I have a 112.5 KVA transformer that is usually grid fed; but when Reddy Kilowatt goes off on a bender, we will loadshed down to his skivvies, and use 15KW of SMA Sunny Island inverters, with an intermittent generator as well.
The SI's are limited to 8500W for less than one minute, I think. They'll just trip off or smoke trying to get past the inrush spec of the xfmr.
I consulted a transformer designer friend with long experience on both large and small transformers [audio signal to MW ferroresonant size]. He reminded me that the inrush is only for ~4 cycles, until the residual flux is back in tune with the feed. So an obvious approach is series resistance to limit the current until the shunting contactor closes. That looks much like a ....resistance type reduced voltage starter.....
I've looked at various solid-state starters, and have several fears the guru shares. One is, I bet they use zero-crossing detection for timing, and may have an issue with the faux-sinewave of any inverter [1]. Secondly, I can't see how they limit the instantaneous peaks; keeping the RMS down is not hard, but do they somehow turn off during a halfcycle if the current goes out of bounds?
One issue is: the starting current needed is actually less than running; I must be able to start off the inverters, but the generator will come up as needed.
I'm not sure how autoformers will react under these conditions.
I'm also looking at TSD's, which seem to be big in the EU. No idea if we could use a EU-approved device in sunny Califuuny.
1] A friend designs another zero-crossing detection device. At one cement kiln, the VFD for a multi-thousand HP mixer motor bit such big pieces out of the plant grid that they'd not turn on/off correctly; with the results the boards would literally blow traces across the cabinet....not pretty. But it only happened at some speeds.....took many trips to find.