Winding Resistance Challenge

[xptpcrewx]

A two-part challenge for the electrical test technicians and/or engineers…

Consider a Δ-Y transformer with the following winding resistance measurements taken in the field:

R_X1-X2: 2.667^mΩ
R_X2-X3: 2.672^mΩ
R_X3-X1: 2.645^mΩ

R_H1-H2: 2.428^mΩ
R_H2-H3: 2.315^mΩ
R_H3-H1: 2.445^mΩ

Note: Aside from X1, X2, X3 and H1, H2, H3 terminals, all other connections are inaccessible with the X₀ buried.

Question #1 (20 points): What is the value of the single lowest Y connected phase winding?

Question #2 (80 points): What is the value of the single lowest Δ connected phase winding?

Show your work or no credit.

 

[petersonra]

I am having brain fade on the second part. Can't remember how to get the variables out of a denominator.

 

[xptpcrewx]

I am having brain fade on the second part. Can't remember how to get the variables out of a denominator.

It’s significantly more difficult, hence the higher points…

 

[xptpcrewx]

For anyone attempting this challenge DM first so no one copies your solution. I will post who gets credit.

 

[junkhound]

A two-part challenge for the electrical test technicians and/or engineers…

Consider a Δ-Y transformer with the following winding resistance measurements taken in the field:

R_X1-X2: 2.667^mΩ
R_X2-X3: 2.672^mΩ
R_X3-X1: 2.645^mΩ

R_H1-H2: 2.428^mΩ
R_H2-H3: 2.315^mΩ
R_H3-H1: 2.445^mΩ

Note: Aside from X1, X2, X3 and H1, H2, H3 terminals, all other connections are inaccessible with the X₀ buried.

Question #1 (20 points): What is the value of the single lowest Y connected phase winding?

Question #2 (80 points): What is the value of the single lowest Δ connected phase winding?

Show your work or no credit.

Simple by examination
Or, are the field readings with all connections made and you are asking the value of each winding with both ends floating?
Question phrasing is ambiguous, you know what you mean but I don't <G> e.g you mean "individual winding unconnected"
BTW, ha ha, don't forget sqrt 3, not.

 

[xptpcrewx]

Simple by examination
Or, are the field readings with all connections made and you are asking the value of each winding with both ends floating?
Question phrasing is ambiguous, you know what you mean but I don't e.g you mean "individual winding unconnected"
BTW, ha ha, don't forget sqrt 3, not.

Field measurements are terminal to terminal readings with the delta and wye connections made-up in the tank. Connections in the tank are not accessible. The challenge is to determine what the individual winding values are without disturbing the transformer; i.e. not having to pump down the fluid, open the tank, break the connections and measure each unconnected winding.

 

[junkhound]

A two-part challenge for the electrical test technicians and/or engineers…

Consider a Δ-Y transformer with the following winding resistance measurements taken in the field:

R_X1-X2: 2.667^mΩ
R_X2-X3: 2.672^mΩ
R_X3-X1: 2.645^mΩ

R_H1-H2: 2.428^mΩ
R_H2-H3: 2.315^mΩ
R_H3-H1: 2.445^mΩ

Note: Aside from X1, X2, X3 and H1, H2, H3 terminals, all other connections are inaccessible with the X₀ buried.

Question #1 (20 points): What is the value of the single lowest Y connected phase winding?

Question #2 (80 points): What is the value of the single lowest Δ connected phase winding?

Show your work or no credit.

Spoiler: equations for wye

a+b=2.667;
b+c=2.672;
c+a=2.645;
3 equations, 3 unknowns, solve for a, b, c.

delta a bit tedious with one winding in parallel with the other 2 in series,
too lazy to even write out today <G>

 

[junkhound]

whoops, too late, Xpt asked that I delete the 3 equations, asked I not give the answer, think there is a time limit on editing a post.
oh well, did not do the full calculations anyway

 

[GoldDigger]

whoops, too late, Xpt asked that I delete the 3 equations, asked I not give the answer, think there is a time limit on editing a post.
oh well, did not do the full calculations anyway

I edited your post to use SPOILER tags, Those who want to see it can; those who do not want to look can work on their own.

 

[xptpcrewx]

I edited your post to use SPOILER tags, Those who want to see it can; those who do not want to look can work on their own.

Awesome thanks


Sent from my iPhone using Tapatalk

 

[GoldDigger]

Awesome thanks


Sent from my iPhone using Tapatalk

You are welcome. The SPOILER feature is something Xenforo provides that our previous software did not, No more having to change text color to white.
For those who are interested the feature is in the vertical dots dropdown at the end of formatting bar.

 

[petersonra]

Writing the equations for the Delta version is the easy part. Figuring out how to get the variables out of the denominator has been making me crazy.

 

[junkhound]

Writing the equations for the Delta version is the easy part. Figuring out how to get the variables out of the denominator has been making me crazy.

Easiest way is to put the simple circuits into the free student version of LT Spice or Orcad PSpice (or other spice tool) and let the resistances be the variable, sweep the values and pick off the answer. Easiest if you already know PSpice or similar.

Think the last time I actually worked a differential equation (needed instead of just algebra with as in the OP example question) if similar task but with complex inductive and reactive cirecuits was 30 years ago. Let the finite element programs do the work now.
Pretty sure if somebody put a differential equation (or even just Laplace) in front of me now I'd spent hours reviewing textbooks before I could work it!

Advanced credit for Xpts query - put a phase angle to each of the impedances

 

[xptpcrewx]

Advanced credit for Xpts query - put a phase angle to each of the impedances

Zero degrees. I thought that was implicit with winding "resistance" measurements, or are you suggesting a Question 3: with complex impedance?

 

[Hv&Lv]

Zero degrees. I thought that was implicit with winding "resistance" measurements, or are you suggesting a Question 3: with complex impedance?

Sure. the winding will have complex impedance rather than “resistance” anyway.
Core loss and winding capacitance can present errors also.

 

[xptpcrewx]

Sure. the winding will have complex impedance rather than “resistance” anyway.
Core loss and winding capacitance can present errors also.

Let's assume for this example the winding resistance test-times for the above measurements were very long, so the readings had enough time to stabilize and are accurate to the digits shown.

So far petersonra was the only one to get the right answer for Q1.

 

[xptpcrewx]

Update: synchro has successfully solved Q1 and Q2. Full points awarded. Congratulations! and thanks for participating.

Where are the NETA/NICET test technicians at???

 

[junkhound]

Zero degrees. I thought that was implicit with winding "resistance" measurements, or are you suggesting a Question 3: with complex impedance?

Yeah, complicate things with a question 3. "Resistance" does tell one it is zero degree phase, no L or C.

 

[petersonra]

Update: synchro has successfully solved Q1 and Q2. Full points awarded. Congratulations! and thanks for participating.

Where are the NETA/NICET test technicians at???

They are still trying to get the variables out of the denominator like I am.

I may be forced to talk to another engineer at work and see if he or she can remember the algebra to do this. I'm pretty sure it's going to make me crazy when I find it out and realize it was just sitting out there waiting for me.

 

[wwhitney]

Well, as far as the algebra and the denominators, try this:

Spoiler

If x, y, z are the unknown conductances of the coils arranged in a delta, and A, B, and C are the measured conductances from the pairs of corners, then the equations are:

x + 1/(1/y + 1/z) = A

and its two analogues under the 3-cycle (x -> y, y -> z, z -> x ; A -> B ; B -> C ; C -> A).

That becomes

x+ yz/(y+z) = A or
xy + xz + yz = Ay + Az

So you get the three equations:

xy + xz + yz = Ay + Az = Bz + Bx = Cx + Cy

as the lefthand side of the exemplar equation is stable under the 3-cycle.

Which is sufficiently elegant that it makes me wonder if there's an even nicer way to frame the physics to make the math even simpler.

Cheers, Wayne