With a high proportion of power electronic devices connected to the power system, the new power system presents low inertia, low impedance, weak stability and other characteristics, and the risk of operational security increases. In this regard, the grid-forming energy storage converter should be emerged, the grid-forming energy storage converter gives inner loop voltage control the amplitude and phase angle through the power external loop control, presenting the voltage source characteristics. It has active anti-interference, active support characteristics, can effectively solve the problems faced by the new power systems. However, when the system is disturbed and the voltage falls to different degrees, the grid-forming energy storage is limited by the power angle curve of the power outer loop and the fixed active and reactive reference values, which will result in a large power angle instability and a disturbance current of more than 5 times. It threats the security and stability of the system operation. To address this problem, this paper firstly establishes a model of grid-forming energy storage converter. Based on the established model, the droop control power angle curve is plotted, and the transient destabilization mechanism of the grid-forming energy storage converter is analyzed under large disturbances. After analyzing the system, it is known that the stability of the system during large disturbances depends on the existence of an intersection between the system power angle curve and the active power reference value. At the same time, the size of the system disturbance current is affected by the degree of power angle change to a certain extent. Secondly, the disturbance current characteristics and its determining factors are analyzed, and the effect of direct current limiting control on the transient stability of the system is revealed. The analysis results show that the direct current limiting control tends to destabilize the system and cannot be directly used to limit the disturbance current. After theoretical analysis in this paper, it is found that the disturbance current size of the system is positively correlated with the difference between the converter out put voltage and the grid-side voltage, and the converter out put voltage size is correlated with the reference value of the power outer loop reactive power of the structural network type control. Therefore, during the disturbance period, the disturbance current can be limited by adjusting the system reactive power and then controlling the converter out put voltage. Based on the above theoretical analysis, an adaptive low-voltage ride-through (LVRT) control strategy for grid-forming energy storage converter is proposed, which can adjust the active and reactive reference values according to the degree of system perturbation, without switching the control strategy and changing the structure of the grid-forming control strategy. The energy storage converter still exhibits the characteristics of the voltage source during the distribution period, and it has the ability of active support for the system. It realizes effective limitation of the distribution current in the course of maintaining the stability of the system. At the same time, the disturbance current is effectively limited. Finally, the effectiveness of the proposed control strategy is verified by simulation and semi-physical experiment.