Electrical Power Systems

Using eqn.( 2.46) as given in Chapter-2, we can write
–7
la0 = 2 ´ 10
Since I a0 = I b0 = I c0 and I n = –3I a0, we have
Since
HG
–7
la0 = 2 ´ 10 I a0
L0 = la0 I a0
Symmetrical Components 231
1 1 1 1
0 0
¢ + + +
I ln I ln ln ln
r D I
D I
a0 b c n
...(9.32)
D
ln
HG
= 02 . ln Dn
rD ¢
D
rD ¢
D Dn
\ L0 = 02 . ln 3 02 . ln
r
D
3
2
I
3
n
2
wb T/ mt ...(9.33)
KJ -
mH/Km
irst term in eqn. (9.34) is positive sequence inductance.
Therefore,
X 0 = X 1 + 3 X n
¢ + HG I KJ mH/Km ...(9.34)
n
I
KJ
...(9.35)
Therefore, zero-sequence impedance of the transmission line is more than three times of the
positive or negative sequence impedance.
9.5 SEQUENCE IMPEDANCES O SYNCHRONOUS MACHINE
Synchronous machine is designed with symmetrical windings and it induces emfs of positive
sequency only. The positive sequence generator impedance is the value found when positivesequence
current flows due to an imposed positive-sequence set of voltages. Neglecting the
armature resistance, the positive sequence impedance of the machine is
Z 1 = jX d ² (if subtransient is of interest) ...(9.36)
Z1 = j Xd¢ (if transient is of interest) ...(9.37)
Z1 = j Xd (if steady-state value is of interest) ...(9.38)
With the flow of negative sequence currents in the stator, the net flux in the air gap rotates
at opposite direction to that of the rotor. Therefore, the net flux rotates twice the synchronous
speed to the rotor.
In this case, field winding has no influence because field voltage is associated with the
positive-sequence variables and only the damper winding produces an effect in the quadrature
axis. Therefore, the negative sequence impedance is close to the positive sequence subtransient
impedance, i.e.,
Z 2 » jX d ²
...(9.39)