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Procedia
Engineering
ProcediaProcedia
Engineering 00 (2011)
Engineering 29 000–000
(2012) 1685 – 1689
www.elsevier.com/locate/procedia

2012 International Workshop on Information and Electronics Engineering (IWIEE)

Research and Simulation of DTC Based on SVPWM of

PMSM
Xu Wang, Yan Xing*, Zhipeng He, Yan Liu
College of Information Science and Engineering, Northeastern University, Shenyang-110819, China

Abstract

Abstract: In order to solve the problem of the flux linkage and the torque ripple in conventional direct torque
control(DTC) for permanent magnet synchronous motor (PMSM), a new method which combines space vector pulse
width modulation(SVPWM) with direct torque control is proposed where the hysteresis controllers and the switch
table in conventional DTC system are replaced by SVPWM. Through the simulation with MATLAB, the theoretical
analyses and simulation results indicate that the proposed control method can reduce the flux linkage and torque
ripple in a large extent and have a better dynamic and static performance.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of Harbin University
of Science and Technology

Key words: PMSM; DTC; SVPWM; MATLAB/SIMULINK;

1. Introduction

The conventional DTC system of PMSM has a simple control structure and fine static and dynamic
performance. However, in the conventional DTC system, the switchover among the basic vectors is
discontinuous because the universal voltage inverter has only eight available basic space vectors, while 6
of them are nonzero and distribute in space every 60 degree. In a control period, only one voltage space
vector can be selected, which could not adjust the direction and control the rangeability of stator flux, so
the flux and torque ripple is unavoidable.
For the disadvantage of flux and torque ripple mentioned above, a SVM-DTC method is proposed in
this paper, that is to say the SVPWM is used to reduce the flux and torque ripple. In a control period, two

* Corresponding author. Tel.: 13889858643.

E-mail address: xingyan086@163.com.

1877-7058 © 2011 Published by Elsevier Ltd.

doi:10.1016/j.proeng.2012.01.195
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/ Procedia Engineering
Engineering 29 000–000
00 (2011) (2012) 1685 – 1689

adjacent nonzero voltage vectors and zero vector are selected and their action time is calculated in order
to synthesize the voltage space vector needed and then control the inverter. This method abandons the
switch-table in conventional DTC system. The performance of simulation indicates that the proposed
method can reduce the torque and flux ripple caused by hysteretic controller efficiently.

2. The Mathematical Model of PMSM

Suppose to ignore the core saturation and eddy current and hysteresis loss of the motor and there is no
damper winding in rotor, the following equations describe the mathematical model of PMSM in the α -β
coordinate system:
⎧⎪uα = Rs iα + Ls diα dt − ωrψ f sin θ
⎨ (1)
⎪⎩uβ =Rs iβ + Ls diβ dt + ωrψ f cos θ
⎧=
⎪ψ α ∫ (uα − Rs iα )dt
⎨ (2)
ψ β ∫ (uβ − Rs iβ )dt
⎪⎩=
3
= Te N p (ψ α iβ −ψ β iα ) (3)
2
where uα , uβ , iα and iβ are the stator voltage and current components in the α -β coordinate system,
respectively; Rs and LS are the resistance and the inductance; ψ f is the flux of permanent magnet; ωr
and θ are the rotor angular speed and position and dθ dt = ωr ; p is the differential operator and
p = d / dt .

3. Space Vector Pulse Width Modulation (SVPWM)

SVPWM deems motor and inverter as one object, trying to provide motor with circular magnetic field
with constant amplitude. According to ideal flux circle generated by three-phase symmetric sinusoidal
voltage, use the effective voltage vector generated by different switch patterns of inverter to approximate
the standard flux circle.

3.1. Judgement of Sector Number

Defining the following variables:

⎧U ref 1 = U β
⎪⎪
⎨U= ref 2 3U α − U β (4)
⎪
⎪⎩U ref 3 =− 3Uα − U β
then the sector number N can be obtained as equation (5):
N =sign(U ref 1 ) + 2 sign(U ref 2 ) + 4 sign(U ref 3 ) (5)
where sign
（x）is the sign function.
The corresponding relation of N and sector number are shown in Table 1.
Table 1 Corresponding relation of N and sector number

N 3 1 5 4 6 2
Sector number 1 2 3 4 5 6
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3.2. Calculation of Action Time

When voltage vector is in different sectors, the conducting time of each inverter switch is different.
Shown in Table 2.
Table 2 T1 and T2 in different sectors

Sector 1 2 3 4 5 6
T1 -Z Y X Z -Y -X
T2 X Z -Y -X -Z Y
where
⎧ X = 3U β T / Vdc
⎪⎪
=⎨Y (3Uα + 3U β )T / 2Vdc (6)
⎪
⎪⎩ Z =
(−3U α + 3U β )T / 2Vdc

3.3. Calculation of switching point of voltage vector

Defining the following variables:

⎧Ta = (T − T1 − T2 ) 4
⎪
⎨ T= b Ta + T1 2 (7)
⎪ T= T + T 2
⎩ c b 2

Assign Tcm1 , Tcm 2 and Tcm 3 according to Table 3, where Tcm1 , Tcm 2 and Tcm 3 are defined as the conducting
time of phase A , B and C ,respectively. Comparing the calculated value of switch point ( Tcm1 , Tcm 2 , Tcm 3 )
with triangular wave, we can obtain the output time of SVPWM.
Table 3 Calculation of switch point Tcmp

Sector number 1 2 3 4 5 6
Tcm1 Tb Ta Ta Tc Tc Tb
Tcm 2 Ta Tc Tb Tb Ta Tc
Tcm3 Tc Tb Tc Ta Tb Ta

4. The Direct Torque Control Based On Space Vector Modulation(SVM-DTC)

In the conventional DTC system, the flux amplitude ψ s (k ) and phase angle θ (k ) can be calculated in
the α -β coordinate system through CLARK transformation and some math operation after stator voltage
and current are sampled. After a control period, the flux amplitude becomes ψ s (k + 1) and the phase
angle becomes θ (k + 1) , with the included angle between θ (k ) and θ (k + 1) is Δθ . As is shown in Fig.1.
Define ψ s ( k +1) = ψ s * ， ψ s ( k ) = ψ s , then
=⎧⎪ψ α ( k +1) ψ s * cos(θ + Δθ ) ⎧⎪ψ α ( k ) =ψ s cos(θ )
⎨ , ⎨ (8)
⎪⎩ψ β ( k +1) ψ s * sin(θ + Δθ )
= ⎪⎩ψ β ( k ) = ψ s sin(θ )
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ψ β ( k + 1)

ψ β ref ψ s (k + 1) Δψ s

ψ β (k )

ψ s (k )
Δθ
ψ α ref
θ
0 ψ α (k + 1) ψ α (k ) α

Fig.1 The flux vector in the SVM-DTC system

Define the flux difference between ψ s (k + 1) and ψ s (k ) as ψ ref , that is to say,=
ψ ref ψ s ( k +1) −ψ s ( k ) ,
then
⎧⎪ψ α=ref ψ α ( k +1) −ψ α=
(k ) ψ s * cos(θ +Δθ ) − ψ s cos(θ )
⎨ (9)
⎪⎩ψ β=
ref ψ β ( k +1) −ψ β=
(k ) ψ s * sin(θ +Δθ ) − ψ s sin(θ )
ψ ref can be calculated in equation (9).
In order to make up for error vector ψ ref , an equivalent reference voltage vector U ref is needed.
ψ s (t )
Through the discretization of equation = ∫ (u (t ) − R i (t ))dt ,ψ
s s s ref = ψ s ( k +1) −ψ s ( k ) = us ( k )Ts − Rs is ( k )Ts
is obtained. Then
⎪⎧u=α ref u=α (k ) ψ α ref / Ts + Rs iα ( k )
⎨ (10)
⎪⎩u=
β ref u=β (k ) ψ β ref / Ts + Rs iα ( k )
Putting equation (9) into equation (10), equation (11) can be acquired:
⎪⎧uα ref= uα ( k =) ( ψ s * cos(θ +Δθ ) − ψ s cos(θ )) / Ts + Rs iα ( k )
⎨ (11)
⎪⎩uβ ref= uβ ( k =
) ( ψ s * sin(θ +Δθ ) − ψ s sin(θ )) / Ts + Rs iα ( k )
Based on the principles mentioned before, combining with the conventional DTC principles, the
system structure of SVM-DTC can be built and shown in Fig.2. The error vector ψ ref can be
compensated by stator voltage components uα * and uβ * . And voltage vector selection, action time and
control signal of inverter can be obtained through SVPWM module.
T* ΔT dθ
ψs* ψ ref uα *
T uβ *
ψs

θ uα
uβ
ψα iα
ψβ iβ

Fig.2 The system structure of SVM-DTC

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Engineering0029(2011)
(2012)000–000
1685 – 1689 5 1689

5. Simulation Results

In order to prove the validity and feasibility of SVM-DTC, the simulation module is built in
MATLAB/SIMULINK.
Set the parameters of PMSM as: pole pairs N p = 2 ; stator resistance RS = 18.7Ω ; flux of permanent
magnet ψ f = 0.1717Wb ; inductance Ld = Lq = 26.82mH ; given revolving speed n* = 1000r / min . The
load torque is changed from 1.5Nm to 2.5Nm at the time of 0.1s . In order to check the validity of the
proposed SVM-DTC system in reducing the flux and torque ripple, the simulation of conventional DTC is
done as well, the simulation results of both methods are shown from Fig.3 to Fig. 4.
0.3
<Electromagnetic torque Te (N*m)>
1500 0.2
3
5 0.1
2 1000

y plot
Te/Nm

r/min
0
0
i/A

1 500
-0.1
0
-5 0 -0.2

-1 0 0.05 0.1 0.15 0.2

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2 -0.2 -0.1 0 0.1 0.2 0.3
t/s x plot
t/s t/s

Fig.3 Performance of conventional DTC of motor

<Electromagnetic torque Te (N*m)> 0.3

3 0.2
5 1000
0.1
2
r/min
Te/Nm

y plot
0 500 0
i/A

1 -0.1
0
-5
-0.2
0

0 0.05 0.1 0.15 0.2 0 0.05 0.1 0.15 0.2

0 0.05 0.1 0.15 0.2 -0.2 0 0.2
t/s t/s t/s x plot

Fig.4 Performance of SVM-DTC of motor

6. Conclusion

A new direct torque control algorithm of PMSM is introduced in this paper. By using SVPWM, the
dynamic and static performance of the control system is better than the conventional DTC system of
PMSM. Simulation results indicate that the proposed SVM-DTC can reduce the flux and torque ripple
efficiently, and has quicker dynamic response and less current harmonic comparing with the conventional
DTC. So the SVM-DTC is feasible and more effective, and has a better application prospect.

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