
Multiphase AC Machines 3-11
v R i
d
dt
v R i
d
dt
v R i
d
dt
v
x s s x s
x s
y s s y s
y s
x s s x s
x s
1 1
1
1 1
1
2 2
2
= +
= +
= +
ψ
ψ
ψ
yy s s y s
y s
s s s
s
R i
d
dt
v R i
d
2 2
2
0 0
0
= +
= +
ψ
ψ
(3.20b)
ψ
ψ
ψ
ds ls m ds m dr
qs ls m qs m qr
dr lr m dr
L L i L i
L L i L i
L L i
= + +
= + +
= + +
( )
( )
( ) LL i
L L i L i
m ds
qr lr m qr m qs
ψ = + +( )
(3.21a)
ψ
ψ
ψ
ψ
ψ
x s ls x s
y s ls y s
x s ls x s
y s ls y s
s
L i
L i
L i
L i
L
1 1
1 1
2 2
2 2
0
=
=
=
=
=
……………
lls s
i
0
(3.21b)
1r-Axis
1s-Axis
ω
a
90°
θ
ω
θ
s
θ
r
Rotor
q-Axis
Stator
FIGURE 3.2 Illustration of various angles used in the rotational transformation of an induction machine’s model
(1s and 1r denote magnetic axes of the rst stator and rotor phas