A Refined Unit Commitment Model for Physical Energy Storage Incorporating Startup and Shutdown Curves

The increasing penetration of variable renewable energy sources necessitates flexible regulation resources, among which physical energy storage (PES) plays an indispensable role. However, unlike electrochemical storage, PES relies on rotating machinery with mechanical inertia, which imposes inherent limitations on instantaneous state transitions. Conventional unit commitment (UC) models typically idealize the startup and shutdown curves (SSCs) of PES as instantaneous events, leading to schedules that are physically infeasible. To address this gap, this paper proposes a refined UC model that explicitly incorporates SSCs into the operational constraints for PES. The proposed formulation introduces additional binary variables and curve-related constraints to enforce gradual power change during state transitions while preserving computational tractability. The model is validated through two case studies: a self-scheduling problem and the IEEE 118-bus system with multiple PESs. The two case studies collectively confirm that the proposed model is computationally tractable for day-ahead scheduling and, more importantly, captures refined operational behaviors.