Short-term Non-convex Economic Hydrothermal Scheduling Using Dynamically Controlled Particle Swarm Optimization

The aim of this paper is to present short-term hydrothermal scheduling (STHS) of power system. This problem is solved in such a way that utilizes available hydro reserves optimally and thus minimizes the fuel cost of thermal plants. A PSO based method is developed which can efficiently deals with hydro constraints like reservoir storage volume limits, water discharge rate limits, water dynamic balance, initial and final reservoir storage volume limits, etc. for a given time horizon. The operators of the PSO are dynamically controlled. Moreover, the cognitive and social behaviors of the swarm are modified for better exploration and exploitation of the search space. The effectiveness of the proposed method has been investigated on a standard test generating system considering several operational constraints pertaining to hydrothermal systems. INDEX TERMS Short-term hydrothermal scheduling, fuel cost minimization, particle swarm optimization, valve-point loading effect, constriction functions INTRODUCTION In the present competitive environment, the short-term hydrothermal scheduling (STHS) plays significant role for economic operation of power systems. The main objective of STHS problem is to schedule the thermal and hydro plants so as minimize the overall cost of energy generation by optimally utilizing the available hydro potentials and thereby reducing the fuel cost of thermal units while satisfying several operational and network constraints pertaining to hydro-thermal units. STHS is a non-convex, complex combinatorial optimization problem having various operational constraints such as power balance, power generation limits, reservoir storage volume limits, water discharge rate limits, water dynamic balance, initial and end reservoir storage volume limits, valve-point loading effect, etc. The classical optimization methods such as Mixed Integer Programming, Dynamic Programming, Gradient Search Method, Nonlinear Programming, Mathematical Decomposition and Lagrange Relaxation, etc. are not suitable to solve such optimization problems due to their inherent shortcoming in handling non-convexity and complex inequalities constraints except dynamic programming which has the curse of dimensionality [1]. Several Artificial Intelligence (AI) based meta-heuristic techniques such as Simulated Annealing (SA), Differential Evolution (DE), Evolutionary Programming (EP), Genetic Algorithm (GA), Cultural Algorithm (CA) Particle Swarm Optimization (PSO), etc. have successfully attempted the STHS problem [2]. PSO is a population based meta-heuristic optimization technique in which the movement of particles is governed by the two stochastic acceleration coefficients, i. e., cognitive and social components and the inertia component. It has several advantages over other meta-heuristic techniques in terms of simplicity, convergence speed, and robustness [3]. It provides convergence to the global or near global point, irrespective of the shape or discontinuities of the cost function [4]. The performance of the PSO greatly depends on its parameters and it often suffers from the problems such as being trapped in local optima due to premature convergence [5], lack of efficient mechanism to treat the constraints [6], loss of diversity and performance in optimization process [7], etc. In order to enhance its exploration and exploitation capabilities, the components affecting velocity of particles should be properly managed and controlled. Several methods have been reported in the recent past to enhance the computational efficiency of the conventional PSO. A constriction factor was suggested in the control equation to assure convergence of PSO [8-10]. However, the exact determination of this factor is computationally demanding. Selvakumar and Thanushkodi [11] modified cognitive behavior of the swarm by considering worst experience of the particle. This method provides some additional diversity but showing