Abstract

Efficient and reliable power production is necessary to meet both the profitability of power systems operations and the electricity demand, taking also into account the environmental concerns about the emissions produced by fossil-fuelled power plants. The economic emission load dispatch problem has been defined and applied in order to deal with the optimization of these two conflicting objectives, that is, the minimization of both fuel cost and emission of generating units. This paper introduces and describes a solution to this famous problem using a new metaheuristic nature-inspired algorithm, called firefly algorithm, which was developed by Dr. Xin-She Yang at Cambridge University in 2007. A general formulation of this algorithm is presented together with an analytical mathematical modeling to solve this problem by a single equivalent objective function. The results are compared with those obtained by alternative techniques proposed by the literature in order to show that it is capable of yielding good optimal solutions with proper selection of control parameters.

Highlights

  • Biology-inspired metaheuristic algorithms have recently become the forefront of the current research as an efficient way to deal with many NP-hard combinatorial optimization problems and non-linear optimization constrained problems in general

  • We can see that the total number of 600 function evaluations 12 fireflies ∗ 50 generations is sufficient, and as a result, the algorithm stably converges to the optimal solution very quickly approximately from the 10th generation/iteration

  • This algorithm differs from other alternative approaches in the selection procedure in which each firefly constructs its own solution based on a weighted sum of the objective functions, where the weight attached to multiobjective criteria is constant

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Summary

Introduction

Biology-inspired metaheuristic algorithms have recently become the forefront of the current research as an efficient way to deal with many NP-hard combinatorial optimization problems and non-linear optimization constrained problems in general. In this research paper we will show how the recently developed firefly algorithm can be used to solve the famous economic emissions load dispatch optimization problem This hard optimization problem constitutes one of the key problems in power system operation and planning in which a direct solution cannot be found and metaheuristic approaches, such as the firefly algorithm, have to be used to find the near optimal solutions.

Multiobjective Optimization and Problem Formulation
Pareto Optimal Solutions
The Utility Function Method
The Economic Emissions Load Dispatch Problem
The Fuel Cost Objective
The Emissions Objective
The Necessary Constraints of the Problem
The Goal Attainment SQP Method
The Goal Attainment Method
The Sequential Quadratic Programming Method
Description
Attractiveness
Distance
Movement
Convergence and Asymptotic Behavior
Special Cases
Hybridization
Application Example
Application of the Proposed Firefly Algorithm
Results and Discussion
Application to the Test System
Comparison with Other Optimization Algorithms
Conclusions and Future Work
Full Text
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