A Framework for the Analysis of Probabilistic Demand Response Schemes

We describe the class of probabilistic demand response (PDR) schemes, which are particularly suited for dynamic load management in the residential sector. Our main contribution is a new methodology for implementing and analyzing these schemes based on an operational objective function that balances the total cost of meeting demand, which includes the costs of supply generation, and spinning reserves, with the total revenue from the met demand and the gain from storage/deferment. We derive structural results for the design of PDR schemes in terms of sufficient conditions that yield a well-posed joint optimization problem for the two decision variables: the planned supply generation level and the real-time PDR signal magnitude. These results are used to evaluate the suitability of various proposed PDR schemes in single-period and multiple-period contexts. Finally, using simulations, we illustrate the application and effectiveness of the proposed methodology for a collection of thermostatically-controlled residential loads.