"emily" wrote in message
Hi,
I am looking for a closedform equation for the equivalent admittance
between any two points in a nbus power system with a given Ybus
matrix.
Any ideas?
Thanks!
Emily
If you are simply looking at the transfer impedance , you have it in the
corresponding element of the Ybus. Since this is so simple, I assume that
you are looking for something else.
Are you looking at the network with all sources set to 0  essentially
seeking the Norton equivalent between terminals i,j?
If so, I suggest that you take 1/((1/(YiiYii) + 1/(YjjYij)) +Yij (1)
This will agree with the Zbus method as given by Paul (expressed as a rake
with the reference node open.
Here is a simple example:
1 2
oj0.01o j0.1oj0.1o
  

V1 j0.5 j0.5
V2
  

oooo
reference
Ybus = j (22 10) Zbus =j(0.05729 0.02604)
(10 22) (0.02604 0.05729)
Zbus may be represented by a T
1 2
oj0.03125oj0.03125o

0.02604
ooreference
From the Ybus Y11Y12 =Y22Y21 leading to Yin
Note that the Zbus T model with the reference floating gives Y12 input
In general it would take more effort to find Zbus than to simply use the
expression (1) above
Without having explored a more complex case, I would suggest that using
either Zbus or expression (1) above would result in the same value but it
looks as if (1) applies in all cases.
Life would be easier with better diagrams but consider node i connected
directly to node j and also to a blob representing a network which also
lies between i and j through any and possibly all nodes other than i, j
all essentially related to Norton/Thevenin
Don Kelly
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