  We study an ensemble of diverse (inhomogeneous) thermostatically controlled
loads aggregated to provide the demand response (DR) services in a
district-level energy system. Each load in the ensemble is assumed to be
equipped with a random number generator switching heating/cooling on or off
with a Poisson rate, $r$, when the load leaves the comfort zone. Ensemble
diversity is modeled through inhomogeneity/disorder in the deterministic
dynamics of loads. Approached from the standpoint of statistical physics, the
ensemble represents a non-equilibrium system driven away from its natural
steady state by the DR. The ability of the ensemble to recover by mixing faster
to the steady state after its DR's use is advantageous. The trade-off between
the level of the aggregator's control, commanding the devices to lower the rate
$r$, and the phase-space-oscillatory deterministic dynamics is analyzed. We
discover that there exists a critical value, $r_c$, corresponding to both the
most efficient mixing and the bifurcation point where the ensemble transitions
from the oscillatory relaxation at $r>r_c$ to the pure relaxation at $r<r_c$.
Then, we study the effect of the load diversity, investigating four different
disorder probability distributions (DPDs) ranging from the case of the Gaussian
DPD to the case of the uniform with finite support DPD. Demonstrating
resemblance to the similar question of the effectiveness of Landau damping in
plasma physics, we show that stronger regularity of the DPD around its maximum
results in faster mixing. Our theoretical analysis is supported by extensive
numerical validation, which also allows us to access the effect of the
ensemble's finite size.
