Space Vector Modulated – Direct Torque Controlled (DTC – SVM ...

2. Voltage Source Inverter Fed Induction Motor Drive
The times t 1 and t 2 are obtained from simple trigonometrical relationships and can be
expressed in the following equations:
2 3
t
1
= MTs
sin( π 3 −α
)
(2.24a)
π
2 3
t
2
= MTs
sin( α )
(2.24b)
π
Where M is a modulation index, which for the space vector modulation is defined as:
M
U
=
U
c
1( six−step)
U
c
=
2
U
π
dc
(2.25)
where:
U
c
- vector magnitude, or phase peak value,
U1 ( six − step)
- fundamental peak value ( U dc
π )
2 of the square-phase voltage
wave.
The modulation index M varies from 0 to 1 at the square-wave output. The length of
the U c vector, which is possible to realize in the whole range of α is equal to
3
U
3
This is a radius of the circle inscribed of the hexagon in Fig. 2.13. At this condition the
modulation index is equal:
dc
.
M
=
3
U
3
2
U
π
dc
dc
= 0.907
(2.26)
This means that 90.7% of the fundamental at the square wave can be obtained. It
extends the linear range of modulation in relation to 78.55% in the sinusoidal
modulation techniques (Fig. 2.10).
After calculation of t 1 and t 2 from equations (2.24) the residual sampling time is
reserved for zero vectors U 0 and U 7 .
t =
s
− ( + = t + t
(2.27)
0 ,7
T t1
t2
)
0
7
24