## 4 Results  
The method is illustrated by the example of the hybrid system shown in Figure 1. The system consists of a solar power plant with a rated power of P = 100 kW, one EV charger with a rated power of 22 kW, and a battery with a capacity of C = 30 kWh. The expected EV charging is 60 kWh from 6-12 h and 60 kWh from 16-22 h. Other input values are presented in Table 1.  
The energy price for the 24 h period is presented in Figure 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline SOC(0) & 20 kWh & \(P_{B}\) max & 20 kW \\ \hline SOC\({}_{S}\)(0) & 10 kWh & \(P_{EV}\)max & 20 kW \\ \hline SOC\({}_{G}\)(0) & 10 kWh & \(P_{G}\)max & 70 kW \\ \hline SOC min & 0.1 C & \(\eta_{C}\) & 0.9 \\ \hline SOC max & 0.9 C & \(\eta_{D}\) & 0.9 \\ \hline \(c_{B}\) & 0.4 €/(kWh-day) & \(C\) & 30 kWh \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Input values for the optimization. For the sake of simplification, all of the inverters are working in unity power factor mode, without the reactive power generation. The optimization is performed in two steps: in the first step, utility functions for each criterion are determined. In the second step, a multi-attribute approach is used for the battery and EV charging schedules. Because the battery capacity is not changing during the first simulation, battery costs are not taken into account. Single-criterion optimizations were performed for all three criteria: minimum procurement costs, minimum battery aging, and maximization of car charging from solar energy by the Equations (13)-(15). The optimization problem is solved with the genetic algorithm in MATLAB (The MathWorks, Inc., Natic, MA, USA). The maximal generation number for the GA algorithm is 100, with the population size set to the array length of 200. Optimization is performed on Intel(R)Xeon(R) CPU E5-26670@ 2.90 GHz processor (Intel, Santa Clara, CA, USA) with 32 GB RAM. The total time of optimization is 47 s.  
The results are shown in Table 2.  
Results of the maximization of the solar energy share in the EV charging process are presented in Figure 5. Figure 5a presents, besides the forecasted values for the PV production (\(P_{S}\)) and load demand (\(P_{L}\))--the power from the grid (\(P_{g}\)), battery power (\(P_{bat}\)), and the optimized EV charging power (\(P_{ev}\)). Figure 5b represents the state of charge (SOC) of two virtual \"battery compartments\"--for renewable solar energy (\(SOC_{S}\)) and energy from the grid (\(SOC_{S}\)). Figure 5c gives the EV solar (\(P_{ev}\)) power component and grid component (\(P_{evg}\)), while Figure 5d represents the share of battery power from renewables (\(P_{bs}\)) and battery power coming from the stored grid energy (\(P_{bg}\)) in the optimized charge and discharge battery schedule. The weighting factors for each criteria are the same: \(k_{1}=k_{2}=k_{3}=0.33\). Results are presented in Figure 6.  
The absolute and relative values of individual criteria are presented in Table 3. Relative values \(U_{i}\) for single criteria are obtained using the scalarization expressions (24)-(26). Optimization results for the complementary multi-attribute case are presented in Figure 7. \begin{table}
\begin{tabular}{c c c c} \hline  & **F1 (kWh)** & **F2 (c)** & **F3 (\%)** \\ \hline max \(F1\) & 103.91 & 12,518 & 0.69 \\ \hline min \(F2\) & 46.71 & 11,869 & 0.48 \\ \hline min \(F3\) & 63.17 & 12,631 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Single-criterion optimization results. Figure 4: Energy prices for the next 24 h period. Using the optimization model, the analysis of the optimal battery capacity for different weighting coefficients in the optimization function was performed. Two cases were compared: (a) greater importance is given to one of the criteria, and (b) a balanced distribution of criteria values (complementary case).