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

Md Musabbir Hossain and Asatur Zh. Khurshudyan
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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

Mathematics, 2019, vol. 7, issue 6, 1-8

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.

Keywords: PDE; power consumption; TCLs; control; minimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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