An aggregate model of the flexible energy demand of thermostatically controlled loads with explicit outdoor temperature dependency

In this paper we describe an aggregate model of Thermostatically Controlled Loads (TCLs) for Demand Response (DR) scheduling that, through a new approximation, makes explicit the dependency between the feasible control region and the time series of outdoor temperatures. In turn, the model can easily account for non-constant, stochastic temperatures during the control period, expressing the feasible load control through a set of linear equations and constraints with stochastic parameters. To highlight this feature we present a stochastic optimization formulation for the management of the DR-TCL and compare it with its deterministic counterpart, and with various equivalent models aimed at reducing the complexity of the constraints in the market optimization.