Datasheet

The magnetic flux linkages 
i
are composed by two items, one due to the stator currents, one to the permanent magnets.
The permanent magnet creates a magnetic field that is constant in amplitude and fixed in position in respect to the rotor.
This magnetic field can be represented by vector 
m
whose position in respect to the stator is determined by the angle 
between the vector direction and the stator reference frame.
The contribution of the permanent magnets in the flux linkages depends on the relative position of the rotor and the
stator represented by the mechanical-electric angle.
It is, in every axis, the projection of the constant flux vector 
m
in the direction of the axis:
)
3
4
cos(
)
3
2
cos(
)cos(








mcc
mbb
maa
Li
Li
Li
Supposing that the rotor is rotating at constant speed  (that is: (t) = t) the flux linkages derivatives can be calculated,
and we obtain:
)
3
4
sin(
)
3
2
sin(
)sin(








m
b
bSc
m
b
bSb
m
a
aSa
dt
di
LiRv
dt
di
LiRv
dt
di
LiRv
A “three phase system”, may be represented by an equivalent “two phase system”. So there by using specific
transformations, our three equations system is equivalent to a two equations system. It is basically a mathematical
representation in a new reference coordinates system.
In the two phases (,) fixed system the above equations become:
dt
d
iRv
dt
d
iRv
S
S










m
a
a’
b
c
c’
b’
a axis
b axis
c axis
Real axes (a, b, c) and equivalent ones (, ); a fixed amplitude vector can be completely determined by its
position respect the (, ) system (angle )

’
 axis
’
’
 axis