How do transformer taps affect fault calculations?

[bacon4life]

General question: For a typical +/- 10% LTC, what is the expected variation in fault current.

Detailed question:
I am attempting to calculate faults when using a transformer with the off nominal taps, but I haven't found a good example to follow yet. When calculating the per unit impedance of a tranformer with taps, do you use the same voltage & MVA base, or do you use the new voltage and the same MVA base?

As an example, if I have a 4 kVA, 3 phase, 230 to 115 tranformer with 10 primary turns at 0.1 ohm per turn and 20 secondary turns at 0.05 ohms per turn, then the Zpu is 0.094.

1: If I add 1 primary turn and use the same MVA and voltage base, the per unit impedance would be 0.106, a change of 12%.

2: If I add 1 primary turn and instead use the same MVA and use 207 for the voltage base, the per unit impedance would jump up to 0.13, a change of 38%.

3: Since I neither of these seemed quite right, I also tried calculating the fault current with real units as follows:

Nominal
Zprimary= 1.0 ohm
Zsecondary 1.0 ohm
Ztotalrefered to high side = 1.25 ohm = 1.0 + 1.0* (10/20)^2

Iprimary = 106A= 230/1.25/1.73
Isecondary = 212A = 106A * 20/10

One extra highside winding:

Zprimary= 1.1 ohm
Zsecondary 1.0 ohm
Ztotalrefered to high side = 1.4025 ohm = 1.1 + 1.0* (11/20)^2

Iprimary = 94.7A= 230/1.4025/1.73
Isecondary = 172A = 94.7A * 20/11

A change of 26%

 

[dpc]

I'm not sure where are you getting 0.1 ohm/turn?

The impedance of a transformer is primarily the leakage reactance. I don't think this is going to vary linearly with the number of turns.

I have some test data from a transformer with a 32-step LTC:

For the same primary tap:

16R: 6.84
N: 6.68
16L: 6.11


For neutral position of LTC:

Primary Tap A: 6.84
Primary Tap E: 6.68

It gets confusing in per unit because I'm not sure what they are using for the base voltage.

 

[prc]

In power transformers, % leakage impedance will change with tap positions based on where the regulating winding is placed with respect to other windings.So a generalised statement is not possible esp with respect to auto transformers.Generally designers try to place the regulating winding such a position that impedance variation with tapping positions is minimum so that fault current variation is also less. But exceptions are common and then fault current will vary with tapping position.

 

[jghrist]

prc is correct. Inspection of several power transformer test reports shows that there is no simple formula to determine the impedance at different taps. In some cases, the impedance increases from neutral going both ways with the taps.

 

[bacon4life]

You are right, I should have gone all the back to the thinking about the magnetic circuit instead of making an assumption about a linear leakage impedance.

dpc
So for your transformer on the 16L tap, the fault current would increase by 12% due to the reduction in impedance, and then increase by another 10% to account for the turns ratio?