**5. Case Study**

The performance of the proposed approach is evaluated in this section. In the simulation, assume that there are |*I*| = 50 residential communities. At the beginning of the DR project (i.e., the 1st week), there are |*N*| = four residential communities who are willing to participate in DR, and other |*M*| = 46 communities are in a waiting state. For these communities participating in DR, they have to take part in the day-ahead bidding market to obtain the dispatching amount. Generally, the daily peak hours appear in 10:00–14:00 and 18:00–21:00. Here, energy consumption scheduling during 18:00–21:00 in one day of each week is taken as an example. Accordingly, suppose that peak shaving hours are 18:00–21:00 and a scheduling interval is 15 minutes. That is, residential communities in group *N* will bid for a load shaving amount in time slots *T* = [1, 2, ..., 12]. Furthermore, bidding price parameters are shown as (unit: 10<sup>3</sup> dollars/MWh): *a<sup>t</sup> <sup>h</sup>* <sup>=</sup> <sup>−</sup>0.068, *bt <sup>h</sup>* <sup>=</sup> 0.553 (*<sup>t</sup>* <sup>=</sup> 1–5 and 11–12); *at <sup>h</sup>* <sup>=</sup> <sup>−</sup>0.058, *bt h* = 0.774 (*t* = 6–10). Utility model parameters are shown as (unit: 10ˆ3 dollars/MWh): *ct <sup>h</sup>* <sup>=</sup> 0.012, *<sup>d</sup><sup>t</sup> <sup>h</sup>* = 0.117 (*t* = 1–5 and 11–12); *ct <sup>h</sup>* <sup>=</sup> 0.013, *dt <sup>h</sup>* = 0.126 (*t* = 6–10). Transition probability model parameters are shown as: β is in [0.02,0.04], η is in [0.3,0.4]. As for the available DR resource in the community, we

assume that the maximal value and minimal value of the DR resource are set as in Figure 2. And each community's DR resource is given with a random value among the range.

**Figure 2.** Range of available DR resource of each residential community.
