## 1 Introduction  
With the development of modern power systems, the proportion of wind energy and other new energies in power systems is increasing. Doubly-fed induction generators (DFIGs), as the most commonly used wind turbine type, often need to transmit over long distances during power transmission [1]. In the process of long-distance power transmission, in order to reduce the energy loss in the line and improve the transmission efficiency, a scheme for connecting compensation capacitors in series in the transmission line is often adopted [2]. However, due to the fact that the DFIG converter contains a large number of power electronic components, the interaction between the converters and the series compensation capacitors may cause sub-synchronous oscillations (SSO) in the wind power system [3; 4]. Mild SSOs can cause the output power of wind-driven generators to oscillate, which can affect the lower line; if it is serious, it can cause the wind-driven generator to be disconnected from the grid, and the thermal power and other generator sets will be cut off [5; 6; 7]. In 2009, the power system of the US state of Texas experienced high line series compensation, causing sub-synchronous oscillation resulting in wind generator failures [8]. Since 2012, due to the high degree of series compensation in transmission lines, a number of synchronous oscillation accidents have occurred in doubly-fed wind farms in Guyuan district, Hebei Province, China, resulting in the waste of wind energy and the off-gridding of a large number of wind turbines [9]. Therefore, research on the suppression of SSO in DFIG grid-connected systems has important significance. In order to suppress the accidents caused by the SSO of DFIG grid-connected systems, scholars from various countries have proposed many methods. Among them, addingan SSO damper and improving the control strategy for the converter are the most common [10; 11]. [PERSON] introduced an SSO damper on the dq axis of the RSC current control to alleviate the influence of SSO by improving the damping of the RSC control system [12]. [PERSON] proposed to add a double-damping compensation filter to the RSC to improve the system damping and increase the flexibility of the control system, reducing the oscillation and overshoot of the rotor voltage and thereby mitigating the SSO phenomenon in DFIG wind farms [13]. The abovementioned suppression measures involving addition of dampers are relatively traditional, and the difficulty of implementation is low. However, the applicability of these strategies is not strong, and the suppression effect on the SSO is not flexible enough; furthermore, they can generally only eliminate oscillations at specific frequencies. Improving the converter control strategy is also a common way of suppressing SSOs in DFIG systems. [PERSON] et al. designed a notch filter on the power feedback branch and current feedback branch of an RSC in accordance with the impedance scanning method [14]. This scheme has excellent inhibitory effects on low-frequency oscillations but no obvious inhibitory effects on oscillations at 15 Hz and above. [PERSON] et al. utilized a quasi-resonant controller's static-free adjustment capability for AC signals. The quasi-resonant controller was used on the rotor side to suppress the stator sub-synchronous current and also on the grid side to suppress the sub-synchronous oscillation of the DC side voltage and reactive power, but the case of SSO frequency variation was not considered [15]. Aiming at the SSO problem in DFIG systems, this paper proposes an RSC back-stepping SSO suppression strategy based on an adaptive quasi-resonant controller. First, the mechanism of SSO generation was analyzed and the mathematical model for the RSC under the SSO state was established. By analyzing the process of the interference of grid SSO on RSC control, it was determined that there are three propagation paths for the SSO in the RSC control system, and the influence of SSO frequency changes on the generator stator current was also analyzed.