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# Percentage Differential Mismatch

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## Percentage Differential Mismatch

Calculate the percentage differential mismatch for an electromechanical relay protecting a 138kV-69kV Delta-Wye 50MVA Transformer with 250:5 CTs on the primary and 500:5 CTs on the secondary, with CT ratio taps on the relay set to 5A on the high side and 9A on the low side.

I need help with this problem, the answer is supposedly 3.78%. Thanks.

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Originally Posted by Uguessus
Calculate the percentage differential mismatch for an electromechanical relay protecting a 138kV-69kV Delta-Wye 50MVA Transformer with 250:5 CTs on the primary and 500:5 CTs on the secondary, with CT ratio taps on the relay set to 5A on the high side and 9A on the low side.

I need help with this problem, the answer is supposedly 3.78%. Thanks.
Now, I got a slightly different answer, so someone correct me if I'm mistaken.

First calculate HV currents.

Primary:
50000000/sqrt(3)*138000 = 209.18

Secondary:
50000000/sqrt(3)*69000 = 418.37

Now calculate CT currents. An electromechanical scheme on a Delta-Wye will have Wye-Delta CT's to account for the phase shift. Delta CT current must be multiplied by sqrt(3).

Primary - Wye CT:
209.18/50 = 4.18

Secondary - Delta CT:
418.37/100 = 4.18
4.18*sqrt(3) = 7.24

Calculate the percent mismatch as follows: On two-winding transformers,
determine the ratio of the two relay currents and the tap values selected. The
difference between these ratios, divided by the smaller ratio, is the percent
mismatch.

((4.18/5)-(7.24/9)) / (7.24/9) = 0.0392

3.92% with rounding errors.

Looks like your answer came from incorrectly dividing by the larger ratio.

(4.18/5)-(7.24/9) / (4.18/5) = 0.0377

3.77% with rounding errors.

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This is awesome! Thanks a lot, Erased.

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