Whoops, I missed that this was a _delta_ system with a center tap.

Dnk, The equation that you were using, and which I said was 'spot on', applies when you have a 120 degree phase angle to phases A,B, and C around the neutral. If the power factors deviate at all from being the same, so that the current flows are no longer 120 degrees out of phase, then the equation no longer applies.

Remember that voltage is always measured relative to some reference zero. If you pick a different reference point, then you will measure _different_ voltages. No matter which reference point you select, if you do all of the math and calculate the total work involved to move an electron from on point to another, the overall result will come out the same, but some of the numbers in the middle will look different.

Generally we use the grounded transformer terminal as our reference zero. But remember the discussions of corner grounded delta systems; _any_ transformer terminal could be grounded, and any transformer terminal could be our reference zero for calculations.

From the 'point of view' of the center tap in the delta system, phases A and C _are_ 180 degrees out of phase. If we created a virtual neutral (say by using a zig-zag transformer) and used that virtual neutral as our reference zero, then phases A and C would be 120 degrees out of phase. If we picked phase B as our reference zero, then phases A and C are only 60 degrees out of phase.

It probably makes the most sense to pick the center tap as the voltage reference zero. *grin*

I am going to assume that all of the loads are resistive, just to go through the calculation. This is almost certainly an incorrect assumption; there are probably motors in that three phase load. But if you know the power factors for the various loads, then you can adjust the phase angles for the individual current flows appropriately.

In my calculations below, I calculate the current flowing _into_ each terminal. This gives a current phase angle that is approximately 180 degrees out of phase with the voltage phase angle of that terminal. It is interesting to note that even with the assumption of resistive loads, the current flowing from each terminal is not quite in phase with the voltage at each terminal. An unbalanced three phase resistive load does not have unity power factor.

I am also assuming a total KVA of 315; 240KVA of 3 phase load plus 75KVA of single phase load. You will get different numbers if you read the question differently.

Finally, in my calculations below, the loads are very carefully double counted, because I count the current from phase C to phase A and again as the current from phase A to C. This is compensated by the phase angle calculations; as a check, take the sum of all phase currents times 240/root(3) and you will get roughly the same total VA as the sum of the original specifications.

I will select the voltage measured from phase A to the Grounded center tap as the phase reference zero.
This gives us the following voltage phase angles for the single phase loads:
A to G 0 degrees 120V
G to A 180 degrees 120V
C to G 180 degrees 120V
G to C 0 degrees 120V

For the three phase loads, we assume that 80 KVA is connected between each pair A-B, B-C, C-A, so we need the three phase angles:
A to C 0 degrees 240V
C to B 120 degrees 240V
B to A 240 degrees 240V
A to B 60 degrees 240V
B to C 300 degrees 240V
C to A 180 degrees 240V

First the neutral current:
Our A to G load is 34 KVA at 120V, so 283.33A at 0 degrees
Our C to G load is 41 KVA at 120V, so 341.67A at 180 degrees
283.33A at 0 plus 341.67A at 180 gives
58.33A at 180 degrees

Now the phase A current:
Our G to A current is 283.33A at 180 degrees (just the opposite of the A to G current)
Our B to A load is 80 KVA at 240V, so 333.33A at 240 degrees
Our C to A load is 333.33A at 180 degrees
Now we add up 283.33 at 180 degrees with 333.33 at 240 degrees and 333.33 at 180 gives
834.83A at 200 degrees

Phase B current:
Our G to B current is 0
Our A to B current is 333.33A at 60 degrees
Our C to B current is 333.33A at 120 degrees
gives 577.35A at 90 degrees

Phase C current
G to C is 341.67A at 0 degrees
A to C is 333.33A at 0 degrees
B to C is 333.33A at 300 degrees
gives 889.8A at 341 degrees

I'll leave selection of OCPD and conductor size for someone else [Linked Image]

-Jon