The GFCI Trip issue is definitely due to Current "Leaking" someplace in the Circuitry.

Since the Voltage is increased via an Autotransformer - as opposed to an Isolated Transformer, the Circuitry leaving the Transformer will also be "Monitored" by the GFCI Device - as will the Circuitry at the input side of the Transformer.

If the Transformer was an Isolated type (separate non-interconnected Primary and Secondary Windings), the GFCI Device will only "Monitor" the Circuitry which it is connected to - i.e.: the "Input" to the Transformer.

Since the OP's scenario uses an Autotransformer, all Currents flowing through the connected Equipment's Circuitry will flow through the GFCI Device (through the Device's CT).

Judging from the trip events:
after running a short time & particularly on spin-up
the trip issue may be One of the following:

A: VFD is shunting TV Surges via MOVs,
B: MOVs at the VFD are "Leaking" at an increasing rate during usage,
or,
C: Current is "Leaking" from One or more Windings - either at the Motor, at the Transformer, or both.

All Three of the above possible causes have a common link: Heat

I would bet the trip issue is related to an L-G connected Component at the VFD - most likely an MOV or other type of TVSS / SPD.

The GFCI Device is tripping due to an imbalance of Current flowing between the Ungrounded Conductor ("Hot"), and the Grounded Conductor ("Neutral"), as sensed via the Device's CT (Current Transformer).
Somewhere in the Circuitry, there is an L-G (or even an N-G) Leakage of Current.

The "Reverse Connection" of the Autotransformer will not cause an L-G Current Leak, and is not an Operating issue.
There should not be any L-G Current flowing "Directly" from the Autotransformer, unless a Winding Tap is directly Bonded to the Equipment Grounding Conductor.

If the trip issue turns out to be normal operation of the VFD's MOVs, the Autotransformer may need to be replaced with a Standard Isolated Transformer.

-- Scott (EE)


Scott " 35 " Thompson
Just Say NO To Green Eggs And Ham!