A tractable formulation for multi-period linearized optimal power flow in presence of thermostatically controlled loads

This paper presents a convex reformulation of a nonlinear constrained optimization problem for Markov decision processes, and applies the technical findings to optimal control problems for an ensemble of thermostatically controlled loads (TCLs). The paper further explores the formulation and solution of a (linearized) AC optimal power flow problem when one or more ensembles of TCLs are connected to a power network. In particular, a receding horizon controller is proposed, to simultaneously compute the optimal set-points of distributed energy resources (DERs) in the grid and the optimal switching signal for the TCLs. This formulation takes into account hardware constraints of the DERs, operational constraints of the grid (e.g., voltage limits), comfort of the TCL users, and ancillary services provision at the substation. Numerical results are provided to verify the effectiveness of the proposed methodology.