On the maximum likelihood duty cycle of an appliance and its validation

A physically based load model that incorporates the effects of random variations of load behavior is used to derive the probability density function (PDF) of the duty cycle of a residential thermostat-controlled heating unit. The PDF of the duty cycle is a function of the house parameters, outside temperature, and the statistics of random influences on the load. From the PDF, the maximum likelihood estimate of the duty cycle is deduced numerically. Simulations using real data were carried out to assess the influence of the temperature gradient, appliance rating, and the random disturbance. Two households were selected for verifying the maximum-likelihood duty cycle prediction of heat pumps during winter. Very good correlation exists between the prediction and measurement