  Thermostatically controlled loads (TCLs) have the potential to be a valuable
resource for the Balancing Authority (BA) of the future. Examples of TCLs
include household appliances such as air conditioners, water heaters, and
refrigerators. Since the rated power of each TCL is on the order of kilowatts,
to provide meaningful service for the BA, it is necessary to control large
collections of TCLs. To perform design of a distributed coordination/control
algorithm, the BA requires a control oriented model that describes the relevant
dynamics of an ensemble. Works focusing on solely modeling the ensemble date
back to the 1980's, while works focusing on control oriented modeling are more
recent. In this work, we contribute to the control oriented modeling
literature. We leverage techniques from computational fluid dynamics (CFD) to
discretize a pair of Fokker-Planck equations derived in earlier work [1]. The
discretized equations are shown to admit a certain factorization, which makes
the developed model useful for control design. In particular, the effects of
weather and control are shown to independently effect the system dynamics.
