This paper proposes a double integral sliding mode (DISM) controller-based supercapacitor interfaced by a dc-dc bidirectional converter to improve the fault ride-through (FRT) capability of a wind energy conversion system (WECS) that is based on a doubly fed induction generator (DFIG). Initially, the dynamical model is obtained for the dc-dc bidirectional converter in conjunction with the supercapacitor to accurately represent the system’s behavior during normal and fault conditions. Subsequently, DISM controller is designed for the system using the obtained dynamical modelling that complies with the Lyapunov stability criterion. Afterwards, a single integral sliding mode (SISM) controller and conventional sliding mode (CSM) controller are designed for the same system to evaluate the efficacy of the proposed method. Additionally, to address the well-known chattering phenomenon associated with all sliding mode controllers, smooth functions are employed to minimize chattering effects. Comparative studies which have been done in this paper show that DISM controller performs significantly better than SISM and CSM controllers in every metric regarding settling time, overshoot and undershoot.