Aggregate capacity of TCLs with cycling constraints

Thermostatically Controlled Loads (TCLs) such as air conditioners and water heaters typically maintain their temperature within a preset range using on/off actuation. These types of loads are inherently flexible: many different power consumption trajectories exist that can keep the temperature within range. Decades of research has shown that flexible loads can provide valuable grid services. Quantifying the power and energy capacities of a collection of TCLs is a well-studied problem. However, most works focus on temperature constraints. In this work, we present a characterization of the capacity of a collection of TCLs that considers not only temperature, but also cycling and energy constraints. The characterization leads to a set of convex constraints. A grid operator can use this characterization to compute a feasible power consumption trajectory for an ensemble of TCLs that comes closest to what the operator needs to maintain demand-supply balance. Unlike prior attempts at capacity characterizations incorporating cycling constraints, our results are independent of the algorithm used to coordinate the TCLs.