Except that it means you will have the problems that you are having with the voltage. If your primary is corner-grounded, then I bet your secondary is not grounded, which presents a real hazard to personnel. There may not be enough short-circuit current to trip a breaker on the secondary. Another problem is that the secondary voltages-to-ground are now "floating" and may jump around....there is nothing wrong with having a corner grounded 480 volt system.
In my opinion grounded delta 480 volt power systems present real safety hazards and should be prohibited. One phase is already shorted to ground. When a second phase faults, then there is a phase-to-phase fault, much more severe than the normal fault-to-ground. Phase-to-phase faults usually result in something getting burned up.
There is the case of an outside contractor coming in for a job. "Better check the voltage to make sure this circuit is off, Joe". "Moe, I checked to phase C and it shows 0 volts, so the main breaker must be off." Joe then sticks his hand in a box and gets fried.
I must have missed the requirement for a corner-grounded Delta primary. Would you kindly point me to the NEC Article that requires that grounding method? I do not find that requirement in either Article 250 (Grounding) or 450 (Transformers).According to NEC the 480 must be grounded either corner or with a center tapped phase (which gives 240/480) and the secondary must also be grounded (in this case wye) to give me 120 / 208.
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