Gradient Revision Method for Demand Response Stimulus Parameters of the Integrated Energy System

Integrated Demand Response (IDR) enhances the operational flexibility of Integrated Energy Systems (IES) and promotes renewable energy integration. However, limited interaction between the Integrated Energy Operator (IEO) and users during actual energy transactions can lead to biases in IDR planning, compromising user response effectiveness. To address this, this paper proposes a method for revising IDR stimulus parameters in IES based on gradient descent within a Stackelberg game framework. First, an IDR model based on consumer psychology principles is constructed to establish an IES Stackelberg game, in which the IEO acts as the leader and the load aggregator acts as the follower. Subsequently, during the game, the IEO utilizes users’ energy consumption strategies to adjust the stimulus threshold parameters of the dead zone and saturation zone along the negative gradient direction, thereby updating its decision for the next round. Furthermore, a response adjustment mechanism is designed to refine the IDR plan, enhancing its feasibility. Finally, comparative analyses across diverse scenarios demonstrate that the proposed method reduces deviations in planned IDR, thereby enhancing the low-carbon performance and renewable energy integration capacity of IES.