## 4 Results and Discussion
### Optimization Results  
#### 4.2.1 The Impact of the Reserve Activation Probability  
With the wind farm's aggregated capacity of 30 MW and the power curve (in p.u.) given in Section 4.1, we have the forecasted wind power and demand data presented in Figure 6. To evaluate the effect of the reserve activation probability on the VPP's optimal schedule, we randomly generate three scenarios \(p_{1},\ p_{2}\), and \(p_{3}\) of the reserve probability and apply them to the proposed model. Moreover, we consider a scenario with a reserve activation probability of 0.05 for all hours to see the effect of this uncertain parameter on the optimal results. The VPP's optimal reserve capacity corresponding to each scenario is presented in Figure 7. It can be seen that the ESS provides all the reserve capacity. Figure 5: Forecasted Demand. Figure 6: Forecasted wind power and demand. Figure 6 shows that the wind farm's available power output from hour 3 to hour 5, hour 9 to hour 16, and hour 22 to hour 24 is relatively higher than the demand. Therefore, it is clear that the VPP can provide reserve service during these periods; on the contrary, this service is unlikely to be available during the rest of the day. Figure 7a shows the VPP's optimal reserve contract if the probability of reserve activation is 0.05 for every hour. It can be seen that the VPP only provides reserve service when the power output of RES is redundant. By contrast, the optimal results in the scenario \(p_{1}\) show that the VPP's reserve service is available in hours 6 and 17 while wind power is equal to or even less than the demand (Figure 7b). This is due to the high probability of calling reserve during these hours. Note that the main role of ESS is to store the excess energy of RES or buy low-priced electricity from the network; then the ESS energy will be discharged to provide reserve or supply the load when the RES' power output is low and avoid the VPP having to buy electricity at a high price from the system. It is easy to see that the VPP provides a reserve service when the RES power output is not high enough will to cause the VPP to reduce the selling power or buy more electricity at other times to recharge ESS. This means that the probabilities of calling reserve in hours 6 and 17 are high enough so that the VPP expects the profit obtained from the BC market will be greater than the profit decline in the energy market. The optimal results in scenarios 2 and 3 also show the same thing. Even in scenario 3, the wind power in hours 15 and 16 is higher than the load by approximately the minimum threshold \(SR_{min}\), but VPP still decide not to provide reserve service during these hours due to the very small probability of calling reserve (less than 1%) (Figure 7d). As discussed in Section 2, the energy trading scheme during the period without reserve contract is assumed to be adjustable in the intraday market to utilize the RES available power output and maximize the VPP profit. This adjustment is not allowed to affect the performance of the reserve contract next period, even in an extreme case. Figure 8 shows the energy trade between the VPP and the main grid in scenario \(p_{1}\) for two extreme cases: (a) the full reserve capacity is called and generated for the entire contract duration, and (b) the reserve capacity is not called and generated. Similarly, the operating plans of ESS and RES corresponding to two cases are described in Figures 9 and 10, respectively. In the proposed model, VPP selling/buying energy and the operating parameters of ESS and RES in each hour are second-stage variables considering the uncertain nature of RESs and  
Figure 7: The VPP’s reserve bidding with (**a**) \(p=0.05\) for all hours, (**b**) scenario \(p_{1}\), (**c**) scenario \(p_{2}\), and (**d**) scenario \(p_{3}\) of the reserve probability. It is clear that with a relatively small probability of reserve activation, the energy trading scheme in Figure 8b can be applied in the DA market.