Ok, an inductor is a coil of wire around a piece of iron or similar material that can store a magnetic field. This magnetic field acts to resist changes in the rate of electron flow, aka current.
Why does an AC GFCI trip? All I can visualize is, when the AC signal shifts high and the electrons “surge forward”, the inductor slows them down so they don’t “push” as hard to shove the electrons ahead of them into the other side of the GFCI (the neutral wire). (when AC goes low the same happens in reverse) This leads to a detected imbalance in current between the AC high wire and neutral and the GFCI goes off.
Inductors don’t actually store electrons, they just resist changes in their flow.
Is this what’s really happening? Circuit classes in a state school, they were obsessed about making you solve the various equations by hand. The labs are obsessed with making your lab report be formatted correctly. I don’t have a good intuitive explanation of why some of these happen, which is what I need more in the field than anything else.
Online calculators and discrete circuit solvers are far more useful than integrating circuits with symbolic math - I’d go so far as to say that the integration methods and the various circuits they forced us to solve for all the nodes using KCL/KVL was worthless - I’ll never use those methods for the rest of my days. (Spice is more accurate and can handle time varying circuits)
I suspect you are overthinking the problem.
Inductors cause temporary high inrush currents due to magnetization.
This high current might put the differential transformer in the GFCI out of it’s linear operation area, or might expose any slight imbalance in the two coils of the transformer, resulting in nuisance tripping.
A GFCI uses a differential transformer to measure the difference in current between the hot wire and the neutral wire. If, for example, the hot wire has a current of 2.38723 A at an instant in time, and the neutral wire has a current of 2.38721 A at the same instant in time, the differential transformer will measure 20 μA (and not trip). If the hot wire has a current of 2.389 A, and the neutral wire has a current of 2.381 A, the differential transformer will measure 8 mA (and trip). A GFCI will trip when it detects a difference in current of around 5 mA.
For a properly-functioning load, the difference in current between the hot and neutral wires is very very small… on the order of μA or even nA. The reactance of the load does not matter; for a properly-functioning load, the magnitude of the current in the hot wire will be the same (or nearly the same) as the current in the neutral wire regardless of how “inductive” or “capacitive” the load is.
So back to your question: I do not know why a GFCI would falsely trip due to an “overly-inductive” load. I am wondering if something else is going on. I am wondering if some large motors have poor isolation to ground, and thus the GFCI trips (as it should).
And here’s something else to think about: an appliance can be designed to have very good isolation from ground for DC (e.g. 1 GΩ) but not for AC @ 60Hz due to capacitance to ground.