Direct Torque Control with Space Vector Modulation (DTC-SVM) of ...

Voltage source PWM inverter for PMSM supply
The three-phase output voltage of the inverter can be described by space vector
definition as:
U
k
⎧2
⎪ U
3
⎪
= ⎨
⎪⎪⎪ 0
⎩
DC
e
π
j( k−1) 3
for k =1,2...,6.
for k=0,7.
, (3.3)
where k denotes numbers vector.
Vectors from 1-6 are called active vectors, whereas vectors 0,7 are called zero vectors
or non active vectors. The voltage space vector
U
k
in complex plane forms a regular
hexagon and divides in into six equal sectors (one sector takes 60 electrical degree) Fig.
3.8.
Im
U 4
(011)
U 3 (010)
sector3
sector4
sector2
sector5
U (110) 2
sector1
U (000) U 1
(100)
0 U (111) 7 Re
sector6
2
U
3 DC
U (001)
U (101)
5 6
Figure 3.8 Representation of the inverter states in the complex space.
In practice the real voltage source inverter has non-linear characteristic due to [19]:
• the dead-time,
• a voltage drop across the power switches,
• pulsation of the DC link voltage.
Dead time effect [17,20,27,30]
Semiconductors power switches of voltage source inverter operate not ideally. They do
not turn-on or turn-off instantaneously. Therefore it is necessary to include a protection
time to avoid a short circuit in the DC link, when two switching devices are in the same
leg (see Fig. 3.9). This time T d
is included in the control signals and it is called “dead
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