This paper proposes an optimal operational framework for a flexibility-based energy hub management system (FBEH-EMS) that explicitly accounts for uncertainties in renewable energy sources (RESs) and demand profiles. The framework aims to enhance flexibility, minimize operating costs, and reduce emissions in energy hubs (EHs). On the supply side, gas-fired power plants and storage units are modeled as the primary flexibility providers. A quantitative system flexibility index (SFI) is developed, incorporating both the maximum available capacity and the dynamic response times of electrical and thermal units. The proposed EH integrates advanced technologies such as carbon capture, utilization, and storage (CCUS), photovoltaic (PV) panels, INVELOX wind turbines (IWTs), compressed air energy storage (CAES), photothermal (PT) units, electrical heat pumps (EHPs), combined heat and power (CHP) systems, power-to-gas (P2G), and electric vehicles (EVs). On the demand side, demand response programs (DRPs)—particularly time-of-use (TOU) pricing—are employed to facilitate load shifting and mitigate energy not supplied (ENS). To address the multi-objective problem of minimizing costs, emissions, and ENS while maximizing flexibility, a hybrid Bald Eagle Search–Mutant Grey Wolf Optimization (hBES-MGWO) algorithm is implemented. Simulation results demonstrate that the proposed framework achieves up to a 27.2% reduction in operating costs, a 91.2% decrease in emissions, and a 169.7% (2.88-fold) improvement in flexibility, confirming its effectiveness in achieving sustainable, low-carbon EH operation.
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