Analysis and modelling of thermostatically-controlled loads

A general model of electric heating loads regulated by automatically-controlled thermostats is presented. The model is based on the equations of the thermal transients due to the thermostat operation. The power/voltage characteristic of a single load is obtained from the static analysis, showing its dependence on the most significant parameters of the thermostatic control, and the transient behaviour due to a step supply voltage decrease. The dynamic analysis is performed by simulating the response of a community of thermostatically-controlled loads with random initial conditions, subjected to step voltage variations. A theoretical justification of the behaviour of an aggregation of equal loads is given. Simulations are carried out to show the power response to voltage drops of different depth, up to the extreme situation of a load pick up which follows a temporary outage.