# PV-Powered Charging Station for Electric Vehicles: Power Management with Integrated V2G
## 4 Simulation Results and Analyses
### Simulation Results under SPVA  
The second simulation works under SPVA and the EV cannot be charged/discharged until the estimated optimal start operating time of EVs is given by searching the \"peak\" periods and \"valley\" periods of the public grid; \(t_{\textit{EV\_best\_st}}\) represents the optimal start operating time, and \(t_{\textit{EV\_ttest\_st}}\) represents the estimated latest operating time. As shown in Figure 21, the steady DC bus voltage is 400 V within the simulation period, which proves that the power management strategy works well to balance the powers under SPVA. Figure 22 shows the storage _soc_ and distribution coefficient \(k\) under SPVA. The evolutions of the state of charge _soc_ and distribution coefficient \(k\) show the feasibility of SPVA and respect the power flow given in Figure 2.  
Figure 21: DC bus voltage evolution under SPVA. Figure 20: Recording of EV charging under ICDA. Figure 22: Storage _soc_ and distribution coefficient \(k\) under SPVA. Storage current evolution under SPVA is shown in Figure 23. As already mentioned, the absolute value of the storage current is limited to 115 A, and the simulation result shows that the current is successfully limited. The power flow of DC microgrid under SPVA is shown in Figure 24. The grid power is within the imposed power limits during the simulation period, respecting the power flow given in Figure 2. Setting different power limits of the public grid in the \"valley\" period and the \"peak\" period provides a guarantee for the stability of the public grid. Figure 25 shows the parking periods of EVs. In order to compare the two algorithms, all the information about EVs in case one and case two are the same. The theoretical optimal start operating time and latest start operating time of EVs are shown in Table 4, which can be calculated by the EV charging station based on \(T_{\textit{arrive}}\), \(T_{\textit{depatt}}\), \(SOC_{\textit{EV\_in}}\), \(SOC_{\textit{EV\_final\_lin}}\), charging modes, and discharge power. Figure 23: Storage current evolution under SPVA. Figure 24: Power flow of DC microgrid under SPVA. Figure 25: Parking periods of EVs at each charger. The power evolutions under SPVA are shown in Figure 21:0 Compared with Figure 13, the 4 th and the10 th EVs are farther away from the \"peak\" periods of the public grid, while the 12 th EV directly avoids the \"peak\" periods of the public grid, thereby preventing the public grid from overloading, meanwhile reducing charging costs, which proves the effectiveness and superiority of SPVA. Figure 27 shows the \(soc_{EV}\) evolutions under SPVA. The operating time of EVs connected to charger 1 is shown in Figure 21:1 Compared with Figure 15, due to SPVA, the 12 th EV did not choose to be charged immediately after arrival but waited for the optimal start operating time, which saved the user's charging costs and avoided adding peak loads to the public grid. The operating time of EVs connected to charger 2 is shown in Figure 21:2 Compared with Figure 16, due to SPVA, the 4 th EV did not choose to be charged immediately after arrival but waited for the optimal start operating time. The operating time of EVs connected to charger 3 is shown in Figure 30, and the 8 th and the 16 th EVs have the same operation results as Figure 21:3  
The operating time of EVs connected to charger 4 is shown in Figure 21:4 The operating time of EVs connected to charger 5 is shown in Figure 32 and the 9 th EV has the same operation result as Figure 21:5 Compared with Figure 19, due to SPVA, the 10 th EV did not choose to be charged immediately after arrival but waited for the optimal start operating time. Figure 21:6 Operating time of EVs connected to charger 4 under SPVA. Figure 21:7 Operating time of EVs connected to charger 2 under SPVA. There are 11 EVs with a completion degree of 100%, while the 1 st, 11 th, 14 th, and 16 th EV have a completion degree of 0%, among which, the 11 th EV directly left after arriving at the charging station because the charging station could not meet the user need.