# PV-Powered Charging Station with Energy Cost Optimization via V2G Services
## 4 Simulation Results for PVCS with V2G Service  
Several simulation cases are presented to demonstrate the effectiveness of the energy cost optimization method. Finally, the cases with optimization, denoted as \"Sim w/ opti\", are compared with the cases without optimization, denoted as \"Sim w/o opti\". The \"Sim w/o opti\" is operated under a simple control scheme based on a storage priority, where \(k_{D}\) is set to one in this operation mode [52]. The optimization problem is solved by CPLEX [53], where CPLEX is a high-performance mathematical programming solver for linear programming, mixed-integer programming, quadratic programming, and convex optimization, developed by IBM. The optimization is performed with 1-min intervals, while the simulation is performed with 1-s intervals. The data for the irradiance and ambient temperature were recorded at 10-s intervals using proper instruments of measurement, and through interpolation, the data are reduced to 1-s intervals.  
In this section, two case studies are presented for a PVCS that includes five chargers, with EVs equipped with 50 kWh lithium-ion batteries. The PVCS has 84 PV panels with 28.9 kWp, and the stationary storage has a capacity of 130 Ah, with 288 V providing 37.44 kWh. However, there is no defined power injection limit for the public grid. Table 1 lists the parameters that are used in the following simulation cases for the PVCS with V2G service.  
Table 2 presents the EV users' data and preferences. \(SOC_{EV\_ar\_r}\), \(SOC_{EV\_des}\), \(t_{arr}\), \(M_{v}\), and V2G participation are generated randomly. \(SOC_{EV\_ar\_r}\) and \(SOC_{EV\_des_{v}}\) are generated in the intervals [20%, 50%] and [70%, 100%], respectively. It is assumed that EV battery capacity is capable of handling fast charging.  
Additionally, two scenarios in each study case are taken into consideration:  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(P_{G\_J\_max}\) & - & \(SOC_{S\_min}\) & 20\% & \(c_{G\_NH}\) & 0.1 \(\epsilon\)/kWh \\ \(P_{G\_S\_max}\) & 50 kW & \(SOC_{S\_max}\) & 80\% & \(c_{G\_PH}\) & 0.7 \(\epsilon\)/kWh \\ \(P_{S\_max}\) & 7 kW & \(SOC_{EV\_min}\) & 20\% & \(c_{S}\) & 0.01 \(\epsilon\)/kWh \\ \(P_{EV\_fast\_max}\) & 50 kW & \(SOC_{EV\_max}\) & 100\% & \(c_{PVS}\) & 1.2 \(\epsilon\)/kWh \\ \(P_{EV\_aver\_max}\) & 22 kW & \(SOC_{S_{0}}\) & 50\% & \(c_{EV\_penalty}\) & 2.5 \(\epsilon\)/kWh \\ \(P_{EV\_slow\_max}\) & 7 kW & \(v_{S}\) & 288 V & \(c_{SW}\) & 0.05 \(\epsilon\) \\ \(E\) & 50 kWh & \(C_{Bat}\) & 130 Ah & \(p_{PV\_MPPT}\) & 28.9 kWp \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter values used in the simulations for the V2G service.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**EVs** & \(SOC_{EV\_art}\) & \(SOC_{EV\_des}\) & \(t_{arr}\) & \(t_{est\_ch}\) & \(M\) & **V2G** \\ \hline EV1 & 31\% & 85\% & 09:20 & 03 h 52 min & Slow & Yes \\ EV2 & 35\% & 75\% & 10:00 & 0 h 24 min & Fast & No \\ EV3 & 50\% & 80\% & 12:05 & 02 h 8 min & Slow & Yes \\ EV4 & 25\% & 78\% & 13:45 & 01 h 13 min & Average & No \\ EV5 & 29\% & 72\% & 14:25 & 03 h 5 min & Slow & No \\ \hline \hline \end{tabular}
\end{table}
Table 2: Data and preferences of EV users [43].  
* Scenario a: during peak periods, EVs discharge at a constant power and then recharge with the same constant charging power as set by the user until departure time;
* Scenario b: during peak periods, EVs discharge at a maximum power of 50 kW and then recharge again with a variable charging power, irrespective of the charging mode selected by the user, to achieve the desired SOC at departure after V2G service.