Abstract:
Grid-impedance steps can induce multi-time-scale transient current surges in grid-forming virtual synchronous generator (VSG) systems, thereby challenging the safe operation of renewable-energy converters. This paper establishes a three-time-scale transient analysis framework to systematically reveal the physical mechanism underlying the impedance-mutation-induced current surge. The central finding is that the surge originates from a mismatch between the step change of the controlled plant and the continuity of the control variables. In the electromagnetic transient stage, inductive flux-linkage conservation forces each phase current to jump instantaneously by the reactance ratio, producing the initial surge peak. Although the proportional channel of the current inner loop rapidly suppresses the post-jump mismatch and restores the sinusoidal trajectory, the voltage outer loop and the active-power frequency loop lag behind due to their time constants being much larger than the peak window; the fundamental of the modulation voltage therefore retains its pre-mutation value, and this legacy voltage, applied to the reduced reactance, generates the dominant transient current peak. Building on this mechanism, the suppression effect of virtual inductance on current surges is investigated. Considering bidirectional grid-strength variations, a lower-bound constraint and an upper-bound constraint on the virtual inductance are derived for grid-strengthening and grid-weakening scenarios, respectively. Results show that the strong-grid constraint is governed by overcurrent suppression requirements, whereas the weak-grid constraint is dictated by power transfer capability and power-angle stability margins. The findings offer a theoretical foundation for the engineering design of VSG virtual impedance and over-current protection strategies in renewable energy generation equipment.