Optimal Joint Energy and Flexibility Market Clearing Considering Uncertain Renewable Resources Using Information Gap Decision Theory

The increasing penetration of renewable energy resources (RERs) introduces significant intermittency and uncertainty into power systems, challenging real-time balancing and flexibility provision. To address these challenges, this paper proposes a novel bi-level market-clearing framework that co-optimizes energy and flexibility dispatch while accounting for severe uncertainty in photovoltaic and wind generation. The model is structured as a Stackelberg game between the Independent System Operator (ISO) and multiple Distributed Flexibility Providers (DFPs), including demand response aggregators, distributed generators, and electric vehicle fleets. Unlike conventional probabilistic methods, the proposed approach employs Information Gap Decision Theory (IGDT) to evaluate risk-averse and risk-seeking strategies without relying on historical probability distributions. This enables the ISO to explicitly trade off operational cost against immunity to renewable forecast deviations. The framework is validated on the modified IEEE 24-bus Reliability Test System. Results demonstrate a 10.2% reduction in flexibility procurement costs through DFP integration, along with actionable robustness – opportunity curves. For instance, accepting a 5% cost increase immunizes the system against up to 18% wind power uncertainty. The proposed model offers a non-probabilistic, risk-aware decision-making tool for system operators, enhancing both economic efficiency and operational resilience in renewable-dominated grids.