Frequency regulation with thermostatic load participation in power networks

We consider the problem of controlling thermostatic loads such that ancillary services are provided to the power network within the secondary frequency control timeframe. This problem has been widely studied in the literature, where stochastic control schemes have been proposed to avoid the possibility of load synchronization, which induces persistent frequency oscillations. However, stochastic schemes introduce delays in the response of thermostatic loads that may limit their ability to provide support at urgencies. In this paper, we present a deterministic control mechanism for thermostatic loads such that those switch when prescribed frequency thresholds are exceeded in order to provide ancillary services to the power network. For the considered scheme, we propose appropriate conditions for the design of the frequency thresholds that bound the coupling between frequency and thermostatic load dynamics, so as to avoid synchronization phenomena. In particular, we show that as the number of loads tends to infinity, there exist arbitrarily long time intervals where the frequency deviations are arbitrarily small.