
192 Electrotechnical Systems
Here θ is the angle between the phase A axis and the axis q of the reference frame. It
is supposed that IM windings are connected in a three-wire Y conguration with an
insulated middle point, so that the zero sequence current is null.
Because the line (phase-to-phase) voltages are applied to IM, after substitution of
the formulas,
UUUU
UU
U
UU
U
ca ab bc a
ab ca
b
bc ab
c
ca bc
==
––,
–
,
–
,
–
(5.18)
it follows for the stator:
UU U
UU
qs abs bcs
ds abs
=++
=+−
1
3
1
3
2
cos(cossin )
sin(sin
θθθ
θθ
33cos )θ U
bcs
(5.19)
Analogous for the rotor
UU U
UU
qr abr bcr
dr abr
=++
=+
1
3
3
1
3
2cos cos sin
2sin sin
βββ
ββ
( −−
)3 cosβ U
bcr
(5.2 ...