Optimal Power Flow Analysis Based on Hybrid Gradient-Based Optimizer with Moth–Flame Optimization Algorithm Considering Optimal Placement and Sizing of FACTS/Wind Power

Optimal power flow (OPF) is one of the most significant electric power network control and management issues. Adding unreliable and intermittent renewable energy sources to the electrical grid increase and complicates the OPF issue, which calls for using modern optimization techniques to solve this issue. This work presents the optimal location and size of some FACTS devices in a hybrid power system containing stochastic wind and traditional thermal power plants considering OPF. The FACTS devices used are thyristor-controlled series compensator (TCSC), thyristor-controlled phase shifter (TCPS), and static var compensator (SVC). This optimal location and size of FACTS devices was determined by introducing a multi-objective function containing reserve costs for overestimation and penalty costs for underestimating intermittent renewable sources besides active power losses. The uncertainty in the wind power output is predicted using Weibull probability density functions. This multi-objective function is optimized using a hybrid technique, gradient-based optimizer (GBO), and moth–flame optimization algorithm (MFO).