Transformer Impedance Calculation from Test Data

[Tinh123]

Hi,

I'm trying to determine the appropriate way to represent 3-winding Delta transformer to its equivalent Wye representation. The given data were: Primary : Secondary voltages, its MVA rating, MW loss, and %Z. I saw an old note in the past which indicates the calculated resistance as %R = MW loss * 100 / rated MVA. I didn't see any logic in this resistance calculation. If you have any links or advices to the above subject, please let me know. Thanks.

 

[magoo2]

The formula you gave is more understandable if you write it as:
%R = I^2 R * 100 / (I^2 Z)

I^2 * R = the resistive losses

I^2 * Z = MVA rating

Expressing the losses as a % of the MVA rating is what the formula does. It is common to all transformers - be they 2 winding, 3 winding or more.

A test report should give you the %Z between pairs of windings. With a 3 winding transformer, let's call the terminals H, L and T (high, low and tertiary).

Get 3 values from test report:
Z_H-L = impedance between H and L
Z_H-T = impedance between H and T
Z_L-T = impedance between L and T


Z_H = 1/2 (Z_H-L + Z_H-T - Z_L-T)

Z_L = 1/2 (Z_H-L + Z_L-T - Z_H-T)

Z_H = 1/2 (Z_H-T + Z_L-T - Z_H-L)

Looks better if you can use subscripts, but this should give you what you want. These impedances, Z_H, Z_L and Z_T are the wye equivalent values.

 

[Tinh123]

Magoo2,

Truly appreciate for your help. Have a great day.

 

[Tinh123]

One more question. What is the difference between the above Delta-Wye conversion and that of the typical formula: Z_H = (Z_H-L * Z_H-T)/ Z_sum, where Z_sum = Z_H-L + Z_H-T + Z_L-T ? I'm trying to facilitate the equations above with full representation of Z = R + jX and compare with the one you gave, but have a tough time of seeing the corresponding relationship. Thanks for any help.