Power tracking control of heterogeneous populations of thermostatically controlled loads with partially measured states

This paper presents a new aggregate power tracking control scheme for populations of thermostatically controlled loads (TCLs). The control design is performed in the framework of partial differential equations (PDEs) based on a late-lumping procedure without truncating the infinite-dimensional model describing the dynamics of the TCL population. An input-output linearization control scheme, which is independent of system parameters and uses only partial state measurement, is derived, and a sliding mode-like control is applied to achieve finite-time input-to-state stability for tracking error dynamics. Such a control strategy can ensure robust performance in the presence of modeling uncertainties, while considerably reducing the communication burden in large-scale distributed systems similar to that considered in the present work. A rigorous analysis of the closed-loop stability of the underlying PDE system was conducted, which guarantees the validity of the developed control scheme. Simulation studies were performed while considering two TCL populations with a significant difference in their size, and the results show that the developed control scheme performs well in both cases, thereby confirming the effectiveness of the proposed solution.

Uncontrolled Keywords

• aggregate power tracking control
• finite-time input-to-state stability
• input-output linearization
• partial differential equations
• thermostatically controlled loads