
22-16 Power Electronics and Motor Drives
Trigonometric functions of the angle between two vectors may be calculated as follows:
cos( ) ,ϕ
α α β β
rs
r
r
r
s
r
r
r
s
r
i i i i
i
=
+
2
(22.55)
sin( ) ,ϕ
α β β α
rs
r
r
r
s
r
r
r
s
r
i i i i
i
=
−
2
(22.56)
where superscript r, s denote the current vector components determined respectively in the frame of
references connected to the rotor and the stator.
Components of the rotor current vector
r
r
α β
can be measured directly, but
r
r
α β
have to be estimated.
e main dependence of any induction machine is as follows (Figure 22.3):
i i i
m s r
= + ,
(22.57)
where i
m
, i
s
, i
r
are the magnetizing, stator and rotor current vectors. ...