Power-Duration Characterization of Aggregated Thermostatically Controlled Loads via Reach and Hold Sets
For power grid operators, this provides a practical ex-ante quantification of TCL flexibility to inform grid decisions.
This paper develops a method to quantify the flexibility of aggregated thermostatically controlled loads (TCLs) using reach-and-hold sets, which define how much power can be shifted and for how long. The method uses a Markov-chain model and a tractable optimization to compute inner approximations, validated through simulations.
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.