an investigation of dual stator winding induction machines

while the second three-phase winding set wound for P2 poles is called the XYZ winding
set.
V = r i + pλ
− jω
λ
(10.55)
qdsi
ri qdri
si qdsi
qdri
qdsi
ei
qdsi
( ωei
ωri
) qdri
0 = r i + pλ
− j − λ
(10.56)
where, the complex variable forms of the voltages and flux linkages are defined as
V V +
jV
qdsi = qsi dsi , qdri qri dri
V = V + jV , λ qdri = λqri
+ jλdri
, λ qdsi = λqsi
+ jλdsi
. The
frequencies of the supply voltages are ω ei and the rotor electric speeds are ω ri . In all
these and subsequent equations, i = 1,
2 represent the state variables for ABC winding set
and XYZ winding set respectively.
where,
The stator and rotor currents are expressed in terms of the flux linkages as:
L L
= (10.57)
ri
mi
iqdsi λqdsi − λqdri
Di
Di
L L
= (10.58)
si
mi
iqdri λqdri − λqdsi
Di
Di
D = L L − L
i
si
ri
2
mi
Substituting equations (10.57-10.58) into (10.55-10.56) to eliminate the currents, the
voltage equations can be expressed in terms of flux linkages as:
r L r L
= (10.59)
si ri
si mi
Vqdsi λqdsi − λqdri
+ pλqdsi
− jωeiλqdsi
Di
Di
r L r L
0 = λ −
(10.60)
ri si
ri mi
qdri − λqdsi
+ pλqdri
− j
Di
Di
( ωei
ωri
) λqdri
If the stator and rotor flux linkages are chosen as state variables,
X i
⎡λ
= ⎢
⎣λ
qdsi
qdri
⎤ ⎡1
0⎤
⎡Vqdsi
⎤
⎥ , B = ⎢ ⎥ , U
i =
⎦ ⎣0
1
⎢ ⎥
⎦ ⎣ 0 ⎦
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