TY - JOUR
T1 - Super-relaxation of space–time-quantized ensemble of energy loads to curtail their synchronization after demand response perturbation
AU - Luchnikov, I.
AU - Métivier, D.
AU - Ouerdane, H.
AU - Chertkov, M.
N1 - Funding Information:
The work at LANL was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. DE-AC52-06NA25396, and it was partially supported by DOE/OE/GMLC, US and LANL/LDRD/CNLS, US projects. The work at Skoltech was supported by the Skoltech NGP Program (Skoltech-MIT joint project).
Funding Information:
The work at LANL was carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy under Contract No. DE-AC52-06NA25396 , and it was partially supported by DOE/OE/GMLC, US and LANL/LDRD/CNLS, US projects. The work at Skoltech was supported by the Skoltech NGP Program (Skoltech-MIT joint project).
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2021/3/1
Y1 - 2021/3/1
N2 - Ensembles of thermostatically controlled loads (TCL) provide a significant demand response reserve for the system operator to balance power grids. However, this also results in the parasitic synchronization of individual devices within the ensemble leading to long post-demand-response oscillations in the integrated energy consumption of the ensemble. The synchronization is eventually destructed by fluctuations, thus leading to the (pre-demand response) steady state; however, this natural desynchronization, or relaxation to a statistically steady state, is too long. A resolution of this problem consists in measuring the ensemble's instantaneous consumption and using it as a feedback to stochastic switching of the ensemble's devices between on- and off-states. A simplified continuous-time model showed that carefully tuned nonlinear feedback results in a fast (super-) relaxation of the ensemble energy consumption. Since both state information and control signals are discrete, the actual TCL devices operation is space–time quantized, and this must be considered for realistic TCL ensemble modeling. Here, assuming that states are characterized by indoor temperature (quantifying comfort) and air conditioner regime (on, off), we construct a discrete model based on the probabilistic description of state transitions. We demonstrate that super-relaxation holds in such a more realistic setting, and that while it is stable against randomness in the stochastic matrix of the quantized model, it remains sensitive to the time discretization scheme. Aiming to achieve a balance between super-relaxation and customer's comfort, we analyze the dependence of super-relaxation on details of the space–time quantization, and provide a simple analytical criterion to avoid undesirable oscillations in consumption.
AB - Ensembles of thermostatically controlled loads (TCL) provide a significant demand response reserve for the system operator to balance power grids. However, this also results in the parasitic synchronization of individual devices within the ensemble leading to long post-demand-response oscillations in the integrated energy consumption of the ensemble. The synchronization is eventually destructed by fluctuations, thus leading to the (pre-demand response) steady state; however, this natural desynchronization, or relaxation to a statistically steady state, is too long. A resolution of this problem consists in measuring the ensemble's instantaneous consumption and using it as a feedback to stochastic switching of the ensemble's devices between on- and off-states. A simplified continuous-time model showed that carefully tuned nonlinear feedback results in a fast (super-) relaxation of the ensemble energy consumption. Since both state information and control signals are discrete, the actual TCL devices operation is space–time quantized, and this must be considered for realistic TCL ensemble modeling. Here, assuming that states are characterized by indoor temperature (quantifying comfort) and air conditioner regime (on, off), we construct a discrete model based on the probabilistic description of state transitions. We demonstrate that super-relaxation holds in such a more realistic setting, and that while it is stable against randomness in the stochastic matrix of the quantized model, it remains sensitive to the time discretization scheme. Aiming to achieve a balance between super-relaxation and customer's comfort, we analyze the dependence of super-relaxation on details of the space–time quantization, and provide a simple analytical criterion to avoid undesirable oscillations in consumption.
KW - Demand response
KW - Energy consumption dynamics
KW - Thermostatically controlled loads
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U2 - 10.1016/j.apenergy.2020.116419
DO - 10.1016/j.apenergy.2020.116419
M3 - Article
AN - SCOPUS:85098956783
VL - 285
JO - Applied Energy
JF - Applied Energy
SN - 0306-2619
M1 - 116419
ER -