Abstract: With the proposal of the “carbon peaking and carbon neutrality” goal, wind and photovoltaic power generation technologies have found a wide application. However, the coupling effect between the power electronics of wind and photovoltaic farms, as well as the dynamic interaction between the renewable energy station and the series compensation, poses a risk of sub-synchronous oscillation to the system and affects the consumption capacity of renewable energy. Therefore, it is of great importance to study the stability of the hybrid wind-PV farm via series compensation grid connection system. Firstly, the state-space method is used to establish the mathematical model of doubly fed induction generator and PV unit, and the impedance transfer functions of the two are derived. Secondly, based on the complex torque coefficient method, the electrical damping characteristics expressed by the one-dimensional residues are generalized to the impedance characteristics expressed by the two-dimensional residues. The determination of the main oscillation mode is achieved by the weight of residues, thereby realizing simplification of the high-order transfer function and facilitating the analysis of the impedance characteristics of specific frequency bands. Also, the effectiveness of the simplified method is verified by the Bode diagram. Finally, by solving the eigenvalue participation factor and the residue observability and controllability correlation factors, the strongly correlated state variables and dominant parameters which affect the sub-synchronous oscillation are obtained based on the simplified transfer function. The influence of these dominant parameters on the sub-synchronous oscillation stability of system is studied through PSCAD simulation, which provides a theoretical basis for the formulation of sub-synchronous oscillation suppression measures.