The vast majority of variable frequency drives (VFDs) are the "voltage-source inverter" (VSI) type with a diode front-end. These non-regenerative VSI-type VFDs, do not contribute to upstream fault current as the input diodes block any current that might flow from the dc bus to the mains.
For regenerative VSI VFDs, the actual front-end regenerative circuit can be either transistors (IGBT, etc.) or thyristors. The VFD controls will respond very quickly. The controls will sense either a loss-of-voltage or an increase in current. Either one will cause the VFD to turn-off very quickly, on the order of micro-seconds for a transistor to sub-cycle for a thyristor. If possible, get the actual values and duration from the VFD manufacturer.
There are still many older "current-source inverter" (CSI) type VFDs that are still in operation that use thyristors in the front-end. Though these CSI-type VFDs are inherently regenerative, they do not contribute to upstream fault current as the large dc link inductor keeps the current close to pre-fault levels. In addition, the CSI's controls will turn the appropriate thyristors off or on to internally circulate the VFDs dc link current to keep it out of the mains (actual implementation will vary with manufacturer) and to keep an interruption of dc link current from damaging the thyristors.
Determine the types of VFDs that will be part of your SC study. If they are the CSI-type VFD or the basic non-regenerative VSI-type VFD, then they do not have a SC contribution. If it's a regenerative type of VSI VFD, then include it in the study at the appropriate SC level and duration.