## 4 DR Uncertainty Model  
DR potential refers to the ability of consumers to participate in response to load adjustment, including load increase and load reduction. Due to the randomness of residential consumers' electricity consumption, there are many uncertainties in their willingness to participate in DR projects. The LA accurately estimates the response potential and response willingness of consumers and can better formulate day-ahead bidding strategies. The three main factors influencing the willingness of residents to participate in DR are the response quantity, awareness and external incentive [21; 22]. The response quantity factor refers to the responsiveness of residents during the DR period, which can be calculated by \(Q^{\text{DR}}_{\text{HVAC},i,j^{\prime}}\)\(Q^{\text{DR}}_{\text{EWH},i,j^{\prime}}\)\(Q^{\text{DR}}_{\text{EV},j,j}\). When the response quantity of residents is low, the willingness of residents to participate in DR is low, otherwise it is high. Awareness factors include two aspects. One is the degree of subjective identification of the residents themselves to DR, and the other is the consideration of the residents' herd mentality, that is, the degree of identification of the surrounding environment to DR. Both can be obtained by means of questionnaire surveys. When residents' awareness level is high, residents' willingness to participate in DR is high. The external incentive factor is the compensation that residents get after participating in DR. In this paper, the compensation that residents get is paid by the LA. Figure 7: Electric vehicle (EV) charging load curve and charging feasible region. It can be found that there are many influencing factors affecting residents' willingness, and the randomness of residents' willingness is large. Reference [23] adopted questionnaire survey and data statistics to analyze the DR willingness of typical urban residents, which is difficult to implement and the data set is not wide enough. In addition, there are expert judgment method, analytic hierarchy process (AHP), fuzzy comprehensive evaluation method (FCEM), dynamic weighted round-robin (DWRR) and other non-data-driven methods. These methods can consider a variety of factors and build an evaluation model of residents' willingness to participate in DR. However, there are some problems in the above methods, such as the influence of subjective experience, one-sided results, low precision, low efficiency and lack of real-time performance. With the development of artificial intelligence, data-driven and machine learning methods represented by artificial neural network (ANN), extreme learning machine (ELM) and support vector machine (SVM) have been widely applied in many aspects [24]. However, these models need high requirements for data quantity and representativeness, and the mobility of the models between different residential communities is relatively poor. In the early stage of demand response, it is difficult to obtain a large amount of data such as residents' electricity consumption behavior and willingness. Fuzzy inference system can consider the advantages of both non-data-driven and data-driven methods. In the initial stage of DR, the fuzzy inference system is mainly built by expert experience in the absence of sample data. Then, an adaptive neuro-fuzzy inference system (ANFIS) can be constructed based on the user's electricity consumption data and willingness data combined with the neural network. Neural network is used to adjust the parameters of fuzzy inference system to make the evaluation result of willingness more accurate, [25]. This paper uses a fuzzy inference system to establish the relationship between residents' willingness to participate in DR and influencing factors, so as to construct DR uncertainty modeling. The fuzzy inference system imitates human thinking mode and is easy to understand and use. As a universal approximation system, fuzzy inference system can approximate any non-linear system with arbitrary precision in a closed bounded domain.