Help with Nodal Admittance/Impedance Matrix 1

[Wfg42438]

Hello Everyone!

I have a sample SC calculation I'm looking at but can't seem to match the 3x3 impedance matrix found in the sample.

I have formed the Y matrix following the guidelines from Annex B in IEC 60909.

Attached are the system impedance details (pgs 1 to 2 of attachment), the sample Z matrix results (highlighted in yellow on pg 3 of the attachment), and my Y matrix diagram set up (pg 4 of attachment using mathcad).

If someone can help me find my error it would be much appreciated, thanks!

Im sure im making a simple mistake in one of the Y matrix components

https://files.engineering.com/getfi...-a290-401f-93cb-57f0d67a8490&file=Summary.pdf

 

[xnuke]

Your first term in the parentheses for Y₂₂ is wrong.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Wfg42438]

Hello Xnuke,

Thank you for pointing out Y_22.

Attached is the revised Y and Z matrix however I still don't match the sample document. (see pg 3 of "Summary2.pdf")

I found in the document a summary of the majority of the expected Y matrix components. (see pg 1 of "Summary2.pdf")

All of my Y values in yellow match those listed in the sample calculation document.

The only value that does not match is Y_33 for which details are not given by the reference document instead only the final Y value.
In this case, I don’t see how Y_33 is not simply based on ZL1 and ZWP.

However, I did notice that even if I define Y_33 using the value they provide my Z matrix still does not match so there is something else wrong in addition to Y_33.

Additionally, the document does not mention that Y_13 or Y_31 are however I'm fairly confident they are zero as there is no way to travel from node F1 to F3 without passing through node F2.

 

[xnuke]

Why are you using the absolute value of each term in Y to create Y? Shouldn't you find Y as a signed matrix, then invert it to get Z, then find the absolute elements of Z?

I concur that Y₁₃ and Y₃₁ should be 0.

xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[Wfg42438]

You are correct!
I shouldn't have taken the absolute value of the admittance that was the final issue aside from my Y_22 initially that you pointed out.

Taking the absolute value of each of the elements of the impedance matrix calculated now got me the same Z matrix as the sample calculations in the document.

On a side note, it seems that the Y_33 in the document is a typo. I say this since my Y_33 is not the same however with all of your suggested changes I match the final matrix for the magnitude of the impedances.

Thank you Xnuke!