Optimizing flexibility rewards for aggregator–consumer interactions: a bilevel multi-follower approach

Flexibility is increasingly central in power systems with high shares of variable renewable generation, as it enables the modulation of consumption to support grid balancing. Aggregators play a key role by consolidating individual demand-side resources and trading their combined flexibility with grid or market operators with benefits for all stakeholders. This work proposes a bilevel multi-follower mixed-integer nonlinear programming model to explicitly capture the hierarchical interaction between a flexibility aggregator (upper level) and multiple residential consumers/prosumers (lower level). The aggregator sets reward values to incentivize consumers' flexibility. Consumers adjust their energy use across a comprehensive set of resources (shiftable loads, thermostatic loads, electric vehicles, stationary batteries, microgeneration, and grid exchanges) to minimize their cost considering rewards for flexibility, electricity prices and comfort preferences. To address the nonlinear mixed-integer structure of the followers' problems, a hybrid optimization approach is developed. A particle swarm optimization explores the upper-level reward space and an exact MILP solver optimizes each consumer's lower-level problem. Computational experiments using real residential data and diverse consumer profiles demonstrate that the proposed approach can efficiently identify high-quality solutions under realistic computational budgets. The results show that the aggregator can achieve a profit while ensuring reductions in consumers' energy costs, and that consumers' flexibility contributions are heterogeneous across profiles and flexibility slots. These findings highlight how reward design can exploit the diversity of residential flexibility, enhance aggregator profitability and promote prosumer engagement. From a practical perspective, the framework supports aggregators in defining incentive strategies, estimating achievable flexibility and designing operational programs compatible with existing demand response platforms.