Network Protection & Automation Guide
5-8
Generally, the leakage reactance X
L
is equal to the effective
field leakage reactance
X’
f
, about 0.1-0.25p.u. The principal
factor determining the value of
X’
f
is the field leakage. This is
largely beyond the control of the designer, in that other
considerations are at present more significant than field
leakage and hence take precedence in determining the field
design.
X
L
can be varied as already outlined and, in practice,
control of transient reactance is usually achieved by varying
X
L
.
5.8.3 Sub-Transient Reactance X’’
d
=X
L
+X’
kd
The sub-transient reactance determines the initial current
peaks following a disturbance and in the case of a sudden fault
is of importance for selecting the breaking capacity of
associated circuit breakers. The mechanical stresses on the
machine reach maximum values that depend on this constant.
The effective damper winding leakage reactance
X’
kd
is largely
determined by the leakage of the damper windings and control
of this is only possible to a limited extent.
X’
kd
normally has a
value between 0.05 and 0.15p.u. The major factor is
X
L
which, as indicated previously, is of the order of 0.1-0.25p.u.,
and control of the sub-transient reactance is normally achieved
by varying
X
L
.
Good transient stability is obtained by keeping the value of
X’
d
low, which therefore also implies a low value of
X”
d
. The fault
rating of switchgear, etc. is therefore relatively high. It is not
normally possible to improve transient stability performance in
a generator without adverse effects on fault levels, and vice
versa.
5.9 NEGATIVE SEQUENCE REACTANCE
Negative sequence currents can arise whenever there is any
unbalance present in the system. Their effect is to set up a
field rotating in the opposite direction to the main field
generated by the rotor winding, so subjecting the rotor to
double frequency flux pulsations. This gives rise to parasitic
currents and heating; most machines are quite limited in the
amount of such current which they are able to carry, both in
the steady–state and transiently.
An accurate calculation of the negative sequence current
capability of a generator involves consideration of the current
paths in the rotor body. In a turbine generator rotor, for
instance, they include the solid rotor body, slot wedges,
excitation winding and end-winding retaining rings. There is a
tendency for local over-heating to occur and, although possible
for the stator, continuous local temperature measurement is
not practical in the rotor. Calculation requires complex
mathematical techniques to be applied, and involves specialist
software.
In practice an empirical method is used, based on the fact that
a given type of machine is capable of carrying, for short
periods, an amount of heat determined by its thermal capacity,
and for a long period, a rate of heat input which it can
dissipate continuously. Synchronous machines are designed to
operate continuously on an unbalanced system so that with
none of the phase currents exceeding the rated current, the
ratio of the negative sequence current
I
2
to the rated current I
N
does not exceed the values given in Table 5.2. Under fault
conditions, the machine can also operate with the product of
2
N
I
I
¸
¸
¹
·
¨
¨
©
§
2
and time in seconds (t) not exceeding the values
given.
Rotor
construction
Rotor
Cooling
Machine
Type/Rating
(SN) (MVA)
Maximum
I
2
/I
N
for
continuous
operation
Maximum
(I
2
/I
N
)
2
t for
operation
during faults
indirect motors 0.1 20
generators 0.08 20
synchronous
condensers
0.1 20
direct motors 0.08 15
generators 0.05 15
Salient
synchronous
condensers
0.08 15
indirectly cooled
(air)
all 0.1 15
indirectly cooled
(hydrogen)
all 0.1 10
directly cooled <=350 0.08 8
351-900 Note 1 Note 2
901-1250 Note 1 5
Cylindrical
1251-1600 0.05 5
Note 1: Calculate as
4
103
350
08.0
2
u
N
S
N
I
I
Note 2: Calculate as
3500054508
2
2
»
»
¼
º
«
«
¬
ª
N
S.t
N
I
I
Table 5.2: Unbalanced operating conditions for synchronous machines
(with acknowledgement to IEC 60034-1)
5.10 ZERO SEQUENCE REACTANCE
If a machine operates with an earthed neutral, a system earth
fault gives rise to zero sequence currents in the machine. This
reactance represents the machines’ contribution to the total
impedance offered to these currents. In practice it is generally
low and often outweighed by other impedances present in the
circuit.
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