## 4 Case Results and Discussion
### Comparison and Discussion of Different Incentive Mechanisms  
To verify the advantages of the proposed model, the proposed DCIM is compared with two other mechanisms commonly used in practice. Case 1 adopts the proposed DCIM based on the CEF theory. Both Case 2 and Case 3 incentivize energy storage planning from an energy perspective, using the capacity subsidy incentive mechanism and discharge subsidy incentive mechanism, respectively. The actual subsidy prices in Cases 2 and 3 are 23 $/MWh and 20 $/MWh, respectively.  
* Case 1: The hierarchical two-stage robust DES planning model with the proposed DCIM.
* Case 2: The hierarchical two-stage robust DES planning model with capacity subsidy incentive mechanism.  
Figure 5: DES planned capacity and load bus carbon intensity fluctuation variance in Case 1.  
Figure 6: Demand response values and power demand before and after planning.  
* Case 3: The hierarchical two-stage robust DES planning model with discharge subsidy incentive mechanism.  
The total configured capacity and system carbon reduction rate of demand-side energy storage in three cases are shown in Figure 8. It can be found that optimization results in Case 1 have the least total configured DES capacity and the least incentive subsidy cost, yet the best carbon reduction effect. Therefore, it can be proved that compared with the other two mechanisms, the proposed DCIM can effectively lead the low-carbon oriented DES configuration and operation.  
Figure 9 displays the planned capacities of DES and variances of carbon intensity fluctuations for load buses in the three cases. The essence of DES carbon reduction comes from the time shift of the power demand. Therefore the carbon reduction effect will be better if the load carbon intensities fluctuate sharply. It can be found in Figure 9 that the variance of carbon intensities at bus 15 is the least. The DES in Case 1 is not configured at bus 15, which differs from the results in Cases 2 and 3. Comparative analysis reveals that the proposed DCIM can effectively guide the carbon-oriented DES configuration and avoid the DES configuration in some specific buses which is weak for carbon reduction. In addition, the DES capacity configured at each load bus in Case 1 is almost the least among the three cases, but the carbon reduction effect of Case 1 is the best. These highlight the advantages of the proposed DCIM based directly on a carbon perspective.  
Figure 8: Optimization results of the three cases.  
Figure 7: (a) 24-h load carbon emission responsibility map in Case 0; (b) 24-h load carbon emission responsibility map in Case 1.  
The 24-h load carbon emission responsibilities in Cases 2 and 3 are shown in Figure 10. Compared with Figure 7, it is clear that the load carbon emission responsibilities in Cases 2 and 3 are overall lower than the system carbon emission in Case 0, but in same periods, the load carbon emission responsibilities in Cases 2 and 3 are significantly increased instead. Case 1 shows a significant reduction in load carbon emission responsibilities compared to Cases 2 and 3. The comparison result proves that the proposed DCIM can efficaciously lead the low-carbon oriented DES configuration and operation and carbon emission reduction.