## 4 Example Analysis  
The verification study was performed in a modified IEEE 30-bus test system. This system, which is shown in Figure 2, has six thermal units, three DRs and one wind farm. Assume that the three DRs, DR1, DR2 and DR3, are located at Buses 5, 7 and 21, respectively. DR1 contains three IDRs, DR2 contains two IDRs and one TL and DR3 contains one PDR. Additionally, the wind farm with a total capacity of 45 MW is located at Bus 28. The simulation time horizon is set to 24 h with intervals of 1 h.  
To demonstrate the impact of different scenarios on the system dispatch strategy, we design three cases as follows:  
Figure 2: Topology of the modified 30-bus test system. The basic system dispatch without any DR participation. * Impact of DR (with multiple response modes) on system dispatch. * Impact of DR on system dispatch cost and wind power consumption. Case 1: In this case, no DR resources are involved in system scheduling. Parameters related to the system topology, thermal units and load forecast were obtained from Refs. [30; 31], which are shown in Tables A1 and A2. The outputs of six thermal units are optimized based on the scheduling model established in Section 3.2, as shown in Figure 3. The six thermal units are represented as G1-G6. Here, the height of each color block represents the output of each generator at each period. The total cost of system operation is USD 96,808.25, of which the unit operating, startup and shutdown costs are USD 96,171.25 and USD 637, respectively. Additionally, the unit startup/shutdown status can be found in Table 3.  
The total cost of system operation is USD 93,987.2, of which the unit operating, startup and shutdown costs are USD 90,248.2 and USD 536. The DR cost is USD 3202. Figure 4: Response values of DRs at each period in Case 2. Figure 5: Outputs of thermal units at each period with DR participation in Case 2. Figure 6: Daily load with DR participation in Case 2. Compared with Case 1, although the participation cost of DR increases to USD 3203, the total cost decreases from USD 96,808.25 to USD 93,987.20 (2.91% lower). The main reason is that the participation of DR reduces the pressure on the peak load regulation of thermal units and makes their startup and shutdown operation more infrequent. Case 3:  
To verify the impacts of DR on wind power consumption, we consider the uncertainties of wind power based on the previous case. After the scenario reduction process, the probabilities of each wind power output scenario can be obtained, as shown in Table 5. The forecast curves of each scenario can be found in Figure 7, which describes the predicted output of wind power in each scenario. We set \(\beta\) = 0.9 and the unit price of wind curtailment penalty as 100 USD/MW. The responding values of DRs and the thermal unit output are listed in Figures 8 and 9, respectively. Furthermore, the daily load with DR participation and the amount of wind curtailment can be found in Figures 10 and 11, respectively. Additionally, to analyze the impacts of DR participation on the total system operation cost, the comparison between the two subcases is listed in Table 6. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Unit No.** & **Startup Time** & **Shutdown Time** \\ \hline
1 & \\
2 & 11:00 & 21:00 \\
3 & 19:00 & 3:00 \\
4 & & 4:00 \\
5 & 3:00 & \\
6 & & 3:00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The unit start/stop status within the simulation period with DR participation. Figure 7: Predicted output of wind power under each scenario. Figure 8: Response values of DRs at each period in Case 3. Figure 10: The daily load with DR participation in Case 3. Figure 9: Outputs of thermal units at each period with DR participation in Case 3. As shown in Figure 7 and Table 6, the participation of DRs in the system scheduling reduces both the thermal unit operation cost and wind curtailment penalty cost.