Smart$, this was really well done, but I don't think that it works. In post 66 you mention that the accuracy depends on the "values adding to zero." While this should be true for the line currents Ia+Ib+Ic=0, using the triangle centroid also means that is necessarily true for the phase currents too Iab+Ibc+Ica=0. I don't believe that this should be the case.
For instance, imagine a 208V, 3ph system with phase voltages of Vab=208<-60, Vbc=208<180 and Vca=208<60. If you connect a 2080W (resistive) load between A-B and a 1560W (resistive) load between B-C, and connect no load between C-A, then you would have phase currents of Iab=10<-60 and Ibc=7.5<180 and Ica=0
We know that Ia=Iab-Ica (etc) so, Ia=10<0, Ib=15.2<145.3 and Ic=7.5<0. If you add Ia+Ib+Ic, you will find that the sum is zero. However, if you add Iab+Ibc+Ica, you will find that the sum is 9<-106.1
If you took the line vectors and graphed them, and then used the centroid lines for the phase currents, you'd have a value for Ica which was not zero. But in the example, there is no load between C-A, so Ica must be zero. I don't think the triangle centroid method will provide the correct phase currents in all cases.
I agree, except that Ia=10<-60.
If you take Ia = 10, Ib = 15.21, and Ic = 7.5 and put it in Smart's equations, you get:
Iab = 8.21, Ibc = 7.26, Ica = 3
Clearly incorrect.
If you use symmetrical components to back-calculate the delta load currents, assuming no zero-sequence delta load current you get
IL0 = 0, IL1 = 10.1<-90?, IL2 = 5.2<16.1?
ID0 = 0, ID1 = 5.83<-60?, ID2 = 3<-13.9?
IAB = 8.21<-44.7?, IBC = 7.26<156.59?, ICA = 3<73.9?
Also, clearly incorrect. The intuitive assumption that there is no zero-sequence delta load current is incorrect. With the actual starting delta load currents, the sequence currents are:
ID0 = 3<-106.1?, ID1 = 5.83<-60?, ID2 = 3<-13.9?
I say intuitive assumption because I was thinking of the zero-sequence currents circulating in the delta and with one leg open, they can't circulate. My mistake. The zero-sequence currents can flow through the open leg because they are offset by the positive- and negative-sequence currents. The zero-sequence network does not have an open leg.
So where does that leave us in seeking a solution?