Observer Design for Boundary Coupled PDEs: Application to Thermostatically Controlled Loads in Smart Grids

This paper develops methods for state estimation of aggregated thermostatically controlled loads (TCLs) in smart grids, via partial differential equation (PDE) techniques. TCLs include on/off controlled devices, such as heat pumps, HVAC systems, and deep freezers. Control of aggregated TCLs provides a promising opportunity to mitigate the mismatch between power generation and demand, thus enhancing grid reliability and enabling renewable energy penetration. However, persistent communication between thousands of TCLs to a central server can be prohibitive. To this end, this paper focuses on designing a state estimation scheme for a PDE-based model of aggregated TCLs, thus reducing the required communication. First, a two-state linear hyperbolic PDE model for homogenous TCL populations is presented. This model is extended to heterogeneous populations by including a diffusive term. Next, a state observer is derived, which uses only measurements of how many TCLs turn on/off at any given time. The design is proven to be exponentially stable via backstepping techniques. Finally, the observer's properties are demonstrated via simulation examples. The estimator provides system-critical information for power system monitoring and control.