Page 10 - Mathematical Models and Algorithms for Power System Optimization

Preface

In addition, this chapter has mathematically proven that the newly constructed state space
is observable, decoupled, and topologically equivalent to the original state space of the system.
Based on the two stage control criteria given in the chapter, new mathematical models for stage
control and integrated computing processes have been developed. Finally, the chapter explores
the realistic feasibility of the defined criteria and methodologies via the case study of the offline
calculation.
Chapter 9 focuses on the decision-making model in the power market. This chapter studies the
single commodity market with transactions of only active power and the multicommodity
market with transactions of both active and reactive power, using the power pool mode. This
chapter establishes an optimal decision model, and illustrates that this model and the
competition equilibrium model are consistent in form. It indicates that the result of decision
optimization has reached a competitive equilibrium. Based on the characteristics of the power
systems, the accounting pricing method is used to distribute the loss of a power transmission
network and the cost of transmission congestion reasonably among market participants. This
eliminates market surpluses and avoids unfair posttrade distribution issues.

There are three appendices in this book. Appendix A describes the approximate algorithm
for MIP (which has been applied in Chapters 4 and 6). Appendix B presents the derivation of the
difference expressions for transformer T and shunt capacitor C in the optimization model
proposed in Chapter 6. Appendix C introduces the derivation of the decoupling benchmark δ ei
proposed in Chapter 8 by using the DC power flow calculation method.
Finally, the authors gratefully appreciate the edification and inspiration of several respected
mentors, the contributions of collaborators, as well as the participation of several graduate
students, especially the assistance of Dr. Su Aoxue, who made the book more concise and
more reflective of the authors’ most innovative work. The authors are also particularly grateful
to Dr. Liu Yunren, a retired engineer from the California Independent System Operator
(CAISO) in the United States, who carefully read the manuscripts of the book and made
valuable comments. The authors also thank to Dr. QianXin, who provided support on the
English proof reading and promoted the publishing of the book.

The authors hope to help improve the professional skills of power engineers as well as senior
undergraduates and graduates from the relevant universities in their work on the modeling
technology of power system optimization.

Fan Mingtian
Zhang Zuping
Wang Chengmin
August 2017

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