## 5 Numerical Results
### Influence of Wind and EV Penetration  
This section shows the simulation results with different wind power and EV penetration levels. It is assumed that the forecasting error and short-term variations linearly increase according to the wind farm capacity.  
Figure 9 shows the scheduled spinning reserve and curtailed wind energy with different wind penetration levels. At lower wind penetration levels, wind farms are allowed to generate their available wind generation without any curtailment. At higher wind penetration levels, a good amount of wind energy is scheduled to be curtailed because of the increased forecasting error and short-term variations as well as the increased oversupply. Both spinning reserves are significantly increased as the wind penetration increases. However, at higher wind penetration levels, there is a decrease in the increasing  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Case without Wind Curtailment** & **Case with Wind Curtailment** \\ \hline Generation Cost & 1,331,004 \$/day & 812,309 \$/day \\ Reserve Cost & 138,529 \$/day & 123,387 \$/day \\ Total Cost & 1,469,533 \$/day & 935,696 \$/day \\ \hline \hline \end{tabular}
\end{table}
Table 1: Operational costs of unit commitment (UC) with and without wind curtailment.  
Figure 8: System-wide ramping capability with and without wind power curtailment: (**a**) ramping-up capability and (**b**) ramping-down capability.  
rates of spinning reserves because more wind curtailment is scheduled to relieve the oversupply and wind power uncertainty is mitigated.  
Figure 10 shows the scheduled wind energy with different wind penetration levels. During 2-6 h, wind farms are not allowed to generate their available wind energy beyond 1500 MWh through wind capacity increases because of an oversupply of wind generation. During the remaining periods (1 h and 7-24 h), it is observed that curtailed wind energy is exponentially increased as the wind penetration increases. This is attributed to the reason that the incremental cost of one MW spinning reserve is increased as the required spinning reserve increases.  
Figure 11 shows the operational costs incurred with different wind power penetration levels. It can be figured out that unit wind energy value is decreased as a greater number of wind generators are installed, and wind energy beyond a certain penetration level cannot give economic benefits to the power system.  
Figure 11: Operational cost with different wind power penetrations.  
Figure 10: Scheduled wind energy with different wind penetrations.  
Figure 9: Scheduled spinning reserve and curtailed wind energy with different wind penetrations.  
Figure 12 shows the daily curtailed wind energy and average operation costs for different EV penetration levels. As the EV penetration level increases, the EV charging load is expected to have less effect on the wind power curtailment. The average cost decreases as the EV penetration increases up to 30%, because more wind energy can be used as a result of relieving the oversupply by the additional demand of EVs. Beyond 30%, the oversupply is sufficiently relieved, and EVs act as additional demands, thereby leading to an increase in the average cost.