A reliable model based load shifting incorporating users' uncertain behavior to price fluctuations in demand response mechanisms

With the widespread implementation of demand response (DR) mechanisms, the dynamic response behaviors of users to price fluctuations have become increasingly important. To address the constraints of user response delays and behavioral uncertainties on the effectiveness of DR, this paper proposes a load shifting model that incorporates delay effects, aiming to accurately capture user response behaviors and support reliable grid scheduling. The model uses first- and second-order lag systems to represent user response delays under time-of-use pricing (TOU) and real-time pricing (RTP) mechanisms, combined with a variable-parameter logistic function to describe dynamic response behaviors. A corresponding parameterization methodology and reliability assessment framework is also developed. Case studies demonstrate that the proposed model effectively captures the response characteristics of different user types, with an average DR deviation rate reduced by approximately 30% compared to traditional models. The paper also quantifies the negative impact of delays on DR capabilities, showing that response delays significantly weaken the system's scheduling effectiveness. This model provides theoretical and practical support for precise grid scheduling in uncertain environments.