GA Based FGP to Solve BLP Model of EEPGD Problem

GA Based FGP to Solve BLP Model of EEPGD Problem

Bijay Baran Pal (University of Kalyani, India) and Papun Biswas (JIS College of Engineering, India)
Copyright: © 2014 |Pages: 17
DOI: 10.4018/978-1-4666-5202-6.ch094
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Introduction

The demand of electric power has increased in alarming rate in recent years owing to rapid growth of human development index across the countries in modern world. It is to be mentioned here that the main supply source of electric energy is thermal power plant, where fossil-fuel used as main power generation resource, discharges emissions to earth’s environment. The thermal power generation problems are actually optimization problems with multiplicity of objectives and various system constraints in the environment of generation of power. The two most important objectives associated with the problem are minimization of power generation cost and environmental emission.

The general mathematical programming (MP) model for optimal power generation decision was introduced by Dommel, & Tinney (1968). The deep study made in the field in the past century was surveyed by (Momoh, El-Hawary, & Adapa, 1999). The constructive optimization model for minimization of thermal power plant emissions was first studied by Gent, & Lament (1971).

Here, it is to be noted that the objectives of such a problem are incommensurable in nature and often conflict each other in optimizing them in actual practice. As such, a balanced decision could not be achieved there concerning simultaneous optimization of objectives. To overcome the difficulty, Goal Programming (GP) (Lin, 1980) approach as a robust and flexible tool for multiobjecive decision analysis was employed to economic-environmental power generation and dispatch (EEPGD) problem (Nanda, Kothari, & Lingamurthy, 1988) to obtain goal-oriented solution in a crisp environment.

However, in most of the practical decision situations, it is to be observed that decision parameters of problems with multiplicity of objectives are inexact in nature owing to inherent impressions in parameter themselves as well as imprecise in nature of human judgments of setting parameter values. To cope with the situation, Fuzzy programming (FP) approach (Zimmermann, 1987) based on Fuzzy Set Theory (Zadeh, 1965) to EEPGD problems have been discussed (Wang, & Singh, 2007) in the past. Further, to overcome the computational difficulty with nonlinear and competitive in nature of objectives, genetic algorithms (GAs) (Deb, 2002) based on natural selection and natural genetics have also been employed to EEPGD problems (Abido, 2003; Gong, Zhang, & Qi, 2010). But, deep study in this area is at an early stage.

Now, it is to be observed that the objectives of minimizing power generation cost and environmental emission highly conflict each other owing to current accelerating demand rate of electricity as well as increasing social pressure for controlling pollutions. As an essence, optimization of objectives in a hierarchical structure on the basis of needs of decision maker (DM) can be considered. As such, bilevel programming (BLP) (Pal, & Moitra, 2003) in hierarchical decision system might be an effective one for solving EEPGD problems. Although, the problem of balancing thermal power supply and market demand have been studied (Bertsimas, Litvinov, Sun, Zhao, & Zheng, 2013; Zhang, Zhang, Gao, & Lu, 2011; Pal, & Kumar, 2013) in the recent past, BLP approach to EEPGD problem by employing GA based Fuzzy Goal Programming (FGP) method (Pal, Moitra, & Maulik, 2003) is yet to appear in the literature.

In this chapter, the GA base FGP approach studied by Pal, & Chakraborti (2013) to solve quadratic BLP problem (QBLPP) is extended to solve the proposed problem. A case example of IEEE 6-Generator 30-Bus System is considered to illustrate the potential use of the approach.

Key Terms in this Chapter

Bilevel Programming: It is a special field in mathematical programming for multistage decision analysis in a hierarchical decision situation. Here, objective functions are assigned to two decision levels for optimizing them by two decision makers.

Fuzzy Programming: It is the modeling aspects of optimization problems in which parameter values are defined in an imprecise way in the decision environment.

Economic-Environmental Power Generation and Dispatch: It is a thermal power plant problem for optimal power generation and dispatch by minimizing the fuel-cost and environmental emission in a planning horizon.

Genetic Algorithm: It is an adaptive heuristic search algorithm based on the evolutionary ideas of natural selection and genetics in living system.

Fuzzy Goal Programming: It is an extension of conventional goal programming to solve multiobjective problems with fuzzily described model parameters.

Membership Function: It is an algebraic structure for representing degree of achievement of a fuzzy goal defined in an imprecise environment.

Goal Programming: It is a goal-oriented optimization technique to solve decision problems with multiplicity of objectives in a crisp environment.

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