The rapid growth of distributed energy resources (DERs) is transforming distribution networks and increasing the need for coordinated flexibility management to maintain secure and economically efficient operation. In this work, we examine how uncertainty in load demand and photovoltaic (PV) generation affects incentive-based flexibility coordination within a hierarchical three-level framework. The proposed architecture integrates household energy management systems (HEMSs), an aggregator responsible for incentive allocation, and a distribution system operator (DSO) model based on AC optimal power flow. To account for demand and PV variability, a Γ-budget-robust optimization approach is adopted. Also, an incentive–penalty mechanism is introduced to allocate compensation according to each prosumer’s actual flexibility contribution while promoting economic fairness. The entire framework is implemented in PYOMO and tested on the IEEE 33-bus distribution system. A comparative evaluation between deterministic and uncertainty-aware cases is conducted to quantify the cost of robustness and to analyze its influence on flexibility participation, incentive distribution, household net cost, and voltage regulation performance. The results indicate that uncertainty can lead to deviations from initially scheduled flexibility commitments, thereby triggering penalty signals during re-optimization and strengthening contractual compliance. Although the robust formulation results in a moderate increase in operational cost, it substantially improves voltage compliance and overall system reliability. Overall, the findings highlight the importance of explicitly incorporating uncertainty in multi-level flexibility coordination to ensure both technical consistency and practical enforceability in modern distribution networks.
Alrumayh et al. (2026) studied this question.