**5. Conclusions**

SSCI can severely influence stability of series-compensated DFIG-based wind power systems and damage electrical devices. This study proposes a novel VGSTSM damping control strategy for SSCI mitigation. After analyzing the series-compensated model and SSCI mechanism, it is assumed that SSCI were mainly caused by the interaction between current dynamics in the RSC side and the transmission line. Rotor current dynamics are desired to track the prescribed values from MPPT and grid demand. State feedback was firstly carried out in the control law design, and then super-twisting control algorithm was designed. Adaptive control gain was conceived via barrier function. Stability for the series-compensated system was proved, based on the Lyapunov function. The proposed method can achieve chattering suppression of RSC control signals. More importantly, control gains can indeed be adjusted according to uncertainty variation. It did not require the upper bound of uncertainty derivative in advance. Contrastive control simulations were verified to show superiority. Future works will focus on experimental realization.

**Author Contributions:** Conceptualization, R.M. and Y.H.; Funding acquisition, Y.H. and W.P.; Methodology, R.M.; Supervision, R.M.; Writing—original draft, R.M.; Writing—review & editing, Y.H. and W.P. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China under Grant 61803230,61773015; A Project of Shandong Province Higher Educational Science and Technology Program under Grant J18KA330; University Outstanding Youth Innovation Team Development Plan of Shandong Province under Grant 2019KJN023; and Key R & D project of Shandong Province under Grant 2019GSF109076.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statemen:** Not applicable.

**Data Availability Statement:** Data sharing not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.
