Page 6 - Mathematical Models and Algorithms for Power System Optimization

Preface

The practical models for power system planning, operation, control, and electricity markets are
provided in this book based on the authors’ research achievements in the development of
mathematical models and algorithms. The models include optimization models (linear,
nonlinear, mixed integer, nonlinear mixed integers), differential equations, difference
equations, and time series models. This book not only uses numerical algorithms (mathematical
programming methods), such as linear programming, nonlinear programming, mixed
integer programming and dynamic programming, but also uses some non-numerical algorithms
such as Genetic Algorithm (GA), Simulated Annealing (SA), and Expert System (ES). The
mathematical models and calculation methods provided in this book have been proven by
typical calculation examples or applied in engineering practices. Therefore, this book follows a
highly original and very practical approach.

The current research results on modeling technology for power systems can be found in
research papers and textbooks. However, research papers mainly focus on related theoretical
aspects, whereas textbooks emphasize general knowledge, but neither describes the modeling
process in detail. Considering both theoretical and practical aspects, this book not only
introduces the methods and processes for the development of optimization models but also
provides some practical techniques, such as mutual transformation of variables and functions,
transformation of equation types, and transformation of constraints. It also provides some
special techniques such as setting of variable types and preprocessing of data and parameters.
The practical techniques mentioned above allow us to solve the modeling problems
encountered in new generation power systems more effectively.
The power system is a typical large-scale man-made system, though all the conventional
components have a complete model, any new component needs to have a new model so as to be
connected to the power system. To properly handle the new coming problems in power
system planning, operation, and control, the development of corresponding optimization
mathematical models and investigation of feasible algorithms should take many
relationships into consideration, such as the relationships between old and new components,
between old and new models, between the power system and the external environment, to name
a few.

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