## 5 Simulation Results
### Coordinated Preheating Results and Comparison  
The simulation will be implemented within the time range of 04:00-24:00. In order to comprehensively analyze the performance of the coordinated preheating algorithm, this paper compares several cases, and the results are shown in Figure 8. The gray area in the figure represents the base load, and the yellow area represents the wind power output. The base load is not adjustable. The black solid line is the baseline heating schedule, in which all users set heating schedules by on-off mode according to the set temperature. The solid red line is the result of coordinated preheating. It can be seen that the curve is smoother than the baseline because part of the peak load is shifted to the valley. And the red solid line is almost all above the yellow area, so the wind power consumption is greatly promoted. Another two cases were analyzed to demonstrate the superiority of the coordinated preheating strategy. In case 1, all households schedule their heat load curves based on the baseline electricity price to reduce the energy bill on the premise of meeting the temperature demand. The baseline electricity price curve is the marginal generation cost curve in the baseline case. It can be seen that in case 1, a forward and higher peak is formed due to the neglect of marginal cost change, which leads to excessive preheating and heat loss instead. Therefore, concentrated scheduling in the absence of coordination will lead to preheating failure and increase the cost of power generation. To further illustrate the necessity of coordination, case 2 is used for comparison. In case 2, all households schedule their heat load curves based on the marginal cost curve of the coordinated preheating case, which can be regarded as the optimal electricity price curve. However, it also failed to reduce the peak, indicating that the scheduling based on a single price curve is not feasible and the coordination is necessary. A total of 30 adjustment rounds were conducted in the simulation, namely Round # 1-Round # 30. In Round #1, Group #1 performs rescheduling based on the electricity price given by the central controller. Similarly, Group #10 performs rescheduling in Round #10. In Round # 11, it returns to Group # 1. The change of each evaluation index with the number of rounds, is shown in Figure 9. Figure 9a shows the change of total generation cost, which is reduced by 36.8% due to coordinated preheating. Figure 9b shows that the total electricity bill of users has decreased by 48.3%. In addition, it can be seen from Figure 9c that wind power curtailment is significantly reduced, and almost all wind power can be consumed. It is worth noting that the total user bill decre  
Figure 8: Total load under different conditions. generation cost, which is attributed to the smoother load curve after preheating adjustment. The two values are quite close when reaching the group equilibrium, which indicates that the proposed algorithm achieves the optimal adjustment. In addition, it can be found that all indicators have reached a balance in ten rounds. At this time, all groups performed a round of adjustment, and subsequent optimization produced only slight fluctuations. In the simulation, limited by the computing power of a single computer, users in the group need to schedule one by one, so it takes a long time. However, in practical applications, with the help of users' edge computing capabilities, users in the group solve optimization problems in parallel, and the adjustment time for each round is within 10 s. The whole coordinated preheating process can reach equilibrium within 2 min, which is suitable for day-ahead scheduling. In addition, the time-consuming is related to the number of groups, but not related to the user scale due to the group-by-group coordination method, which is extensible for super-large-scale coordination.