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

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

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...

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Bibliographic Details
Main Authors: Md Musabbir Hossain, Asatur Zh. Khurshudyan
Format: Article
Language:English
Published: MDPI AG 2019-06-01
Series:Mathematics
Subjects:
PDE
power consumption
TCLs
control
minimization
Online Access:https://www.mdpi.com/2227-7390/7/6/523
Description
Summary: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.
ISSN:2227-7390

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