Modeling Uncertainties in Aggregated Thermostatically Controlled Loads   Using a State Queueing Model
  To study the impacts of price responsive demand on the electric power system requires better load models. This paper discusses the modeling of uncertainties in aggregated thermostatically controlled loads using a state queueing (SQ) model. The cycling times of thermostatically controlled appliances (TCAs) vary with the TCA types and sizes, as well as the ambient temperatures. The random consumption of consumers, which shortens or prolongs a specific TCA cycling period, introduces another degree of uncertainty. By modifying the state transition matrix, these random factors can be taken into account in a discrete SQ model. The impacts of considering load diversity in the SQ model while simulating TCA setpoint response are also studied. 
Ning Lu, David P. Chassin, Steve E. Widergren