How to Compute The Power Transformer Resistance And Reactance Given The Percent Impedance?

If you happen to see a power transformer nameplate, it is very rare (or impossible) to see the value for the resistance and reactance for the equivalent circuit of that transformer. The only valuable information that you can get from the transformer nameplate for this purpose is the percent impedance (%Z) and the voltage rating.

Using the 64 MVA Mitsubishi transformer in this article http://www.jcmiras.net/jcm/item/116/ , as a real case example;
the actual value of the impedance of this transformer, referred to the high voltage side, can be computed as %Z x baseZ, where baseZ =KV^2/MVA; From the table, baseZ = 230^2/64 = 826.5 ohms thus, Z = 112.404 ohms (this is referred to the high voltage side). baseZ is the base impedance.

From here, if only the value of either resistance or reactance is known, we’ll be able to compute the remaining unknown variable using this equation , Z = sqrt(r^2 + x^2), where Z is the impedance, r is the resistance and x is the reactance.

The value of the resistance can be obtained using short circuit test or heat run test, but practically, for power transformers that are generally of large MVA and high kV rating, like in this example, these tests are hard to perform.

For this transformer in our example, we are well informed that the actual load loss or copper loss of this transformer at 64MVA load is 275,000 Watts. Using P = I^2R equation, we should obtained a 3.5 ohms value for the resistance. Hence, the value of the reactance should be 112.35 ohms.

Observe that the value of the reactance, x, is very close to the value of the impedance, Z. (the difference between the reactance and the impedance is actually only 0.048% while the x/r ratio is 32.1). This is enough justification to assume, for transformer and grid modeling purposes, that the reactance is equivalent to the impedance and the resistance value is negligible. This assumption is a common practice in transformer modeling for power system analysis. But take note that this is only applicable for transformer of large sizes like for the one mentioned in the example.




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