3 phase transformer problem

Question

We were given the following problem. We spent a night but could not even get close to solve it. It would be great if you could help us solve it.

Three identical 10 kVA, 19920/220 transformers are used to build a three-phase transformer in Y-Δ connection. An open-circuit test is performed on the low-voltage side of this threephase transformer: Vline (line-to-line)=220 V, Iline=5 A, P3ϕ(total power in three phases)=430 W. A short-circuit test is performed on the high-voltage side: Vline=500V, Iline=0.5 A, P3ϕ=86 W. a. Determine the equivalent circuit of the three-phase transformer bank. b. Find the efficiency of the transformer bank with a three-phase full-load for a power factor of 0.8 (lagging).

Answer 1

Start with the equivalent circuit for a single phase transformer: -

• Lp is the primary leakage inductance

• Rp is the primary copper loss

• Rc is the core losses due to eddy currents and hysteresis

• Lm is the magnetization inductance

• Ls is the secondary leakage inductance

• Rs is the secondary copper loss

Picture from here.

Then think about the open circuit test; losses are 430 watts so, divide that by three to get the single phase losses and, recognize that those losses are consumed on the primary AND, the only lossy component that fits the bill is Rc. You know the voltage and you know the power so calculate Rc.

Then think about the short circuit test and where the power is dissipated. Your schooling should inform you that Rp and Rs are the main culprits because Rc will have little effect on power wasted with only 500 volts applied.

You can also modify the equivalent circuit I produced at this point; clearly the question isn't formed in such a way that Lp and Ls are significant so they can be shorted out AND, given that you only know the total power of the short circuit test you can assume all that waste is delivered by Rp so, make Rs a short circuit.

Can you take it from here?