## 1 Introduction
To determine the optimal size and control scheme of an EV charger supported by BES, different optimization or control algorithms are proposed with various criteria and constraints. An optimization model for deploying the energy storage system for minimizing the load variance from the grid point of view and cost reduction from the customer's perspective is given in [18]. The minimization of the operating cost using real-time electricity price is developed in [19]. The financial model was also used as the objective in [20], using a particle swarm optimization (PSO)-based optimization model to size the PV and BES in a grid-connected PV/BES combination. EV charging cost represented as a convex function of load demand is minimized in [21]. In [22; 23], a genetic algorithm was employed to solve the optimization model for the design of an EV fast-charging station, optimizing the number of chargers, installed power of renewable energies and storage, and minimizing the imported power from the grid. The uncertainty of the EV power demand is simulated by the Erlang B queuing model. The isolation niche immune genetic algorithm (INIGA) and price-incentive model is applied in [24] for the scheduling of generators, intelligent management of energy storage units and optimization of operating efficiency of the network, and the ordinal optimization theory into the microgrid operation, considering the wind power uncertainty is used in [25]. The additional criteria, as the minimization of the lifecycle cost, taking into account environmental emissions, is presented in [26], and different energy sources such as renewable energy technology-based and diesel generators are considered. The number of chargers and capacity of PV and BES using an operator to maximize the net present value are determined in [27], while [28] developed an energy management system to optimize the energy flow among PV, BES, and the grid. A mixed-integer linear programming (MILP) model to coordinate the charging/discharging pattern of EVs with a BES is used in [29], and an optimization model to determine the optimal sizes of PV and BES in a grid-connected photovoltaic/battery energy storage/electric vehicle charging station and investigate the optimal energy management and the interaction with the utility grid is solved by the MAPSO method in [30]. In [31], a 15 kW PV-grid system connected with a 40 kWh Li-ion battery is tested for different load scenarios for minimizing the energy imported from the utility, using the simulation results without any optimization algorithm. The smart charging scheme for individual homes with EV chargers and PV installation is presented in [32], but only on user's preferences, not taking the grid connection into account. The majority of the already mentioned research is dealing with the day-ahead scheduling of battery operation. In [33], real-time control is introduced besides the hour ahead optimization. A four-stage optimization and control algorithm is proposed to minimize total operating cost for a charging station integrated with PV, fixed battery storage and a commercial building. Total operation costs consist of the cost of power from the distribution grid, BES and PV operating costs, cost of unsupplied demand, cost of discharging EVs, and profits from charging EVs and selling the excess power to the grid. Chance-constrained optimization is used to cope with the optimization parameter uncertainties. Although the model offers higher tolerability for uncertain parameters, the origin of the energy that is charging and discharging the battery is not taken into account. Besides various criteria used in current optimization methodologies, the exact amount of renewable energy in the EV charging process has not been taken into account in all of the previous research. Another disadvantage of the current research methodologies is the single-criterion optimization instead of the multicriteria approach.