many new problems have emerged and new methods have been developed. Many optimization theories and approaches have acquired industrial application and introduced technical and economic benefits. The mathematical optimization methods applied in power systems include linear programming, nonlinear programming, mixed integer programming, dynamic programming, artificial intelligence, stochastic programming, etc. This book focuses on the advanced theories and approaches from the perspective of large-scale complex systems, rather than the traditional ones. However, to begin with the fundamentals, we will first review the basic optimization applications in power system planning and operation.
The aims of this chapter are as follows:
To present a broad review of mathematical optimization applications to power system planning and operation, which is the foundation for the theories and approaches presented in the subsequent chapters.
To explain the basic concepts to those interested in the optimization field, but unfamiliar with power system problems and terminology. It is hoped that this chapter may motivate some people to become involved in the challenging power field.
To summarize the results of traditional power system research, to allow the reader to understand the differences among them and the more advanced approaches presented in books, and to encourage new development and further research.
To give the reader a unified mathematical description of different power system optimization problems, the generalized notation used in this book, such as and for variables, and , , and for functions, and their power system meanings are explained. Vectors (lower-case) sometimes and matrices (upper-case) usually are in bold face; and matrix transposition is indicated by a superscript , such as .
The problems discussed include generation, transmission, and distribution expansion planning, optimal operation problems such as hydrothermal unit commitment and dispatch, optimal load flow and volt-ampere reactive (VAR) optimization, and optimization models of electricity markets based on theories of microeconomics.
Numerous important works have appeared on these topics in books and journals all over the world. It is an impossible task to discuss all of them. Since the objective of this chapter is to introduce the basic concepts and methods of power system optimization, we will lay the emphasis of our discussion on research reported by IEEE papers in IEEE Transactions on Power Systems and Technical Meetings.
1.1 Power System Optimal Planning
Power system expansion planning is traditionally decomposed into load forecasting, generation planning, and transmission planning. Load forecasting is the basis for power system planning, which provides the basic data for calculation of electric power and energy balance. Although generation planning and transmission planning are essentially indivisible, these two issues have to be decomposed and solved separately and further coordinated due to their different focuses and the difficulty in solving them as a whole.
Traditional power system planning is based on scheme comparison, which selects the recommended scheme from a few of the viable options with some technical and economic criteria. However, because this approach is empirical, the final result is not necessarily optimal. With the fast development of power technologies, the rapidly growing demand for electricity, and the increasingly diversified energy resources used in power generation, the generation mix becomes increasingly complicated. On the other hand, large-scale interconnected systems across different areas have been formed gradually. All these factors have brought difficulties to the economic and technical assessment of power system planning schemes, and traditional planning approaches are difficult to adapt to these challenges. Fortunately, the development of computer science, systems engineering, operational research, and other research areas has provided new means for the optimization of power system planning. Theory and practice in power system optimal planning have made considerable progress in recent years. A number of commercial planning software packages have emerged and their benefits have been affirmed in the power industry.
The objective of power system planning is to determine what schemes are the most beneficial from the overall and long-term perspective. This requires us to choose the best planning scheme from all possible choices. The application of power system optimal planning theories and methods not only canhave more accurate and comprehensive technical and economic evaluation, but also can evaluate the impacts of various uncertainties by sensitivity analysis, so that the planning results are produced with a higher referential value.
1.1.1 Generation Expansion Planning
The objective of generation expansion planning is to choose the least expensive expansion scheme (type, number, capacity, and location of generating units), in terms of investment and operation costs, that satisfies certain constraints. The key constraints are electric power and energy balance, which means that the total power and energy produced by all the generating units can meet the requirement of demand. Other technical constraints, such as limitation of resources, also need to be met. Generally, generation expansion is carried out over a planning horizon of many years, which turns into a dynamic optimization problem.
Several key issues should be analyzed quantitatively in generation expansion planning, such as: annual investment flow and operating cost, quantity of primary energy resources used in generation, reliability of electric power supply, etc. The investment cost of building a particular plant in a given year is independent of the other decisions in a given scheme. However, the operating cost is much more complicated, and is related to the generation mix, system load, generating unit outages, transmission network losses, availability and cost of energy from neighboring systems, fuel costs, etc. Some influencing factors are intrinsically random, such as generating unit outages. The fact that units must be added in discrete sizes presents a further complication. Considering all these conditions, the mathematical model of generation expansion planning is large-scale, nonlinear, discrete, and stochastic, which is a very difficult problem to solve.
Generation expansion planning has long been of interest to researchers, and many sophisticated and effective techniques have been developed. The approaches differ in the questions they are intended to answer, the model details, and the optimization methods.
The early work often used linear programming models [2, 3]. The objective functions takes the following form:
where denotes the capacities of different types of generating units installed in each year and specifies the energy produced by each power plant (or plant type). A number of different load levels are considered here. The investment cost and the operating cost should be calculated with the method of technological economics. The load levels related to and are obtained by dividing estimates of the load duration curves into a number of discrete segments (Figure 1.1). The variables and are related through linear constraints so that a plant cannot produce power exceeding its installed capacity. Other constraints limit the capacity of certain types of units and require total capacity to exceed expected load. This formulation is a high-dimensional optimization problem. Decomposition techniques such as Dantzig–Wolfe decomposition may be needed to solve it.
Figure 1.1 Typical load duration curve.
A dynamic programming based model of generation planning has been presented by Booth [4, 5]. The method can handle integer variables and nonlinear constraints. The random variables are treated with a probabilistic approach. As a significant innovation, the expected outage rates for various units are considered by modification of the load duration curve. The problem is formulated as: choose (capacity additions in year ) to minimize
where
The function is related to probabilistic load models, fuel models, etc. A variety of technical and economic constraints are considered.
The problem is decomposed into a series of forward dynamic programming problems. A pretreatment is employed to dynamically reduce the dimensionality of the problem. However, the computational burden is still heavy.
A more advanced generation planning model JASP has been proposed by Chen [6], which decomposes the generation planning problem into a high-level power plant investment decision problem and a low-level operation planning problem and solves them by a decomposition–coordination method. Lagrangian relaxation is used to solve the power plant investment decision problem, and a probabilistic production simulation based on the equivalent energy function method is used to solve the operation planning problem. Simulation results show that JASP can not only overcome the “curse of dimensionality” but also find an economical and technically sound generation planning scheme.
1.1.2 Transmission Expansion Planning
Transmission expansion planning is an important part of power system planning, whose task is to determine the optimal power grid structure according to the load growth and generation planning schemes during the planning horizon to meet the requirements of economic and reliable power delivery. In general, transmissionplanning should answer the following points:
