## 4 Results and Discussion
### Optimization Results
#### 4.2.1 The Impact of the Reserve Activation Probability
Meanwhile, Figure 8a shows that the VPP's highest adjustment in the intraday market if the reserve capacity is fully called and generated during the entire contract period. On the other hand, the ESS provides all reserve capacity; therefore, the ESS energy is maintained at the maximum level during the contract period to be available for reserve provisioning (Figure 9b). After each provisioning period of the reserve, the VPP's adjustment should bring the ESS's energy back to its maximum level just before the next reserve period (Figure 9a). This is still necessary even if the actual provisioning level is lower than the extreme case in this paper. Moreover, Figure 10 shows that the RES power output is fully utilized in both cases of providing reserve. Table 3 shows the optimal profit of the VPP corresponding to each scenario of \(p\) and compares them with the case where VPP does not participate in the BC market. It is easy to see that the VPP becomes more profitable when entering the BC market because reserve energy is 30% higher than the wholesale price. Even if the reserve capacity is not activated, they still profit from the provision of reserve capacity. Paying attention to the difference between the reserve activation probabilities during the hours helps the VPP sell reserve at the higher probability hours, thereby earning a higher profit. Next, the change of the optimal results as the probability of contingencies increases or decreases is evaluated. Note that in the above section, we assume that the maximum  
Figure 10: The RES operational scheduling with scenario \(p_{1}\) of the reserve probability: (**a**) The reserve bid is called on to produce; (**b**) the reserve bid is not called on to produce. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Scenario** & **No Reserve** & \(p\) **= 0.05** & \(p_{1}\) & \(p_{2}\) & \(p_{3}\) \\ \hline
**The optimal profit (USD)** & 3548 & 4134 & 4168 & 4230 & 4499 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The VPP’s optimal profit. probability of active reserve is 0.05. However, in practice, depending on the penetration level of the RESs in the power system, this probability may be higher. Figure 11 shows the VPP's optimal reserve capacity if the reserve activation probabilities in scenario \(p_{1}\) are multiplied by two, four, and six times, corresponding to the maximum value of 0.1, 0.2, and 0.3. It can be seen that, as the reserve activation probability increases, the number of hours that the VPP can provide the reserve service decreases. It seems that the VPP expects to profit from the provision of reserve control rather than from the actual reserve energy called and generated. This can be explained because RES power output is not enough to supply the load, especially in the period from hour 17 to hour 21, so that the ESS needs to provide a part of the load. An activated reserve contract period will use most of the ESS energy so that the VPP must purchase electricity from the main grid (hour 18 in Figures 8a and 9a). However, the peak-load price of 129.6 USD/MWh is higher than the total reserve capacity and reserve energy price; consequently, the operating cost increases.