Optimal demand response aggregation in wholesale electricity markets: Comparative analysis of polyhedral; ellipsoidal and box methods for modeling uncertainties

This paper presents an optimal framework for demand response aggregators in wholesale electricity markets. Demand response aggregators provide customers with flexible contracts in the proposed model. These contracts allow for hourly load reductions through load curtailment, load shifting, onsite generation utilization, and energy storage systems. The study suggests the price-based self-scheduling model for demand response aggregators, which seeks to maximize the aggregator's payoff for participation in day-ahead energy markets. The proposed model is implemented on a sample demand response aggregator with uncertainty and without uncertainty. Three methods, box, polyhedral, and ellipsoidal, based on robust optimization, are proposed for uncertainty modeling in this work, and their effectiveness is compared with each other. The results show that if the uncertainty is modeled using the polyhedral method, the value of the objective function will deviate by only 22.72 % compared to the case without uncertainty. However, this deviation in box and ellipsoidal methods is 118.48 % and 49.20 %, respectively, which shows the superiority of the polyhedral method compared to the oval and box methods.