Page 11 - Mathematical Models and Algorithms for Power System Optimization

CHAPTER 1
Introduction

Chapter Outline
1.1 General Ideas about Modeling 1
1.2 Ideas about the Setting of the Variable and Function 3
1.3 Ideas about the Selection of the Model Type 4
1.4 Ideas about the Selection of the Algorithm 5
1.5 Ideas about the Applications of Artificial Intelligence Technology 7

1.1 General Ideas about Modeling

Many practical power system problems can be represented as mathematical models and sets
of rules that connect the model’s elements. Because of the mathematical model’s good
reproducibility, the inherent law of practical problems can be found via numerical algorithms.
Therefore, it is necessary to study the model and algorithms of power systems in depth.

An appropriate approximation is reasonable for guiding practical theory. It is generally
believed that, as long as human observation of practical problems reaches 10-6 orders
of magnitude, it can meet actual needs of measurement. Beyond this limit, only theorists
are interested. As the famous mathematician Klein has said, approximation mathematics
is the very part of mathematics applied to practical applications, whereas precision
mathematics is the solid framework on which approximation mathematics is built.
Approximate mathematics is not “approximate mathematics” but “precision mathematics
about approximate relationships.” Therefore, the priority of modeling is to determine how to
approximately solve a problem by taking advantage of the existing solvable conditions of
the problem.

In modeling research of power system optimization, it is necessary to dialectically deal with
the different types of variables, such as discreteness and continuous variables; the different
types of models, such as linear and nonlinear; and the different types of algorithms, such as

Mathematical Models and Algorithms for Power System Optimization. https://doi.org/10.1016/B978-0-12-813231-9.00001-7
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