Capacitor Bank Resizing in Islanded Power Grid Fed by Induction Generator

Abstract

In a power grid with distributed different resources, a capacitor bank is used for overall compensation purpose. However, when a part of this grid is islanded, the capacitor bank will be used for induction generator operation in the case of wind energy source. If a same capacitance is permanently connected, it may cause a severe over-voltage due to an abnormal phenomenon ferro-resonance when it is high. In this work, a new approach is developed for reselecting an adequate size of this capacitor for islanding grid. This approach is based on numerical technique and simulation, which leads to determine the optimal value of the required capacitance for three-phase self-excited induction generator operation as well as to identify the region of operation where the magnetizing reactance of induction generator is unsaturated and hence a ferro-resonance may be avoided. Moreover, the simulation utilizing Simulink/MATLAB may be useful for the validation of this approach. The obtained results are very encouraging.

Appendix

Genetic algorithms emulate the mechanics of natural selection by a process of randomized data exchange. In this way they are able to solve of range of difficult problems which cannot be tackled by other approaches. The fact that they are able to search in a randomized, yet directed manner, allows them to reproduce some of the innovative capabilities of natural systems.

In genetic algorithms, evolution towards a global optimum occurs as a result of pressure exerted by a fitness-weighted selection process and exploration of the solution space is accomplished through combination and mutation of existing characteristics present in the current population. Other optimization techniques (such as gradient descent methods) search a region of the solution space around an initial guess for the best local solution [7, 8, 15].

The general scheme of a GA can be given as follows:

begin

INITIALIZE population with random candidate solutions;

EVALUATE each candidate;

repeat

SELECT parents;

RECOMBINE pairs of parents;

MUTATE the resulting children;

EVALUATE children;

SELECT individuals for the next generation

until TERMINATION-CONDITION is satisfied

end

The tasks that a genetic algorithm must perform lead to the existence of three phases in the genetic algorithm optimization [9].

Initiation means filling the initial population with encoded, usually randomly created parameter strings or chromosomes.

Reproduction consists in three main operators: selection, crossover and mutation.

30.1.1 Selecting the Variables and the Fitness Function

A fitness function generates an output from a set of input variables (a chromosome). The fitness function may be a mathematical function, an experiment, or a game. The object is to modify the output in some desirable fashion by finding the appropriate values for the input variables. GAs is usually suitable for solving maximization problems. Minimization problems are usually transformed into maximization problems by some suitable transformation. In general, fitness function F(X) is first derived from the objective function and used in successive genetic operations.

Certain genetic operators require that fitness function be non-negative, although certain operators do not have this requirement. Consider the following transformations: F(X) = f(X) for minimizing problem. Where f(x) can be solved using Eqs. (30.9) and (30.10).

30.1.2 Components of Genetic Algorithm

The GA begins, like any other optimization algorithm, by defining the optimization variables, the fitness function, and the fitness. It ends like other optimization algorithms too, by testing for convergence. In between, however, this algorithm is quite different. Then, the most important components as shown in a GA flowchart (see Fig. 30.A) are:

Fig. 30.A

Flow chart of genetic algorithm

• 1. Representation (definition of individuals),

• 2. Evaluation function (or fitness function),

• 3. Population,

• 4. Parent selection mechanism,

• 5. Variation operators (crossover and mutation),

• 6. Survivor selection mechanism (replacement).

A path through the components of the GA are shown as a flowchart in Fig. 30.A; the main operators of GA are selection, crossover and mutation.