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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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## Still the "wrong" answer in practice test

If the below explanation is correct, the practice test question is still incorrect as of Feb 2021. Just want to confirm...the correct answer is 3.92%?

Originally Posted by Erased
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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