This paper presents both application and comparison of the metaheuristic techniques to multi-area economic dispatch (MAED) problem with tie line constraints considering transmission losses, multiple fuels, valve-point loading and prohibited operating zones. The metaheuristic techniques such as differential evolution, evolutionary programming, genetic algorithm and simulated annealing are applied to solve MAED problem. These metaheuristic techniques for MAED problem are evaluated on three different test systems, both small and large, involving varying degree of complexity and the results are compared against each other.
Static economic dispatch (SED) allocates the load demand which is constant for a given interval of time, among the online generators economically while satisfying various constraints including static behavior of the generators. Dynamic economic dispatch (DED) is an extension of static economic dispatch problem. DED is the most accurate formulation of the economic dispatch problem, but it is the most difficult to solve because of its large dimensionality. The first paper in this area appeared in 1972 [1] by Bechert and Kwatny. Since the DED was introduced, several methods [2-13] such as Lagrangian relaxation, gradient projection method, dynamic programming, hybrid EP and SQP, hybrid HNN-QP, hybrid differential evolution, etc., have been employed for solving this problem. However, all of these methods may not be able to find an optimal solution and usually stuck at a local optimum solution. Recently, stochastic search algorithms [14-27] such as simulated annealing (SA), genetic algorithm (GA), evolutionary programming (EP), particle swarm optimization (PSO), and differential evolution (DE) have been successfully used to solve power system optimization problems due to their ability to find the near-global solution of a nonconvex optimization problem.
This paper presents opposition-based differential evolution to determine the optimal hourly schedule of power generation in a hydrothermal system. Differential evolution (DE) is a population-based stochastic parallel search evolutionary algorithm. Opposition-based differential evolution has been used here to improve the effectiveness and quality of the solution. The proposed opposition-based differential evolution (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. The effectiveness of the proposed method has been verified on two test problems, two fixed head hydrothermal test systems and three hydrothermal multi-reservoir cascaded hydroelectric test systems having prohibited operating zones and thermal units with valve point loading. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed opposition-based differential evolution based approach is able to provide better solution.
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