Demand response with moving horizon estimation of individual thermostatic load states from aggregate power measurements

We present an optimization-based state estimation method that allows us to estimate the states of individual thermostatically controlled loads (TCLs), such as air conditioners and space heaters, from measurements of the power consumption of small aggregations of TCLs. The state estimator can be used together with a controller to provide ancillary services to power systems such as frequency control. The main advantage of this method is that it is designed to work with existing communication infrastructure. We assume that aggregate power measurements are available from distribution substations every few seconds, while TCL state measurements are available from smart meters only every 20 minutes. We model TCLs as hybrid systems and propose a moving horizon state estimator (MHSE), which is formulated as a mixed-integer linear program. We demonstrate the performance of the MHSE in two case studies: (a) estimation of TCL states in the absence of external control actions, and (b) a power tracking problem with closed-loop control using broadcast control inputs. To demonstrate the robustness of the method, we conduct a parametric analysis with respect to aggregation size and diversity, process noise characteristics, and control trajectory characteristics. The results show that the method generally provides accurate estimates of TCL states, resulting in improved controller performance in most cases, and is implementable in real-time with reasonable computational power.