An enhanced equilibrium optimizer for strategic planning of PV-BES units in radial distribution systems considering time-varying demand

The integration of the distributed generations with the distribution systems provides several advantages to the utility and customers, such as enhancing the stability and voltage profile, reducing the system losses, and reducing the fossil-fuel dependability. However, the integration represents a great challenge, especially with the associated uncertainty in load and generation powers. In this paper, the enhanced equilibrium optimizer (EEO), a modified version from the equilibrium optimizer (EO) algorithm, is derived, proposed, and implemented to allocate PV-BES units optimally. The EEO algorithm optimizes the PV-BES size, location, and power factor to reduce the total system power and energy losses during 24-h and a year operation periods. Detailed modeling of photovoltaic modules and battery energy system combination (PV-BES) units are provided and analyzed. The current study includes optimizing PV-BES combinations from one to five units operating either with unity or optimal power factors. Moreover, the proposed EEO algorithm's obtained results are favorably compared to SCA and EO algorithms in terms of the mean, standard deviation, and standard error of different optimization problems. The standard 69-bus radial distribution system is taken as a test system. The obtained results show the proposed EEO algorithm's superiority and effectiveness compared to other algorithms in terms of convergence speed and optimal values. Moreover, EEO algorithms can continuously optimize different PV and BES units during the 24-h and an entire year, taking the probabilistic nature of load and distributed generations.