To maintain the frequency stability of power systems integrated with large-scale renewable energy sources (RESs), a frequency-constrained unit commitment (FCUC) model is proposed, which incorporates a coordinated frequency control strategy of wind turbines and energy storage system (WT-ESS), a vital component for enhancing frequency regulation capacity of wind farms. Analytical formulations for the maximum rate of change of frequency (RoCoF) and steady-state frequency deviation are derived for both serial control and parallel control, accounting for the output-limited state of energy storage under serial control. To address the problem of solution slowness caused by the strong nonlinear frequency nadir constraints, a model-based multi-directional bilayer solution method is proposed. This method employs the simulation model to detect whether the frequency nadir constraint is active and generates parallel optimized cuts in three directions. Simulation results on the IEEE 39-bus test system demonstrate that the proposed FCUC model and solution method could accurately reflect the primary frequency regulation (PFR) characteristics of WT-ESS. Furthermore, the coordinated frequency control strategy effectively reduces overall operating costs while ensuring frequency security.