ISSN: 1693-6930
TELKOMNIKA
Vol. 9, No. 3, August 2011 : 539 – 546 542
The tested motor is a 15kw interior PMSM. Its parameters are shown in Table. 1. The reference amplitude of stator flux is 0.06Wb. According to equ. 8 and Table. 1, k=0.238.
According to 12, M versus α
with 0
°
δ 90
°
and k=0.238 is shown in Figure 4. Figure 4 shows if the angle between stator flux vector and the applying voltage vector is within 0
°
, 103
°
, voltage vector increases torque and if the angle is within 180
°
, 282
°
, voltage vector decreases torque.
Table 1. The Parameters of tested PMSM Parameters
Notations values
Pole pairs p
6 Stator resistance
R
s
0.0142Ω d-axis stator
inductance L
d
0.6660mH q-axis stator
inductance L
q
0.8745mH Permanent flux
ψ
f
0.06Wb
Figure 4. M versus α
3. Voltage vector selecton strategy
According to effects of voltage vector on the amplitude of stator flux, torque angle and torque of the tested PMSM, the selection area for V
11
voltage vector to increase the amplitude of stator flux, torque angle and torque is
δ
s
, δ
s
+90
°
， the selection area for V
01
voltage vector to decrease the amplitude of stator flux and increase torque angle and torque is
δ
s
+90
°
, δ
s
+103
°
， the selection area for V
00
voltage vector to decrease the amplitude of stator flux, torque angle and torque is
δ
s
+180
°
, δ
s
+270
°
， the selection area for V
10
voltage vector to increase the amplitude of stator flux and decrease torque angle and torque is
δ
s
+270
°
, δ
s
+283
°
, where
δ
s
is the angular position of stator flux vector in the stationary reference frame. According to voltage vector selection area, a simplified voltage vector selection strategy
for the tested motor is proposed shown in 13.
+ ∠
= ∠
+ ∠
= ∠
+ =
∠ +
= ∠
° °
° °
° °
° °
360 ,
180 mod
360 ,
180 mod
360 ,
100 mod
360 ,
60 mod
01 10
11 00
01 11
V V
V V
V V
s s
r r
r r
r r
δ δ
13
The angular position of voltage vector obtained by equ. 13 is arbitrary, so the technology of space vector modulation SVM must be used to generate the applying voltage
vector. In the SVM, the amplitude of the applying voltage vector is constant which is the radius of the inscribed circle of the hexagon shown in Figure 5. According to Figure 5, it is shown in
14, where U
dc
is the dc-link voltage.
dc s
U V
3 3
=
14
TELKOMNIKA ISSN: 1693-6930
A Simplfied Voltage Vector Selection Strategy for Direct Torque Control Li Yaohua 543
We assume that the applying voltage vector locates between V
1
and V
2
shown in Figure 6, where
γ is the angle between V
1
and the applying voltage vector V
s
. According to the law of sine, 15 holds true.
° °
= −
= 120
sin 3
3 60
sin 3
2 sin
3 2
1 2
s dc
dc dc
T U
T U
T U
γ γ
15 Thus the applying time of V
1
, V
2
and V in a sampling period is shown in 16.
−
− =
⋅ =
⋅ −
=
°
2 1
2 1
sin 60
sin T
T T
T T
T T
T
s s
s
γ γ
16
The diagram of the PMSM DTC system using voltage vector selection strategy is shown in Figure 7.
1
V r
2
V r
3
V r
4
V r
5
V r
6
V r
s
V r
Figure 5. The amplitude of the applying voltage vector
1
V r
s s
V T r
2
V r
1 1
V T ⋅
r
2 2
V T ⋅
r 120
°
γ
Figure 6. The SVM
Motor
S
A
Stator flux comparator
+
−
+
Inverter
Angular position of stator flux vector
SVM
s
V ∠
r Voltage
vector selection
strategy S
B
S
C
s
δ
Torque comparator
φ
τ
e
T
e
T
s
ψ
s
ψ
−
Figure 7. The PMSM DTC system using voltage vector selection strategy
4. Experimental results 4.1. Test bench
