A Semidefinite Programming Method Weighted Sum Based for Solving a Multi-area Emission (Environmental) Economic Dispatch Problem

Abstract

This paper presents a semi-definite programming (SDP) optimisation approach for solving multi area, emission/economic dispatch (MAEED) problems in thermal power systems. The multi-objective problem was transformed into matrix form as an SDP relaxation problem and subsequently solved with a MATLAB programming suite. The system inequality and equality constraints were entered into a Self-Dual Minimisation (SeDuMi) parser. Simulations were tested on four (4) IEEE benchmark models to validate the efficiency of the proposed SDP method. However, in the generation of the Pareto-fr ont solutions, ideal minimum points were used in the determination of the maximum spread out of the Pareto solutions by the algorithm. This involves the use of a standard weighted sum method in generating the Pareto-optimal solution between two objective functions. Twenty-one (21) runs were carried out for the parameter value to explore the effect of control weight selection k1. A comparative study demonstrated the effectiveness of tie-line constraint and without tie-line constraint, respectively on the optimi sation model for the power dispatch problems solved by using the proposed SDP approach. The optimisation results for the minimum fuel cost using the SDP approach for the case when a tie-line constraint is included was US$ 2,151.7 /hr with minimum emission of 3.4687 Ton/hr. This is lower than US$ 2,162.2 /hr with minimum emission of 3.6662 Ton/hr obtained when the tie-line constraint is not included in the optimisation model on IEEE four-area, sixteen network. Additionally, the comparative results with all other methods reported in the literature for different test cases were also presented in this paper. Lower operational costs were obtained for both tie-lines and no tie-lines power transfer cases, showing that the SDP method performed well in accuracy compared to other methods. The SDP method was employed in this research to deal with the multi-area emission economic power dispatch problem due to its inherent advantages in achieving a global optimal solution and, this approach would also assist the power administrator to come up with an improved decision making in attaining an optimum power dispatch of power generation.