Combined economic and emission dispatch with valve-point loading of thermal generators using modified NSGA-II

Abstract

This paper discusses the application of evolutionary multi-objective optimization algorithms namely Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and Modified NSGA-II (MNSGA-II) for solving the Combined Economic Emission Dispatch (CEED) problem with valve- point loading. The valve-point loading introduce ripples in the input-output characteristics of generating units and make the CEED problem as a non-smooth optimization problem. IEEE 57-bus and IEEE 118-bus systems are taken to validate its effectiveness of NSGA-II and MNSGA-II. To compare the Pareto-front obtained using NSGA-II and MNSGA-II, reference Pareto-front is generated using multiple runs of Real Coded Genetic Algorithm (RCGA) with weighted sum of objectives. Furthermore, three different performance metrics such as convergence, diversity and Inverted Generational Distance (IGD) are calculated for evaluating the closeness of obtained Pareto-fronts. Numerical results reveal that MNSGA-II algorithm performs better than NSGA-II algorithm to solve the CEED problem effectively.