Preprint Article Version 1 This version is not peer-reviewed

The Green’s Type Matrices for Consumption Reduction in a Heterogeneous Population Model of TCLs with Diffusion

Version 1 : Received: 29 April 2019 / Approved: 7 May 2019 / Online: 7 May 2019 (10:18:05 CEST)

A peer-reviewed article of this Preprint also exists.

Hossain, M.M.; Khurshudyan, A.Z. Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach. Mathematics 2019, 7, 523. Hossain, M.M.; Khurshudyan, A.Z. Controlling Power Consumption in a Heterogeneous Population Model of TCLs with Diffusion: The Green’s Function Approach. Mathematics 2019, 7, 523.

Journal reference: Mathematics 2019, 7, 523
DOI: 10.3390/math7060523

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.

Subject Areas

PDE; Power Consumption; TCLs; Control; Minimization

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.