Dynamic estimation of the price-response of deadline-constrained electric loads under threshold policies

The paper presents a consistent and unbiased estimator for dynamic, one-step-ahead prediction of the aggregate response of a large number of individual loads to a common price signal, using only aggregate past response data. The price per unit of consumption is an exogenous signal which is updated at discrete time intervals. It is assumed that individual loads arrive in the system at random times with random demands and random consumption deadlines, and may defer their consumption up to the deadline in order to minimize their total cost. It is further assumed that the individual loads adopt a threshold policy in the sense that they only consume when the price is below a certain threshold. A dynamic aggregate model is constructed from models of independent individual loads. A consistent and unbiased estimator which only uses aggregate data, i.e., the price and aggregate consumption time-series is presented for estimating the aggregate consumption as a function of price.