## 4 Results and Discussion
Then, the optimization problems proposed by Equations (13) and (14) can be decomposed into 9 independent optimization problems and solved separately in this study. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Class:**} & **EV Groups** \\ \hline SoC:class = 1, AVDTi:class = 1 & EV15, EV16, EV17, EV19, EV21, EV41, EV42, EV44, EV46 \\ \hline SoC:class = 1, AVDTi:class = 2 & EV30 \\ \hline SoC:class = 1, AVDTi:class = 3 & EV4, EV9, EV11, EV28, EV31 \\ \hline SoC:class = 2, AVDTi:class = 1 & EV1, EV10, EV13, EV35, EV47 \\ \hline SoC:class = 2, AVDTi:class = 2 & EV26, EV32, EV38, EV39 \\ \hline SoC:class = 2, AVDTi:class = 3 & EV12, EV14, EV24, EV27, EV43 \\ \hline SoC:class = 3, AVDTi:class = 1 & EV7, EV22, EV23, EV25, EV33, EV36, EV37, EV45 \\ \hline SoC:class = 3, AVDTi:class = 2 & EV3, EV6, EV8, EV20, EV29, EV49 \\ \hline SoC:class = 3, AVDTi:class = 3 & EV2, EV5, EV18, EV34, EV40, EV48, EV50 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reorganized EV Groups. Figure 6: Auto-classified electric vehicle group map. Set \(x\%\) = 100%, \(y\%\) = 0.5%, \(Cp\) = 0.002, \(q\) = 500 kW/Hz, \(\Delta f\) = 0.02 Hz, \(S_{i,max}\) = 5000, \(S_{i,min}\) = 20,000, \(Pr_{\textit{f,max}}\)=5000, \(Pr_{\textit{f,min}}\) = -5000, \(T\) = \(t_{\textit{ave}}\) = 1 h, the weight of the two optimization targets \(w_{r}\) = (\(w_{1}\)\(w_{2}\)) = (0.4;0.6), the map of pareto front of the nine independent optimization problems are as Figure 7 shown. The optimization is indicated in Figure 7 shows the Pareto Front of the nine EVs groups. The optimization results of each electric vehicle group are independent. Each figure is the best solution for the nine EV groups (Nine maps correspond to the nine groups). By applying Equation (17) and Equation (18), the best compromised solution is selected from the pareto front, which is marked red in Figure 5. The value of the nine compromised solution, corresponding to the nine EV groups, are as Table 3 shown. Note that the total charging power is determined by both _Pref_, and \(S_{i}\) according to Equation (6), where _Pref_ determines the initial charging power and \(S_{i}\) determines the power adjustment rate according to the grid frequency deviation. From Table 3, it can be seen that,  
Figure 7: Pareto Front of EVs group of: (**a**) SoC.iclass = 1,AVDTi.class = 1; (**b**) SoC.iclass = 1,AVDTi.class = 2; (**c**) SoC.iclass = 1,AVDTi.class = 3; (**d**) SoC.iclass = 2,AVDTi.class = 1; (**e**) SoC.i class = 2,AVDTi.class = 2; (**f**) SoC.iclass = 2,AVDTi.class = 3; (**g**) SoC.i class = 3,AVDTi.class = 1; (**h**) SoC.i class = 3,AVDTi.class = 2; (**i**) SoC.i class = 3,AVDTi.class = 3.  
as for SoCi.class = 1, which means the state of charge is relatively low, to minimize the energy gap between the drive needs and EVs charging volume, the total charging power of this class is relatively high; as for SoCi.class = 2, which means the state of charge is relatively high, so that the total charging power of this class is relatively low. As for SoCi.class = 3, the total charging power of this class is medium. As for AVDT\({}_{i}\).class = 1, which means average daily drive distance is long, hence the total charging power of this class is relatively higher compared with EVs in the same SOC class and different AVDT class. As for AVDT\({}_{i}\).class = 2, which means average daily drive distance is short hence the total charging power of this class is relatively lower compared with EVs in the same SOC class and different AVDT class. Test the simulation case on the Matlab/Simulink simulation platform. The circuit parameters, as shown in Figure 1 are listed in Table 4.  
Set the simulation timing as follows:  
1. 0-1s, Initialization, set grid frequency = 50.02 Hz, inverters are grid-connected;
2. 1s, set active power \(P_{\textit{ref}}\), the real power flow to EVs are as \(P_{\textit{ref}}\);
3. 2-4s, Droop mechanism enable, the charging power of EVs changes according to different \(S_{i}\);
4. 4s, end simulation. The simulation results are as Figure 8 shows: