Optimal placement and sizing of photovoltaic generators and static reactive power compensators in distribution systems for minimizing the annual energy purchase cost using the fractional optimization algorithm

This paper presents an innovative algorithm, termed the Fractional Optimization Algorithm (FOA), which utilizes the properties of fractional functions to enhance the integration of photovoltaic (PV) systems and distribution static compensators (D-STATCOMs) into distribution systems (DSs). The FOA employs a discrete-continuous encoding approach to determine the optimal placement and sizing of PV and D-STATCOM devices. A master-slave optimization framework is adopted, where the FOA operates in the master stage, and the successive approximations method is used for power flow analysis in the slave stage. The algorithm's efficacy is tested on 33- and 69-bus grids, demonstrating significant cost reductions over traditional optimization approaches such as the Vortex Search Algorithm (VSA) and the Sine-Cosine Algorithm (SCA). Furthermore, the FOA achieves superior computational efficiency, underscoring its promise as a robust optimization strategy.