Environmental Engineering Reference
In-Depth Information
where L s =
L
+
M , and the field flux linkage can be rewritten as
f
=
L f i f +
M f
i
,
cos
θ ,
(18.2)
where
· , ·
denotes the conventional inner product. The second term M f
i
,
cos
θ
is constant
if the three phase currents are sinusoidal (as functions of
) and balanced. Assume that the
resistance of the stator windings is R s , then the phase terminal voltages
θ
v c ] T
v =
[
v a
v b
can
be obtained from (18.1) as
d
dt
d i
dt +
v =−
R s i
=−
R s i
L s
e
,
(18.3)
e c ] T
where e
=
[ e a
e b
is the back EMF due to the rotor movement given by
M f d i f
θ sin
˙
e
=
M f i f
θ
dt
cos
θ.
(18.4)
Similarly, according to (18.2), the field terminal voltage is
d
f
dt ,
v f
=−
R f i f
(18.5)
where R f is the resistance of the rotor windings. However, this is not used here because the
field current i f , instead of
v f , is used as an adjustable constant input. This completes modelling
the electrical part of the machine.
18.1.2 Mechanical Part
The mechanical part of the machine is governed by
J ¨
D p ˙
θ =
T m
T e
θ,
(18.6)
where J is the moment of inertia of all parts rotating with the rotor, T m is the mechanical
torque, T e is the electromagnetic toque and D p is a damping factor. T e can be found from the
energy E stored in the machine magnetic field, i.e. ,
1
2 i
1
2 i f f
=
, +
E
1
2
1
2 i f ( L f i f +
=
i
,
L s i
+
M f i f
cos
θ +
M f
i
,
cos
θ
)
1
2
1
2 L f i f .
=
i
,
L s i
+
M f i f
i
,
cos
θ +
 
Search WWH ::




Custom Search