Page 216 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 207

6.6 Discrete VAR Optimization based on GA

6.6.1 Overview

In Sections 6.3 and 6.4, an approximation discrete optimization algorithm was proposed to
solve large-scale nonlinear integer programming problems. In Section 6.5, expert rules were
introduced to seek better initial values, and the discrete optimization was discussed from the
perspective of programming mathematics. Because traditional optimization algorithm is not
always able to provide global optimal solutions, to search for a solution close to global
optimum, a stochastic searching method is used in this section to solve local optimal solution
problems in optimization calculation.
GA and simulated annealing (SA) are typical stochastic optimization algorithms that try to
consider optimization from another perspective, that is, biological or physical perspectives
rather than an engineering perspective. The process of biological evolution is a process of
survival of the fittest, and the process of metal sintering annealing is a process to change
crystalline structure; both are capable of developing toward optimization. Scientific researchers
make use of mathematical measures to simulate these processes, so as to solve the optimization
problem.

The SA method was used in Chapter 4 to solve ill-conditioned power flow problems. The
method solves the optimization problem through four main steps. However, there was no
common method for selecting parameter and initial value, so it cannot be simply used in the
optimization calculation.

GA is a stochastic optimization algorithm based on natural selection of biology and was
proposed by University of Michigan, US, in recent years, which is characterized by the use of
chromosomes to represent problem variables and the use of multispot searching in the solution
space. Thus, the objective function and constraint function of the problem are continuous, so it
is applicable to the discrete optimization problem.

The basic approach of the generic algorithm is to test the occasional new parts under random
conditions. However, this procedure is not a simple arbitrary search. Instead, it only maintains
searching with performance that may be possibly improved. Moreover, it can effectively
make use of the system information to suspect new searching spots. The strategy of biological
evolution is to change its own structure and function to adapt to the surrounding environment.
Such biological evolution strategy can be simulated with mathematical measures to solve the
discrete optimization problem.

GA technology also has the problem of how to set an initial searching spot. However, the
algorithm itself does not have any requirement for an initial searching spot. To accelerate a
solution procedure, expert rules are used in this section during the calculation process to control
basic operations of GA.