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3-Winding Transformer Equivalent Model 2

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ahmedradi

ahmedradi

Electrical
Feb 2, 2009
5
Hi everyone,

I'm confused about how to model a 3-winding transformer as three 2-winding transformers in star-formation. I was under the impression that it is a simple Delta-to-Star conversion of the impedances, but it is not according to some.

I've got an Autotransformer with a delta tertiary winding 330/132/22kV, 490MVA with the following impedances based on its rate:

Zps = 0.2081 pu
Zpt = 1.0045 pu
Zst = 0.7530 pu

If I follow a conventional Delta-to-Star transformation, then:
Zp=(Zps*Zpt)/(Zps+Zpt+Zst) = 0.10635 pu
Zs=(Zps*Zst)/(Zps+Zpt+Zst) = 0.01967 pu
Zt=(Zpt*Zst)/(Zps+Zpt+Zst) = 0.38481 pu

However, according to a different formula it should be:
Zp = (Zps + Zpt -Zst) / 2 = 0.2298 pu
Zs = (Zps + Zst -Zpt) / 2 = -0.0217 pu
Zt = (Zpt + Zst -Zps) / 2 = 0.7747 pu

Which of these calculations is right and on what bases?!
Thanks in advance for your help.

-Radi
 
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The second formula is the correct one. You can refer it to the references like Protective Relaying Principles & Relaying by Blackburn or Elements of Power System Analysis by Stevenson.

regards,
 
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Ok... I can see that almost everyone saying that it is the second formula. My problem is to do with the resistance.
I can still accept a negative reactance (as shown above), but will also yeild negative resistance, which is hard to accept!

Thanks
 
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The negative impedance is a mathmatical construct the has no physical meaning. The star point of the three impedances has no physical meaning, but simply exists to make the math work. It is only terminal-to-terminal that has physical meaning and all those impedances work out correctly.
 
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ahmedradi,Transformer engineers were getting baffled by these negative reactances and resistances during the first half of last centuary.Then the GE veteran, A.Boyajian removed the mystery by his classic AIEE 1933 paper" Progress in Three Circuit Theory"You can read a summary in Chapter 4 of Blume's famous book "Transformer engineering" where the meaning of negative reactance and resistance are explained.

In factory we find out the resistance value of each circuit by measuring losses by pair and applying formula similar to the one you mentioned for impedances to arrive at losses of each circuit.From that R is calculated out. Then from measured impedance of each circuit, reactances are calculated.
 
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