This paper proposes the random drift particle swarm optimization (RDPSO) algorithm to solve economic dispatch (ED) problems from power systems area. The RDPSO is inspired by the free electron model in metal conductors placed in an external electric field, and it employs a novel set of evolution equations that can enhance the global search ability of the algorithm. Many nonlinear characteristics of a power generator, such as the ramp rate limits, prohibited operating zones and nonsmooth cost functions are considered when the proposed method is used in practice for optimizing the generators' operation. The performance of the RDPSO method is evaluated on three different power systems, and compared with that of other optimization methods in terms of the solution quality, robustness, and convergence performance. The experimental results show that the RDPSO method performs better in solving the ED problems than any other tested optimization techniques.