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

1
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
2
Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
3
Department on Dynamics of Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, Yerevan 0019, Armenia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(6), 523; https://doi.org/10.3390/math7060523
Received: 29 April 2019 / Revised: 30 May 2019 / Accepted: 5 June 2019 / Published: 8 June 2019
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. View Full-Text
Keywords: PDE; power consumption; TCLs; control; minimization PDE; power consumption; TCLs; control; minimization
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Hossain, M.M.; Zh. Khurshudyan, A. Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach. Mathematics 2019, 7, 523.

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