Analytical Calculation Method and Influencing Factors Analysis for Short-Circuit Current of Grid-Forming Converters

Virtual synchronous generator control offers a practical grid-forming (GFM) solution for converter-rich power networks by enabling power-electronic units to reproduce selected electromechanical responses of conventional synchronous generation. Nevertheless, severe fault currents may arise when grid disturbances occur. A tractable analytical description is therefore required to reveal the temporal evolution of the converter current, identify the principal control-dependent variables, and support the design of effective overcurrent mitigation measures. A full-order model that retains every control loop, however, leads to a highly coupled nonlinear system and is not well suited to closed-form analysis. This study develops a reduced analytical framework for a grid-connected VSG equipped with virtual impedance-based current restriction under a balanced three-phase fault. A fault-specific circuit representation is first established to characterize the electrical interaction between the converter and the external network. The reactive power relation obtained from this representation is then introduced into the voltage-regulation dynamics, yielding a time-domain expression for the internal voltage magnitude. This result is subsequently embedded in the network current equation to obtain an explicit formulation of the phase current without assuming a constant internal voltage. The derived current response is separated into a sustained fundamental term, an exponentially attenuating DC offset, and an exponentially attenuating fundamental-frequency term. The effects of virtual impedance, retained grid voltage, reactive power–voltage integral gain, and transient decay constant are further examined. Comparisons with electromagnetic transient simulations under multiple disturbance levels and parameter configurations show that the proposed formulation captures the principal fault current characteristics and the corresponding parameter-dependent trends over the investigated operating conditions. The present formulation is restricted to balanced three-phase voltage-magnitude disturbances in an infinite-bus system with unity-power-factor pre-fault operation (Q_ref = 0) and fixed virtual impedance voltage-source operation. Its applicability has not been demonstrated for unbalanced faults, nonzero fault impedance, substantial grid-voltage phase jumps, nonzero pre-fault reactive power operation, active current limiting, or broader weak-grid conditions.