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I have got a simple network for my assignment:

enter image description here

I know bus admittance matrix have certain properties that let us form the matrix without writing so many lines of KCL. But is there any property such that one could, without matrix formation, say sum of values in row 2 of the matrix is zero, whereas the sum of values in row 4 is –j1?

I have formed the admittance matrix and I can confirm that above statement is true but I was wondering what is the rationale behind that statement?

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  • \$\begingroup\$ Can you be more clear what's meant by the "Y bus matrix". That isn't a term that's used universally in the EE field, as far as I know. Are you making an admittance matrix for the network? What are the ports of the network (all the nodes numbered 0 thru 6)? What is the reference node? \$\endgroup\$
    – The Photon
    Apr 16, 2016 at 14:36
  • \$\begingroup\$ @ThePhoton I thought it is pretty self explanatory but maybe I was wrong. I edited the post and replaced the term 'Y bus'. The reference node is node 0. I don't really know what you mean by network ports?! \$\endgroup\$
    – Bababarghi
    Apr 16, 2016 at 14:52
  • \$\begingroup\$ When you make an admittance matrix, you're making a way to calculate the current at one port due to a voltage applied at another port. But you first have to define what are the ports of your network. \$\endgroup\$
    – The Photon
    Apr 16, 2016 at 14:56
  • \$\begingroup\$ Wikipedia says that the "bus admittance matrix" is used in power engineering. Is that the context you're asking this question in? \$\endgroup\$
    – The Photon
    Apr 16, 2016 at 14:58
  • \$\begingroup\$ Looking at Wiki, I think the answer is that the sum of values in any row is equal to the self-admittance to ground (so for row 4 it's 1j). The sum in row 2 is zero because bus 2 has no self-admittance (no admittance from bus 2 to ground). \$\endgroup\$
    – The Photon
    Apr 16, 2016 at 15:05

1 Answer 1

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Thanks to The Photon for the heads up. I found the comprehensive answer in following textbook:

Rau, NS 2003, 'Appendix B: Network Equations', in Optimization Principles: Practical Applications to the Operation and Markets of the Electric Power Industry, Wiley, p. 310.

In a nutshell:

In an admittance matrix the algebraic sum of values in any row is equal to shunt admittance connecting that particular node to the reference node (ground).

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