A New Improved Particle Swarm Optimization for Solving Nonconvex Economic Dispatch Problems

A New Improved Particle Swarm Optimization for Solving Nonconvex Economic Dispatch Problems

Jirawadee Polprasert (Energy Field of Study, School of Environment, Resources and Development, Asian Institute of Technology, Pathumthani, Thailand), Weerakorn Ongsakul (Energy Field of Study, School of Environment, Resources and Development, Asian Institute of Technology, Pathumthani, Thailand) and Vo Ngoc Dieu (Department of Power Systems, Electronic Electrical Engineering Faculty, Ho Chi Minh City University of Technology, Ho Chi Minh City, Vietnam)
Copyright: © 2013 |Pages: 18
DOI: 10.4018/ijeoe.2013010105
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This paper proposes a new improved particle swarm optimization (NIPSO) for solving nonconvex economic dispatch (ED) problem in power systems including multiple fuel options (MFO) and valve-point loading effects (VPLE). The proposed NIPSO method is based on the self-organizing hierarchical (SOH) particle swarm optimizer with time-varying acceleration coefficients (TVAC). The self-organizing hierarchical can handle the premature convergence of the problem by re-initialization of velocity whenever particles are stagnated in the search space. During the optimization process, the performance of TVAC is applied for properly controlling both local and global explorations with cognitive component and social component of the swarm to obtain the optimum solution accurately and efficiently. The proposed NIPSO algorithm is tested in different types of non-smooth cost functions for solving ED problems and the obtained results are compared to those from many other methods in the literature. The results have revealed that the proposed NIPSO method is effective and feasible in finding higher quality solutions for non-smooth ED problems than many other methods.
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1. Introduction

Economic dispatch (ED) is a fundamental issue of optimization problems in power system. Its objective is to economically schedule the committed generating unit outputs so as to minimize total generation costs while satisfying all physical and operational constraints. In general, the ED problems can be divided into two types, i.e. static and dynamic. The power balance constraints and generation limits are considered in the static ED problem. The extension of the static ED problem is dynamic ED problem which is subject to ramp rate limits and prohibited operating zone of the generating units (Zare, Haque, & Davoodi, 2012). Customarily, the fuel-cost function for each generator has been approximately represented by a single quadratic cost function. Practically, the cost curve of generating units is highly nonlinear and discontinuities due to the effects of valve-point loading, or multiple fuels options. Accordingly, the cost function is more realistically expressed as a piecewise nonlinear function rather than a single quadratic cost function (Chiang, 2005). The practical ED problem with VPLE is represented as a non-smooth optimization problem having complex and non-convex characteristics with considering equality and inequality constraints, making hardly to obtain the global optima. In addition, many generating units are particularly supplied with multiple fuel sources such as coal, oil or natural gas, which have different heat characteristics leading to the problem of determining the most economical fuel to burn (Jayabarathi, Jayaprakash, Jeyakumar, & Raghunathan, 2005).

Previously, solutions to ED problems have applied various mathematical programming techniques (Amita, Vishu, & Saroj, 2009), such as lambda iteration method, the gradient method, Newton method, bundle method, linear programming (LP), nonlinear programming (NLP), mixed integer linear programming (MILP), quadratic programming (QP), Lagrange relaxation (LR) method, network flow programming (NFP) method, direct search (DS) method and dynamic programming (DP). Unfortunately, these techniques are sensitive to initial estimates and converge into local optimal solution leading to high computation time. Typically, lambda iteration and gradient method can solve simple ED problem, which is not sufficient for real world complex applications. Newton methods have difficulty in handling a large number of inequality constraints. LP methods are fast and reliable but they have the disadvantage of being associated with the piecewise linear cost approximation. NLP methods have complexity in algorithm and problems of convergence. DP may suffer from the problem of dimensionality.

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