Power-Duration Characterization of Aggregated Thermostatically Controlled Loads via Reach and Hold Sets

TL;DR

This paper presents a practical method to quantify the power flexibility of aggregated thermostatically controlled loads using reach-and-hold sets, enabling better grid management.

Contribution

It introduces a Markov-chain-based model and optimization approach to accurately characterize and compute the reach-and-hold flexibility sets of TCL aggregations.

Findings

The method accurately characterizes fleet flexibility.

Simulation validates effective power control.

Robustness analysis shows resilience to uncertainties.

Abstract

Aggregations of thermostatically controlled loads (TCLs), such as air conditioners, offer valuable flexibility to the power grid. The aggregate power consumption of a TCL fleet can be controlled by adjusting thermostat setpoints. An \textit{ex-ante} quantification of the flexibility that results from such setpoint change can inform grid operator decisions. This paper develops a rigorous, yet practical method to quantify flexibility in terms of the `reach-and-hold' set of TCL aggregations, which defines how much power can be shifted (reach) and for how long (hold). To quantify the reach-and-hold set, we employ a Markov-chain-based model of the TCL aggregation that captures second-order TCL dynamics, enabling accurate characterization of reach-and-hold sets. A tractable optimization problem is then formulated to numerically compute an inner approximation of these sets. Simulation results validate that our method accurately characterizes the fleet's flexibility and effectively controls its power consumption. Furthermore, a robustness analysis is carried out to investigate the effects of uncertainty in initial conditions and TCL parameters.