## 7 Numerical Results
### Simulation Results  
Figure 7 shows the simulation result of the proposed model for calculating the load profile of the EVs charging station. This figure is the result of using maximum numbers of charging station's capacity (i.e., 70 EVs) during the operating day because we have considered 70 EVs for type of EVs random values. The batteries' capacities for these EVs are based on their market share that have been mentioned in Table 5. As can be seen, given the changing behavior of the EVs charging program, the charging station will be considered as a power generator from the beginning of the peak period (i.e., hour 8) in response to the price changes at this time. In other words, due to Table 1, the probability of discharging at peak times is 85%. So, most of the EVs discharge at this period and hence we can consider charging stations as a power generator. On the other side, the probability of charging at off-peak times is 95%. Therefore, most of the EVs charge at hours 1-8 and hence we can consider a charging station as a load during this period. Table 8 shows the output values of the proposed DA operation. It contains mean and SD values of 200 scenarios and includes generation of micro-turbines and PV unit and buying from upstream grid. As can be seen, the amount of power purchases from the upstream grid is reduced between hours 11-17. However, the MG demand, as well as the market price will peak at these times. The reasons for this can be stated as follows. The PV unit generation in these period reaches the maximum, i.e., 50 kW and more. Furthermore, according to Figure 6, during these hours, the EVs charging station produces most of its energy between 40 kW and 65 kW because the high market price at these periods encourages the EVs to sell the stored energy to the MG. On the other hand, the high market price forces the MG to dispatch more of micro-turbines. In this regard, the production of micro-turbines is increased in these hours. Therefore, the MG can use its internal power resources instead of purchasing costly power from the upstream grid. Figure 7: Load curve of the EVs charging station according to the proposed method. The maximum amount of purchased power from the upstream grid is 265 kW at hour 21 and at a price of 8.4 $/kWh. At this time, the micro-turbine generation is reduced to 44 kW. The output of PV unit is zero and the station's generation is reduced to 21 kW because the market price is low and most of EVs will be discharged to the MG. So, the MG's manager increases its DA power procurement from the main grid in this situation. The minimum amount of purchased power from the upstream grid is 98 kW at hour 14 and at a price of 21.31 $/kWh. However, the MG's demand is high at this time (329.28 kW). The PV output is 57 kW and also the station sells 54 kW to the MG. Therefore, with increasing consumption and market prices, the MG manager will reduce its cost by operating more than internal power sources such as micro-turbines and PV units. The EVs charging station will be operated as an internal power source by engaging the EVs in the demand response program. The total cost of the operation in this simulation case study is $717. In order to realize the effectiveness of the proposed MCS based algorithm for estimating of charging station load, a sensitivity analysis is performed. Table 9 shows the results of this sensitivity analysis on the uncertain parameters of EVs. i.e., each time the simulation of the proposed algorithm is performed, one of the uncertainty parameters is not considered. As it appears, the uncertainty of EVs type has not had much impact on the curve. In contrast, other parameters have changed the curve. If the uncertainty of the charger type is not taken into account (that means all EVs are charged \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Time (h)** & **Micro-Turbines (kW)** & **Upstream Grid (kW)** & **PV Unit (kW)** \\ \hline  & **Mean** & **SD** & **Mean** & **SD** & **Mean** & **SD** \\ \hline  
\hline \end{tabular}
\end{table}