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A PDE-Based Aggregate Power Tracking Control of Heterogeneous TCL Populations

In: Handbook of Smart Energy Systems

Author

Listed:
  • Jun Zheng

    (Southwest Jiaotong University
    Polytechnique Montreal)

  • Guchuan Zhu

    (Polytechnique Montreal)

  • Meng Li

    (Shenzhen Technology University)

Abstract

This chapter presents the development and the analysis of a scheme for aggregate power tracking control of heterogeneous populations of thermostatically controlled loads (TCLs) based on the theory and techniques for partial differential equation (PDE) control. By employing a thermostat-based deadband control with forced switching in the operation of individual TCLs, the aggregated dynamics of TCL populations are governed by a pair of Fokker-Planck equations coupled via the actions located both on the boundaries and in the domain. The technique of input-output feedback linearization is used for the design of aggregate power tracking control, which results in a nonlinear system in a closed loop. As the considered setting is a problem with time-varying boundaries, well-posedness assessment and stability analysis are carried out to confirm the validity of the developed control scheme. A simulation study is conducted to evaluate the effectiveness and the performance of the proposed approach.

Suggested Citation

  • Jun Zheng & Guchuan Zhu & Meng Li, 2023. "A PDE-Based Aggregate Power Tracking Control of Heterogeneous TCL Populations," Springer Books, in: Michel Fathi & Enrico Zio & Panos M. Pardalos (ed.), Handbook of Smart Energy Systems, pages 47-76, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-97940-9_11
    DOI: 10.1007/978-3-030-97940-9_11
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