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This paper presents a convex reformulation of a nonlinear constrainedoptimization problem for Markov decision processes, and applies the technicalfindings to optimal control problems for an ensemble of thermostaticallycontrolled loads (TCLs). The paper further explores the formulation andsolution of a (linearized) AC optimal power flow problem when one or moreensembles of TCLs are connected to a power network. In particular, a recedinghorizon controller is proposed, to simultaneously compute the optimalset-points of distributed energy resources (DERs) in the grid and the optimalswitching signal for the TCLs. This formulation takes into account hardwareconstraints of the DERs, operational constraints of the grid (e.g., voltagelimits), comfort of the TCL users, and ancillary services provision at thesubstation. Numerical results are provided to verify the effectiveness of theproposed methodology.

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