Excitation Transformer Sizing

Can any one help me. I am preparing a calculation sheet for sizing an Exitation transformer, so far I have this

Generator Data:

Rated output: Sgn = 108 MVA

Rated voltage: Un = 13.8 kV

Rated frequency: f = 60 Hz

Rated speed: n = 276.9 rpm

Preliminary Assumed Excitation Data:

Excitation power: Pfn = 540 kW | 0.5% Sn

Rated excitation voltage: Ufn = 320 V | adopted value

Rated excitation current: Ifn = 1687.5 A | Pfn/Ufn

Maximum excitation voltage: Ufmax = 640 V | 2.0*Ufn

Maximum excitation current: Ifmax = 1856.3 A | 1.1*Ifn

Corresponding values on the ac-side:

Uac = 547.4 V | 1.05*1.1*[?/(3?2)]*Ufmax

Iac = 1515.6 A | ?(2/3)*Ifmax

S = 1436.9 kVA | ?3*Uac*Iac

Excitation Transformer

Rated output: Sn = 1500 kVA | adopted value

Rated voltage at LV side: Uac = 550 V | adopted value

Rated current at LV side: Iac = 1574.6 A | Sn/(?3*Uac)

Rated current at HV side: In = 62.8 A | Sn/(?3*Un)

Rated CT ratio at HV side: 100/5 A | adopted value

My question is if there is a method to calculate the Rated excitation voltage, normally this value is given by the manufacturer. But I need to know how they calculate this value.

Thanks