Wire sizing of a feed conductor is based on the amperage that a device draws. To calculate amperage from KVA a voltage of the supply has to be stated. Without this voltage and whether the transformer is single or three phase an answer can not be given.
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A 10 mm cable is most commonly used for a 500 KVA transformer, 240 volt, 3 phrase. The size of the wire that is used in a transformer is based on the voltage.
The size of grounding wire is based on the amperage output of the transformer. The voltage of the transformer needs to be stated. Without this voltage a calculation can not be made. Amps = Watts/Volts = 30000/?.
transformer action doesn't depend on power factor that is why we indicate its rating in KVA
The V stands for volts and A is amps. If for example you have a 12kVA device and are running off a voltage of 120 volts then Amps = 12000/120 = 100. You then use the calculated amps in a wire size table to get the correct size.
Sounds like the wrong size fuse protection was used. The transformer should be protected to its kva capacity.