A Modified Differential Evolution Algorithm for Solving NonConvex Dynamic Economic Dispatch Problems

Abstract

Abstract-In this paper, a modified differential evolution (MDE) algorithm is presented to solve non-convex dynamic economic dispatch (DED) problems considering valve-point effects, the ramp rate limits and transmission losses. The practical DED problems have non-smooth cost function with equality and inequality constraints, which make the problem of finding the global optimum difficult when using any mathematical approaches. The proposed MDE algorithm is inspired by three ideas: (1) use of opposition based learning to generate the initial population, (2) use of tournament best process to generate mutant vector to explore the region around the tournament best individual, (3) use of a single set population in contrast to the two set population as in basic DE. The feasibility of the proposed method is validated on 5 and 10 units test system for a 24 h time interval. The results are compared with the results reported in the literature.Keywords-Modified differential evolution, dynamic economic dispatch, non-smooth cost functions, ramp rate limits, valve-point effects I. INTRODUCTIONThe electrical power systems are interconnected in order to obtain the benefits of minimum generation costs, maximum reliability and best operational conditions, such as sharing of power reserve, improving the stability and operating on emergency situations. Thus, the optimization problem of the economic dispatch of electrical power system is relevant to accomplish requirements of quality and efficiency in power generation. Dynamic economic dispatch (DED) is one of important problems in power system operation and control, which is used to determine the optimal schedule of generating outputs on-line so as to meet the load demand at the minimum operating cost under various system and operating constraints over the entire dispatch periods. DED is an extension of the conventional economic dispatch (ED) problem that takes into consideration the limits on the ramp rate of generating units to maintain the life of generation equipment [1,2].Since the DED problem was introduced, several optimization techniques and procedures have been used for solving the DED problem with complex objective functions or constraints. There were a number of classical methods that have been applied to solve this problem such as gradient projection method, Lagrange relaxation, and linear programming [3][4][5]. Most of these methods are not applicable for non-smooth or non-convex cost functions. To overcome this problem, many stochastic optimization methods have been employed to solve the DED problem, such as genetic algorithm (GA) [6], simulated annealing (SA) [7], differential evolution (DE) [8,9], particle swarm optimization (PSO) [10], hybrid EP and SQP [11], deterministically guided PSO [12], hybrid PSO and SQP [13], and imperialist competitive algorithm (ICA) [14]. Many of these techniques have proven their effectiveness in solving the DED problem without any or fewer restrictions on the shape of the cost function curves.Differential evolution (DE) algorithm introd...