## 5 Case Study
### Simulation Results  
Figure 7 shows the generator's ability to smooth the wind fluctuation in Case 1. It is clear that the generator capability deviated from the imbalanced power. The generator capability varies owing to the wind fluctuation, negative or positive, and the different generator output for every time interval. The generator capability was smaller than the imbalanced power most of the time, which indicates that the AGC units cannot smooth the wind prediction error, and hence the curtailment of renewable generation, or even load shedding, are inevitable during large fluctuations. The estimated load shedding was 130.77 kWh. It can be obviously anticipated that additional balancing reserves are required in order to accommodate the wind output as much as possible. As discussed earlier, the smart appliances--including AC, WH, and EV loads--are highly flexible, and the shifting of the smart appliances in time to smooth the wind power fluctuation will bring greater benefits. The questions of how the smart appliances respond and how much DRP supports the balancing of wind power forecasting error are now explored. Figure 6: The actual and prediction wind power. Figure 7: The system operational power without DR. Figure 8 indicates the DRP and AGC unit capabilities and the unbalanced power. The red line represents the AGC unit capability, which is assumed negative when it provides reserve, and vice versa. The green line expresses the summation of DRP and AGC unit capability. The DRP is unlocked thanks to the domestic thermal storages that enable load shifting in order to smooth the wind forecast error. It is worth stating that the customers' comfort--including the temperature preferences, travel distance,and charging times--are respected at all times. However, as has been discussed in an earlier part of this paper, the DR strategy is not restricted to some specific method. The DR strategy could affect the following DRP, which varies at different time intervals. The DRP may not likely be large enough to smooth the wind forecast error. This phenomenon is observed during 01:50-02:44 a.m. The load-supply matching is disturbed because of large wind forecast error and little DRP. Consequently, the utilization of wind power could be enhanced if the system had more allowed DRP. It is worth revealing that the mismatching, wind power curtailment, and load shedding are a result of large fluctuations and DRP uncertainty. Figure 9 shows the smart appliance results with and without the proposed method. In the process of optimization, the smart appliances provide up and down reserve based on the time-varying DR potential. It is obvious from the upper figure that the smart appliance power before DR is different from the power with no DR, which means the DR potential under these two conditions are also different. The difference between smart appliance power after DR and before DR is within the DR potential value. When the DR potential is not sufficient with negative unbalanced power, some other loads would be shed, like the green line of the lower figure. Figure 8: DRP and AGC unit capabilities and wind prediction error power. Figure 9: The smart appliance results with and without the proposed method. The conventional DRP is calculated in advance, such that the DRP is constant. It is assumed that the upward DRP is 100 MW and the downward DRP is 45 MW. Figure 10 shows the comparative results between the proposed time-varying DRP and constant DRP. During 00:00-01:20 a.m., the total fluctuation is positive and the smart appliances respond to the increment signal. The lower figure depicts that the green shadow is the wind curtailment energy because the DRP is lower than the required response capacity of the load side. During 01:29-03:00 a.m., the total fluctuation is negative and the smart appliances respond to the reduction signal. The purple shadow is the load shedding energy. The amount of load shedding is greater with constant DRP than with the time-varying DRP.