As a younger one in electronics, I want to know from the top engineers int his EDABoard, how I can calculate the capacity of my IGBT/MOSFET switch in my Inverter designs.
1 & 2 - Are the Mosfets for the primary or secondary? If the later, my experience tells me you should use an IGBT, but read further:
As you know BJT's are not known to have nice current sharing characteristics.
An IGBT is a transistor controlled with a mosfet, for convenience and simplicity, therefore the same principle applies. You can get around this using colector sharing resistors, but this is not desirable due to additional power losses. There are however, many decent "brick" power modules capable of several amperes. The actual rating will be not less that 2x your maximum output current. So if you expect 15A output the device must be rated 30Amp or higher.
Is this for a production run or one off unit?
If this is a one off get yourself an intelligent power modules. These devices have the IGBT's, drivers and fault protection circuitry already built in and therefore the extra you pay is assured as reliability. Unless you ignore the fault signals the device should be virtually indestructible. Snubber design is also greatly simplified. I assume you know and will implement them on your design.
If this is for the low side, mosfets are the best option, again for this outputs I would advise to use a brick module, rather than small individual devices. The later can be done, but experience tells me it is not worth the effort. You can either choose to trust my experience or learn by yourself. You also want to use 100V devices, due to the lower RDS(on).
3. No. Unless your load is purely restive. Reactive loads, loads without power factor correction, etc., they all reduce the output capability. Your output will be 3600VA, assuming no filtering, etc. If unsure, look at the ratings of any computer UPS and use them as reference.
4. Assuming 24V.
No. Your load will be nearer to 200A RMS. Power devices losses, transformer losses, battery sag, wiring drops, etc. All these account significant power losses. Hardly a DIY design can get better than 70% efficiency, with mainstream commercial devices on the low 80's and high quality custom designed (expensive) sine wave inverters in the low 90's. You also need to account no load losses on the transformer. Using a thyroidal transformer will largely reduce these, but prepare the wallet.
Another option is to use a small High frequency transformer. These are somewhere in between the above, however extra losses exist due to high switching frequencies and the need to reconvert the primary from HVAC to HVDC and modulate/filter this back into a 50Hz square/sine wave.
4. Read answer 4 and 5. With that in mind the output does increase , but a different transformer, rated to 48V (and not 24) must be used, otherwise core saturation will occur