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Fig. 3. Determination of the voltage-rise during
short-circuit.
Ego voltage immediately before the short-circuit
Eg, internal voltage immediately after the
short-circuit
rt time of the short-circuit
tm magnetization time
where Ego is the voltage at the moment of
short-circuit.
Since the short-circuit time in question is
relatively short (^æ 0.2 sec.), it is possible to substitute
the voltage-rise curve during this period by a straight
line with the slope tan oc’, fig. 3, and to use for the
voltage the expression
EgT=Eg0+r tana’ (8)
In accordance with the supposition, the
short-circuit current should be kept constant during the
short-circuit time tly which in this case is achieved
with very good approximation if the current has the
same value at r = 0 and r = r^
Thus, considering eq. (7) the following relations
are valid
Ejn
x,i
where Euo + r1 tan oc’ is now the internal voltage
at the time r^
With
In order to obtain a constant current it is thus
necessary to apply an exciter voltage which gives
the same transient current at the voltage Ego
immediately before the short-circuit as the stationary
current at the end value Egs of the corresponding
voltage-rise curve. The appropriate exciter voltage
is to be taken from the stationary short-circuit
characteristic of the machine.
It can be seen that the condition for constant
short-circuit current eq. (14) contains no time constants.
This result is not surprising, considering that the
d.c. part of the field current follows instantly the
short-circuit current and constant short-circuit
current requires constant field.
The stationary short-circuit current
The determination of the appropriate exciter
voltage assumes that the stationary short-circuit
characteristic is known for as high values of current as
the value of the transient short-circuit current.
The experimental determination of the stationary
short-circuit current by increasing the field current
is impossible because of the excessive thermal
stresses on the machine. To avoid the overheating,
excitation tests of short duration with different
values of the exciter voltage on the machine, which
is short-circuited in advance, are however, suitable,
because the short-circuit current follows the field
current without delay. However, when the stator
leakage reactance xs of the generator is known, it
is possible to plot graphically the stationary
short-circuit characteristic if corresponding values of the
stationary short-circuit current and the field current
are known at one point.
The field current for the stationary short-circuit
is namely
lf=cIgs+Io (15)
where c is a constant and I0 = / (Iys • x*) the field
current corresponding to the voltage Igs • xs for the
no-load characteristic of the machine, fig. 4.
If the voltage Igs ■ xs for the maximum current value
is on the linear part of the no-load characteristic,
eq. (9) yields
Ego [*+^r]+T»,an [* +p ^p] (10)
and
ri Lp + O (l+p) J v ;
When —> 0, eq. (11) becomes the tangent of the
voltage-rise curve (tan ac), and thus
I — Ego
lim (tan oc’) = ^ [I -11 = tan =
To La J To
(12)
where Egs is the end value of the voltage-rise curve
(tm = oo).
Hence
Ego \~-l\=EgS-Eg
Li d J
and
Ego
m"
Egs
X,l
I <10 — /</
(13)
(14)
Fig. A. The no-load characteristic.
Igs x.s leakage voltage
If field current
ELTEKN I K 1959 ] 3 1
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