## 4 Numerical Results
### Case Studies and Discussions
#### 4.2.3. The CVPP's Optimal Schedule in an Extreme Operating Scenario: Plan 2 of the BC Contract  
This section evaluates the proposed model's effectiveness in an extreme scenario. It is easy to see that if there is no BC contract all day or the total power output of RESs within CVPP is much higher than the local demand, deciding CVPP's operating schedule in the DA and BE markets is not a complicated problem. In these situations, dividing the CVPP's capacity into the DA and BE markets seems to depend only on how high the reserve activation probability is. On the contrary, if the CVPP's BC contracts last over the day and the total power output of RESs is not higher than the local demand, operational planning for CVPP becomes much more difficult. Note that the BC contract should be signed at least a few days before the DA market; at that time, the CVPP may have over-forecasted the power output of RESs or underestimated the customers' consumption. Another possible case is that a RES unit has a sudden problem and must be shut down. However, CVPP must ensure compliance with the signed BC contract; otherwise, they will be penalized. Figure 15 depicts the CVPP's optimal trading strategy, as well as the operating schedule of ESS and RESs in the DA and BE markets with Plan 2 of the BC contract (Table 2). The upward reserve capacity in the BC contract is 3 MW. This means the CVPP must maintain the upward reserve capacity of at least 3 MW throughout the day. Besides, the reserve activation probability is 1%, and other input data is the same as in the base case. Results in Figure 15 show that ESS does not participate in maintaining the BC contract; only PV and WP are responsible. To guarantee the BC contract, a part of the available power output of PV and WP is always kept for reserve provision. Therefore, the selling power of CVPP in the DA market is reduced while its purchasing power is more than in the base case. For example, the CVPP must buy nearly 15 MW at 4:00-7:00, while the buying power in the base case is only around 10 MW during the same period (Figure 9). Consequently, in this section, CVPP suffered a loss of 4,602,625 USD in the DA market. Although a profit of 9,024,775 USD could be obtained from the BE market when the reserve was called, it is still difficult for CVPP to profit due to the probability of reserve activation of only 1%. Then, still, with Plan 2 of the BC contract, we increase the upward reserve capacity to 4 MW, and the other input data is the same as in the base case. With such an extreme scenario, the proposed model is infeasible, meaning the CVPP cannot meet this BC contract. However, as argued above, this can be considered a rare situation in which the temporary solution of abandoning the cyclical nature of the model is acceptable. So, Equation (14), which guarantees that the ESS reserve energy provision does not affect its DA scheduling, can be relaxed by allowing the ESS's end-of-day energy level to differ from its beginning-of-day energy level. Assuming that the difference between the two energy levels can be up to 5% of the ESS's rated capacity, the results are obtained in Figure 16. It can be seen that CVPP has secured the required upward reserve power for the entire day. Besides, the ESS provided a very small amount of upward reserve energy, concentrated when the RESs' power output is low, such as at 5:30-8:30 or 18:00. \begin{table}
\begin{tabular}{c c c c c} \hline
**Case Study** & **Base Case** & **Case 1** & **Case 2** & **Case 3** \\ \hline
**Upward Reserve Energy (MWh)** & 109.54 & 116.89 & 126.69 & 138.88 \\ \hline
**Downward Reserve Energy (MWh)** & 96.59 & 103.37 & 112.49 & 124.71 \\ \hline
**DA Profit (USD)** & 612.69 & 608.78 & 592.3 & 566.11 \\ \hline
**BE Profit if Reserve Activated (USD)** & 6374 & 6911.23 & 7672.93 & 7956.05 \\ \hline
**Total Profit Considering Reserve Activation** & & & & \\
**Probability (USD)** & 676.43 & 747.01 & 975.95 & 1361.71 \\ \hline \end{tabular}
\end{table} 
Table 3: Impact of reserve activation probability on CVPP’s profit.