Transformer Copper Losses pu calcs

[tiftif]

I have a delta/wye transformer. I want to get transformer pu copper losses.

The transformer is 60MVA, 25/13.8 y/d, Z% = 10%, X/R = 23.5

Zb = V2/S = 13.8*13.8/S = 13.8*13.8/60 = 3.174 ohms
Xactual = Zb*Zpu = 0.3174 ohms
R = X / (X/R) = 0.013506383 ohms
I = V/Z = 13.8/SQRT(3)/SQRT(0.013506383* 0.013506383 + 0.3174 * 0.3174) = 25.07948924 kA
Ploss = 3*I2*R = 25.48576593
Ploss pu = 25.48576593/60 = 0.42476 pu??

or
Zb = V2/S = 13.8*13.8/S = 13.8*13.8/60 = 3.174 ohms
Xactual = Zb*Zpu = 0.3174 ohms
R = X / (X/R) = 0.013506383 ohms
P = V2/R = 13.8*13.8/0.013506383 = 13 MW??
Ploss = 14/60 = 24%

This does not make any sense. Can you please advise?

 

[rcw retired EE]

The per unit copper loss will be based on the per unit current. It looks like you used a short circuit current instead of the base operating current.
60 MVA @ 13.8kV = 2510 amps = 1.0 per unit.

If your resistance calculations are correct P = I x I X R = 2,510A x 2,510A x 0.01350 ohms =85,089 Watts = 85kW
Per Unit = 85.089 kW / 60,000 kVA = 0.001418 per unit per phase. This would be for one winding, x 3 = 0.00425 per unit copper loss.

We get about the same answer using the 25 kV equivalent resistance and current.

While that number may be in the ball park, there are some inaccuracies due to: resistance changes with temperature, allocation of the resistance between the 25 kV "Y" winding and the 13.8kV delta winding and other effects. If you need to get accurate data, look at the factory test report that should show the measured load losses adjusted for operating temperature.

Or you could just use per unit. Zpu= 0.1 = sqrt(R^2 + X^2), and X/R = 23.5. X=23.5R.
Substituting for X: 0.1^2 = R^2 + (23.5 R)^2 = R^2 (23.5^2 + 1). Solving for R = sqrt (0.1^2 / (23.5^2 +1) = .00425.

I*I*R = 1.0 x 1.0 x .00425 = 0.00425 per unit copper loss.