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An old fashioned inverter that produced a squarewave or modified "sinewave" used a huge iron core or toroid transformer. If you make one yourself then you would probably buy a few expensive transformers to find one that produces the correct output voltage that is not adjustable. A modern inverter produces a pure sinewave with high frequency PWM and the smaller high frequency transformer has a ferrite core. Simply adjusting its PWM adjusts the output voltage or its circuit can regulate the voltage.
A transformer made to step down mains voltage might have a 12VAC output at full load but produce 14V with no load. Then it is actually a 14V transformer whose output voltage drops tp 12V when loaded. If you use it in your 50Hz inverter then the output voltage will be much too low.
You are very unlikely to find an off the shelf transformer that will exactly suit your needs.
Getting a special custom transformer especially designed and would for you, will not be cheap, it will cost far more than an off the shelf transformer of similar size.
Only realistic solution is to buy a second hand transformer of the power level you want, and strip off the original secondary winding, (which hopefully is on top).
Then wind your new heavy duty low voltage primary on top of the existing 230v or 110v winding.
Its then pretty easy to add or remove perhaps one or two turns to get it working exactly right.
You should then end up with something that looks like this :
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