This study presents a non-linear adaptive control (NAC) for the energy storage system (ESS) embedded dynamic voltage restorer (DVR) in enhancing the low-voltage ride through (LVRT) capability of wind farms. The proposed NAC features a perturbation observer to estimate and then compensate the real perturbation of the whole system, including parameter uncertainties, measurement noise, and external disturbances such as different grid faults and intermittent wind power. It can achieve an adaptive and robust control without requiring accurate system model and full-state measurements. This control is then applied to the ESS embedded DVR (ESS-DVR) system, in which the ESS can store the blocked wind power for potential power fluctuation suppression. Simulation studies have verified that the proposed control for ESS-DVR can effectively enhance the LVRT capability of wind farms installed with different types of WTGs under different operating conditions. Moreover, its superiority has also been demonstrated by comparing with fixed gains-based conventional vector control and accurate system model-based feedback linearising control. induction generator (DFIG)-based wind farms [15-18] and the squirrel cage induction generator-based wind farm [19]. On the other hand, an ESS is generally embedded in the DC side of the DVR to store the blocked wind power and suppress potential wind power fluctuation. Various control methods have been employed for DVR controller design, such as the conventional vector control (VC) in [15-21]. However, this control method is designed and tuned based on one operating point, easily resulting in weaken control performance under varying operation conditions. To improve the performance of the VC, advanced control methods such as fuzzy control [22, 23], H-inf control [24], neural network control [25], and feedback linearising control (FLC) [26-29] have been proposed. Some of those controllers, such as the FLC, require accurate system models and parameter values, which in turn result in a complex control law and weak robustness. Most importantly, wind farms are generally operated and are subject to varying operational conditions, model uncertainties, and external disturbances. Consequently, a robust DVR control strategy is essential for the field implementation. This paper presents the perturbation compensation-based nonlinear adaptive control (NAC) for the ESS-DVR to improve the LVRT capability of wind farms. The NAC method is one type of disturbance observers-based adaptive control, which have been applied to control the grid-side converter (GSC) and improve the LVRT capability of a permanent magnet synchronous generator (PMSG)-based WTG [30] and also in multi-machine power system stability [31-33]. Based on perturbation estimation and compensation, all coupling non-linear dynamics, uncertainties, and external disturbances, especially different grid voltage dips and the uncertain wind power input, can be fully compensated. Moreover, no accurate system model and full-state feedbacks are required, making t...