Optimization under uncertainty of thermal storage-based flexible demand response with quantification of residential users' discomfort

This paper presents a two-stage stochastic programming model for provision of flexible demand response (DR) based on thermal energy storage in the form of hot water storage and/or storage in building material. Aggregated residential electro-thermal technologies (ETTs), such as electric heat pumps and (micro-) combined heat and power, are modeled in a unified nontechnology specific way. Day-ahead optimization is carried out considering uncertainty in outdoor temperature, electricity and hot water consumption, dwelling occupancy, and imbalance prices. Building flexibility is exploited through specification of a deadband around the set temperature or a price of thermal discomfort applied to deviations from the set temperature. A new expected thermal discomfort (ETD) metric is defined to quantify user discomfort. The efficacy of exploiting the flexibility of various residential ETT following the two approaches is analyzed. The utilization of the ETD metric to facilitate quantification of the expected total (energy and thermal discomfort) cost is also demonstrated. Such quantification may be useful in the determination of DR contracts set up by energy service companies. Case studies for a U.K. residential users' aggregation exemplify the model proposed and quantify possible cost reductions that are achievable under different flexibility scenarios.