## 1 Introduction  
In recent years, the peak power consumption in winter has become more and more obvious. The maximum load in winter exceeds that in summer in many southern provinces in many southern provinces of China [1], and Texas in the United States has also set a record for the peak power consumption in winter in 2021 [2]. Different from the central heating in the north, the household independent heating mode is more common in hot summer and cold winter regions, with the characteristics of intermittent heating on demand [3]. It is important to promote heating electrification to achieve carbon neutrality in winter heating systems. The heat pump, hot air blower/cooling and heating air conditioner follows the reverse Carnot cycle and transfers more heat with less energy consumption, which is highly energy efficient. [PERSON] [4] pointed out that the air source heat pump is the most important way of heating electrification. The European Commission has also set a heat pump development target, that is, 40% of residential buildings and 65% of commercial buildings are expected to achieve electric heating by 2030 [5]. With the increase in power demand in the winter peak period [6], efficient demand management technology can help to reduce system costs, promote the consumption of renewable energy, and achieve carbon neutrality. Residential air conditioning plays an important role in demand response resources. A demand response model for single residential buildings was established in [7], in which heat pumps preheat at low electricity prices to reduce power demand at high electricity prices. The home energy management system with integrated intelligent heat load has been studied in [8; 9] and the corresponding optimization problems were found, with the purpose of minimizing energy consumption cost and ensuring user comfort. Comfort is actually guaranteed by the precooling/preheating. Large scale day-ahead heat load regulation is an attractive solution for power system scheduling due to its economy and security, but there are many difficulties to be solved. The assessment of the maximum adjustable load of the air conditioning cluster can be used for real-time regulation [10; 11], but it cannot be used for day ahead scheduling because of the neglect of load-time coupling. For example, the time point and adjustment amount of preheating/precooling cannot be determined by the above methods. Equivalent energy storage models and cluster models for air-conditioning clusters are studied for day-ahead scheduling [12; 13], in which temperature setpoints are regarded as consistent and fixed. In fact, the temperature setpoints of users are different and time-variant, and are related to their respective travel schedules. Most importantly, the scheduling results are not practical due to the lack of instructions specific to each user. In view of the above problems, some studies have been carried out from the characteristics of intermittent heating/cooling [14; 15; 16] and the respective thermal parameters and thermal demands of households [17]. However, the above methods are only applicable to a single residential or commercial building and will encounter difficulties in solving large-scale problems. It is worth noting that if all participants adjust based on the same electricity price curve, it will fundamentally change the marginal cost curve of the system, which will lead to failure of the adjustment. A new coordinated preheating scheme based on game theory was proposed in [18] to ensure the effectiveness of large-scale family collective preheating, which effectively takes into account changes in marginal costs in the coordination process. However, households need to iterate one by one, and the computation time is linearly related to the household scale, which is unacceptable in large-scale problems. Intermittent heating, personalized thermal demand, and computational efficiency are the three major difficulties in large-scale day-ahead thermal load regulation.