Heavy renewable penetrations and high-voltage cross-regional transmission systems reduce the inertia and critical frequency stability of power systems after disturbances. Therefore, the power system operators should ensure the frequency nadirs after possible disturbances are within the set restriction, e.g., 0.20 Hz. Traditional methods utilize linearized and simplified control models to quantify the frequency nadirs and achieve frequency-constrained unit commitments (FCUCs). However, the simplified models are hard to depict the frequency responses of practical units after disturbances. Also, they usually neglect the regulations from battery storage. This paper achieves FCUCs with linear rules extracted from massive simulation results. We simulate the frequency responses on typical thermal-hydro-storage systems under diverse unit online conditions. Then, we extract the rules of frequency nadirs after disturbances merely with linear support vector machine to evaluate the frequency stability of power systems. The algorithm holds a high accuracy in a wide range of frequency restrictions. Finally, we apply the rules to three typical cases to show the influences of frequency constraints on unit commitments.