Existing studies on sub-synchronous oscillation (SSO) in series-compensated/weak grid systems with doubly fed induction generator (DFIG)-based farms generally adopt the leakage inductance model for transformers and neglect the excitation branches. However

real-world SSO events show that transformer core saturation causes nonlinear distortion of excitation branch parameters

leading to engineering problems such as local overheating and abnormal noise. In response to the contradiction between modeling simplifications and real-world phenomena

this paper first reveals the differential impact of transformer excitation branches on SSO characteristics in series-compensated/weak grid systems with DFIG-based farms. The modeling principles for excitation branches in different systems are proposed: for series-compensated systems

the parallel resonant circuit formed by the excitation branch inductance and series-compensated capacitance significantly affects the small-signal stability of systems and SSO nonlinear dynamics

and the transformer model with excitation branches needs to be modeled in detail; for weak grid systems

the influence of excitation branches on SSO characteristics is minimal

and the transformer can be modeled as a leakage inductance. Then

the nonlinear inductance of excitation branches and the pulse width modulation (PWM) limiters are modeled by the describing function method for series-compensated systems. A closed-loop model for equal-amplitude oscillation is developed considering the coupling effect of the two nonlinear dynamics. The mechanism of equal-amplitude oscillation under the dual nonlinear constraints of PWM limiters and core saturation is proposed. Finally

time-domain simulations verify the effectiveness of the theoretical analysis and the proposed model.