Transient Current Behavior and Analytical Expression Derivation for GFM Converters Under Grid Symmetric Faults

The calculation of transient current during threephase symmetrical short-circuit faults is essential for designing the overload capacity of grid-forming (GFM) inverters and coordinating relay protection strategies. Since transient current behavior is closely related to the power synchronization dynamics, this paper first derives the power angle trajectory by solving the active power control equation. The Unperturbed-Result-Based (URB) method is adopted to deal with the non-linearity of the power expression. With the simplified trajectory, an explicit analytical expression of transient current can be obtained after solving the circuit current differential equation. The Matching Degree (MD) between the simulation and analysis reaches higher than 95 %, validating the correctness of the expression. It is found that the damping coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$D$</tex> and inertial coefficient <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> have great impacts fault current response. The boundary of these two parameters is then quantitatively identified based on the maximum current the device can withstand. The above analysis and discussion are well-validated in simulation platform.