Optimal Siting and Sizing of FACTS in Distribution Networks Using the Black Widow Algorithm

The problem regarding the optimal placement and sizing of different FACTS (flexible alternating current transmission systems) in electrical distribution networks is addressed in this research by applying a master-slave optimization approach. The FACTS analyzed correspond to the unified power flow controller (UPFC), the thyristor-controlled shunt compensator (TCSC, also known as the thyristor switched capacitor, or TSC), and the static var compensator (SVC). The master stage is entrusted with defining the location and size of each FACTS device using hybrid discrete-continuous codification through the application of the black widow optimization (BWO) approach. The slave stage corresponds to the successive approximations power flow method based on the admittance grid formulation, which allows determining the expected costs of the energy losses for a one-year operation period. The numerical results in the IEEE 33-, 69-, and 85-bus grids demonstrate that the best FACTS device for locating in distribution networks is the SVC, given that, when compared to the UPFC and the TCSC, it allows for the best possible reduction in the equivalent annual investment and operating cost. A comparative analysis with the General Algebraic Modeling System software, with the aim to solve the exact mixed-integer nonlinear programming model, demonstrated the proposed BWO approach's effectiveness in determining the best location and size for the FACTS in radial distribution networks. Reductions of about 12.63% and 13.97% concerning the benchmark cases confirmed that the SVC is the best option for reactive power compensation in distribution grids.