Multiobjective Bees Algorithm with clustering technique for Environmental/Economic Dispatch N. Leeprechanon, Member, IEEE and P. Polratanasuk, Student Member, IEEE Department of Electrical and Computer Engineering, Thammasart University 99 Moo 18 Pahonyotin Road ,Pathumthani,12120, Thailand. Email: nopporn@ieee.org Abstract-This paper presents the solution of environmental/ economic dispatch (EED) problem by using a multiobjective bees algorithm (MBA) with clustering technique. EED problem is to minimize simultaneously the total fuel cost and environmental pollution of generation while satisfying various constrains. The MBA is modified from Bees Algorithm in order to solve EED problem through compromised fuzzy and clustering techniques. The IEEE 30 Bus system was selected for testing purpose. The results show that the proposed method has effectiveness and potential for solving EED problem. Index Terms — Economic Dispatch (ED), Clustering Technique, Environmental/Economic Dispatch (EED), Multiobjective Bees Algorithm (MBA), Power System Economics. I. INTRODUCTION The Global Warming is currently a serious problem for world population. Power generation industry is one of pollution sources which produce the amount of pollutant emissions. Thus power producers must also consider environmental pollutions in addition to power generation cost. The power system industry should reduce simultaneously both cost of generation and environmental pollution. A new optimization technique is needed to minimize these objectives in a power system planning model. The Environmental/Economic Dispatch (EED) is an optimization problem formulated as a set of nonlinear and complex mathematic equations. EED problem in this paper is formulated as a multiobjective environmental economic dispatch or as an emissions constrained economic dispatch problem. An EED problem is to minimize simultaneously the total fuel cost and environmental pollution of generation subject to equality and inequality constrains. The EED can be complicated even if generator’s cost function is non-convex and other constrains are also considered (e.g., branch flow limits). This will find the environmental economic problem very difficult to be solved due to the complexity and highly nonlinear nature of the resulting problem. Conventionally, multiobjective optimization problem were treated as a single objective optimization problem. The objective function is formed as a weighted sum of all objectives using suitable weighting factors. This approach has the disadvantage of finding only a single solution which does not express the tradeoff between the different objectives. Generating multiple solutions using this approach requires several runs with different weighting factors and hence elongates the running time. As an alternative to this approach, recent studies consider the EED as a true multi- objective optimization problem in which the objectives are treated simultaneously and independently [1]. Evolutionary algorithm is recently developed to solve EED problem based on the principle of Pareto optimal set. Abido [2] developed a Multiobjective Evolutionary Algorithm EED that determined the Pareto optimal set using the strength Pareto evolutionary algorithm. Other implementations were attempted for solving EED such as: neural network [3], Bacteria Foraging [4] and multiobjective PSO [5]. The purpose of this paper is to solve the environmental/ economic dispatch problem using Bees algorithm (BA). The MBA is implemented in order to minimize simultaneously the total fuel cost and environmental pollution of generations while satisfying various constrains based on the principle of Pareto optimal set. The clustering techniques are used to manage the size of Pareto fronts. A satisfying fuzzy method is used to compromise the set of Pareto optimal solution. II. PROBLEM FORMULATION The objective of environmental/economic dispatch is to minimize the economic and environmental cost function while satisfying various equality and inequality constrains. A. Objectives Objective1: Minimization of generator cost The total US$/h fuel cost F(P G ) can be expressed as ∑ = + + = N i Gi i Gi i i P c P b a u x f 1 2 ) , ( (1) where and are the cost coefficients of the generator, and is the real power output of the generator and can be defined as i i b a , i c th i th i Gi P (2) T G G G Gi N P P P P ] , , , [ 2 1 K =