an investigation of dual stator winding induction machines

The expressions of t1 i and t2 i are given in (10.75-10.80). Equation (10.119) can also
be function expressed as:
H
i
= −
( ω − ˆ ω )
L
( ω t + pt ) + j(
pt − ω t )
2
ˆ
mi ei 1i
2i
1i
ei 2i
λ qdri ⋅ rm rm ⋅ ⋅
. (10.127)
2 2
Di
t1i
+ t2i
Then the imaginary and real parts of (10.127) are given as:
Im
Re
L
D
2
( ) ˆ
mi 1i
H
( ˆ
i = − λqdri
⋅ ωrm
− ωrm
) ⋅ ⋅ 2 2
i
L
D
pt − ω t
t + t
2
( ) ˆ
mi ei 1i
H
( ˆ
i = − λqdri
⋅ ωrm
− ωrm
) ⋅ ⋅ 2 2
i
1i
1i
2i
395
ei 2i
ω t + pt
t + t
To simplify the analysis, the following definitions are made:
f
1i
f
2i
L
pt
−ω
t
2
( ) ˆ mi 1i
p = qdri ⋅ ⋅ 2 2
2i
2i
(10.128)
(10.129)
ei 2i
λ (10.130)
Di
t1i
+ t2i
L
pt
+ ω t
2
( ) ˆ mi 2i
p = qdri ⋅ ⋅ 2 2
ei 1i
λ (10.131)
Di
t1i
+ t2i
Then (10.125) can be rewritten as:
ˆ ω
rm
= G ⋅ P ⋅ k
1
+ G ⋅ P ⋅
2
{ f ( p)
k f ( p)
} ( ω ˆ
11 + 1 ⋅ 21 ⋅ rm − ωrm
)
( 1−
k ) { f ( p)
+ k ⋅ f ( p)
} ⋅ ( ω − ˆ ω )
12
2
22
rm
rm
(10.132)
The first idea of speed estimation is an adjustable combination of the error signals
from both stator winding sets. The computed error function is expressed as:
ε = k
+
*
*
{ k1
Im[
ˆ λ ( ˆ ) ] ( ) [ ˆ ( ˆ
qdr1
iqds1
− iqds1
+ 1−
k1
Re λqdr1
iqds1
− iqds1)
] }
*
*
( 1−
k)
{ k Im ˆ λ ( i − iˆ
) + 1−
k Re ˆ λ i − iˆ
}
2
[ ] ( ) [ ( ) ]
qdr 2
qds2
qds2
2
qdr 2
qds2
qds2
(10.133)
where, k is used to partition the error signals from two stator windings and 0 ≤ k ≤1
; 1 k
is used to partition the active power and reactive power of ABC winding set and