Optimal power flow of power systems with controllable wind-photovoltaic energy systems via differential evolutionary particle swarm optimization

The produced energy from varied sources in modern power systems is to be optimally planned for planning and operating of power system under the determined limit conditions. Recently, the rising overall people population of the world, the increasing of people requirements, improvements of technology, and ecosystem and global climate changes have caused with the increasing of electric energy demand. One of the most important solution methods to meet this energy demand is considered as utilization of renewable energy sources (RESs) in power systems. The structure of power systems has become with the usage of RESs more complex. The optimal power flow (OPF) from planning and operation problems has converted to difficult problem with RESs integrated into modern power systems. This paper presents the OPF problem of power systems with a high penetration of controllable renewable sources. These kinds of sources are able to inject a determined power since they have a back-up unit (storage). Uncertain solar irradiance and wind speed are simulated via log-normal and Rayleigh probability distributions, respectively. The proposed OPF problem with controllable renewable sources is solved by the differential evolutionary particle swarm optimization (DEEPSO) algorithm. Simulations conducted on various test systems illustrate the effectiveness and efficiency of DEEPSO as compared with other algorithms including moth swarm algorithm, backtracking search algorithm, and differential search algorithm. In addition, the Wilcoxon signed-rank test is applied to show the supremacy, effectiveness, and robustness of DEEPSO algorithm.