Environmental Engineering Reference
In-Depth Information
a)
b)
Fig. 3.17
Torque characteristic in grid operation.
(a)
Turbo-type machine;
(b)
Salient polema-
chine,
X
q
<
X
d
Figure 3.17a shows the torque vs. load angle. Theoretical limits of stable opera-
tion are right angles,
|
ϑ
|
=
π
/
2, where generating and motoring breakdown torques
appear, respectively.
The simple model of Fig. 3.15 is no longer sufficient to describe salient pole
machines, where due to magnetic inhomogenity the synchronous reactances in di-
rect and quadrature axis are of different magnitude,
X
q
=
X
d
. The current loci
then form Pascal conics instead of circles. A variable-reluctance torque compo-
nent, proportional to the square of the voltage and the sine of double load an-
gle, is generated in addition to the synchronous component. Figure 3.17b shows
an example for a machine where
X
q
<
X
d
; now the break down torque appearing
at
|
ϑ
| ≤
π
/
2.
3.3.2.4 Operation at Given Passive Load
Different from grid operation with given terminal voltage and frequency, in stand-
alone operation the voltage is load-dependant. Assuming a passive resistive/induc-
tive load as indicated in Fig. 3.18a, and using frequency
ω
1
which reflects the speed
as independent variable, armature current and terminal voltage are expressed by:
U
p
R
tot
1
1 +
j
R
L
R
tot
1 +
j
ω
1
τ
L
1 +
j
I
1
=
−
;
U
1
=
U
p
(3.20)
ω
1
τ
ω
1
τ
where
τ
L
=
L
L
R
L
=
L
tot
R
tot
=
L
d
1 +
L
L
/
L
d
1 +
R
1
/
R
L
R
tot
=
R
1
+
R
L
;
L
tot
=
L
d
+
L
L
;
;
τ
R
L
The inductor voltage (r.m.s. value) is proportional to the impressed inductor flux
linkage
Ψ
p
(amplitude value) and angular speed
Ω
=
ω
1
/
z
p
:
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