International Journal of Engineering Research and Development e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com Volume 5, Issue 12 (February 2013), PP. 57-64 57 Stochastic Optimization Tools for ELD Problem Santosh Kumar Mishra 1 , Neelakantha Guru 2 1,2 Department of EEE, Silicon Institute of Technology, Bhubaneswar. Abstract:- ELD determines the power to be generated by the committed units so that the total cost can be minimized while satisfying the required constraints. Here the cost function is highly non linear, non-convex and non differentiable. Therefore, classical optimization methods usually face problem to converge. This paper presents a comparative study of three different algorithms i.e. MPSO, clonal selection algorithm and gravitational search algorithm for solving the ELD problem. Simulation results were performed with different test cases and comparisons are performed. The simulation result reveals the comparative performance and suggested the best technique which is easy to implement, with less execution time. Keywords: - Economic Dispatch, valve point effect, PSO, Clonal Selection, GSA I. INTRODUCTION Economic load dispatch is a vital part of the optimization task in power system generation, whose characteristics are complex and highly non linear, is to schedule the committed unit outputs, So that the required load demand can be fulfilled at minimum cost while satisfying equality and inequality constraints. In conventional ELD the cost function of all generators is approximately represented by a simple quadratic function and is solved by different optimization technique such as dynamic programming and non-linear programming techniques. However non-off these methods may be able to provide an optimal solution for they usually get stuck at a local optimum [1],[2]. Recently, as an alternative to the conventional mathematical approaches, modern heuristic optimal technique such as simulated annealing (SA), evolutionary programming (EP), genetic algorithm (GA), particle swarm optimization (PSO), neural networks and tabu search have been given much attention by many researches due to their ability to find global or quasi global optimum solutions. Although these heuristic methods do not always guarantee the global optimal solution in finite time, they often provide fast and reasonable solution. PSO is a population based, self-adaptive search optimization technique introduced by Kennedy and Eberhart in 1995.It solves nonlinear and non-continuous optimization problems very effectively and proves its success for many power system problems [17],[20].This paper proposes new optimization approaches, to solve ELD problems using improved gravitational search algorithm has shown the efficiency of GSA over others. In order to establish the capability of GSA to optimize the non-smooth cost function of 3 and 40 generator systems. The results obtained are compared with these of EP, PSO and AIS. The proposed methodology emerges out to be a robust optimization technique for solving ELD problem for various curve natures and power systems. II. NONCONVEX ECONOMIC LOAD DISPATCH The economic load dispatch problem can be described as an optimization (minimization) process with the following objective function Subject to: Energy balance equation And power balance equation (i=1, 2….NG) Here the loss part is not considered for simplicity. The fuel cost function without valve- point loading of the generating unit by And the fuel cost function considering valve point loading (as shown in fig.1) of the generating unit are given as