Environmental Engineering Reference
In-Depth Information
stator inductance. The total self-inductance of a stator winding is taken as total
turns in series squared times the magnetic circuit permeance, which, in terms of its
constituent parts, can be stated as
L
p
¼
N
s
G
L
p
¼
L
ms
þ
L
sl
þ
L
et
ð
Hy
Þ
ð
5
:
18
Þ
where phase inductance,
L
p
, is composed of magnetizing inductance defined as that
fraction of the total stator flux that links the rotor, a slot leakage term for flux
that crosses the stator slots transversely and does not cross the airgap, and an end
turn leakage flux due to flux on the ends of the machine that neither crosses the
airgap nor links the rotor. At this point, it is essential to clarify what is meant by
airgap. Let
k
c
be the carter coefficient, the modifier to physical airgap that accounts
for the presence of open slots. Then the magnetic equivalent airgap,
g
0
, for the
various machine types is as given in Table 5.7.
Table 5.7 Air gap of various electric machines
BDCM
SPM
IPM
IM
VRM
SRM
g
0
=
k
c
g
+
L
m
g
0
=
k
c
g
+
L
m
g
0
=
k
c
g
0
=
k
c
g
0
=
g
0
=
g
The constituents of phase inductance listed in (5.19) are
ð
2
p
m
0
D
si
h
2
g
0
N
2
L
ms
¼
ðqÞ
d
q
0
ð
Hy
Þ
ð
5
:
19
Þ
2
pm
0
D
si
h
2
g
0
N
s
P
L
ms
¼
There can be some discrepancies in the interpretation of (5.19), particularly in
the definition of the winding function,
N
(
q
), in the case of a
P
-pole machine. The
second expression in (5.19) gives the magnetizing inductance of a
P
-pole machine
in terms of its stator bore, stack length,
h
, and total series connected turns:
L
sl
¼
12
N
s
h
r
s
Q
s
ð
5
:
20
Þ
where the variable
r
s
is the slot geometry describing the slot permeance and
Q
s
is
the number of stator slots, which is equal to the number of coils in a 2-layer
winding. Slot leakage inductance is very design dependent, but the relationship
given in (5.20) is what is typically used to compute its value:
m
0
PN
c
D
et
2
ln 4
D
et
L
et
¼
GMD
2
r
S
a
2
ð
5
:
21
Þ
GMD
¼
0
:
447
