
706
Electric Power Distribution Handbook
react to other stator currents that are not 50- or 60-Hz positive-sequence
currents (significantly, negative-sequence currents and harmonic currents).
The negative-sequence impedance determines the current flow due to
negative-sequence voltages. The impedance to harmonic voltages is also
approximately the negative-sequence impedance. The negative-sequence
impedance is the same whether the generator is under steady-state, transient,
or subtransient conditions.
The zero-sequence impedance of a synchronous machine can have
extremely low impedance. It is enough of a problem that many generators
are ungrounded or grounded through an impedance to prevent the flow of
zero-sequence current. Many generators are not braced to handle the fault
current for a line-to-ground fault at the terminals of the machine. Single-
phase faults cause more mechanical stress and are higher magnitude. Ground
fault currents are 30 to 40% higher than three-phase fault currents (
E
/
X
d
" vs.
3
E
/(2
X
d
"+
X
0
)
ª
1.3 to 1.4
E
/
X
d
"). The zero-sequence impedance is the same
whether it is under steady-state, transient, or subtransient conditions.
The reason that the zero-sequence impedance is so low is that magnetic
fields from zero-sequence currents in the stator winding tend to cancel each
other. If the fields cancel and couple very little to the rotor, the impedance
is very low.
The zero-sequence impedance varies significantly with design. The most
prominent difference is due to the pitch of the stator winding. A pole pitch
is the number of degrees that the rotor has to move to change from one pole
to the other. In a 2-pole machine, one pole pitch is 180
∞
, and in a 4-pole
machine, it is 90
∞
. The
pitch factor
(or just the
pitch
) of the stator winding is
the portion of the pole pitch that the stator winding spans. A full-pitch stator
winding spans the full pitch. A fractional pitch winding spans less than the
full pitch. Figure 14.2 shows a comparison of a full-pitch winding and a 2/
3-pitch winding. In this figure, each phase has two windings (
a
1
and
a
2
for
example); the current in each winding goes out on one slot conductor (like
a
1
) and returns in another slot conductor labeled with the prime notation
(like
a
¢
1
). The 2/3-pitch winding reduces the zero-sequence impedance the
most. Because the two conductors in each slot have current in opposite
directions, the fields cancel almost completely (since
a = b = c =
-
a
¢
=
-
b
¢
=
-
c
¢
for zero-sequence current). Other common pitch factors are 5/8 and 3/4.
Synchronization is important when connecting synchronous generators. If
a large machine is out of synch with the utility when it is connected, the
sudden torque can damage the generator, and the connecting switch and
other devices will have a large voltage disturbance. To avoid these problems,
synchronizing relays are required for synchronous generators to ensure that
the voltage, frequency, phase angle, and phasing are the same on the utility
and generator. Normally, the generator is brought up to speed, and the field
current is adjusted to bring the voltage close to the utility system. The
frequency is more precisely adjusted to bring it within 0.5 Hz of the power
system. Then, the synchronizing relay allows closing when the two voltages
are within 10
∞
(CEA 128 D 767, 1994).
1791_book.fm Page 706 Monday, August 4, 2003 3:20 PM
(C) 2004 by CRC Press LLC