Ungrounded Wye Unbalance Detection Discussion
Section 1 | Section 2 | Section 3 | Library Index

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).

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:

E_BA - V_N’A’ + V_N’B’ = 0

E_BC - V_N’B’ + V_N’C’ = 0

E_AC - V_N’C’ + V_N’A’ = 0

Substituting

V_N’A’ = I_A’N’Z₁, V_N’B’ = I_B’N’Z₂, V_N’C’ = I_C’N’Z₃,

Then we have

E_BA = I_A’N’Z₁-I_B’N’Z₂

E_CB = I_B’N’Z₂-I_C’N’Z₃

E_AC = I_C’N’Z₃-I_A’N’Z₁

The current law (Kirchhoff’s) at node N’ will be

I_A’N’ + I_B’N’ + I_C’N’ = 0

I_B’N’ = -I_A’N’ - I_C’N’

Substituting for I_B’N’ we get

Rewritten we have

Using determinants

=

I_A’N’=

Appling Kirchhoff’s voltage law

E_BA+E_AC+E_CB = 0 or, E_BA+E_CB = -E_AC

Substituting E_BA+E_CB with -E_AC

I_A’N’=

or

I_A’N’=

I_C’N’=

I_B’N’=