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Ungrounded Wye Unbalanced Detection Discussion (Page 2 of 3)

The polyphase analysis for an unbalance three phase, three wire system, where all three phases are unequal will take some math to determine the extent of unbalance.

For this ungrounded WYE connected bank (See Figure 2). Figure 2

We can look at polyphase circuit analysis to try to develop more user-friendly equations. However, before we attempt to simplify anything we need to do the math. The analysis can be shown in this case with , the following formulas were developed:

Appling Kirchhoff’s voltage law around each closed loop from Figure 1 we have the following

EBA - VN’A’ + VN’B’ = 0
EBC - VN’B’ + VN’C’ = 0
EAC - VN’C’ + VN’A’ = 0

Substituting

VN’A’ = IA’N’Z1, VN’B’ = IB’N’Z2, VN’C’ = IC’N’Z3,

Then We Have

EBA = IA’N’Z1-IB’N’Z2
ECB = IB’N’Z2-IC’N’Z3
EAC = IC’N’Z3-IA’N’Z1

The Current Law (Kirchhoff’s) at Node "N" will BE
IA’N’ + IB’N’ + IC’N’ = 0
IB’N’ = -IA’N’ - IC’N’

Substituting for IB’N’ We Get  Rewritten We Have Using Determinants  IA’N’ Appling Kirchhoff’s Voltage Law

EBA+EAC+ECB = 0 or, EBA+ECB = -EAC

Substituting EBA+ECB with -EAC
IA’N’ Or

IA’N’ IC’N’ IB’N’ Page 2 | Page 3