Winding Resistance Challenge

xptpcrewx

Power System Engineer
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:

RX1-X2: 2.667
RX2-X3: 2.672
RX3-X1: 2.645

RH1-H2: 2.428
RH2-H3: 2.315
RH3-H1: 2.445

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

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

xptpcrewx

Power System Engineer
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

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

junkhound

Senior Member
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:

RX1-X2: 2.667
RX2-X3: 2.672
RX3-X1: 2.645

RH1-H2: 2.428
RH2-H3: 2.315
RH3-H1: 2.445

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

Power System Engineer
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

Senior Member
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:

RX1-X2: 2.667
RX2-X3: 2.672
RX3-X1: 2.645

RH1-H2: 2.428
RH2-H3: 2.315
RH3-H1: 2.445

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.
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>

Last edited by a moderator:

junkhound

Senior Member
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

Moderator
Staff member
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

Power System Engineer
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

Moderator
Staff member
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

Senior Member
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

Senior Member
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

Power System Engineer
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?

Last edited:

Hv&Lv

Senior Member
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

Power System Engineer
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

Power System Engineer
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

Senior Member
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

Senior Member
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

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

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