## 1 Introduction
Therefore, if the residents' willingness is not considered or not accurately evaluated, it will bring some problems to the LA and the PSO. On the one hand, this will reduce the revenue of the LA, and on the other hand, it is not conducive to ensure the balance of power supply and load demand. In addition, the willingness of different residential consumers to participate in DR is different. In conventional bidding strategies, the LA mostly ignores the differences between residential consumers when selecting target residents for DR, which will increase the LA's response cost. It is very important for the LA to provide personalized DR projects according to the electricity consumption characteristics and DR willingness of different residents. Aiming at the above research gaps, this paper focuses on how the LA formulate the optimal bidding strategy considering the uncertainty of residents' participation in DR. Firstly, the physical models of flexible loads are established to evaluate the ideal DR potential. Then, to quantify the uncertainty of the residential consumers, this paper considers the influence of various factors on the uncertainty and uses the fuzzy logic system to establish the residents' willingness to participate in DR evaluation model. Based on the model, the LA can quantify the uncertainty of the residential consumers and evaluate the corresponding DR willingness. Then, an optimal bidding decision-making model considering the uncertainty of residents is proposed. Based on the model, the LA can give priority to the residents with high DR willingness to participate in DR, which has two main benefits. On the one hand, the LA can reduce the incentive cost to residential consumers. On the other hand, the LA can reduce the risk of under-response or over-response in the response process. Finally, a case study of a residential community is carried out, and the results show that compared with the conventional bidding strategy, the optimal bidding model considering the uncertainty of residents' participation in DR can reduce the response cost of the LA and increase the LA's income. The contributions of this paper can be summarized as follows:  
1. Based on the residents' ideal DR potential, this paper also considers the influence of incentive and awareness on the uncertainty, which makes the DR potential evaluation result more in line with the reality. 2. The willingness evaluation model is established to quantify the uncertainty of the residential consumers. This is important to implement DR projects and accurately predict the effect of DR.
3. The LA optimal bidding decision-making model considering the uncertainty is constructed. This can guide the LA to provide different incentive packages for different residents, which not only improves the willingness of residents but also reduces the response cost of the LA. The rest of this paper is organized as follows: Section 2 is the research framework of the LA bidding. Section 3 constructs residents' multiple flexible load models and analyzes demand response strategies. In Section 4, the fuzzy logic system is used to establish the residents' willingness to participate in DR evaluation model. Section 5 proposes a method for formulating optimal bidding strategies for the LA. A case study is presented in Section 6. Section 7 concludes the paper.