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This paper proposes a combination of phasor particle swarm optimization (PPSO) and a gravitational search algorithm, namely a hybrid PPSOGSA algorithm, for optimal power flow (OPF) in power systems with an integrated wind turbine (WT) and solar photovoltaic (PV) generators. The OPF formulation includes the forecasted active power generation of WT and PV as dependent variables, whereas the voltage magnitude at WT and PV buses is considered as control (decision) variables. Forecasting the output power of WT and PV generators is based on the real-time measurements and the probabilistic models of wind speed and solar irradiance. The proposed OPF approach and the solution method are verified on the IEEE 30-bus test system. The robustness and efficiency of the proposed PPSOGSA algorithm in solving the OPF problem are evaluated by comparing with 20 well-established metaheuristic optimization methods under the same system data, control variables, and constraints. The statistical features of the OPF results are estimated by using the Monte Carlo method.

A Solution to the Optimal Power Flow Problem Considering WT and PV Generation