Power Flow Genetic Algorithm In Matlab

Abstract

A genetic algorithm (GA) to solve Optimal Power Flow (OPF) problems, optimizing electricity generation fuel cost. The GA based OPF is a derivative free optimization technique that relies on the evaluation of several points in the parameter search space strictly on the objective function. A 3 bus system and the IEEE 30 bus test system are used to validate the developed GA based OPF by means of comparisons with an interior point based optimal power flow.

Introduction

Since the emergence of electric power systems, there has always been a search for increasingly efficient methods to solve the power flow problem. The power flow consists of solving a set of nonlinear algebraic equations with quadratic and trigonometric terms. When its solution is found, state variables of a power system are available and several information about the system may also be used, for example, to system planning and stability studies. Among the most successful algorithms applied on the power flow solution are those that use the Newton-Raphson method, proposed by Van Ess and Griffin. This method underwent improvements in who introduced matrix techniques using sparsity as a means of implementing the Newton-Raphson method for large networks. Early developments of digital power flow calculations were reviewed by Tinney and Powell. Currently there are several books and computer programs that explain and solve the power flow problem.

Optimal Power Flow (GAOPF) problem is solved based on the use of a genetic algorithm load flow, and to accelerate the concepts it propose the use of gradient information by the use of the steepest decent method. The method is not sensitive to the starting points and capable to determining the global optimum solution to the OPF for range of constraints and objective functions. But GAOPF requires two load flow to be performed per individual, per iteration because all controllable variables are included in the fitness. In this paper we develop a simple genetic algorithm applied to the problem of optimal power flow in large power distribution systems. To accelerate the processes of GAOPF, the controllable variables are decomposed to active constraints that effect directly the cost function are included in the Genetic algorithms process and passive constraints which are updating using a conventional load flow program, only, one time after the convergence on the GAOPF. In which the search of the optimal parameters set is performed using into the account that the power losses are 2% of the power demand. The slack bus parameter would be recalculated in the load flow process to take the effect of the passive constraints.

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Description of Genetic Algorithms

The genetic algorithms are part of the evolutionary algorithms family, which are computational models, inspired in the Nature. Genetic algorithms are powerful stochastic search algorithms based on the mechanism of natural selection and natural genetics. GAs works with a population of binary string, searching many peaks in parallel. By employing genetic operators, they exchange information between the peaks, hence reducing the possibility of ending at a local optimum. GAs are more flexible than most search methods because they require only information concerning the quality of the solution produced by each parameter set (objective function values) and not lake many optimization methods which require derivative information, or worse yet, complete knowledge of the problem structure and parameters.

There are some difference between GAs and traditional searching algorithms. They cold be summarized as follows:

• The algorithms work with a population of string, searching many peaks in parallel, as opposed to a single point.
• GAs work directly with strings of characters representing the parameters set not the parameters themselves.
• GAs use probabilistic transition rules instead of deterministic rules.
• GAs use objective function information instead of derivatives or others auxiliary knowledge.
• GAs have the potential to find solutions in many different areas of the search space simultaneously.

PROBLEM FORMULATION

The standard OPF problem can be written in the following form,

                    Minimise F(x)                                                   (the objective function)

subject to :

hi(x) = 0, i = 1, 2, ..., n                                   (equality constraints)

gj(x) = 0, j = 1, 2, ...,m                                   (inequality constraints)

where x is the vector of the control variables, that is those which can be varied by a control center operator (generated active and reactive powers, generation bus voltage magnitudes, transformers taps etc.);
The essence of the optimal power flow problem resides in reducing the objective function and simultaneously satisfying the load flow equations (equality constraints) without violating the inequality constraints

Item 1 is a part of the problem's input data and all the features in items 2 and 3 are

A. Objective Function

The most commonly used objective in the OPF problem formulation is the minimisation of the total cost of real power generation. The individual costs of each generating unit are assumed to be function, only, of active power generation and are represented by quadratic curves of second order. The objective function for the entire power system can then be written as the sum of the quadratic cost model at each generator.

where ng is the number of generation including the slack bus. Pgi is the generated active power at bus i. ai, bi and ci are the unit costs curve for ith generator.

B. Types of equality constraints

While minimizing the cost function, its necessary to make sure that the generation still supplies the load demands plus losses in transmission lines. Usually the power flow
equations are used as equality constraints.

where active and reactive power injection at bus i are defined in the following equation: