Electrical Power Systems

230 Electrical Power Systems
Now
A T A* = 3
L
NM
1 0 0
0 1 0
0 0 1
\ S = 3VsI 3V I 3V I 3V
I
T s *
a1 a1
*
a2 a2
*
a0 a0
*
= + +
O
QP
= sum of symmetrical component powers. ...(9.29)
9.4 SEQUENCE IMPEDANCES O TRANSMISSION LINES
Parameters of transmission lines were derived in Chapters 2 and 3. Transmission line is a static
device and hence the phase sequence has no effect on the impedance because currents and
voltages encounter the same geometry of the line. Therefore, positive and negative sequence
impedances of transmission lines are equal, i.e., Z 1 = Z 2.
As mentioned earlier, zero-sequence currents are in phase and flow through the phases (a,
b, c conductors) to return through the grounded neutral. The ground or any shielding wire are
in the path of zero sequence and zero-sequence impedance (Z 0), which includes the effect of the
return path through the ground, is different from Z 1 and Z 2.
To get an idea of Z 0 of transmission line, consider 1-mt length of a three phase line as shown
in ig. 9.2. The ground surface is approximated to an equivalent fictious conductor located at
the average distance D n from each of the three phases. The phase conductors carry zerosequence
currents with return paths through a grounded neutral.
ig. 9.2: low of zero-sequence current with earth return.
We can write,
Ia0 + Ib0 + Ic0 + In = 0 ...(9.30)
Since Ia0 = Ib0 = Ic0, we get,
In = –3Ia0 ...(9.31)