Page 7 - Mathematical Models and Algorithms for Power System Optimization

Preface

In recent years, there has been an evident tendency for a large number of distributed
resources, such as distributed generation, energy storage devices, and interactive loads, to
be connected to the power grid. In addition, information and communication technologies have
been widely applied in many fields of power systems. To adapt to this new progress, many new
relationships need to be dealt with and many new models need to be developed, and traditional
mathematical models of power systems need to be further improved.
The modeling of power systems is extremely challenging due to the complexity of practical
problems, which requires fairly good mathematical knowledge and deep understanding of the
physical system. Although the reasonable reproducibility of mathematical models allows us to
simulate practical problems more effectively, the selecting of an optimization model nearly
always involves compromise among conflicting goals, such as discrete versus continuous,
accurate versus approximate, simple use versus comprehensive analysis, etc. The modeling
techniques for power system optimization deserve to be discussed in depth in this book.

Four types of basic variables are considered in the steady-state analysis and calculation of the
power system in this book: active power, reactive power, voltage, and phase angle (namely P,
Q, U, and θ). Among them, active power and reactive power can be divided into active power
generation output and reactive power generation output (P G , Q G ), and active load and reactive
power load (P L , Q L ), respectively. Occasionally, the “P” and “Q” on the node are considered as
the corresponding impedances rather than the variables. Besides the basic variables described
previously, two more variables are considered in the transient calculation of the power system:
the power angle δ and the angular frequency or rotational speed of the generator ω¼2πf (where
f is the system frequency).

Chapter 1 introduces the fundamental issues of modeling techniques deduced from practical
engineering problems, including some general and special modeling techniques. It provides
some ideas for the setting of variables and functions, the selection of model types, and the
selection of algorithms, all of which provide main aspects for power system model
constructions and solutions.
The rest of the book is divided into four parts: operation, planning, control, and marketing for
power systems. All four parts describe the mathematical models and the calculation methods to
optimize the variables P, Q, U, and θ, from different points of view. The first part comprising
Chapters 2 and 3 focuses on the power generation operation plan, which optimizes the
generated output of the generator hourly, daily, and yearly. The second part of the book,
Chapters 4, 5 and 6, focuses on the investment and operation planning of the power network,
which optimizes the variables active power P (including P G and P L ), reactive power Q G ,
voltage U, phase angle θ, transformer ratio T, capacitor bank C, and reactor bank R in hourly
and yearly cycles. The third part of this book, Chapters 7 and 8, describes the power system
control on small or large disturbances in a second and millisecond time cycle, which mainly
optimizes variables such as the generator output P G , the power angle δ of the generator, and the

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