With the increasing wind power penetration in the power system, the auxiliary frequency control (AFC) of wind farm (WF) has been widely used. The traditional system frequency response (SFR) model is not suitable for the wind power generation system due to its poor accuracy and applicability. In this paper, a piecewise reduced-order frequency response (P-ROFR) model is proposed, and an optimized auxiliary frequency control (O-AFC) scheme of WF based on the P-ROFR model is proposed. Firstly, a full-order frequency response model considering the change in operating point of wind turbine is established to improve the applicability. In order to simplify the full-order model, a P-ROFR model with second-order structure and high accuracy at each frequency response stage is proposed. Based on the proposed P-ROFR model, the relationship between the frequency response indexes and the auxiliary frequency controller coefficients is expressed explicitly. Then, an O-AFC scheme with the derived explicit expression as the optimization objective is proposed in order to improve the frequency support capability on the premise of ensuring the full release of the rotor kinetic energy and the full use of the effect of time delay on frequency regulation. Finally, the effectiveness of the proposed P-ROFR model and the performance of the proposed O-AFC scheme are verified by simulation studies.