Constrained Evolutionary Programming Approaches to Power System Economic Dispatch K. Shanti Swarup Abstract - This paper proposes a novel methodology of Constraint evolutionary programming for solving dynamic economic dispatch. Dynamic Economic Dispatch is one of the main functions of power generation operation and control. It determines the optimal settings of generator units with predicted load demand over a certain period of time. The objective is to operate an electric power system most economically while the system is operating within its security limits. Ten units test system with smooth and non- smooth fuel cost functions are considered to illustrate the suitability and effectiveness of the proposed method. Keywords: Constrained Optimization, Evolutionary Programming, Stochastic Optimization techniques, Power system operation and control, Dynamic Economic Dispatch. I INTRODUCTION Dynamic Economic Dispatch is a method to schedule the online generator outputs with the predicted load demands over a certain period of time so as to operate an electric power system most economically [1-4]. It is a dynamic optimization problem taking into account the constraints imposed on system operation by generating ramping rate limits. The dynamic economic dispatch is not only the most accurate formulation of the economic dispatch problem but also the most difficult to solve because of its large dimensionality. Normally it is solved by dividing the entire dispatch period into a number of small time intervals, and then a static economic dispatch has been employed to solve the problem in each interval. However all of those methods may not be able to provide an optimal solution and usually getting stuck at a local optimal. Recently, stochastic optimization techniques [5-15] such as Simulated Annealing (SA), Genetic Algorithm (GA) and Evolutionary Programming (EP) have been given much attention by researchers due to their ability to seek for the near global optimal solution. Appropriate setting of the control parameters of the SA algorithm is a difficult task and the speed of the algorithm is slow when applied to a real power system. Genetic Algorithm, invented by Holland [15] in the early 1970s, is a stochastic global search method that mimics the metaphor of natural biological evaluation. The GA uses only the objective function information, not derivative or other auxiliary knowledge. Therefore GA can deal with the non-smooth, non-continuous and non differentiable functions, which actually exist in a practical optimization problem. Evolutionary Programming (EP) introduced by Lawrence J. Fogel in the 1960s, on the other hand, is also a global search method starting from a population of candidate solutions, and finds solution in parallel using evaluation process. Both GA and EP can provide a near global solution. However the encoding and decoding schemes essential in the GA approach are not needed in dynamic economic dispatch problem. Therefore EP is faster in speed than GA in this case. Any evolutionary computation technique applied to a particular problem should address the issue of handling infeasible individuals. The presence of constraints significantly affects the performance of optimization algorithm, including evolutionary search methods. The general way of handling constraints is by penalizing the infeasible points. Constraint handling in evolutionary computation is more or less problem dependent [21-23]. In this paper, the application of constrained optimization using Evolutionary programming technique for solving dynamic economic dispatch has been proposed. The proposed method starts with only feasible candidate solutions generated by an iterative procedure of correcting violations. In order to show the effectiveness of the proposed method, 10 units test system with smooth and non-smooth fuel cost functions are considered in this paper. The results of the proposed method are compared with those reported in literature [18-20]. II PROBLEM FORMULATION The dynamic economic dispatch problem can be formulated as follows. The objective function: Min ( ) ∑∑ = = = T t N i it it P F F 1 1 (1) Where, Proceedings of the 6th WSEAS Int. Conf. on EVOLUTIONARY COMPUTING, Lisbon, Portugal, June 16-18, 2005 (pp160-166)