Stochastic Optimization for Residential Demand Response under Time of Use

Demand response (DR) is one of the most economical methods for peak demand reduction, renewable energy integration and ancillary service support. Residential electrical energy consumption takes approximately 33% of the total electricity usage and hence has great potentials in DR applications. However, residential DR encounters various challenges such as small individual magnitude, stochastic consuming patterns and privacy issues. In this study, we propose a stochastic optimal mechanism to tackle these issues and try to reveal the benefits from residential DR implementation. Stochastic residential load (SRL) models, a generation cost prediction (GCP) model and a stochastic optimal load aggregation (SOLA) model are developed. A set of uniformly distributed scalers is introduced into the SOLA model to efficiently avoid the peak demand rebound problem in DR applications. The SOLA model is further transformed into a deterministic LP model. Time-of-Use (TOU) tariff is adopted as the price structure because of its similarity and popularity. Case studies show that the proposed mechanism can significantly reduce the peak-to-average power ratio (PAPR) of the load profile as well as the electrical energy cost. Furthermore, the impacts of consumers' participation levels in the DR program are investigated. Simulation results show that the 50% participation level appears as the best case in terms system stability. With the participation level of 80%, consumers' electrical energy cost is minimized. The proposed mechanism can be used by a residential load aggregator (LA) or a utility to plan a DR program, predict its impacts, and aggregate residential loads to minimize the electrical energy cost.