Question

How do you calculate the short-circuit impedance of a three-phase transformer?

Answer 1

Calculating the short-circuit impedance of a three-phase transformer involves determining the equivalent impedance as seen from the primary side when the secondary side is short-circuited. The short-circuit impedance is an important parameter that helps in assessing the transformer's behavior during fault conditions.

To calculate the short-circuit impedance, you need the following information:

Rated primary voltage (Vp) in volts.
Rated secondary voltage (Vs) in volts.
Rated apparent power (S) in volt-amperes (VA) or kilovolt-amperes (kVA).
Transformer connection type (e.g., Y-Y, Delta-Delta, Y-Delta, etc.).
Transformer phase configuration (e.g., three-phase, single-phase).

The formula to calculate the short-circuit impedance is different for different transformer connections. Let's take two common types as examples:

For a three-phase transformer with a "Y" (Wye) connection on both the primary and secondary side:

Short-Circuit Impedance (Zsc) = (Vp / Isc) * (1 / √3)

Where:
Vp = Rated primary voltage
Isc = Short-circuit current on the secondary side (symmetrical rms value, in amperes)

For a three-phase transformer with a "Delta" connection on the primary side and a "Y" (Wye) connection on the secondary side:

Short-Circuit Impedance (Zsc) = (Vp / Isc)

Where:
Vp = Rated primary voltage
Isc = Short-circuit current on the secondary side (symmetrical rms value, in amperes)

To determine the short-circuit current (Isc), you may need to perform a short-circuit test on the transformer. In this test, you apply a known voltage on the secondary side with the primary side open, and then measure the resulting short-circuit current on the secondary side.

Keep in mind that the short-circuit impedance is usually given as a percentage of the transformer's rated apparent power (S). You can convert the impedance to a percentage by dividing the impedance value (in ohms) by the rated apparent power and then multiplying by 100.

It's crucial to have accurate data for the transformer and consult the manufacturer's documentation or seek assistance from a professional engineer for precise calculations and safe operation. Transformers are complex equipment, and any faults or misinterpretations during short-circuit conditions can lead to severe consequences.