Adaptive Teaching Learning Based Optimization Applied to Nonlinear Economic Load Dispatch Problem

Adaptive Teaching Learning Based Optimization Applied to Nonlinear Economic Load Dispatch Problem

Sk Md Ali Bulbul (Department of Electrical and Electronics Engineering, Bengal College of Engineering and Technology, West Bengal, India) and Provas Kumar Roy (Department of Electrical Engineering, Jalpaiguri Government Engineering College, West Bengal, India)
Copyright: © 2014 |Pages: 16
DOI: 10.4018/ijsir.2014100101
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Abstract

Economic load dispatch (ELD) is a process of calculating real power dispatch by satisfying a set of constraints such a way as fuel cost can be minimized. Inclusion of the effect of valve-points and prohibited operation zones (POZs) in the cost functions make ELD problem a non-linear and non-convex one. For solving ELD in power system a newly proposed evolutionary technique namely adaptive teaching learning based optimization (ATLBO) is presented in this article. TLBO mimics the influence of a teacher on students in a classroom environment by social interaction. ATLBO is an improved version of TLBO which makes TLBO faster and more robust. An adaptive dynamic parameter control mechanism is adopted by the proposed ATLBO algorithm to determine the suitable parameter settings for teaching and learning phases of TLBO algorithm. The proposed ATLBO algorithm is tested in three different cases like 10-unit, 40-unit, and 80-unit systems. A comparison of numerical results with other well established techniques reveals optimization superiority of the proposed scheme both in quality of solution and computational efficiency.
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1. Introduction

The economic load dispatch (ELD) problem is an essential area for power system operation and planning. Its objective is to find the optimal combination of output power of all the committed generating units that minimizes the fuel cost, while satisfying a group of equality and inequality constraints. The input-output characteristics of the generating units are highly nonlinear, non-smooth and discrete in nature because of prohibited operating zones (Mohammadi-Ivatloo, Rabiee, Soroudi & Ehsan, 2012; Neto, Bernert & Coelho, 2011), ramp rate limits (Pereira-Neto, Unsihuay & Saavedra, 2005), valve point loading (Walters & Sheble, 1993) and multi-fuel effects as fuel sources like coal, natural gas or oil lead to the problem of determining the most economic fuel to burn. That makes ELD problem a challenging optimization task. Therefore traditional calculus-based techniques like linear programming (LP) (Jabr, Coonick & Cory, 2000), non-linear programming (NLP) (Chen, 2007), Lagrangian relaxation (LR) (Hindi & Ghani, 1991), quadratic programming (QP) (Papageorgiou & Fraga, 2007) and gradient method (Bakirtzis, Petridis & Kazarlis, 1994; Lee & Breipohl, 1993) are infeasible in practical cases. Also classical optimization methods are highly sensitive to starting points and frequently converge to local optimum solution which is not desirable to solve complex ELD problem. Though dynamic programming (Liang & Glover, 1992) has excellent ability to solve complexity inherited in ELD problem but it suffers from large dimension with increase of system size and has a tendency to trap into local optimal point.

To solve modern complex ELD problem, various population based heuristic optimization techniques are used in recent years. Some population based techniques mentioned in the literature are simulated annealing (SA) (Wong & Fung, 1993), evolutionary programming (EP) (Venkatesh, Gnanadass & Padhy, 2003),differential evolution (DE) (Nomana & Iba, 2008), genetic algorithm (GA) (Basu, 2008), bacteria foraging optimization (BFO) (Hota, Barisal & Chakrabarti, 2010), particle swarm optimization (PSO) (Eberhart & Shi, 2001; Ho, Yang, Ni, Lo & Wong, 2005; Selvakumar & Thanushkodi, 2007; Gaing, 2003), chaotic ant swarm optimization (CASO) (Cai, Ma, Li, Yang, Peng & Wang, 2007), artificial bee colony (ABC) (Basu, 2013). Amongst these techniques, EP is much faster than SA for its internal parallel search technique. EP has other advantages of minimum information requirement and constraint handling. However, it has a tendency to converge prematurely in local optima. DE is one of the most popular and simple optimization technique but it also has stagnation and premature convergence problem. In case of GA, where variables are highly correlated, its crossover and mutation operators do not always generate individuals with better fitness. Also premature convergence as well as high computational burden degrades its robustness. PSO technique has great potential to solve ELD problem due to its simplicity, superior convergence characteristics and high solution quality. But for modern complex functions having multiple minima, it also suffers from premature convergence. CASO is based on the chaotic behavior of individual ants and its intelligent organized actions in a colony. ABC imitates foraging behavior of bees in a hive, though it uses fewer parameters for simplicity, flexibility and robustness, it suffers from a variety of decision making problem (Jadhav & Roy, 2013).

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