Optimal placement and sizing of FACTS devices for optimal power flow in a wind power integrated electrical network

Optimal power flow (OPF) is one of the challenging optimization problems in power domain. The complexity of the problem escalates with incorporation of uncertain and intermittent renewable sources into the electrical network. Flexible AC transmission system (FACTS) devices are also becoming more commonplace in modern power system to mitigate growing demand and to relieve congestion from the network. This paper aims to solve the OPF where the generation cost is optimized with incorporation of stochastic wind power and several types of FACTS devices such as static VAR compensator, thyristor-controlled series compensator and thyristor-controlled phase shifter. Case studies with both fixed and uncertain load demands are performed. The stochastic wind energy and load demand are modeled using suitable probability density functions. Optimization objective considers cost of thermal generation, direct cost of scheduled wind power, penalty cost for underestimation and reserve cost for overestimation of the wind power. In addition, both locations and ratings of the FACTS devices are optimized to minimize total generation cost of the system. Success history-based adaptive differential evolution (SHADE), a powerful evolutionary algorithm, is adopted to perform the optimization task. The constraints of OPF problem are handled using superiority of feasible solutions (SF) method. The integration approach of SF method with several popular metaheuristic algorithms has been proposed in this work, and a detailed comparative analysis among various algorithms establishes SHADE algorithm to be the best performer.