an investigation of dual stator winding induction machines

varying inductances excited by four independent angular frequencies (ω1, ω2, ωs1, ωs2)
are expressed as :
m ⋅ P
( mω
+ nω
+ kω
+ zω
)
+∞ +∞ +∞ +∞
1 2 3 4
∑∑∑∑
=
m= 0 n= −∞k=
−∞z=
−∞ mω1
+ nω2
+ kω3
+ zω4
n ⋅ P
( mω
+ nω
+ kω
+ zω
)
+∞ +∞ +∞ +∞
1 2 3 4
∑∑ ∑∑
=
n= 0 m= −∞ k= −∞z=
−∞ mω1
+ nω2
+ kω3
+ zω4
k ⋅ P
( mω
+ nω
+ kω
+ zω
)
+∞ +∞ +∞ +∞
1 2 3 4
∑∑∑∑
=
k= 0 m= −∞ n= −∞z=
−∞ mω1
+ nω2
+ kω3
+ zω4
+∞
+∞
+∞
+∞
∑∑∑∑
z ⋅ P
( mω1
+ nω2
+ kω3
+ zω4
)
= 0
z= 0 m= −∞ n= −∞ k= −∞ mω1
+ nω2
+ kω3
+ zω4
181
0
0
0
(4.13)
The average input power into the machine is assumed to be positive, average power
going out of the machine is negative and P( ω ω ) = P(
−ω
−ω
)
( mω
nω
+ kω
zω
)
1
2
3
4
a
+ .
P + + is the average real power flow at angular frequency
( m ω nω
+ kω
+ zω
)
1
+ . In using (4.13), all sources of loss (such as copper and core
2
3
4
losses in the electrical circuit and the mechanical and frictional losses in the mechanical
subsystem) are considered to be external to the energy converting electric machines.
Hence, (4.13) in the context of dual stator winding induction machines, the average
powers are the input and output powers of the time varying inductances between the
stator and rotor windings. The angular frequency of the voltages impressed on the ABC
winding set is ω 1 and the angular frequency of the rotor currents due to this voltage is
ω s1
, the angular frequency of the voltage connected to the XYZ winding set and the
corresponding angular frequency of the rotor currents induced by this impressed voltage
source are 2
ω , s2
ω respectively. The dependent angular frequency is the mechanical
b
a
b