Flexibility capacity of thermostatically controlled loads with cycling/lock-out constraints

Thermostatically Controlled Loads (TCLs), e.g., A/Cs and water heaters, are a source of flexible power demand for the power grid: many different power consumption trajectories exist that can maintain consumers' quality of service (QoS). Extensive research has shown that flexible loads can provide valuable grid services. Quantifying the flexibility capacity of a collection of TCLs is a well-studied problem. However, many studies consider temperature constraints alone, while most TCLs are on/off loads that have cycling (or lock-out) constraints. Studies that have considered lock-out constraints have proposed quantifications that depend on the control algorithm used to coordinate loads to provide grid services. In this work, we present a characterization of the capacity of a collection of TCLs that considers not only temperature, but also cycling and total energy constraints. Our characterization is independent of the algorithm used to control the TCLs; it depends only on the QoS constraints on the individual TCLs. The proposed characterization can be used for planning a feasible power deviation trajectory for a collection of TCLs by solving a convex optimization problem.