The virtual synchronous generator (VSG) technology for energy storage is an important measure to ensure system frequency and voltage stability. During faults, power fluctuations cause nonlinear changes of the output angular frequency of the active power-frequency loop, significantly impacting the transient fault characteristics of energy storage VSG. Existing research on the fault characteristics of energy storage VSG mainly focuses on the discharging state and often neglects changes in angular frequency, making it difficult to ensure the accuracy of analytical calculations for electrical quantities such as voltage and current. To address this, this paper studies the transient characteristics of energy storage VSG in different operating states and during rapid switching of states. A new fault characteristic analysis method of energy storage VSG is proposed that takes into account the dynamic characteristics of the active power-frequency loop. Taking symmetrical short-circuit faults as the scenario, the mechanism of angular frequency variation after the fault is analyzed, and a simplified method based on the equal area principle is proposed to clarify the nonlinear characteristics of the grid voltage change under the influence of angular frequency changes. Furthermore, by analyzing how the transient characteristics of voltage affect the short-circuit current, the analytical expression of short-circuit current is established by comprehensively considering the dynamic response of the reactive power-voltage loop and the virtual impedance loop. Compared with traditional analytical methods that ignore the dynamic characteristics of the active power-frequency loop, the proposed method can accurately characterize the transient fault characteristics of electrical quantities such as voltage and current in energy storage VSG, while the conclusions can provide valuable references for protection strategy research in grid-forming scenarios.