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# 3-Winding Transformer Model

## 3-Winding Transformer Model

(OP)
I was provided the data to model a 230/34.35 kV 3 winding transformer for a wind farm with the +/- 12.5 % regulation and +/- 8 taps. The primary-secondary impedance value for the transformer is 11.80% at nominal and 12.4% (8R tap position, 258.75 kV) and 11.81% (8L tap position, 201.25 kV) all using 124 MVA base - Voltage control is on the primary (230 kV) and secondary (34.5 kV) is held constant. Recently, however, realizing that the voltage regulation should be on the secondary, the transformer mfr provided the impedance values of 15.72% (for the 8R, 30.667 kV), 11.87% (for Nominal, 34.5 kV), and 9.03% (for 8L, 39.481 kV). They suggested this as the same impedance value. I have 2 questions, 1. Is what they stated valid and if so, would the short circuit calculation at the lowest tap position still valid? 2. If you were provided the 2 sets of impedance data as above, which one would you use for the short circuit evaluation since the 9.03% impedance would represent a much larger than the 11.81% ? Thanks for any advice.

### RE: 3-Winding Transformer Model

First of all,what is the third winding? Stabilising winding or another loaded secondary? In the later case, what is the MVA and impedance for each pair of secondaries.Since the tappings are already provided on the primary for constant flux variation, manufacturer cannot do anything more to get variation on secondary.Of course you can operate transformer for constant primary voltage to get varibale secondary voltage by operating the tap changer.Then the flux density in the core will change based on tapping position ie whether more or less turns are added to the winding with constant preimary volatge.You may get a confirmation from manufacturer the values of B for such operation for the desired secondary voltage range.Also the loading should be controlled to avoid excess heating of winding.

Impedance values will not change with such operation.

### RE: 3-Winding Transformer Model

(OP)
prc, thanks for the response. At the present, there is nothing connected to the tertiary winding of the 3-wnd transformer. The fact that the mfr provided 2 different set of impedance, 1 is for primary voltage regulation while holding the secondary constant, and the 2nd set of impedance for holding the primary constant while regulating the secondary voltage (This would yield a much lower impedance at the lowest tap). The selection of which impedance to model in ETAP is our concern. And if possible, what would be the justification of using one verses the other? Instead of just using the most conservative value.

### RE: 3-Winding Transformer Model

Impedance will not vary whether constant flux or variable flux voltage variation.

### RE: 3-Winding Transformer Model

(OP)
prc, does that imply what the mfr provided is invalid? and I should just stay with what I had modeled previously?

### RE: 3-Winding Transformer Model

YES.But you should ask why he is giving different figures and the reason behind it.

### RE: 3-Winding Transformer Model

(OP)
prc,

The first set of figure with the higher impedance (11.81) at the lowest tap (8L) was for primary voltage (230 kV) regulation between +/- 12.5% from nominal while holding the secondary constant. An engineer suggests the voltage should be held constant at the primary, and secondary voltage should be varied. Thus the mfr provided the later set of impedance to justify that if the 230 kV voltage is held constant, the 34.5 kV could be varied between 30.667 to 39.481 kV - at the lowest tap position (8L) this would constitute to the impedance value of 9.03%. That was what threw me off.

### RE: 3-Winding Transformer Model

The impedance in ohms is the same, but the per unit impedance changed because the selected base voltage changed from 34.5 kV to 30.667 kV and to 39.481 kV.

For example at 8R:
15.72%= 12.4*(30.667/34.5)^2

Which set of per unit impedances you choose to use will depend on which set of base voltages you use for the rest of the ETAP model.

As prc pointed out, it is very important to operate the transformer core within allowable flux levels and the windings within allowable current limits. If the transformer was designed for variable high side voltage, the core may saturate if operated at 230 to 39.481 instead of 201 kv to 39.5 kV. Likewise,the windings may be limited to 110 MVA if operated at 230 kV to 30.66 kV instead of at 258 kV to 34.5 kV.

### RE: 3-Winding Transformer Model

As per standards,the %impedance is always expressed on reference MVA. See IEC60076-1 Power Transformers Clause 3.7.1
%Z =Z/Zref where Z actual series impedance in ohms (R+jX) Zref = UxU/Sr where U is rated voltage or tapping voltage,Sr= rated power of the transformer.

### RE: 3-Winding Transformer Model

(OP)
Thank you very much, prc and bacon4life. This had helped us tremendously in eliminating the unnecessary work of reassessing and more importantly, the needless of sizing equipment based on erroneous results. Truly thankful. If anything more you or others would like to add, I'm all ears. Thanks, again.

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