## 4 Case Results and Discussion
### Optimization Results and Discussion  
The convergence gap for the solution procedure of the model is the percentage change in demand-side energy storage capacity obtained in two adjacent MP. The convergence threshold in the model is 0.1%. The convergence is demonstrated in Figure 4. The model converges after 12 iterations. To study the validity of the proposed model, two cases are set up below for comparison. Case 0 is the normal group without the proposed DCIM. Case 1 is the proposed model with the DCIM. * Case 0: The hierarchical two-stage robust DES planning model without the incentive mechanism. * Case 1: The hierarchical two-stage robust DES planning model with the proposed DCIM. The optimal results of Cases 0 and 1 are shown in Table 6. Case 0 has no incentives and demand-side energy storage is not configured. The total configured DES capacity in Case 1 is 2863.6 MWh. The system in Case 1 reduced carbon emissions by 8.44% after planning compared to pre-planning. Therefore, it shows that the proposed DCIM \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Value** & **Item** & **Value** \\ \hline \(\Gamma^{L}\) & 12 & \(\Delta P^{L}_{i,t}\) & \(\pm\)20\% \\ \(\Gamma^{W}\) & 12 & / & / \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Uncertainty parameters. Figure 3: Wind power and load curves for generating uncertainty sets. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Value** & **Item** & **Value** \\ \hline \(\alpha_{max}\), \(\alpha_{min}\) & 90\%, 10\% & \(c_{\Sigma}^{ES}\), \(c_{\Sigma}^{ES}\) & 100 USD/kW, 250 \\ \(\eta_{char}\), \(\eta_{dis}\) & 95\%, 95\% & \(c_{\Upsilon}^{MT}\) & 25 S/(kW-Year) \\ \(N_{Y,DSB}\) & 8 Years & \(i_{R}\), \(d_{r}\) & 2\%, 10\% \\ \(\Gamma_{N}\) & 8 & \(a_{min}^{DR}\), \(a_{max}^{DR}\) & \(\pm\)30\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Energy storage parameters. can stimulate the system demand-side energy storage configuration and thus reduce the system's carbon emissions. Figure 5 presents the results of demand-side energy storage planning for all load buses in Case 1 and the variance of carbon intensity fluctuations at load buses. Under the proposed DCIM, demand-side energy storage can be profitable by charging and discharging in an environment of fluctuating carbon intensity. When the carbon intensity is high, energy storage is discharged to reduce the demand for high-carbon-intensity electricity. When the carbon intensity is low, the energy storage is charged to promote wind power accommodation. Therefore, it is more favorable for energy storage to be configured on buses where the carbon intensity fluctuates more intensely. When the carbon intensity fluctuates relatively smoothly, it becomes difficult to profit from the configuration of the DES. As there is a coal-fired unit on bus 15, it can be noted from Figure 5 that bus 15 has the smallest carbon intensity variance, which results in insufficient DES planning incentives on bus 15. Since the carbon intensity variances of other load buses reach a certain threshold, DES can all be effectively configured. However, from Figure 5, we can notice no strong correlation between the value of the carbon intensity variance at the load bus and the DES planning capacity. This is because the DES planning capacity depends mainly on the load power values. Comparing the load power size in Table 2 with the demand-side energy storage planning capacity size in Figure 5, it is obvious that there exists a strong correlation between the two. Therefore, the bus carbon intensity variance, i.e., the degree of bus carbon intensity fluctuation, is the threshold of whether demand-side energy storage is suitable for planning. In contrast, the planning capacity of demand-side energy storage mainly depends on the load size. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Case** & **DES Total Capacity/MWh** & **System Carbon Reduction Rate/\%** \\ \hline Case 0 & 0 & 0 \\ Case 1 & 2863.6 & 8.44 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The optimal results of Case 0 and Case 1.