Optimal λ Based Economic Emission Dispatch using Simulated Annealing

The economic emission dispatch (EED) assumes a lot of significance to meet the clean energy requirements of the society, while at the same time minimising the cost of generation. The solution schemes in an attempt to arrive at the global best through the use of evolutionary algorithms are however inadequate to cater to problems of large size. The search based EED approaches are computationally inefficient particularly for problems with large number of decision variables. This paper attempts to develop a new SA based modified approach with a single decision variable to solve the EED problem. The philosophy involves the introduction of a new decision variable through a prudent mathematical transformation of the relation between the decision variable and the optimal generations. It thus yields a reduction in the number of problem variables and contributes to realistically enhance the performance of the existing heuristic strategies. The feasibility of the proposed approach is evaluated through two test systems and the results are compared with the available methods to highlight its suitability for online applications. Nomenclature COST cost function ELD economic load dispatch EED economic emission dispatch PA proposed algorithm SA simulated annealing ESA existing SA based ELD i i i c b a & fuel cost coefficients of th i generating plant i i i f e d & emission coefficients of th i generating plant i IC incremental cost at th i generation plant max min & i i IC IC minimum and maximum values of i IC respectively Sasikala. J Lecturer in Computer Science and Engineering, Annamalai University, Annamalainagar 608 002, India. Ramaswamy. M Professor of Electrical Engineering, Annamalai University, Annamalainagar 608 002, India. ©2010 International Journal of Computer Applications (0975 – 8887) Volume 1 – No. 10 56 ng number of generating plants D P total power demand Gi P generation at th i generating plant max min & i G i G P P minimum and maximum of Gi P respectively ( ) Gi i P F fuel cost function of th i generating plant in h / $ ( ) Gi i P E emission cost function of th i generating plant in h kg / i h price penalty factor of th i generating plant in kg / $ t T current temperature 1 + t T next temperature λ incremental cost of received power max min & λ λ minimum and maximum values of λ respectively Ф objective function to be minimized T Φ augmented objective function to be minimized α cooling coefficient ) (T P transition probability in the interval [0,1] F ∆ reduction in cost of the trial solution compared with the current solution 1.0 INTRODUCTION Economic Load Dispatch (ELD) plays an important role in maintaining a high degree of economy and reliability in power system operational planning. It is a computational process of allocating the total required generation among the available generating units subject to load and operational constraints such that the cost of operation is minimum. Various techniques such as lambda iteration, gradient search, linear programming, dynamic programming and Lagrangian relaxation are used to solve ELD problem [1-2]. Recently intelligent algorithms such as Pattern Search [3], Neural Networks [4-5], Genetic Algorithm [6], Simulated Annealing (SA) [7], Evolutionary Programming [8] and Particle Swarm optimisation [9] are applied to solve ELD problems. Operating at absolute minimum cost can no longer be the only criterion for dispatching electric power due to increasing concern over the environmental considerations. The generation of electricity from fossil fuel releases several contaminants, such as sulphur dioxides, nitrogen oxides and carbon dioxide into the atmosphere. The pressing public demand for clean air and the enforcement of environmental regulations in recent years have changed the dispatch problem with conflicting objectives of minimising both the fuel cost and the emissions. Several methods have been suggested for solving the multiobjective economic emission dispatch (EED) problem. A direct NR method based on alternative jacobian matrix [10], a recursive approach based on dynamic programming [11], a simplified recursive approach [12], a progressive articulation of preference information based optimisation technique [13] and an analytical strategy based on mathematical modelling [14] have been presented to handle combined EED problems. In recent years, heuristic optimisation techniques have aroused greater ©2010 International Journal of Computer Applications (0975 – 8887) Volume 1 – No. 10 57 interest due to their flexibility, versatility and robustness. These evolutionary approaches such as an interactive fuzzy satisfying based SA technique [15], particle swarm optimisation based goal-attainment method [16], a multiobjective genetic algorithm [17] and a fuzzified multi-objective particle swarm optimisation algorithm [18] have been extensively articulated to obtain the global optimal solution. However, on account of the fact that EED problems necessarily involve a large number of problem variables, the heuristic approaches have been found to suffer from huge computational burden and end up with consuming exhaustively large execution times. Therefore an efficient strategy that is independent of the number of generating plants in the system, is formulated with a single decision variable and invokes the use of SA to solve for EED problem in this paper 2.0 Problem Formulation The aim of EED is to minimise the total generation cost and emissions of a power system for a given load while satisfying various constraints [1-2]. The objective function is thus obtained by blending the emission cost function with the fuel cost function through the use of a price penalty factor [19] and the constrained optimisation problem is formulated as Minimise { } ∑ = + = Φ ng i Gi i i Gi i P E h P F 1 ) ( ) ( (1)