Hierarchical optimal allocation of BESS using APT-FPSO based on stochastic programming model considering voltage sensitivity and eigenvalues analyses

Integration of energy storage systems (ESSs) to microgrids (MGs) due to the growing penetration of intermittent energy resources is a great motivation to develop studies in the context of optimal sizing and placement of these systems. In this paper, a multi-objective bi-level optimization problem is addressed based on the stochastic nature and dynamic model of power system elements. As a preliminary step, the optimal size and capacity of the battery energy storage system (BESS) are determined to minimize frequency fluctuations. This level has been performed based on three approaches considering the daily intra-hour stochastic data. In the secondary level, the dynamic behaviour of all MG elements has been considered and correspondingly a dynamic objective function based on system eigenvalues and voltage sensitivity index (VSI) has been developed. According to the proposed objective function, the secondary step for sizing and placement of the battery units has been performed by adaptive particularly tuneable fuzzy particle swarm optimization (APT-FPSO) algorithm to reduce power losses, improve the voltage profile/ stability, and mitigate low-frequency fluctuations. Finally, the effectiveness of the proposed approach is evaluated using time-domain simulations, voltage sensitivity studies, and eigenvalue analysis.