Power System Analysis: Node Elimination Explained

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SUMMARY

The discussion centers on the node elimination method in power system analysis, specifically using a 4x4 matrix as outlined in "Elements of Power System Analysis" by Stevenson. The participant successfully eliminates node 4, resulting in a new 3x3 matrix. Key calculations involve determining new matrix elements using the formula Eij(new) = Eij - (Eik * Ekj) / Ekk. The participant seeks clarification on the criteria for eliminating rows and the underlying rationale for the method's effectiveness.

PREREQUISITES
  • Understanding of matrix operations in power system analysis
  • Familiarity with the node elimination method
  • Knowledge of electrical engineering principles related to power systems
  • Proficiency in using "Elements of Power System Analysis" by Stevenson
NEXT STEPS
  • Research the criteria for row elimination in matrix operations
  • Study the implications of matrix inversion in power systems
  • Explore alternative methods for solving power system equations
  • Learn about the significance of matrix determinants in node elimination
USEFUL FOR

Electrical engineers, students preparing for the PE exam, and professionals involved in power system analysis who seek to deepen their understanding of matrix methods and node elimination techniques.

MitYeltu
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Preface: I am an electrical engineer studying for the PE exam. I am reviewing power system analysis and have come across something I do not remember in any of my classes.

I'll not bore you with the entire problem. Suffice it to say there is a 4x4 matrix that is being partitioned as follows:

[-9.8, 0.0, 4.0 | 5.0]
[0.0, -8.3, 2.5 | 5.0]
[4.0, 2.5, -14.5 | 8.0]
---------------------
[5.0, 5.0, 8.0, | -18.0]

Sorry for the weird formatting.

Now according to my book, "Elements of Power System Analysis" by Stevenson, I need to eliminate node 4 (the bottom row and last column). For ease of understanding I will use subscripts so that element in row 2 column 3 is E23.

I'm not sure how to explain this so let me show you.

the new matrix will be 3x3 and will be constructed thusly:

E11(new matrix) = E11 - (E14xE41)/E44 = -9.8 - (5x5)/-18 = -8.411
E32(new matrix) = E32 - (E34xE42)/E44 = 2.5 - (8x5)/-18 = 4.722

Each element of the new matrix is constructed the same way yielding:

[-8.411, 1.389, 6.222]
[1.389, -6.911, 4.722]
[6.222, 4.722, -10.944]

Now the question.

First, how do I know if I can eliminate a particular row? Is there some method like the inverted matrix has a particular form, or something?

Can anyone help me understand WHEN I can apply this method?

Thanks.
 
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I can follow you up until your Question, but from there on it is unclear what you want to know.

What row from what matrix do you want to eliminate?
 
No, I know whuch one was removed, I just have no idea why THAT row was removed.

If I had a matrix that was not in my textbook, how am I to know which row is to be removed if, indeed, any row CAN be removed? I don't understand how I would know WHEN I can apply this method.

I also don't really understand WHY this method even works.
 

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