## 4 Case Study
### Bidding Results  
To show the effectiveness of the proposed trading strategy, a two-play game is as follows: one wind power producer (WPP 1) and one DR aggregator (DRA) are considered. The following three bidding cases are proposed for comparison. The bidding strategies and market participation details of different entities in various cases are presented in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **Bidding Entity** & **Bidding Scenarios** & **Market(s) Involved** \\ \hline \multirow{3}{*}{Case 1} & WPP 1 without DR & S1 & Energy market \\ \cline{3-4}  & aggregators & & Energy and frequency \\ \cline{3-4}  & & S2 & regulation markets \\ \hline \multirow{3}{*}{Case 2} & DRA without wind & S3 & Energy market \\ \cline{3-4}  & power producers & & S4 & regulation markets \\ \hline \multirow{3}{*}{Case 3} & Coalition of WPP 1 & S5 & Energy market \\ \cline{3-4}  & and DRA & S6 & Energy and frequency \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Market participation of bidding entities: comparative analysis in multiple cases. Figure 4: Expected hourly prices in energy and regulation markets. Figure 3: Wind power data for a sample day. The profit for different bidding strategies is shown in Figure 5, along with the additional costs for market participants in the regulation market. Specifically, the orange bar depicts the revenue loss incurred by WPPs when providing upward regulation services, whereas the green bar indicates the additional purchase costs incurred by DRAs when enabling downward regulation. The cyan bar, on the other hand, represents the overall profits. If the WPP and DRA form a coalition, these costs can be avoided. The profit in the coordinated case is higher than in the uncoordinated cases. For example, the expected profit of the coalition in Case S6 is USD 85,375.4, a 5.0% increase compared to the combined profits of Cases S2 and S4. The expected profits from each market are plotted in Figure 6. Specifically, the green bars depict the percentage of the expected profit derived from the energy market, while the cyan bars represent the percentage of the expected profit originating from the regulation market. Additionally, the red bars indicate the imbalance costs incurred in the real-time energy market. Note that the energy imbalance represents the profit loss caused by the wind forecast error. Comparing Case S1 and Case S5, by coordinating with DR resources, the energy imbalances of the WPP decreased by 6%. In addition, by strategically allocating the resources in different markets, the coalition obtains the market profits with 70.36% energy, 46.54% frequency regulation, and 5.9% energy imbalance in Case S6. It indicates that the coalition obtains significant profits from frequency regulation provision, thus it is beneficial for market participators to bid in both the energy and regulation markets. Comparing Case S2, S4, and S6, the market profit of the cooperation case resulting from the regulation market is larger than the sum of revenues in independent cases. The results show that the proposed coordinated trading strategy can bring higher benefits for WPPs and DR aggregators, taking advantage of their complementary characteristics when participating in the regulation market. The comparison of cooperative case (S6) based on the profits allocation methods and individual cases (Case S2 and Case S4) is presented in Table 2. The results show that the expected profit for the WPP in the coordinated case is USD 57,563.95, a 3.7% increase compared to the uncoordinated case. The total surplus profit amounts to USD 4058.9, clearly indicating that effective coordination between the WPP and a DR aggregator can generate additional profits, highlighting the potential benefits of collaborative strategies in this context. Note that in the two-player game, the additional revenue is allocated equally based on cooperative game theory methods. Figure 5: Total expected profit in each case.