Transformer loss from %Z and X/R

[traj123]

Hi all,

Is it possible to calculate/ make an educated guess about iron and copper losses from the following information:

1) Transformer ratings: 20MVA (34.5kV -> 70kV)
2) %z = 10% impedance at base
3) X/R = 23

I need to make some preliminary assessments and I'm not a power systems engineer so I'm lost. Thanks for the help!!!

 

[magoo2]

You have Z and X/R, so this will give you the load (copper) loss.

Z^2 = R^2 + X^2

= R^2 [ 1 + (X/R)^2 ]

So, taking sqrt and rearranging, you get

R = Z / SQRT[ 1 + X/R)^2 ]

Now Z in ohms can be derived from your %Z and the base ohms.

Base ohms = kV^2 / MVA or 34.5 * 34.5 / 20 if you are looking at the 34.5 kV side

Zpu = 0.10

Z(ohms) = Zpu * Base ohms

Plug and chug


You won't be able to estimate the iron or core losses from what you've provided.

 

[prc]

You have to add 10-20% more to I2R to get load loss to take in to account the eddy loss in winding and stray losses in metal parts.

 

[AusLee]

Hi Magoo2,

From your equation, it seems that the whole result will change based on "if" the primary or secondary voltage is chosen.

What is the actual rule please?

Thanks.

 

[magoo2]

Hey AustLee

It depends on what you're using the results for. As you said, you'll get a different result if you base it on 34.6 kV than you will if you do it for 70 kV.

 

[dpc]

The losses (in watts) are the losses. If you're getting different losses when calculating from the primary side and secondary side, there is an error in the calculation method.

 

[magoo2]

DPC is correct. I was thinking in terms of base ohms and not losses. My mistake.

 

[AusLee]

Ok so what is the correct formula then, as the value of the losses in the above equation will vary depending on the voltage used

 

[davidbeach]

Losses don't changed when voltage changes. Z base changes when voltage changes, ohms change when voltage changes. Current changes when voltage changes. But losses are independent of which side "supplies" the losses.

 

[7anoter4]

I agree with prc if the X/R value is "calculated " and not measured. I think if it is measured –at the steady state [100% load] in the rated ambient, it has to include the eddy current and stray losses[ except iron core losses]. Usually the"R" losses are extracted from load losses and no-load losses.
As per IEC 60076-8 ch.7.2
"The test permits separation of the series impedance into a resistance, representing the load loss, and a reactance:
Z = R + jX "
As per IEC 60076-1
ch.10.4 Measurement of short-circuit impedance and load loss:
"the a.c. resistance derived from the load loss"