Sequential Set-Point Control for Heterogeneous Thermostatically Controlled Loads Through an Extended Markov Chain Abstraction

This paper investigates utilizing a heterogeneous group of thermostatically controlled loads (TCLs) for long-term demand response applications. The steady-state services are achieved through manipulating the stored thermal-energy with minimal impact on devices' switching rates and the operating duty-cycles. The Markov chain abstraction method has been developed in literature for aggregating the TCLs at fixed temperature set-point. In this paper, an extended Markov model (EMM) is proposed to account for the dynamics involved in modifying various set-point magnitudes in both directions. The EMM is formulated online based on linear mapping and fast restructuring to Markov chains developed offline at fixed set-points, where a training process is used to construct each Markov chain. Set-point adjustments force devices to operate in a synchronized pattern, causing the aggregated power to oscillate or traverse extreme conditions. Therefore, model predictive control with direct ON/OFF switching capability is proposed to apply the set-point change sequentially and control devices' movement toward the new operating set-point. The performance of the proposed modeling and control techniques are compared against existing methods which rely on the direct ON/OFF control solely rather than adjusting the thermal-energy level.