Two-Stage Stochastic Frequency-Security-Constrained Unit Commitment for Thermal-Storage Joint Frequency Regulation Under High Renewables Using Analytical Criterion and Linear Surrogates

In modern power systems, the rapid growth of renewable energy capacity, such as wind and solar photovoltaic (PV) power, has led to a decline in system equivalent inertia and primary frequency regulation margin. At the same time, net load fluctuations have intensified across multiple time scales, making it more likely for the RoCoF, frequency nadir, and quasi-steady-state frequency deviation to approach safety limits following disturbances. To achieve a balance between frequency security and economic operation, this paper proposes a two-stage stochastic frequency-security-constrained unit commitment (FSC-SUC) model tailored for scenarios with high renewable energy penetration. The day-ahead hourly dispatch stage jointly determines the on/off status and reference output of synchronous units and the reservation of slow frequency regulation capacity, as well as energy storage charging and discharging plans, SoC trajectories, and the reservation of fast frequency regulation capacity. The intraday minute-level real-time dispatch stage accommodates prediction errors through scenario-based rescheduling and ensures the deliverability of both slow and fast frequency regulation capabilities via commitment consistency constraints. To address the challenge of directly embedding frequency nadir constraints into mixed-integer optimization, this paper employs a modeling approach that combines analytical criteria with linear surrogate constraints. The RoCoF and quasi-steady-state frequency deviation are specified via aggregated analytical constraints, while the nadir is embedded into the main problem after generating samples offline using a simplified frequency response model and training a polyhedral linear surrogate for external approximation. The safety margin is then calibrated using high-quantile residuals from the validation set to ensure conservativeness. Case studies on the IEEE 33-bus system under different renewable penetration levels demonstrate that the proposed method significantly reduces the probability of frequency nadir violations and load-loss risk with only a modest cost increase while also improving coordination between fast and slow frequency regulation.