A residential demand-side management strategy under nonlinear pricing based on robust model predictive control

This paper presents a real-time demand side management framework based on robust model predictive control (RMPC) for residential smart grids. The system incorporates a number of interconnected smart homes, each equipped with controllable and non-controllable loads, as well as a shared energy storage system (ESS). We aim at minimizing the users' energy payment and limiting the peak-to-average ratio (PAR) of the energy consumption while taking into account all device/comfort/contractual constraints, specifically the feasibility constraints on energy transferred between users and the power grid in presence of load demand uncertainty. We consider a quadratic cost function for energy bought from the grid. Firstly, the energy price and related constraints of the system are modeled. Then, a min-max robust problem is established to optimally schedule energy under an interval-based uncertainty set. We finally adopt model predictive control (MPC) to solve the resulting robust optimization problem iteratively over a finite-horizon time window based on the receding horizon concept. Moreover, the robustness of the proposed real-time approach against the level of conservativeness of the solution is addressed. The effectiveness of the method is validated through a simulated case study.