Set-Membership Dual Predictive Control for Thermoelectric Flexible Loads

Abstract

Flexible loads, such as Thermostatically Controlled Loads, are emerging as key elements for power balancing in smart grids, particularly under increasing renewable energy penetration. However, exploiting their flexibility requires knowledge of their aggregated dynamics, which are difficult to derive analytically. This challenge naturally leads to a dual control problem, where the controller must learn the system dynamics while simultaneously regulating the power consumption, to provide flexibility service to the grid. This paper presents a Set-Membership Dual Model Predictive Control (MPC) framework for the aggregated control of flexible loads that performs simultaneous system identification and optimal control of a set of loads, using Autoregressive with Exogenous Inputs models. The proposed approach actively reduces model uncertainty by minimising the volume of the Feasible Parameter Set, providing an uncertainty-aware dual control strategy. The performance of the method is evaluated through a comparative study against a passive adaptive MPC scheme in a demand response scenario. Simulation results show that the proposed approach reduces the Integral Square Error by 70.5% and the Integral Absolute Error by 57.9%, relative to the benchmark, demonstrating the benefits of incorporating active learning into the control design.