  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 modelling. 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.
