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Fig. 1. The voltage-rise characteristics.
Eg no-load voltage of the generator (per-unit
values)
E,u no-load voltage of the exciter (per-unit values)
tm magnetization time
where T0 is the no-load time constant of the field
coil of the generator. T() cannot, however, be
determined directly for solid steel rotors or rotors with
damping windings.
The voltage-rise characteristics
If the exciter is switched on at a certain voltage
to the generator field, the generator voltage rises
until the beginning of the saturation according to
an exponential function. The voltage-rise
characteristics for a given machine may be represented by a
family of curves, fig. 1, with the exciter voltage Em
as parameter.
The field current for laminated rotors where eddy
currents cannot develop shows a similar course as
the generator voltage and deviates only with higher
voltages under the influence of saturation. Such a
proportionality between the generator voltage and
the field current does not occur with solid rotors
where eddy currents can develop freely, and the
deviation increases with increasing exciter voltage.
The deviation between the two values can be best
displayed by means of curves, fig. 2, showing the
generator no-load voltage E(J and the corresponding
field current If as functions of the magnetization
time.
This deviation of the field current from the
exponential characteristic makes the determination of
the time constant T0 in eq. (4) impossible. The
generator voltage is, however, caused by the common
flux of the field current and the eddy currents and,
like laminated rotors, has an exponential
characteristic until the beginning of the saturation. If the
time constant of the voltage-rise curves is applied
in eq. (4), the influence of the eddy currents with
regard to the time constant is eliminated and the
solid rotor is replaced by a laminated one. It is also
possible to determine the no-load time constant in
eq. (4) by means of the transient short-circuit time
constant T’,i, since
o T„ = T a
Conditions for constant short-circuit current
The voltage-rise characteristics, fig. 1, show that
different exciter voltages Em can be used for
short-circuit tests at a given generator voltage Eg provided
that the magnetization time tm is chosen accordingly.
The problem is to determine the value of the exciter
voltage that is to be used in order to get a constant
short-circuit current.
The transient short-circuit current at the moment
of short-circuit (r = 0) may be expressed, according
to eq. (2), in the following form
The leakage coefficient is
Igs_x’ d
1 go Xd
(5)
where x’d is the transient reactance and Xd the
synchronous reactance of the generator.
In the presence of external reactance x, eq. (5)
changes to
1+-
0 =
x’d+x
Xd + x Xd
x’d x’d
X d
x
(6)
which shows that o depends only on the
reactance-ratio x/x’d, because the ratio xd/x’d is constant, being
influenced by the dimensions of the machine.
Using the transient and synchronous reactances,
eq. (2) now gives
x’d Xd L g J
(7)
Fig. 2. Excitation-time characteristic.
Eg no-load voltage of the generator (per-unit
values)
If field current (per-unit values)
tm magnetization time
] 130 ELTEKN I K 1959
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