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

Jun Zheng (), Guchuan Zhu () and Meng Li
Additional contact information
Jun Zheng: Southwest Jiaotong University
Guchuan Zhu: Polytechnique Montreal
Meng Li: Shenzhen Technology University

A chapter in Handbook of Smart Energy Systems, 2023, pp 47-76 from Springer

Abstract: 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.

Keywords: Partial differential equations; Thermostatically controlled loads; Aggregate power control; Well-posedness; Stability (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-97940-9_11

Ordering information: This item can be ordered from
http://www.springer.com/9783030979409

DOI: 10.1007/978-3-030-97940-9_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().