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Chapter 8: Transmission Lines and Cables
Figure 8-17 – Two Modes of a Two-Conductor Transmission Line
For the ground mode, the current flows down both conductors and
back through the ground. The current flows down one conductor and
back on the other for the metallic mode. Each of these modes can
be differentiated by defining the direction in which current flows as
either a +1 or -1. The modal transformation matrix is then:
[ ​1 ​ ​-1 ​]
​[ Te ]​= ​  ​1   ​  ​1    ​  ​
(8-50)
and when normalized it becomes,
[ 
]
0.707 0.707
​[ Te ]​= [​ Ti ]​= ​  ​     ​  ​     ​  ​
(8-51)
​0.707 ​ ​-0.707 ​
It is interesting to note that the transformation matrix for a single and
double-conductor flat configuration does not change with frequency,
this is because the conductors are always balanced. If a threephase line is balanced, then the transformation is also constant with
frequency. This is the case for ideally transposed lines, or a delta
configured line very high in the air. Under these conditions, the
transformation matrix becomes that consisting of Clark components:
[ 
] 
1 1 -1
​ 0  ​  ​2 ​   ​
TI = ​  ​ 1  ​ 1 -1 -1
and when normalized becomes,
[ 
(8-52)
] 
0.5774 0.7071 -0.4082
TI = ​  0.5774 
​
 
​  ​  0   
 
 
​  ​0.8165 
 
​  ​
0.5774 -0.7071 -0.4082
180
EMTDC User’s Guide
(8-53)