Composing Thermostatically Controlled Loads to Determine the Reliability against Blackouts

Power grids are parallel systems in which consumers demand a shared resource independent of each other. A blackout occurs when the total demand increases or decreases too rapidly. This paper combines methods and concepts from three domains. The first stems from estimating the power consumption based on thermostatically controlled loads via Markov chains. The second domain provides the composition of parallel systems enriched by intermediate lumping to construct a minimal aggregate transition model, in this case of a community of housings. The third domain provides reasoning about fault tolerance properties by introducing limiting window reliability as measure, suitable to account for the continuous risk of blackouts. Combined, the three methods and concepts allow to determine the risk of blackout of a community over time.