Negative value of transformer impedance 1

[Beengineer]

We have a 3-winding transformer with the negative value of secondary winding impedance. What's the physical meaning of the "Negative Impedance"?

Thanks

 

[PHovnanian]

What exactly does the nameplate and/or manufacturer's specs say?

 

[magoo2]

The actual measurements between any 2 windings will always give a positive result.

In deriving a 3 terminal equivalent for a three-winding transformer, it is possible that one of the impedances will be negative. I wouldn't try to attach anything of significance to it. It's just a derived quantity.

 

[waross]

Primary voltage-600V
Secondary voltage-120V
Impedance voltage-3%
????

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[Beengineer]

Zps=20%
Zpt=30%
Zst=6.5%

Under same MVA base

Zp=1/2(Zps+Zpt-Zst)=21.75%
Zs=1/2(Zps+Zst-Zpt)=-1.75%

-1.75% is what I was talking about

 

[pwrtran]

Have you convert Zst to the primary base first?
Zps and Zpt are no problem since they are on the primary MVA base, however, Zst is normally on the secondary winding MVA base.

 

[Beengineer]

Reply to pwrtran -

In this case, OEM test sheet shown 75MVA for all three windings.

 

[pwrtran]

I would say it might be some error. You are doing transformation from pair value to Tee equivalent, and maybe your next step is to convert to delta equivalent for doing a load flow calculation for a three-winding transformer. I don't see a negative value will make sense.

 

[waross]

Remember that %impedance voltages may be verified by testing. A negative value may not be verifiable.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[magoo2]

Beengineer,

Your math looks OK. So what if one of the impedances is negative? It's not a big deal. I've seen it before and there's nothing wrong with it.

You are working with a wye equivalent, where you have Zp, Zs and Zt connected in a wye arrangement. Where is the junction of this wye in an actual transformer? It doesn't exist.

Testing won't verify any negative impedances because all you can measure is impedances between pairs of windings, and these are all positive.

There is no physical meaning of the negative impedance value.

 

[Beengineer]

Thank you magoo2, you have given me the answer. Yes, Zp, Zs, and Zt connected in a Wye, with fititious common point.

 

[pwrtran]

magoo2

Zps=Zp+Zs
Zpt=Zp+Zt
Zts=Zt+Zs
then you have below
Zp=(Zps+Zpt-Zst)/2
Zs=(Zps+Zst-Zpt)/2
Zt=(Zpt+Zst-Zps)/2

Like a triangle, you have the sum of the length of any two sides, then you solve the individual length of each three side. How can you get a negative number of the length for a triangle? Same as the each individual winding leakage impedance, could you please explain why a negative impedance is okay?

 

[magoo2]

I'm afraid your triangle analogy doesn't apply here.

If you take your last set of equations:
Zp=(Zps+Zpt-Zst)/2
Zs=(Zps+Zst-Zpt)/2
Zt=(Zpt+Zst-Zps)/2

If Zps is close to Zpt, and Zst is noticably less, you'll consistently get a negative impedance result for one of the legs.

The math is basically doing a delta to wye conversion, where the actual measurements are legs of a triangle. The calculated legs (Zp, Zs & Zt) apply to a wye arrangement.

 

[davidbeach]

magoo2 is absolutely correct. Perfectly normal and not representative of anything physical. Impedances from a fictitious wye point to each terminal. As long as all of the terminal to terminal impedances are positive you are fine.