Alternating renewal process models for electric power system loads

Results are derived for a class of stochastic processes called alternating renewal processes that appear particularly suitable for modeling air-conditioning loads on electrical power systems. Expressions for the Laplace transforms of the nonstationary mean and the stationary autocorrelation function are obtained. If the on-duration and off-duration random variables have gamma distributions of the particular type known as Erlang-n, then the transforms will turn out to be rational functions. Therefore, this class of air-conditioning loads can be characterized by the poles and zeros of these functions. Moreover, pole and zero locations determined empirically under quasi-equilibrium conditions can be used to predict the payback transient. How these results permit the prediction of transient behavior after an outage based on measurements taken under nominal conditions is explained