## 1 Introduction  
The power system is developing towards increasing the proportion of renewable energy generation and forming a low-carbon power supply system. At the same time, there are a lot of flexible loads on the demand side, such as electric vehicle (EV), heating ventilation and air conditioning (HVAC) and electric water heater (EWH) [1; 2]. The traditional single control mode of power supply following the load change has been unable to meet the development needs of the power system. As an important part of the power system, demand side resources gradually play an important role in ensuring the supply-demand balance of the power system [3]. Among the demand side resources, on the one hand, the proportion of electricity consumed by residents to the total electricity consumption of society is increasing; on the other hand, the advanced metering infrastructure (AMI) is gradually becoming popular among residents. Therefore, the DR potentials of residents are increasing [4; 5]. However, the distribution of residents is relatively scattered, and the load elasticity level of individual residents is low, which cannot reach the minimum level of participation in demand response (DR). Load aggregator (LA) can integrate the flexible load resourcesof residents to achieve the minimum level of participation in DR and thus participate in power system operation. In the power market, the LA integrates demand side resources to participate in demand side bidding to gain benefits [6]. The bidding interaction process between power system operator (PSO) and LA is as follows: The PSO publishes demand response information to multiple LAs, including response period and response quantity. Each LA evaluates the response potential of the residents within its jurisdiction and reports the response quantity and bidding unit price to the PSO with the maximum net income. The PSO selects LAs from low to high according to the bidding unit price until the total response demand is reached [7; 8]. However, the DR behavior of residential consumers is uncertain, and different residential consumers have different willingness to participate in DR. In addition, there is intense competition among LAs. Therefore, the LA should consider the willingness of residents to participate in DR, accurately estimate the response potential, and formulate reasonable bidding strategies to obtain the maximum revenue [9]. Remarkable work has been done with respect to the resident load DR method under the LA management. Reference [10] proposed that residential consumers can participate in DR by means of the LA arranging load reduction contracts. The results verified that the participation of the LA is beneficial to reduce the peak valley difference of the power system. In Reference [11], a pre-day bidding model was built with the objective of maximizing profit of the LA. The above studies considered direct load control from the perspective of the LA, ignoring the willingness of residents and the impact of external factors on the responsiveness and willingness of residents in the process of DR. Reference [12; 13; 14] modeled the uncertainty of consumers' response behavior based on consumer psychology principles, and obtained the relationship between consumers' response probability and electricity price and incentives. Reference [15] used quantile regression to characterize the responsiveness of residents to economic incentives with probability. These studies only consider the influence of incentive or electricity price factors on residents' willingness to participate in DR. The existing studies on the LA bidding do not consider residents' willingness or only consider the influence of incentive factors on the willingness. However, in practice, consumers' response willingness is affected by many factors, such as residents' own response ability and DR awareness [16]. Due to the uncertainty of residential consumers' willingness to participate in DR, the LA has to face the risk that residents may refuse to participate in some DR projects.