AN1931D Freescale Semiconductor / Motorola, AN1931D Datasheet - Page 6

• Manufacturer Part Number: AN1931D
• Description: 3-Phase PM Synchronous Motor Vector Control
• Manufacturer: Freescale Semiconductor / Motorola

Target Motor Theory
6
The space vector defined by
space vector is equal to the instantaneous value of the direct-axis stator current component, i
whose imaginary part is equal to the quadrature-axis stator current component, i
current space vector, in the stationary reference frame attached to the stator can be expressed as:
In symmetrical three-phase machines, the direct and quadrature axis stator currents i
quadrature-phase (two-phase) current components, which are related to the actual three-phase stator
currents as follows:
where k=2/3 is a transformation constant.
The space vectors of other motor quantities (voltages, currents, magnetic fluxes etc.) can be defined in
the same way as the stator current space vector.
Figure 3-2. Stator Current Space Vector and Its Projection
phase- b
Freescale Semiconductor, Inc.
3-Phase PM Synchronous Motor Vector Control
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i
s
(EQ 3-2.)
i
s
i
s
=
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i
s
=
k i
=
can be expressed utilizing two-axis theory. The real part of the
k
sa
------ - i
i
2
s
3
–
1
-- - i
2
+
sb
sb
ji
–
s
–
i
sc
1
-- - i
2
sc
s
s
. Thus, the stator
, i
s
MOTOROLA
are fictitious
(EQ 3-3.)
(EQ 3-4.)
(EQ 3-5.)
s
, and