# Circulating Current in Two Transformers on Different Taps

From a NETA 4 practice exam:

There are two identical LTC transformers (12/16/20 MVA, 115 kV to 13.8kV, 9%Z, +/-10% in 5/8% steps) which are operating on differing taps, one step removed from each other. Calculate the resulting circulating current from a one-step tap discrepancy.
a. 17.413 Amps
b. 27.664 Amps
c. 47.916 Amps
d. 55.329 Amps
e. 95.833 Amps

I tried multiple different ways of figuring this one out but none of my answers matched the choices. I’m not sure what “5/8% steps” means: is it a choice of 5% steps or 8% steps? Or is it 5/8% = 0.625%? Then there are multiple MVA values given, which I would normally think are for different cooling modes (ONAN/ONAF/ONAF). So I assume I should use the highest one.

If I think of this as a circuit with a voltage source and two windings in series, where the voltage is 13800 V x 0.625% = 86.25 V, then the current would be I = E / Z. I’m not sure how to convert a %Z to an actual impedance in ohms.

I can calculate the “base impedance” as 13.8^2 / 20 = 9.522 ohms. There are two windings in series, so maybe it’s double: 2 x 9.522 = 19.044 ohms.

So:
I = E / Z
I = 86.25 V / 19.044 ohms
I = 4.529 A

Or:
I = E / Z
I = 86.25 V / 9.522 ohms
I = 9.058 A

Or:
I = (E x 1.732) / Z
I = 149.385 / 9.522
I = 15.688 A

Or:
I = 149.385 / 19.044
I = 7.844 A

None of these options are available.

Another way I looked at it is 0.625% of short circuit current at 13.8 kV:

I_SC = S / (E x 1.732 x %Z)
I_SC = 20000 / (13.8 x 1.732 x .09)
I_SC = 9297.379 A
9297.379 x 0.00625 = 58.109 A
This option also isn’t available.

This post is getting long but I tried a couple of other ideas and none of them fit the answer choices.

What is the right way to calculate this?

1 Like

%Circulating current = (tap % *100 )/ (Z1%+((MVA1/MVA2) *Z2%)
= 10 *100 / (9+9)
=55.56%

The circulation current will be on the secondary side.
Circulating Current = ((%Circulating current/100) *MVA) / (SQRT OF 3 *kV).
= (0.5556 *20000) / 23.9
= 464.89 A

I believe “d” is the correct answer.

1 Like