## 3 Simulation Results and Analyses
### Case 3--High Irradiation Profile with High Fluctuations  
The case of 12 May 2019, in Compiegne, France, is considered. Figure 13 shows the _ppv mppt prel_, _ppv mppt_. In this case, the irradiations are high, and the weather is cloudy, so there are high fluctuations. The IIREVs demand power is based on the data in Table 2. Figure 14 shows the power flow and storage state of charge for \"Sim w/o opt\" and simulation with optimization \"Sim with opt\" for case 3. Figure 12: (a) Energy system distribution and (b) energy system cost—case 2. Figure 13: PV MPPT real and predicted powers and IIREV demand power—case 3. In Figure 14a, the storage always has priority over the grid, either to be discharged or to be charged. However, when EV5 arrives, the IIREV demand power is greater than the PV and storage power that can be supplied, where the black dotted lines represent the maximum storage power and the red dotted lines represent the maximum grid power that can be reached. Therefore, the grid supplies power to charge the EVs. On the other hand, in Figure 14b, the power flow of the storage and the grid is based on the coefficient \(k_{D}\). Since between 12:00 and 13:00 is considered a peak period, by selling energy to the grid operator, it is possible to make profits. However, after 13:00, the storage can be recharged to be able to charge the future EVs with sufficient storage energy. Therefore, when EV5 arrives, the PV, storage and grid can together supply the EVs. Figure 15 shows the EV energy distribution for \"Sim w/o opt\" and \"Sim with opt\". EV1, EV3, and EV4 depend mainly on PV energy since they charge in slow mode. EV2 depends on PV and storage with a slightly equal percentage. Figure 15 shows that EV5, which is in fast mode, is charged from the grid with a high percentage. This will increase the charging price for the EV user. In Figure 15b, EV3, EV4, andEV5 are charged from the grid with a higher percentage than in \"Sim w/o opt\"; due to the high fluctuations, the power distribution was not as suitable. However, the energy cost obtained from optimization stays better than in \"Sim w/o opt\" and returns profits due to selling energy to the grid. Figure 16a shows the energy system distribution for \"Sim w/o opt\" and \"Sim with opt\". There is no grid injection in the \"Sim w/o opt\", while for the \"Sim with opt\", there is grid injection, which is referred to selling energy to the grid and maintaining a little storage charging energy. Figure 16b shows the energy system cost; due to the high  
Figure 14: Power flow and storage state of charge in (**a**) “Sim w/o opt” and (**b**) “Sim with opt”—case 3.  
coefficient \(k_{D}\) gives better energy distribution for the system to have a lower cost than \"Sim w/o opt\" instead of giving a better energy distribution for EVs. Therefore, the EV user charging in fast mode should be willing to pay a high price. In case 3, due to high fluctuations, the optimization is not very accurate, as the PV prediction is hourly coming from Meteo France. However, the total cost in \"Sim with opt\" is still better than \"Sim with opt\" due to selling energy to the grid and making profits, yet the EV energy distribution is not as well distributed in \"Sim with opt\" as in \"Sim with opt\". In optimization, it is always preferred to sell energy to the grid to make profits. However, the goal, besides minimizing the total cost, is to have better EV energy distribution by reducing the grid energy consumed by the EVs. Therefore, it is important to recharge the storage. For the three cases taken in this study, after the departure of EV2, \(SOC_{S}\) decreases, and in case 2, it has reached the lower limit. It is expected for three more EVs to come for recharging at the IIREVs, and it is supposed that at least one EV could charge in fast mode. The average energy demand for each EV is 25 kWh, and so it is 75 kWh for the three EVs to come. Based on the data from Table 2, the capacity of the storage that can be used is 27 kWh (30% of 90 kWh).