Environmental and economic power dispatch of thermal generators using modified NSGA-II algorithm

This paper presents the solution to the problem in fabricating Environmental and Economic Power Dispatch (EEPD) of thermal generators with valve-point loading effect and multiple prohibited operating zones (POZ). The valve-point effect introduces ripples in the input-output characteristics of generating units, and the existence of POZ breaks the operating region of a generating unit into isolated sub-regions, thus forms a nonconvex decision space. The EEPD problem becomes a nonsmooth optimization problem because of these valve-point effect and POZ. Accuracy of the solution for a practical system is improved by considering the nonlinearities of valve-point loading effect and multiple POZ in the EEPD problem. The multi-objective evolutionary algorithms, namely non-dominated sorting genetic algorithm-II (NSGA-II) and modified NSGA-II (MNSGA-II) have been applied for solving the multi-objective nonlinear optimization EEPD problem. To improve the uniform distribution of non-dominated solutions, dynamic crowding distance is considered in the NSGA-II and developed MNSGA-II. These multi-objective evolutionary algorithms have been individually examined and applied to the standard IEEE 30-bus and IEEE 118-bus test systems. Real-coded genetic algorithm is used to generate reference Pareto-front, which is used to compare with the Pareto front obtained using NSGA-II and MNSGA-II. Numerical results reveal that MNSGA-II is effectively capable for appreciable performance than NSGA-II to solve the different power system nonsmooth EEPD problem. Moreover, three different performance metrics such as convergence, diversity and Inverted Generational Distance are calculated for the evaluation of closeness of obtained Pareto fronts to the reference Pareto-front. In addition, an approach based on Technique for ordering Preferences by Similarity to Ideal Solution is applied to extract best compromise solution from the obtained non-domination solutions. Copyright (c) 2014 John Wiley & Sons, Ltd.