Can you explain? I don't see it. I see this:

.. an infinite parallel load, that would be just as damaging to the transformer and everything else in the circuit. But I don't see 1kV across the variac.

I have to admit I don't see it either being as the physics are concerned the variac is only ever going to have to work with the voltage span between the two ends of its winding. All other voltage references are purely secondary and external to the variac and not of any concern to it voltage wise. As long as the working currents are not above its capable limits for excessive amounts of time I don't see how or where any issues with overheating could happen.

The way I see it if the variac was rated for 10 amps and was set at exactly its center point and a 10 amp load was applied each end of the variac will only be carrying ~5 amps which would be well below its 10 amp continuous duty working limit due to the simple autotransformer effect it uses.
Given that to be honest with a 10 amp rating there is no point in any output setting where there would be more than 10 amps flowing through either end of its windings unless the moving tap was all the way at the end which would then in effect be totally bypassing all of the windings.

Fusing wise any overload that would be sufficiently high enough to damage the triac will be way beyond the the capacity of the main transformer and its related input circuit fusing.

I say go with it and make sure that the variac assy as a whole has sufficient ground plane isolation and leave it at that.

 

what you actually need is a large variable frequency drive. most are adjustable to output voltage, if you dont want to use a variac or other adjustable transformer.

That's plan A. This variac thing is plan B.
The 3kV transformer primary is fed by a VFD already. That's one of the other things I'm looking into; how to make the VFD compensate for voltage drop.
There's no encoder on the motor, and I don't know if flux vector can "see through" a sine filter and a transformer. I don't even know what mode the VFD is in, but I suspect V/Hz is the only thing it could be.
More investigation is due here.

I suspect I can use voltage drop as an analog input to the VFD assigned to voltage boost %.
I should be able use one of these 0-3600Vrms -> 4-20mA signal conditioners, compare to drive o/p voltage setpoint, adjust if necessary. Could be done in the PLC or in the drive (if it's smart enough, I don't know enough about this brand of drive yet).

 

If the output is shorted to ground then there will be ≈1000V from the top of the Variac to the wiper point on the Variac winding

but there will be 900V from the bottom of the variac pushing back against the 1020V, same as when it's not shorted. So in my mind, still only 120V across the variac.
...assuming the output isn't pulled all the way to ground by the short circuit.

 

variacs are not insulated for those voltage levels. just put the variac into the primary.

The variac knob is usually a pretty big chunk of Bakelite - but you'd want to plug/insulate the holes where the grub screws go in to grip the spindle!

 

but there will be 900V from the bottom of the variac pushing back against the 1020V, same as when it's not shorted. So in my mind, still only 120V across the variac.
...assuming the output isn't pulled all the way to ground by the short circuit.

My assumption was that a short will pull the output to ground, leaving 1000V across the top of the winding to the wiper position.

Why did you assume the output wouldn't go all the way to ground?

 

Just calculate your relative impedances of the main transformer Vs the variac being attached to the top 10% of the windings where in a hard short both the 1020 volt and the 900 volt tap would be feeding the variac from opposite ends simultaneously. .

Some basic math should show the primary of the main transformer would be supporting a huge current overload whereas the in comparison the variac being fed from both its own ends simultaneously (thus phase canceling out much of its own impedance) leaving its relatively low winding resistances (going from each end to the tap point) to create its relative voltage drop during the hard short is not.

Basically in a hard short the impedance and power losses of the variac will be trivial due to most of its impedance being canceled out compared to what the main transformer windings are dealing plus on top of that the whole short circuit load has to be carried all the way back to the 480 volt primary input windings of the main transformer which should have the properly sized and rated fuses or circuit breakers to shut the whole system down when such a short occurs.

 

The variac knob is usually a pretty big chunk of Bakelite - but you'd want to plug/insulate the holes where the grub screws go in to grip the spindle!

Better yet, use a insulated shaft coupler like one of these:
https://www.surplussales.com/ShaftHardware/ShaftH-10.html
Being paranoid, I would put a plastic shaft between the coupler and the knob.

... or a metal shaft coupler like this with an insulated shaft between the coupler and the knob.
https://www.servocity.com/html/set_screw_shaft_couplers.html

 

Ideally this wouldn't even be hand operated; it would be motorized controlled by a PLC output for automatic voltage regulation.

Even more ideally there won't even be a variac, and the VFD will do the AVR.

 

Let us know how this works out. This is an interesting puzzle for which I have no answer.

 

Edit

 

If using the smaller variac at the business end, one could add a servo so that the device "auto balances", reducing human error and even adjusting for variation in voltage drop due to increased load. It would also mitigate against having burnt flesh.

Edit
Hmmm, I should have read the whole post! Doh!