  Recently it has been shown that an aggregation of Thermostatically Controlled
Loads (TCLs) can be utilized to provide fast regulating reserve service for
power grids and the behavior of the aggregation can be captured by a stochastic
battery with dissipation. In this paper, we address two practical issues
associated with the proposed battery model. First, we address clustering of a
heterogeneous collection and show that by finding the optimal dissipation
parameter for a given collection, one can divide these units into few clusters
and improve the overall battery model. Second, we analytically characterize the
impact of imposing a no-short-cycling requirement on TCLs as constraints on the
ramping rate of the regulation signal. We support our theorems by providing
simulation results.
