Solving the economic dispatch problem with a modified quantum-behaved particle swarm optimization method

In this paper, a modified quantum-behaved particle swarm optimization (QPSO) method is proposed to solve the economic dispatch (ED) problem in power systems, whose objective is to simultaneously minimize the generation cost rate while satisfying various equality and inequality constraints. The proposed method, denoted as QPSO-DM, combines the QPSO algorithm with differential mutation operation to enhance the global search ability of the algorithm. Many nonlinear characteristics of the generator, such as ramp rate limits, prohibited operating zones, and nonsmooth cost functions are considered when the proposed method is used in practical generator operation. The feasibility of the QPSO–DM method is demonstrated by three different power systems. It is compared with the QPSO, the differential evolution (DE), the particle swarm optimization (PSO), and the genetic algorithm (GA) in terms of the solution quality, robustness and convergence property. The simulation results show that the proposed QPSO–DM method is able to obtain higher quality solutions stably and efficiently in the ED problem than any other tested optimization algorithm.