Much appreciated
@Zach Stone P.E.
I am still wondering why the per unit equation cannot be used here.
If I am understanding your question correctly, then the answer is because when we use percent impedance (Z%) to calculate the impedance of the transformer on either the primary or secondary side, the resulting impedance value is the total referred impedance which is the sum of the impedance already on that side of the transformer, with the impedance that was referred from the other side.
In other words, if you use the percent impedance (Z%) and the base impedance of the transformer to solve for say, the total primary referred impedance (Z1_total), then you are calculating Z1_total = Z1 + a²·Z2, not just the secondary impedance referred to the primary (Z2' = a²·Z2).
For example:
The referred impedance formula is used to calculate the total impedance referred to either primary or secondary.
However, the
total referred impedance is the sum of impedance that is already on that side of the transformer, along with the impedance that is being referred.
The
total impedance referred to primary is the sum of the primary impedance (Z1), and the secondary impedance referred to primary (Z2' = a²·Z2):
Z1_total = Z1 + a²·Z2
The
total impedance referred to secondary is the sum of the secondary impedance (Z2), and the primary impedance referred to secondary (Z1' = Z1/a²):
Z2_total = Z2 + Z1/a²
If we compare this relationship to calculating the impedance of a transformer using the per unit impedance (also known as the percent impedance) with the base impedance (Zb1 or Zb2), then we can calculate the total impedance referred to primary (Z1_total) or the total impedance referred to secondary (Z2_total).
For example, let's say a three-phase transformer has a volt-amp power rating of S, a three-phase voltage ratio of V1:V2, and a percent impedance of Z%.
The base impedance on the primary side of the transformer is equal to:
Zb1 = V1²/S
and the
total impedance referred to primary can be calculated as:
Z1_total = Z%·Zb1
This value is the same as Z1_total = Z1 + a²·Z2
Similarly, the base impedance on the secondary side of the transformer is equal to:
Zb2 = V2²/S
and the total impedance referred to secondary can be calculated as:
Z2_total = Z%·Zb2
This value is the same as Z2_total = Z2 + Z1/a²
It is the sum of two terms (Z1 and a²·Z2, or Z2 and Z1/a²) not just a single term.
