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Selection Of Control Parameters Of Differential Evolution Algorithm For

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Selection Of Control Parameters Of Differential Evolution Algorithm For Economic Load Dispatch Problem

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Y.Narendra Kumar1, Sidhartha Panda2 Department of Electrical and Electronics Engineering Veer Surendra Sai University of Technology (VSSUT), Burla-768018, Odisha, India. E-mails: narenyegireddy@gmail.com1 , panda_sidhartha@rediffmail.com2 Abstract. Differential evolution (DE) is a population based heuristic search algorithm for global optimization capable of handling non differentiable, nonlinear and multi-modal objective functions. The performance of this type of heuristic algorithms is heavily dependent on the setting of control parameters as proper selection of the control parameters is very important for the success of the algorithm. In this paper, a study of control parameters on the performance of DE optimization algorithm for economic load dispatch problem has been addressed. The constrained optimization problem is formulated considering equality constraints on power balance and inequality constraints on generation capacity limits as well as the transmission losses. The effectiveness of the proposed method is illustrated on a standard IEEE 30 bus test system. The results of the effect of the variation of different strategy and control parameters are presented. It is observed that the DE algorithm may fail in finding the optimal value if the strategy and control parameters are not chosen carefully. Keywords: Differential evolution, optimal power flow, control parameters, economic dispatch, IEEE 30 bus test system. 1. Introduction With the development of modern power systems, economic load dispatch (ELD) problem has received an increasing attention. The main objective of ELD is to schedule the committed generation unit outputs so as to meet the load demand at minimum operating cost, while satisfying all unit and system equality and inequality constraints [1]. Over the years, many efforts have been made to solve the problem, incorporating different kinds of constraints or multiple objectives, through various mathematical programming and optimization techniques. The input-output characteristics of modern generators are nonlinear and highly constrained. Hence, conventional methods may fail to provide satisfactory results. Evolutionary computational approaches, on the other hand, gained remarkable importance in this area since they can provide solutions leading to a considerable reduction of generator fuel consumption and also provide these solutions at low computational costs [2]. Differential evolution (DE) is a branch of evolutionary algorithms developed by Rainer Stron and Kenneth Price in 1995 [3] is an

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improved version of genetic algorithm for faster optimization. DE is a population based direct search algorithm for global optimization capable of handling non differentiable, nonlinear and multi-modal objective functions, with few, easily chosen, control parameters. DE differs from other evolutionary algorithms in the mutation and recombination phases. DE uses weighted differences between solution vectors to change the population whereas in other stochastic techniques such as perturbation occurs in accordance with a random quantity. In view of the above, many researchers have applied DE to various engineering problems [4-7]. The general convention used in mutation process, is DE/x/y, where DE stands for differential evolution, x represents a string denoting the type of the vector to be perturbed (whether it is randomly selected or it is the best vector in the population with respect to fitness value) and y is the number of difference vectors considered for perturbation of x. It has been reported in literature that there are ten possible working strategies of DE and proper selection of a particular strategy is very much necessary [8]. The success of DE is also heavily dependent on setting of control parameters namely; mutation strategy, step size F and crossover probability of CR. One of the main problems in evolution strategies of DE is to choose the control parameters and mutation strategy such that it exhibits good behavior. In this paper, tests for various mutation strategy and parameter settings of DE are conducted for the economic load dispatch with generator constraints. The influence of parameter settings of DE is tested on an IEEE 30 bus test system and results are presented. Based on the results obtained, recommendations are suggested for the mutation scheme and suitable range of control parameters of DE for the present problem. 2. Problem Formulation The primary objective of ELD is to allocate the most optimum real power generation level for all the available generating units in the power station that satisfies the load demand at the same time meeting all the operating constraints. The fuel cost characteristics of each generator unit, is represented by a quadratic equation and the valve point effect is modeled. Mathematically, the problem is represented as: Minimiz

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