Estimate of typical resisdential feed utility transformer secondary inductance

[mivey]

Hi Mivey,
Since I did not know what to do I followed the example at the site I posted a link to early on. Being aware of the dangers in relying on arbitrary internet sites ( coupled with my interpretation of same) I was looking for some help here.

The site referenced found a "Zbase" calculated from MVA and KV. From there they used the Zbase and %Z to find the impedance. I was not familiar at all with using "per unit" values that are common in the power distribution realm.

Would you please detail the method you use so that I may learn from it?

Thanks,
Ela

I used some approximate per-unit data to derive the values I posted. You assumed all reactance and you had a combined primary and secondary reactance because the transformer %Z is for the combination of primary and secondary impedance.


You can find approximate X/R ratios for different transformer sizes and use them to help with the X approximation when given %Z.

Example with 2.1%:

If we use 25kVA and 2.1%Z and look at the secondary side:
Zbase = V² / S = 240² / 25000 = 2.304 Ω

If we assume the X/R ratio is about 1.3 and the primary and secondary impedances are about equal on a per-unit basis we get:
Z₁₂² = X₁₂² + R₁₂² = X₁₂² + ((X₁₂ / R₁₂ ) / 1.3 * R₁₂)² = X₁₂² + (X₁₂ / 1.3)²

0.021² = X₁₂² + 0.769² * X₁₂²

0.021² = 1.592 * X₁₂²

X12 ~ sqrt(2.77E-4) = 0.016645 pu = 0.016645 pu * Zbase = 38.35 mΩ

X2 ~ X12 / 2 = 19.18 mΩ


Example with 2.6%:

If we use 25kVA and 2.6%Z and look at the secondary side:
Zbase = V² / S = 240² / 25000 = 2.304 Ω

If we assume the X/R ratio is about 1.4 and the primary and secondary impedances are about equal on a per-unit basis we get:
Z₁₂² = X₁₂² + R₁₂²

0.026² = X₁₂² + 0.714² * X₁₂²

0.026² = 1.51 * X₁₂²

X12 ~ sqrt(4.476E-4) = 0.021157 pu = 0.021157 pu * Zbase = 48.75 mΩ

X2 ~ X12 / 2 = 24.37 mΩ

 

[ELA]

Thank you very much Mivey for the detailed response.
I appreciate your willingness to share your knowledge.