Analysis and optimization control of demand response via networked evolutionary game with memory

Demand response (DR) is a crucial mechanism for dynamically regulating electricity consumption in smart grids. Conventional DR studies often neglect the role of historical information on current decision-making and cost constraints providing users with an upper affordable threshold. This paper proposes a networked evolutionary game (NEG) model for DR that incorporates multi-step memory and cost constraints to more realistically capture user behavior . By employing the semi-tensor product method, the dynamics of the DR system is represented algebraically, enabling tractable analysis of equilibria and controller design. An optimization control strategy is developed to steer the system toward a desired state, reducing both total energy consumption and users’ cost, while ensuring that individual costs remain within a predetermined threshold. The proposed approach provides an effective theoretical framework for DR implementation in smart grids.