On the range of feasible power trajectories for a population of thermostatically controlled loads

Abstract

We study the potential of a population of thermostatically controlled loads to track desired power signals with provable guarantees. Based on connecting the temperature state of an individual device with its internal energy, we derive necessary conditions that a given power signal needs to satisfy in order for the aggregation of devices to track it using non-disruptive probabilistic switching control. Our derivation takes into account hybrid individual dynamics, an accurate continuous-time Markov chain model for the population dynamics and bounds on switching rates of individual devices. We illustrate the approach with case studies.

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

“…1 and the proof is complete. Note that, from (6) and from the definitions of Π t and ρ t , we can write…”

“…The scope of this section is to model a population of TCLs as an MDP and show that, under basic assumptions, Proposition (2.2) can be applied to several finite horizon optimal control problems of interest. Similarly to [6], we build a dynamical model starting with the Fokker Plank equation that describes the evolution of the probability density function of the TCL temperature over time, but we propose an alternative discretization of the dynamics that allows to obtain a valid (as in (2)) transition probability matrix under weaker assumptions.…”

“…The convex reformulation of the constrained MDP problem is then applied to management of TCLs. To this end, we propose a discretization of the Fokker-Plank equations [5] that leads to a discrete MDP model for a system of TCLs under less restrictive assumptions than previously proposed [6]. E Motivated by the recent works demonstrating the potential of TCLs to complement DERs in providing ancillary services to assist the (re)balancing of the grid [1], [2], [7], [8], it is shown how the proposed methodology allows one to embed the MDPs optimization into a (linearized) AC optimal power flow (OPF) problem for distribution systems to coordinate the operation of the TCLs and other distributed energy resources (DERs) in a distribution grid.…”

Optimal power consumption for demand response of thermostatically controlled loads

“…In the work of Paccagnan et al, the range of feasible reference power trajectories was studied. Reulens et al adopted a model‐free approach to schedule a cluster of electric water heaters using batch reinforcement learning.…”

Mean field game based control of dispersed energy storage devices with constrained inputs

“…In [Grammatico et al, 2015], a pricing incentives scheme is implemented for the entire population based on the current aggregated power demand where individual control is bang-bang-like switching. In [Paccagnan et al, 2015], the set of feasible aggregated power trajectories are characterized such that a population of TCLs can follow them, where each TCL has a hybrid dynamics and the mode switching rate is constrained. The control is common to the entire population of TCLs and is announced by the central authority.…”