With the increasing penetration of renewable energy and power electronic devices in modern power systems, frequency security has become one of the bottlenecks affecting safe and stable power system operation. In order to meet the analytical needs from the grid-side for frequency response in large-scale power systems, the simplified model of primary frequency regulation (PFR) for thermal power units employed in the existing analytical methods is first improved. A second-order simplified model is established, which comprehensively considers the characteristics of the load feedback control, valve position limitation, and the influence of steady-state main steam pressure. Then, to accurately reflect the real PFR characteristics of units under different operating conditions, an online method for determining PFR model parameters is proposed based on real-time steady-state operating data. Finally, to enable analytical calculation of system frequency security constraints, the average system frequency model is treated as an open-loop system. By integrating the simplified PFR model into the open-loop average system frequency model, an analytical method for calculating the frequency security constraints is developed. Simulation results indicate that the proposed simplified model and analytical method for frequency security assessment can effectively evaluate the frequency security characteristics with high accuracy.