*5.3. Impact of Bidding Price Parameters*

According to the above analysis, it is clear that bidding price plays an important role in the DR project. It is necessary to analyze how the bidding price affects the DR. Therefore, this section analyzes the influence of bidding price parameters on the population evolution result and the Nash equilibrium. Here, we took initial price parameters (i.e., *at <sup>h</sup>* <sup>=</sup> <sup>−</sup>0.068, *bt <sup>h</sup>* = 0.553 (*t* = 1–5 and 11–12); *at <sup>h</sup>* <sup>=</sup> <sup>−</sup>0.058, *bt <sup>h</sup>* = 0.774 (*t* = 6–10)) as the benchmark, then varied the price parameters by 1.1–2.0 times the benchmark. The corresponding result is presented as follows.

Figure 9 shows the bidding amount of each community and population in group *N* for different bidding price parameters. Note that the optimal bidding strategy in the figure was the Nash equilibrium in the week that evolution equilibrium was reached. Since the bidding strategies of different communities were all the same under the same price parameters, each community had the same bidding amount in dispatching slots *T*. From the figure, it depicts that the bidding amount increased gradually with 1.1–2.0 times the benchmark. Specifically, the population in group *N* increased from 44 to 45 communities when the parameters reached 1.3 times the benchmark. However, the population in group *N* still had only 45 communities even when price parameters reached 2 times the benchmark. Figure 10 shows the total bidding amount of all communities for different bidding price parameters. It is clear that, although the total bidding amount achieved consistent growth, the increment was declined gradually. By analyzing the above result, it demonstrates that raising the bidding price can improve the growth of the bidding amount, but with the market saturation, the dispatching cost increased for the same increment. Therefore, for the dispatching center of the smart grid, it was very necessary to optimize the bidding price parameters to make a balance between the DR amount and the dispatching cost.

**Figure 9.** Bidding amount and population for different bidding price parameters.

**Figure 10.** Total bidding amount for different bidding price parameters.

#### **6. Conclusions**

This paper not only focused on the evolutionary analysis of group population participating in the DR project, but also the optimization of the bidding strategy in a day-ahead bidding market. In the proposed scenario, a residential community's irrationality was considered in the decision-making process. In particular, the dynamic evolutionary process of group population was described with the Markov model, and the bidding strategy for communities participating in DR was optimized with the non-cooperative game approach. Furthermore, the uniqueness of the Nash equilibrium was proved with the mathematical method. Finally, a case study was performed to verify the effectiveness of formulated models. It showed that the group population in DR gradually converges to the fixed value with the implementation of the DR project. In addition, by analyzing the influence of bidding price parameters on DR, it showed that raising the bidding price can improve the growth of the group population in DR and the bidding amount, but the smart grid had to pay for the high dispatching cost with market saturation.

**Author Contributions:** Writing—original draft preparation, X.L.; methodology, Q.W.; validation, W.W. All authors were involved in preparing this manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
