A multi-objective equilibrium optimization for optimal allocation of batteries in distribution systems with lifetime maximization

Many economic, environmental, and technical benefits have been achieved in recent years as a result of the integration of renewable energy resources (RERs) and battery energy storage units (BESUs) through the distri-bution network. However, unplanned allocating of the integrated BESUs and RERs leads to excessive investment costs and insecure system operation. Moreover, the charging and discharging processes have a direct impact on the degradation of the BESUs, and consequently, the stability of the BESUs will be affected as the battery ages. Therefore, this paper presents the trade-off between different conflicting objectives. In the presented multi -objective model, the battery lifetime maximization is considered in the allocation problem, for the first time, by maximizing the battery cycle to failure (CTF). On the other hand, different beneficial objectives are included by minimizing the operation and investment costs of the integrated units, the cost of energy not supplied (CENS), the cost of power loss, and the cost of carbon dioxide (CO2) emissions. For solving this model, a multi-objective equilibrium optimization technique (MOEOT) is proposed to determine the optimum sites and sizes of photo-voltaic (PV) and BESUs, maximum and minimum battery state of charge, and the charge hours. The proposed approach is employed on IEEE standard 30-bus and 69-bus radial distribution networks. The proposed MOEOT successfully acquires Pareto optimal front with diverse candidate options of different CTF and corresponding costs. Also, the impacts of varying depth of discharge (DOD) and charge and discharge hours for BESUs on the system performance are analyzed. For the IEEE 30 bus system, as the hours of the battery charge and discharge are increased from 2 to 12 h, the battery CTF is increased by 1 %; the power losses costs are decreased by 8.6 %; the emission costs are decreased with 1 %, and the life cycle cost is decreased with percentage 1 %. For the IEEE 69 bus system, the battery CTF is increased by 1 %; the power loss costs are decreased by 17 %; the emission costs are decreased by 1.8 %, and the life cycle cost is decreased by 0.1 %.