Electronic – Find impedence given per unit value-transformer

I have 1 kVA, single phase, 250/125 V transformer.

If you can adjust the primary voltage so that the input current is 4 amps RMS when the secondary is shorted, the secondary current will be 8 amps for a 2:1 step-down transformer.

NB - you will probably find that the easiest way to do this is use the output of a variac and raise the primary voltage carefully whilst noting the primary current. Typically the variac output will only need to be around 10V RMS to get full primary current with secondary shorted out.

The primary-secondary turns ratio determines both step-down voltage ratio and step-up current ratio.

This is a modified version of my answer to A-C delta-wye phase shift. In that question the voltage was stepped down. In this one it is stepped up.

^{simulate this circuit – Schematic created using CircuitLab}

Figure 1. A delta-wye (delta-star) transformer connection and phasor diagrams.

• Figure 1 shows a standard delta-wye 3-phase transformer connection. The useful aspect of showing it wired this way is that it is very easy to see that each of XFMR1 primary and secondary pairs must be in phase as they are on the same core.
• Figure 1(i) shows the primary and secondary phasors. Note that we join the phasors wherever they are electrically connected. The secondaries are smaller (representing a step-down in voltage) for clarity and haven't been connected yet. Note that 'a' is in-phase with 'A', etc.
• When we wye-connect the secondaries we join the secondary phasors at the neutral point. This is shown in Figure 1(ii). Note that the phase-neutral voltages are in still phase with the primaries.
• Figure 1(iii) shows the phase to phase phasors in black. Note that these are 30° out of phase with the phasors in Figure 1(i). This is the phase-shift you will be interrogated on.

I think that since the transfer function includes the term \$ e^{-j30°} \$ that all voltages are either phase to phase or phase to neutral. (That would be the large triangle of (i) and the black of (iii).) This would also account for the \$ \sqrt{3} \$ in the transfer function.