Three-winding transformer enigma 1

I can make a suggestion.
%Z is a percentage based on the current at base KVA. If a given transformer is re-rated to a lower KVA, the impedance doesn't change but the percentage does change.
Most of the impedance of a winding pair may be in the higher voltage winding.
You have a 3MVA transformer with a 100KVA tertiary winding.
To test the impedance on the 100KVA winding, the high voltage winding must be de-rated to 100KVA. That is a 30:1 reduction of the base KVA. At 100KVA on a 3MVA winding, the percentage of the primary winding contribution to the impedance of the winding pair drops by a factor of 1/30.
Yes those numbers (0.7% and 0.94%) are possible with a reduced capacity tertiary winding.

Bill
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"Why not the best?"
Jimmy Carter

Although Z[sub]HX[/sub] is not equal to Z[sub]HY[/sub], the table below will provide a rough idea that Z[sub]xy[/sub] could be very small (close to zero).

The impedances of o.7 %& 0.94 % are on base of 100 kVA. On 3 MVA base it will be 21 % &28 %. Please confirm the Z values again. From the pattern given, the physical arrangement of windings seems - core-M-H-L. This gives a Z of H= -0.9%,M=6.3 % and L= 21.9 % . A 3L fault on L with open M can produce 143 times 100KVA. But even though L rating is 100KVA, manufacturers will design it for 600KVA so as to withstand short circuit current and forces.

I sincerely appreciate all the contributions from the respondents so far. Thank you. It certainly keeps me thinking. I've had a look at the nameplate from the client. It is in quite a bad way but I could make out the following:

11kV, 3000kVA, 157A (HV)
6.6kV 3100kVA, 217A (MV)
415V 100kVA, 139A (LV)

Impedance 11/6.6kV = 5.37%
Impedance 11/0.415kV = 0.7%
Impedance 6.6/0.415kV = 0.94%

That's as far as the nameplate goes. My own deductions are as follows:

ZHV + ZMV = 5.37%, ZHV + ZLV = 0.7%, ZMV + ZLV = 0.94%

Problem is nameplate does not specify MVA base at which the impedances are expressed. What we have is 3MVA, 3.1MVA and 100kVA as possible bases. The 5.73% must be at 3MVA as those are the ratings of the HV and MV windings (ignoring difference between 3MVA and 3.1MVA). I would also presume that the 0.7% and 0.94% is at 100kVA for the same reason. If the 0.7% was at 3MVA then at 100kVA it would be 30 times less or 0.0233%. Though I must say with 0%Z and -Z values for 3 winding trfrs anything is possible!

prc - where did you get 600kVA from? Surely it cannot be a continuous rating? Otherwise, I agree with your post, it's in line with what I've stated above.

cuky2000 - interesting table. Thank you very much. One question though - why will you have higher fault duty and losses? When Zxy = 2, then Zhx and Zhy are still equal to 1 so why would the fault duties be higher if one considers faults at X and Y terminals?

waross
"To test the impedance on the 100KVA winding, the high voltage winding must be de-rated to 100KVA. That is a 30:1 reduction of the base KVA. At 100KVA on a 3MVA winding, the percentage of the primary winding contribution to the impedance of the winding pair drops by a factor of 1/30. "
You've lost me here. My understanding is that the impedance of the HV-LV is a function of the physical arrangement of the windings on the core. ZHL is determined by shorting the LV, MV open and applying a source to the HV till rated LV current flows. The measured impedance can then be expressed as a % either at the HV MVA base or LV MVA base. Where does derating of the HV come in?

Aside question - since the 6.6kV winding has a higher rating, does that mean the trfr was originally designed to have source connected to the 6.6kV and load to the other windings?

Thanks.

Normally Transformer windings can stand only 20-25 times rated current. So if the fault current comes 143 times, manufacturer will increase copper section sufficient for 600 KVA (approx.) so that times current is within 25 times.

Hi; Impedance is a fixed value measured in Ohms. The impedance may be expressed as a percentage, but to do so, a base KVA must be chosen.
Consider an ONAN transformer with provision for adding fans. The impedance may be expressed as a percentage based on the base KVA.
Now the base KVA of the transformer is raised by the addition of cooling fans. The base KVA is increased. The impedance in Ohms stays the same but the impedance expressed as a percentage changes with the change in base KVA.
Consider the way that percent impedance is measured;
The percent impedance or more accurately the percent impedance voltage is the voltage needed to force full load current through a short circuit.
Impedance 11/6.6kV = 5.37%. Full load current through the 6.6 kV winding will be based on 3 MVA at 11 kV.
Impedance 6.6/0.415kV = 0.94%. Full load current through the 6.6 kV winding will be based on 100 KVA at 0.415 kV.

Bill
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"Why not the best?"
Jimmy Carter