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.
Highlights
The usage of renewable energy sources is becoming more efficient as an alternative to power sources
Thermostatically controlled loads (TCLs) are the typical control means in such systems and it may be a better option to provide necessary generation-balancing services
We consider the controllability property of the diffusive model of thermostatically controlled loads (TCLs) described by a one-dimensional diffusion equation with variable coefficients
Summary
The usage of renewable energy sources is becoming more efficient as an alternative to power sources. In [6], multi-state operating reserve model of aggregate TCLs has been presented for power system short-term reliability evaluation. A common temperature setpoint offset needs to be manipulated for controlling the aggregate power requirement of a population of TCLs [9]. This opportunity allows to develop efficient elaboration schemes aiming to reduce power consumption by altering the set-point temperature and the minimal and maximal admissible values of the temperature. The set-point temperature of the ith load, Θsp,i , is determined in terms of Θmin,i and Θmax,i as follows: Θsp,i =.
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