Lecture 25 :
Analysis of Power Swings in a Multi – Machine System
Now let the current in the transmission line AB, when it is connected to the network be Iij from the ith end and Iji at the j th end
respectively. Then, under the assumption of linearity, the effect of the transmission line connection can be evaluated by superimposing injected currents and on the network in which line i-j was disconnected. Thus, . Since, we are only interested in characterizing behavior at busses i and j, we can ignore the remaining rows in (2).
Thus, (3)
Now if we assure a simple series model of the line, then,
where Yij is the primitive admittance of the transmission line
Equivalently, (3) can be expressed as follows.
(4)
where matrix is the inverse of corresponding restricted Zbus matrix. Under usual symmetry assumption, .
and 
on the network in which line i-j was disconnected. Thus, 
. Since, we are only interested in characterizing behavior at busses i and j, we can ignore the remaining rows in (2). 
matrix is the inverse of corresponding 
restricted Zbus matrix. Under usual symmetry assumption, 
. 
