## 4 Case Study
### Results  
In order to prove the effectiveness of the proposed hybrid game theory-based energy trading strategy, the following different strategies are set up for comparative analysis. The operation results under different strategies are shown in Table 3. The final benefit pairs of each member of the PVP alliance are shown in Table 4, and the benefit pairs before and after cooperation are shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Time** & \
\begin{tabular}{c} **Electricity Sale Price from** \\ **Outer System/Yuan** \\ \end{tabular} &
\begin{tabular}{c} **Electricity Purchase Price** \\ **from Outer System/Yuan** \\ \end{tabular} \\ \hline
1:00–6:00, 23:00–24:00 & 0.4 & 0.35 \\
7:00–9:00, 15:00–17:00 & 0.79 & 0.68 \\
21:00–22:00 & 10:00–14:00, 18:00–20:00 & 1.2 & 1.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Electricity transaction price between the outer power grid and VPP/SES. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Time Frame** & **Heat Price/Yuan** \\ \hline Heat price maximum & 00:00–24:00 & 0.6 \\ Heat price minimum & 00:00–24:00 & 0.15 \\ Average heat price & 00:00–24:00 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Heat transaction price between the outer grid and VPP. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Strategy** & \begin{tabular}{c} **VPP** \\ **Benefits/Yuan** \\ \end{tabular} & \begin{tabular}{c} **SES** \\ **Benefit/Yuan** \\ \end{tabular} & \
\begin{tabular}{c} **Total Benefit of PVP** \\ **Alliance/Yuan** \\ \end{tabular} &
\begin{tabular}{c} **Overall Total** \\ **Benefit/Yuan** \\ \end{tabular} \\ \hline
1 (our proposed) & 14,925.15 & 4706.73 & \(-\)45,479.42 & \(-\)25,847.54 \\ \hline
2 & 14,969.46 & 4698.13 & \(-\)46,164.85 & \(-\)26,497.39 \\ \hline
3 & 13,110.25 & 5923.96 & \(-\)48,425.16 & \(-\)29,390.95 \\ \hline
4 & 13,368.87 & 5935.48 & \(-\)49,158.27 & \(-\)29,853.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: System operation results under different strategies. Strategy 1 (our proposed strategy): Consider the demand-side response, the master-slave game between SES and VPP, VPP and PVP alliance, and the cooperative game among PVP alliance members, that is, the method proposed in this paper. Strategy 2: Consider the demand-side response and consider the master-slave game between SES and VPP and VPP and PVP alliance, ignoring the cooperative game among PVP alliance members. Strategy 3: Ignoring the demand-side response, the master-slave game between SES and VPP, VPP, and PVP alliance is considered, and the cooperative game among members of the PVP alliance is considered. Strategy 4: Ignoring demand-side response, the master-slave game between SES and VPP and VPP and PVP alliance is considered, and the cooperative game among PVP alliance members is not considered. By comparing Strategy 1 (our proposed strategy) and Strategy 2 in Tables 3 and 4, it can be found that the total benefit for the whole system by using our proposed strategy is the lowest. Due to the cooperative game between PVP alliance members in Strategy 1, the total benefit of PVP alliance in Strategy 1 is increased by CNY 685.43 compared with Strategy 2, and the SES benefit and VPP benefit are slightly increased. The reason is that PVP members can trade P2P electric energy, thus reducing the need for the PVP alliance to purchase energy from outside. As the VPP delivers less power to the PVP alliance, there may be electricity surplus sold back to the grid or SES, resulting in a slight increase in revenue and a slight decrease in SES revenue. As can be seen from Table 5, the benefits of PVP alliance members increased by CNY 244.15, CNY 243.49, and CNY 244.61, respectively, after the cooperative game, and their revenue increased by 1.215%, 1.698%, and 1.661%, respectively, compared with that before cooperation. The results proved that our proposed method can not only improve the benefit of VPP but also would not reduce the total benefit of the PVP alliance.