This article addresses the modeling and control of heterogeneous populations of thermostatically controlled loads (TCLs) operated by model predictive control (MPC) schemes at the level of each TCL. It is shown that the dynamics of such TCLs populations can be described by a pair of Fokker–Planck equations coupled via the actions in the domain. The technique of input–output feedback linearization is used in the design of aggregate power control, which leads to a nonlinear system in a closed loop. Well-posedness analysis is carried out to validate the developed control scheme. The closed-loop stability of the system is assessed by rigorous analysis. A simulation study is contacted, and the obtained results confirm the validity and effectiveness of the proposed approach.

中文翻译：

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由Fokker-Planck方程控制的异质TCL种群的总功率控制

本文介绍了通过模型预测控制（MPC）方案在每个TCL级别上运行的恒温控制负载（TCL）的异构种群的建模和控制。研究表明，此类TCL种群的动力学可以通过一对通过域中作用耦合的Fokker-Planck方程来描述。输入-输出反馈线性化技术用于集合功率控制的设计中，这导致了闭环中的非线性系统。进行了适度分析，以验证开发的控制方案。通过严格的分析评估系统的闭环稳定性。进行了仿真研究，所得结果证实了该方法的有效性和有效性。