Excitation Transformer

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They are different because there are major differences in the power demands between the two systems. In a brushless excitation system the power required for the main field is provided by the prime mover, while in a static excitation system the DC power is produced by stationary (hence the name "static") power components that feed DC through brushes directly to the main field.

How is excitation transformer rating determined? (both in case of static excitation and brushless excitation?)

Regs,

Like any other transformer, by determining the total current drawn by the connected circuit. For brushless the bulk of the power goes into the control field(s) of the PMG (Permanent Magnet Generator), whose output gets rectified and applied directly to the main field. For static the output goes directly into the field so the input rating of the transformer is basically equal to the power consumed by the main field, plus losses. In either case the control electronics and AVR (Automatic Voltage Regulator) are electronic and take a very small percentage of the transformer's rating.

but why is the kVA rating of excitation transformer larger in case of static excitation than the kVA rating in case of brushless excitation?

eg For a generator of 13000 kVA, 428 rpm, what will be the excitation transformer kVA rating?

Regs,

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Hint: It will be vastly different between scenarios. When all else fails, contact the vendor.

It seem that you are getting confused between excitation power requirements and excitation transformer rating. There is no excitation transformer in Brush-less excitation system. It is there only in static excitation system where a part of generator output power is stepped down and after rectification fed in excitation circuit (with necessary control circuit). In brush-less excitation system as stated in other reply, excitation power is developed by coupled exciter mounted on the generator shaft system.

Excitation power requirement of the generator (with same rating) does not change with change of excitation system. What changes with excitation system is excitation current and excitation voltage requirement. Power practically remain same.