This paper presents a frequency constrained economic dispatch (FCED) method designed to prevent frequency violations under N – 1 contingencies, encompassing both generator outages and high-voltage direct current (HVDC) infeed losses. Firstly, the coordinated frequency dynamics of synchronous generators, wind turbines, and HVDC lines are modeled, and the resulting frequency constraints are derived. To address the challenging frequency nadir (FN) constraint, a physics-informed piecewise linearization (PI-PWL) model is introduced to learn the FN security boundary. The formulation of the proposed FCED method is then presented, incorporating frequency constraints under N – 1 contingencies. Additionally, an error-aware constraint cut (EACC) is proposed to eliminate errors introduced by data-driven methods and accelerate solution convergence. Case studies on the modified IEEE 39-bus and IEEE 118-bus test systems validate the effectiveness of the proposed FCED method. Results indicate that the proposed PI-PWL model more accurately captures the FN security boundary than the traditional PWL (T-PWL) model, particularly in scenarios with limited unstable samples. Moreover, the proposed FCED method ensures frequency security under N – 1 contingencies, while the EACC effectively eliminates approximation errors and accelerates convergence compared with fixed-step constraint cuts.