Nice thing about these 23V608 isolation transformers is they have two separate 120 vac primaries and two separate 120vac secondary windings so you can create a lot of different options.
You can wire an isolation transformer as an auto-transformer and get twice the VA capability of full isolation wiring. Just have to get the wiring phasing correct when you wire it for autotransformer.
I've been pondering that.
Certainly you have enough core for 2x the VA. Likely the windings can carry only enough current for half the VA rating of transformer to couple from one secondary winding to the other. Auto-transformer only has to convert half your power, so it can support a 120V load of 1x the VA rating of the transformer.
The way it works with an auto-transformer is that half the VA is coupled magnetically from one 120V winding to the other, and half the VA is current conducted through one 120V winding.
Make sure the neutral connection to the (two) 120V windings can carry 2x the current you're putting it each of L1, L2. It will be exactly the current your 120V load is drawing. One easy way to do this is with four wires, two for one 120V winding to L1, N and two for the other 120V winding to N, L2.
Often, full isolation transformers have a slight turns ratio difference between primary and secondary to make up for transformer losses in output voltage under moderate load. This is minor and typical no more than 2% increase in no-load output voltage compared to input voltage.
Which should work fine in the intended direction of conversion from primary to secondary.
The two 120V secondaries will be identical, which is as good as you can get for 240V isolated in, 120 series with 120 for 120/240V out.
If always stepping down from 240V to 120V, or always stepping up from 120V to 240V, you'll always have a bit of voltage sag. That's where you might prefer to start with +2% voltage no-load, sagging to -2% under full load. Instead, you'll get 0% sag no-load to -4% full load. Not a problem with an inverter delivering rock solid 120Vrms, so long as you don't also have excessively long skinny wires.
I haven't run into a situation of an inverter complaining about powering up a transformer yet, but about my only first-hand experience is 5000W Sunny Island feeding a 9kVA toroid as auto-transformer.
This issue is that a transformer with a winding intended for say 120V, has enough inductance to keep current extremely low (< 1% of rated current) for 1/2 cycle of AC without "saturating". Then polarity reverses, and it again blocks current flow.
When power is removed, leaving the core magnetized to some degree, next time power is reapplied it may magnetize core further in same direction, or demagnetize in opposite direction.
If it gets hit twice in the same direction (positive going cycle just before turn-off, another positive going cycle when turned back on), the core can saturate and cease acting like a big inductor. Instead, only winding resistance limits current to about 10x to 50x nominal.
I'm testing this at work right now. I got 70A peak current through a 12Arms transformer (that's only about 4x or 5x peak.)
One transformer manufacturer recommended using the outer layer winding as the driven one, rather than inner layer. That has more leakage inductance to the air, so saturation of core has less effect.
I would expect cheap undersized transformers to be more of a problem. Also cheap marginally designed inverters.
If you buy an isolation transformer with 2x 240V primary windings and 2x 120V secondary windings, and if each 240V winding can handle the current you want, you can make an auto-transformer that should never saturate.
Connect the two 240V windings in series, 240V + 240V = 240/480V split-phase. Now feed the outer L1 & L2 with your 240V inverter and have center tap as neutral (bonded to ground for an off-grid system; can't help you with autotransformer on a grid-tied system.)
Because you're using a 240V winding for 120V, it has 100% margin and should never be driven into saturation.
Brute force and big iron wins.
I don't expect anyone who isn't a magnetics guy to understand this. I'm just learning it. But avoiding the problem is necessary to prevent tripping of circuit breakers or causing inverter to shut down.
en.wikipedia.org