Symbiotic organisms search algorithm-based security-constrained AC–DC OPF regarding uncertainty of wind, PV and PEV systems

Nowadays, the energy obtained from different generating units in modern power systems must be suitably planned for optimal power system operating conditions. One of the methods applied for this is the optimal power flow (OPF). Thus, the optimal power flow (OPF) problem has become one of the most important power system planning and operation challenges once renewable energy sources are integrated with modern electrical power systems which have a highly nonlinear complex structure. In addition, usage of high-voltage direct current systems increases the complexity of the network in the modern power system. Using a symbiotic organisms search (SOS) algorithm, this paper focused on a solution to the security-constrained AC–DC OPF with regard to the uncertainty of wind, solar and plug-in electric vehicle (PEV) energy systems with thermal generating units. Uncertain wind speed, solar irradiance, and PEV power were modeled using Weibull, Lognormal, and Normal probability distribution functions (PDFs), respectively. Moreover, our study presents solutions to the security-constrained AC–DC OPF by involving test cases of stochastic wind, solar, and PEV energy systems on IEEE 30-bus and 57-bus test systems under various operational conditions. These can be listed as minimization of different total cost functions, improvement of voltage stability, voltage deviation and minimization of fitness function for determined N-1 contingency conditions. The SOS algorithm results were compared to the artificial bee colony, imperialist competitive, moth swarm, shuffled frog-leaping, genetic algorithm, and particle swarm optimization algorithms. These comparison results demonstrated that the SOS algorithm exhibited the capability to provide high-quality solutions to the OPF problem by satisfying both equality and inequality constraints. In addition, nonparametric Friedman and Wilcoxon tests were applied to show the statistical validity of the results obtained from the algorithms.