  As energy markets begin clearing at sub-hourly rates, their interaction with
load control systems becomes a potentially important consideration. A simple
model for the control of thermal systems using market-based power distribution
strategies is proposed, with particular attention to the behavior and dynamics
of electric building loads and distribution-level power markets. Observations
of dynamic behavior of simple numerical model are compared to that of an
aggregate continuous model. The analytic solution of the continuous model
suggests important deficiencies in each. The continuous model provides very
valuable insights into how one might design such load control system and design
the power markets they interact with. We also highlight important shortcomings
of the continuous model which we believe must be addressed using discrete
models.
