an investigation of dual stator winding induction machines

The system equation in matrix form becomes:
•
where,
X = A X + BU
i
i
⎡ rsiLri
⎢−
+ jωei
Di
Ai
= ⎢
⎢ rriLmi
⎢⎣
Di
i
rriL
−
D
i
si
rsiL
D
+
j
mi
( ) ⎥
⎥ ⎥⎥
i
ω − ω
The stator currents are expressed in terms of flux linkages as:
qdsi
i
i
ei
370
ri
⎤
⎦
.
(10.61)
i = C X
(10.62)
⎡ L ⎤
ri Lmi
where, C i = ⎢ − ⎥
⎣ Di
Di
⎦
The electromagnetic torque due to each winding set expressed in terms of the flux
linkages is given as :
3P
L
( λ λ − λ )
ri Tei = dri qsi qriλdsi
4 Di
(10.63)
The total electromagnetic torque of the dual stator winding induction machine is the
sum of the electromagnetic torque components due to the interaction of the separate two
three-phase winding sets with the squirrel-cage rotor.
10.6.2 Full Order Observer Model
The full-order flux observer equations of the machine are defined as:
si ri
si mi
qsi = Vqsi
− λqsi
+ λqri
−ω
eiλdsi
Di
Di
11i
( i − iˆ
)
r L r L
p ˆ λ ˆ ˆ ˆ + K ⋅
(10.64)
si ri si mi
dsi = Vdsi
− λds
+ λdri
+ ωeiλqsi
Di
Di
12i
qsi
qsi
( i − iˆ
)
r L r L
p ˆ λ ˆ ˆ ˆ + K ⋅
(10.65)
dsi
dsi