Aggregate Flexibility Capacity of TCLs With Cycling Constraints

Thermostatically Controlled Loads (TCLs), e.g., an air conditioner, 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. Grid operators need tools for quantifying demand flexibility of a collection of TCLs in order to use them as a resource. However, computationally tractable characterization of flexibility capacity obtained so far has considered temperature constraints alone, ignoring their cycling/lock-out constraints: the length of time a TCL must stay in “on” stage before switching to “off,” or vice versa. In this work, we present a tractable characterization of the flexibility capacity of a collection of TCLs that incorporates not only temperature but also cycling and total energy consumption constraints. Unlike prior attempts at capacity characterizations incorporating cycling constraints, our results are independent of the algorithm used to coordinate the TCLs. The characterization leads to a set of convex constraints. A grid operator can use this characterization to compute a power consumption trajectory for an ensemble of TCLs that comes closest to what the operator needs to maintain demand-supply balance. Numerical results are provided to showcase the effectiveness of the proposed characterization.