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An analytical characterisation of cold-load pickup oscillations in thermostatically controlled loads

Large groups of thermostatically controlled loads can be controlled to achieve the necessary balance between generation and demand in power networks. When a significant portion of a population of thermostatically controlled loads is forced to change their on-off state simultaneously, the aggregate power demand of such population presents large, underdamped oscillations, a well-known phenomenon referred to by power utilities as “cold-load pickup”. Characterising these oscillations and, in general, the aggregate dynamics of the population facilitates mathematical analysis and control design. In this paper we present a stochastic model for the power response and derive simple expressions for the period and envelope of the oscillations.