Econophysical Dynamics of Market-Based Electric Power Distribution   Systems
  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. 
Nicolas Ho and David P. Chassin