Efficiency Calculation of 10-kVA Transformer at 0.85 Power Factor Lagging

[graygoh]

Homework Statement

A 10-kVA, 200:400 V transformer gave these test results:
open circuit (LV winding supplied): 200V, 3.2A, 450W
short circuit (HV winding supplied) : 38 V, 25A, 600W
calculate the efficiency when the transformer delivers its rated kVA at 0.85 power factor lagging

Homework Equations

efficiency = output power / input power

The Attempt at a Solution

I totally don't know how to start. help pls. thanks

 

[cnh1995]

open circuit (LV winding supplied): 200V, 3.2A, 450W

This gives the core loss of the transformer.
P_i=450W

short circuit (HV winding supplied) : 38 V, 25A, 600W

This gives the copper loss of the transformer at full load.
P_cu=600W
Iron loss is fixed loss and doesn't depend on the load. Copper loss varies proportional to the square of the current. In general, copper loss=x²P_cu, where x is the fraction of full load with which the transformer is loaded. Since the transformer is operated at full load, x=1 and the losses will be,
P=P_i+P_cu
=450+600=1.050kW.
Efficiency η= Output power/input power
=Output kW/(Output kW+losses)
∴ η=10×0.85/(10×0.85+1.050)
∴ η=0.89
The transformer is 89% efficient.