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

2. Voltage Source Inverter Fed Induction Motor Drive
In the hexagon trajectory part only active vectors are used. The duration of these
vectors t 1 and t 2 are obtained from trigonometrical relationships and can be expressed in
the following equations:
3 cosα
− sinα
t 1
= T s
(2.37a)
3 cosα
+ sinα
t
= −
(2.37b)
2
Ts
t1
t 0
= t 7
= 0
(2.37c)
The output voltage waveform is given approximately by linear segments for the
hexagon trajectory and sinusoidal segments for the circular trajectory. Boundary of the
segments is determined by a crossover angle θ which depends on the reference voltage
value. As known from Fig. 2.21 the upper limit in mode I is when θ = 0°. Then the
voltage trajectory is fully on the hexagon. The fundamental peak value generated in this
way voltage is 95% of the peak voltage of the square wave [75]. It gives modulation
index M = 0.952.
For the modulation index higher then 0.952 the overmodulation mode II is applied.
The overmodulation mode II is shown in Fig. 2.22. In this mode not only the reference
vector amplitude is modified but also an angle. The reference angle from α to α *
changed.
is
U 3
(010)
U 2
(110)
α h
U c
*
U c
U 4
(011)
U 0
(000)
α
∗
α
α h
U 1
(100)
U 7
(111)
U 5
(001) U 6
(101)
Fig. 2.22. Overmodulation mode II where both amplitude and angle is changed
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