In this paper, we formulate and analyze the optimal set point problem of thermostatically controlled loads in a smart microgrid environment. From an aggregator's perspective, we show that flexibility can be extracted from the thermal inertia embedded in residential customers and be leveraged for maximum utilization of variable generation such as wind and solar. Through rigorous theoretical results we show that there is a fully decentralized mechanism for setting individual household temperature bounds while (a) maximum flexibility is extracted from inertial loads to balance the stochastic generation; (b) optimal staggering of demand responses of inertial loads can be achieved for smoothing out the overall power consumption; and (c) individual customers' comfort zone is taken into account. An easy-to-implement practical control setting is also introduced and tested using a simple model of wind and load distribution.
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