## 3 Simulation Results and Analyses
### Case 2--Low Irradiation Profile without Fluctuations  
The case of 5 October 2018, in Compiegne, France, is considered. Figure 9 shows _PPV MPPT pred_, _PPV MPPT_.  
In this case, the weather is clear, so there are no fluctuations; however, the PV power production is not very high. The IIREV demand power is based on the data in Table 2. Figure 10 shows the power flow and storage state of charge for \"Sim w/o opt\" and simulation with optimization \"Sim with opt\" for case 2.  
Figure 10: _Cont._  
Figure 9: PV MPPT real and predicted powers—case 2.  
In Figure 10a, the storage always has priority over the grid. However, when EV5 arrives, the grid supplies power with the PV and the storage to charge the EVs, where the black dotted lines represent the maximum storage power and the red dotted lines represent the maximum grid power that can be reached. On the other hand, in Figure 10b, the power flow of the storage and the grid is based on the coefficient \(k_{D}\). Since the PV production is not high, the storage reached its lower limit at the departure of EV2. Therefore, the storage is required to 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. However, between 12:00 and 13:00 is considered a peak period, so by selling a little energy to the grid operator, it is possible to make small profits. Additionally, between 15:00 and 16:00 is a peak period, so in \"Sim with opt\", the power flow is better distributed since the storage is kept to supply power instead of grid power, while in \"Sim w/o opt\", the storage reached its lower limit before 16:00, and the grid continued to supply power to the EVs.  
Figure 11 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. Figure 11 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 11b, EV5 is charged from the grid with a higher percentage than in \"Sim w/o  
Figure 11: EV energy distribution in (**a**) “Sim w/o opt” and (**b**) “Sim with opt”—case 2.  
Figure 10: Power flow and storage state of charge in (**a**) “Sim w/o opt” and (**b**) “Sim with opt”—case 2.  
opt\", while EV3 and EV4 have been charged from the storage with a higher percentage than in \"Sim w/o opt\", based on \(k_{D}\) giving a better energy cost as shown.  
Figure 12a 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 a little bit of grid injection, which refers to selling energy to the grid and having approximately the same storage charging energy. Figure 12b shows the energy system cost, where the energy costs in \"Sim with opt\" are closer to the ideal case \"Opt for real conditions\" with 99.37% accuracy and lower cost than in \"Sim w/o opt\" with 164.04% accuracy (overpriced). In this case, the PV production is not high; however, selling a little bit of energy to the grid during the peak time could reduce the total cost of the system. Thus, it proves the superiority of the optimization algorithm over the storage priority algorithm.