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Abstract
This paper addresses the realistic economic emission dispatch (EED) problem by considering the operating fuel cost and environmental emission as two conflicting objectives, and power balance and generator limits as two constraints. A novel dynamic multi-objective optimization algorithm, namely the multi-objective differential evolution with recursive distributed constraint handling (RDC-MODE) has been proposed and successfully employed to address this challenging EED problem. It has been thoroughly investigated in two different test cases at three different load demands. The efficiency of the RDC-MODE is also compared with two other multi-objective evolutionary algorithms (MOEAs), namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swam optimization (MOPSO). Performance evaluation is carried out by comparing the Pareto fronts, computational time and three non-parametric performance metrics. The statistical analysis is also performed, to demonstrate the ascendancy of the proposed RDC-MODE algorithm. Investigation of the performance metrics revealed that the proposed RDC-MODE approach was capable of providing good Pareto solutions while retaining sufficient diversity. It renders a wide opportunity to make a trade-off between operating cost and emission under different challenging constraints.
Highlights
The Economic Load Dispatch (ELD) problem deals with the estimation of the scheduled real power generation from the committed units for best economic operation
The constraint handling mechanism is suitably incorporated in three multi-objective optimization (MOP) algorithms, and the effectiveness of the algorithms has been tested under various load conditions
The multi-objective optimization using differential evolution (MODE) is an evolutionary multi-objective optimization algorithm that retains the diversity of solutions on the Pareto front
Summary
The Economic Load Dispatch (ELD) problem deals with the estimation of the scheduled real power generation from the committed units for best economic operation. In [1,2], the power engineers solved the ELD problem by scheduling of the generation of multi-unit systems using the derivative based Gauss-Siedel and Newton-Raphson algorithms along with the Lagrangian multiplier These conventional methods suffer from the problem of getting trapped in local minima and fail for system discontinuities due to prohibited zones. Muthuswamy et al [10] modified the non-dominated sorting technique by incorporating a dynamic crowding distance to improve the diversity of solutions in the search space These algorithms fail when there are discontinuities in the cost function. The EED problem has been solved to decide the unit commitment of the power system by considering operational power flow and environmental constraints in [22] It again utilized the method of conversion of the multi-objective problem to a single objective one. The constraint handling mechanism is suitably incorporated in three multi-objective optimization (MOP) algorithms, and the effectiveness of the algorithms has been tested under various load conditions
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