This paper proposes a particle swarm optimization (PSO) method for solving the economic dispatch (ED) problem in power systems. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zone, and nonsmooth cost functions are considered using the proposed method in practical generator operation. The feasibility of the proposed method is demonstrated for three different systems, and it is compared with the GA method in terms of the solution quality and computation efficiency. The experimental results show that the proposed PSO method was indeed capable of obtaining higher quality solutions efficiently in ED problems.

Particle swarm optimization to solving the economic dispatch considering the generator constraints

Evolutionary programming has emerged as a useful optimization tool for handling nonlinear programming problems. Various modifications to the basic method have been proposed with a view to enhance speed and robustness and these have been applied successfully on some benchmark mathematical problems. But few applications have been reported on real-world problems such as economic load dispatch (ELD). The performance of evolutionary programs on ELD problems is examined and presented in this paper in two parts. In Part I, modifications to the basic technique are proposed, where adaptation is based on scaled cost. In Part II, evolutionary programs are developed with adaptation based on an empirical learning rate. Absolute, as well as relative, performance of the algorithms are investigated on ELD problems of different size and complexity having nonconvex cost curves where conventional gradient-based methods are inapplicable.

Evolutionary programming techniques for economic load dispatch

This work presents a new approach to economic dispatch (ED) problems with nonsmooth cost functions using a particle swarm optimization (PSO) technique. The practical ED problems have nonsmooth cost functions with equality and inequality constraints that make the problem of finding the global optimum difficult using any mathematical approaches. A modified PSO (MPSO) mechanism is suggested to deal with the equality and inequality constraints in the ED problems. A constraint treatment mechanism is devised in such a way that the dynamic process inherent in the conventional PSO is preserved. Moreover, a dynamic search-space reduction strategy is devised to accelerate the optimization process. To show its efficiency and effectiveness, the proposed MPSO is applied to test ED problems, one with smooth cost functions and others with nonsmooth cost functions considering valve-point effects and multi-fuel problems. The results of the MPSO are compared with the results of conventional numerical methods, Tabu search method, evolutionary programming approaches, genetic algorithm, and modified Hopfield neural network approaches.

/pdf/a-particle-swarm-optimization-for-economic-dispatch-with-46vvxpkotr.pdf

A particle swarm optimization for economic dispatch with nonsmooth cost functions

This paper presents a genetic algorithm (GA) solution to the unit commitment problem. GAs are general purpose optimization techniques based on principles inspired from the biological evolution using metaphors of mechanisms such as natural selection, genetic recombination and survival of the fittest. A simple GA algorithm implementation using the standard crossover and mutation operators could locate near optimal solutions but in most cases failed to converge to the optimal solution. However, using the varying quality function technique and adding problem specific operators, satisfactory solutions to the unit commitment problem were obtained. Test results for power systems of up to 100 units and comparisons with results obtained using Lagrangian relaxation and dynamic programming are also reported.

A genetic algorithm solution to the unit commitment problem

This paper proposes a new version of the classical particle swarm optimization (PSO), namely, new PSO (NPSO), to solve nonconvex economic dispatch problems. In the classical PSO, the movement of a particle is governed by three behaviors, namely, inertial, cognitive, and social. The cognitive behavior helps the particle to remember its previously visited best position. This paper proposes a split-up in the cognitive behavior. That is, the particle is made to remember its worst position also. This modification helps to explore the search space very effectively. In order to well exploit the promising solution region, a simple local random search (LRS) procedure is integrated with NPSO. The resultant NPSO-LRS algorithm is very effective in solving the nonconvex economic dispatch problems. To validate the proposed NPSO-LRS method, it is applied to three test systems having nonconvex solution spaces, and better results are obtained when compared with previous approaches

A New Particle Swarm Optimization Solution to Nonconvex Economic Dispatch Problems

A genetics-based algorithm is proposed to solve an economic dispatch problem for valve point discontinuities. The algorithm utilizes payoff information of candidate solutions to evaluate their optimality. Thus, the constraints of classical LaGrangian techniques on unit curves are circumvented. The formulations of an economic dispatch computer program using genetic algorithms are presented and the program's performances using two different encoding techniques are compared. The results are verified for a sample problem using a dynamic programming technique. >

D.C. Walters

Papers

Genetic algorithm solution of economic dispatch with valve point loading