## 5 Numerical Studies
### Comparative Analysis of Different Uncertainty Settings  
In the above model, the sources of uncertainty considered include two aspects: the uncertainty of PV&WPP output on the energy supply side and the uncertainty on the user side represented by the comfort range. In order to verify the effectiveness of the proposed approach, four scenarios are selected for comparative studies in this subsection. The details are as follows. 1. Scenario 1: No prediction error in the output of PV&WPP, and the occupants' comfort range \(\Delta P^{H}/P^{H}_{load}\) is set to be 0. 2. Scenario 2: No prediction error in the output of PV&WPP, and the occupants' comfort range \(\Delta P^{H}/P^{H}_{load}\) is set to be 0.1. 3. Scenario 3: Considering prediction errors in the output of PV&WPP, and the occupants' comfort range \(\Delta P^{H}/P^{H}_{load}\) is set to be 0. 4. Scenario 4: Considering prediction errors in the output of PV&WPP, and the occupants' comfort range \(\Delta P^{H}/P^{H}_{load}\) is set to be 0.1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline \(\alpha_{CHP_{1}}\) & 0.15 & \(P^{E}_{GT,max}\) & 2 MWh \\ \hline \(\alpha_{CHP_{2}}\) & 0.2 & \(\omega_{CCS}\)[31] & 0.5 MWh/t \\ \hline \(\alpha_{CHP_{3}}\) & 0.8 & \(\eta_{CCS}\) & 0.9 \\ \hline \(\beta_{CHP}\) & 18.18 m\({}^{3}\)/MWh & \(\phi_{P2G}\)[32] & 0.98 MWh/t \\ \hline \(\gamma_{CO_{2}}\) & 0.002 t/m\({}^{3}\) & \(\psi_{P2G}\) & 0.539 MWh/t \\ \hline \(P^{E}_{CHP,min}\) & 0.01 MWh & \(\zeta_{P2G}\) & 274.4 m\({}^{3}\)/t \\ \hline \(P^{E}_{CHP,max}\) & 2 MWh & \(\mu^{C}\) & 260 CNY/t \\ \hline \(\chi_{GT}\)[33] & 0.0044 MWh/m\({}^{3}\) & \(\mu_{ES}\) & 83 CNY/MWh \\ \hline \(P^{E}_{GT,min}\) & 0.01 MWh & \(\sigma\)[34] & 0.8 t/MWh \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Values of parameters in test system. Figure 4: Electricity and heat load on a typical day in summer and winter. First of all, in order to demonstrate the performance of the proposed model without uncertainty, it is assumed that the PV&WPP output forecast error and occupants' comfort range are both 0 in scenario 1; that is, the optimal dispatch of multiple energy scenarios is performed under deterministic conditions. The outputs of PV&WPP in summer and winter are plotted in Figure 5. Taking heat load for example, the dispatch results in summer and winter are shown in Figure 6. It can be seen that since the occupant comfort zone \(\Delta P^{H}\) is eliminated, the heat balance function (31) becomes a rigid constraint, and the heat output of CHP and P2G can just meet the heat load requirements. However, since the constraint relaxation is not performed, the feasible domain of the decision variables is reduced, and the optimal energy cost cannot be obtained. In addition, ignoring the fluctuations in renewable energy output may reduce the system's robustness in the face of worst-case scenarios. Figure 7 shows the actual heat load under different scenarios in summer and winter. In scenarios 1 and 3, since \(\Delta P^{H}/P^{H}_{load}\) is set to 0, the heat load is consistent with the preset value in Figure 4. Scenarios 2 and 4 relax the heat balance constraint, so the actual heat load deviates from the preset value. The cumulative deviation of heat load \(\sum_{t}\Delta t\Delta P^{H}\) for these two scenarios is calculated, respectively. The values for scenarios 2 and 4 are 0.028 MWh and 0.063 MWh in summer and 0.058 MWh and 0.113 MWh in winter. It can be concluded that the deviation in scenario 2 is smaller than that in scenario 4 in both summer and winter. This is because scenario 4 needs to consider the uncertainty of PV&WPP output, and a larger interval is required to meet the constraints in the worst case. Table 3 summarizes the total cost values under different uncertainty setting scenarios. It can be seen that, whether in summer or winter, the total cost of scenario 2 is the smallest,  
Figure 5: Output of PV&WPP in Scenario 1 for summer and winter. Figure 6: Dispatch of heat power in Scenario 1 for summer and winter.