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Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach

Author

Listed:
  • Md Musabbir Hossain

    (School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China)

  • Asatur Zh. Khurshudyan

    (Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
    Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, Yerevan 0019, Armenia)

Abstract

We consider a control problem for a diffusive PDE model of heterogeneous population of thermostatically controlled loads (TCLs) aiming to balance the aggregate power consumption within a given amount of time. Using the Green’s function approach, the problem is formulated as an approximate controllability problem for a residue depending on control parameters nonlinearly. A sufficient condition for approximate controllability is derived in terms of initial temperature distribution, operation time of TCLs and threshold value of the aggregate power consumption. Case studies allow to reveal the advantages of the proposed solution from numerical calculations point of view.

Suggested Citation

  • Md Musabbir Hossain & Asatur Zh. Khurshudyan, 2019. "Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach," Mathematics, MDPI, vol. 7(6), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:6:p:523-:d:238251
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    References listed on IDEAS

    as
    1. Kazmi, Hussain & Suykens, Johan & Balint, Attila & Driesen, Johan, 2019. "Multi-agent reinforcement learning for modeling and control of thermostatically controlled loads," Applied Energy, Elsevier, vol. 238(C), pages 1022-1035.
    2. Ding, Yi & Cui, Wenqi & Zhang, Shujun & Hui, Hongxun & Qiu, Yiwei & Song, Yonghua, 2019. "Multi-state operating reserve model of aggregate thermostatically-controlled-loads for power system short-term reliability evaluation," Applied Energy, Elsevier, vol. 241(C), pages 46-58.
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