Hardware Reference
In-Depth Information
given in the following.
From Figure 4.10, the stator voltages for the three phases can be written
as:
⎨
dt
+M
AB
di
dt
+M
AC
di
dt
= e
B
+ R
B
i
B
+ L
BB
di
dt
+M
BA
di
A
= e
A
+ R
A
i
A
+ L
AA
di
A
V
AN
V
BN
V
CN
dt
+M
BC
di
dt
= e
C
+ R
C
i
C
+ L
CC
di
dt
+M
CA
di
A
(4.75)
⎩
dt
+M
CB
di
dt
or,
[V ]=[e]+[R][i]+[L
p
][
di
dt
],
(4.76)
where,
e
A
, e
B
and e
C
: phase back-EMF of winding A,
B and C, respectively,
R
A
, R
B
and R
C
: resistance of winding A, B and
C, respectively,
L
AA
, L
BB
and L
CC
: self-inductance of winding A, B
and C, respectively,
M
AB
, M
AC
, M
BA
, M
BC
, M
CA
, M
CB
: mutual
inductance
between
windings,
[V ]=[V
AN
V
BN
V
CN
]
T
,
[e]=[e
A
e
B
e
C
]
T
,
[i]=[i
A
i
B
i
C
]
T
,
[
di
di
B
/dt di
C
/dt]
T
,
dt
]=[di
A
/dt
⎡
⎤
R
A
00
0 R
B
0
00R
C
⎣
⎦
[R]=
,and
⎡
⎤
L
AA
M
AB
M
AC
M
AB
L
BB
M
BC
M
AC
M
BC
L
CC
⎣
⎦
[L
p
=
.
As mentioned in the previous chapter, the micro PMSM used in HDDs
has many special characteristics, one of which is that the Y-connected three
phases are symmetrical and the variation of the self-inductances and mutual-
inductances are very small. So, the analysis can be simpli
fi
ed using the as-
sumptions,
R
A
= R
B
= R
C
= R,
