Wye-Delta, Delta-Wye Transfomers

Location
Colorado
Occupation
Engineer
Source to transformer stepped-up from 480/277V to 13.2 kV wye - delta (corner grounded). Then stepped down via delta (corner grounded) to wye (grounded) from 13.2 kV back to 480 V. The load is about 630 kVA and .9 pf. I only have line currents on the load (wye) side of A = 200, B = 16, and C=190 A, I need the neutral current on both wye sides and the line currents traced back to the source. This is a problem I have been working on (purely for myself).
 

wwhitney

Senior Member
Location
Berkeley, CA
Occupation
Retired
The load is about 630 kVA and .9 pf.
What exactly do you mean by the a 0.9 power factor? In the context of single phase, or balanced 3 phase, the meaning is clear. But with unbalanced 3 phase, each line current could have a different phase shift.

I only have line currents on the load (wye) side of A = 200, B = 16, and C=190 A, I need the neutral current on both wye sides and the line currents traced back to the source.
I don't see how those currents can square with your voltages of 480Y/277V and 13,200V delta and the load figure of 630 kVA. For a balanced loading (just for comparison and order of magnitude), that 630 kVA would be 758A at 480Y/277V or 28A at 13,200V delta.

Anyway, given the magnitudes of the 3 line currents on a wye, you can't calculate the neutral current unless you also know the relative phase shifts of those 3 line currents.

For example, say you know the phase shifts are all pairwise 120 degrees. Call the A current 0 degrees and the B current 120 degrees. Then in vector form the A current is (200,0); the B current is (16 cos 120, 16 sin 120); and the C current is (190 cos 240, 190 sin 240). The sum of the 3 vectors is (97, -151). That's the negative of the neutral current, so its magnitude is sqrt(972+1512[/sup) = 179A.

Alternatively, suppose the 3 line current were all in phase (perhaps very unlikely, as that would mean one of the current represents power flowing away from the load). Then the neutral current would be the simple sum of the magnitudes of the line currents, or 406A.

Lastly, suppose the B and C line currents are 180 degrees out of phase from the A line current. Then the neutral current would have magnitude |200-16-190| = 6A.

These last two cases are the two extremes--all you can say with mathematical certainty without relative phase shift information on the line currents is that the neutral current will be somewhere between 6A and 406A.

Cheers, Wayne
 
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