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Snowjob:
You need to find out if the specified voltage ratio is the turns ratio.
Apply 120 V to the 600 volt input. If on the 240 winding you get close to 120* 240 / 600 = 48 V, then the turns ratio equals the voltage ratio. Simultaneously measure both the input voltage and output voltage with accurate meters. If line voltage is not jumping around you can use one meter.
If the no-load output voltage is more like 50.4 V for 120 V input, then the number of secondary turns have been selected to compensate for voltage drop from full load current. I assumed 5% here.
If this transformer with the extra turns on the original secondary is run backwards from 240, then the no load output voltage would be about 5% low, and when operated at full load about 10% low.
You may need to consider the VA rating will be somewhat less when run in the reverse direction. If the transformer will be run at 75% of original rating you should be OK. As an estimate use 15 * 540/600 = 13.5 KVA.
Another view. The original primary current allowed based on the KVA rating is 15,000 / 600 = 25 A. This same maximum current would be allowed in the reversed direction. On that basis the transformer rating would be 540 * 25 = 13.5 KVA.
The normal transformer connection would allow 15,000 /20 = 62.5 A on the secondary. But you can not run it this hard in the reverse direction because of the original primary and which is now the secondary limitation of 25 A. The turns ratio for 5% correction is 600 / (240 * 1.05) = 2.301. Thus the new maximum primary current is 25 * 2.301 = 57.5 A instead of 62.5 A.
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