The manufacturing standards like NEMA MG1 do not define the starting current of Large Synchronous Motors. The manufacturer provides the “Code Letter” which means the kVA per HP demanded at starting with full voltage.
Expect around 5.7 kVA/HP (Code G) for a motor 4,500 HP. This will result in
25,600 kVA starting at full voltage.
For 4160 volts, I start = 25,600/(1.732*4.16) = 3560 amperes.
The synchronous reactance depend on the PF design (1.0 or 0.8)
Typical reactance values are: