2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia)

Direct Torque Control of Permanent Magnet

Synchronous Motor Based on Space Vector
Modulation Control
Ying Yang,Rui Hunag,Yan-pu Yu,Shuang Wang
School of Mechanics Engineering and Automation, Shanghai University, China
E-mail: wang-shuang@shu.edu.cn

Abstract— How to calculate the reference voltage vector is matrix converter and so on. These methods can reduce torque
an important issue in space vector modulation direct torque ripple effectively. However, they increased the hardware or
control (SVM-DTC) of permanent magnet synchronous motor computation to make the system much more complex than
(PMSM). The effect of zero vector on electromagnetic torque conventional DTC. So it is necessary to study how to calculate
during all speed range is analyzed on the basis of the relation
between voltage vector and torque current component. And the
the reference voltage vector in SVM-DTC of PMSM to reduce
analysis shows that in conventional DTC system of PMSM torque ripple and maintain simplicity, robustness of
available voltage vector is only six which is the mainly cause of conventional DTC [7].
high ripple of torque. A robust SVM- DTC method of PMSM is This paper investigates an improved method of SVM-DTC
designed in which the reference voltage vector is calculated with in which the reference voltage is calculated with the flux
the flux position, error of torque and flux. The method is simple position, errors of flux and torque. The method is simple to
to implement and insensitive to motor parameters error. First implement and robust compared with other SVM-DTC. In
order filter cascaded with high pass filter (HPF) is adopted to addition, appropriate modulation method is adopted to
estimate stator flux accurately. The experimental results are decrease dead time effectively. The improved SVM-DTC is
carried out and show that the improved SVM-DTC has the verified by simulation and experiments and proved to decrease
advantage of simplicity, robustness and improved performance. torque ripple effectively and be strong.

Key words: PMSM; direct torque control; space vector II. ANALYSIS OF EFFECT OF VOLTAGE VECTOR ON
modulation; torque ripple ELECTROMAGNETIC TORQUE
The dynamic model of surface-mounted PMSM in the
I. INTRODUCTION rotating reference frame(d,q) can be expressed as follows:
The conventional DTC of PMSM has received  dψ d
considerable investigation for its advantage of quick change of usd = Rs isd + dt − ωrψ sq
 (1)
torque, robustness and simplicity [1]. However, only six valid
u = R i + dψ q + ω ψ
voltage vectors are available in conventional DTC which  sq s sq r sd
dt
induce such problems as large torque ripple and variable
switching frequency [2]. ψ sd = Lsd isd + ψ f
Hence the space vector modulation -direct torque control  (2)
(SVM-DTC) was presented in which the hysteresis control of ψ sq = Lsq isq
torque and stator flux hysteresis controller in conventional 3 (3)
Te = n pψ f isq
DTC are replaced by the reference voltage calculator and 2
space vector modulation unit. The SVM-DTC can provide usd usq isd isq are d-
Where, are d- and q-axis stator voltage,
constant switching frequency and more accurate Stator flux
and torque control. and q-axis stator current, Rs is stator resistance, ψ sd ψ sq are
How to calculate reference voltage vector is an important
issue in SVM-DTC. A lot of methods were carried out to d- and q-axis stator flux, Ld Lq are the d-and q-axis
calculate the space vector voltage. The errors of flux and
torque are compensated by deadbeat control in SVM-DTC [1, inductance,ψ f is permanent magnet flux, ωr is electrical
2]
.However it is sensitive to motor parameters. Two PI
rotor-speed, n p is the number of pole pairs.
controllers are used to control torque and flux [3, 4].However it
is difficult to design the parameters of PI controllers. The The differentiation of Te with respect to time t can be
scheme proposed in [5] and [6] uses three-level inverter,

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978-1-5090-1210-7/16/$31.00 ©2016 IEEE

 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia)

expressed by , ψ s are observed torque and stator flux, KT Kψ are positive

dTe 3 di coefficients.
= n pψ f sq (4)
dt 2 dt Accordingly the voltage vector amplitude is
From (1), we can get U
U s = d × dc (8)
3
disq usq − ωr ( Lsd isd + ψ f ) − Rs isq
= (5) Where U dc is the DC bus voltage, from the (7) and (8),
dt Lsq
the torque and flux ripple will be reduced when lower voltage
From (4) and (5), the differentiation of Te with respect to vector amplitude is obtained according to small errors.
time t can be expressed by B. Voltage vector angle determination
dTe 3 3 ωr ( Lsd isd + ψ f ) 3 Rs isq
= n pψ f usq − n pψ f − n pψ f Supposing the stator-flux angle θs is known as shown in
dt 2 2 Lsq 2 Lsq (6)
Fig.1. In order to obtain better performance, the angle of
= ΔT1 + ΔT2 + ΔT3 voltage vector areas are divided into 4 areas including
Following conclusions can be derived from equation (6): (θs~θs+90o),(θs+90o~θs+1800),(θs+180o~θs+270o)and
1) ΔT1 is determined by q-axis voltage component of the (θs+270o~θs+360o) according to the torque errors and flux
voltage vector. errors and stator flux angle, as shown in Fig.1. The
2) The electromagnetic torque will decrease significantly relationship between voltage vector areas and its influence on
when zero voltage vector is applied in mid-and high-speed. flux and torque are shown in Tab.1. Where “+” means
Because ΔT1 is zero and ΔT2 is proportional to motor speed, increase and “-”means decrease. For example, the stator-flux
and meanwhile ΔT3 can be neglected for its small value. angle θs is known and the torque and flux should be
Hence in order to increase the electromagnetic torque, the q- increased, the candidate vector should be in area 1. When the
axis component of stator voltage must be greater than zero,
torque error is large, the vector near θs + 90 should be

and electromagnetic torque will not rise fast in consequence of
ΔT2. adopted. When the flux error is large, the vector near
3) ΔT2 is small and ΔT3 is also small when motor runs in θs should be adopted.
low speed. The voltage space vector with fixed amplitude
θ s + 1000 θ s + 800
selected according to sector of stator flux, output of torque and
stator flux controller will induce rapid change of Te ↑ψs ↓ Te ↑ψs ↑

electromagnetic torque. Furthermore there is dead band in

digital control system. Therefore large torque ripple occurs in θ s + 100
conventional DTC in low speed. Based on the analysis above,
θ s + 1700
we can get the conclusion that in conventional DTC system 10 0 ψS
θs 00
available voltage vector is only six which mainly causes high
ripple of torque. θ s + 1900 θ s − 100
More voltage vectors with different magnitude and space
Te ↓ψs ↑
angle are available in SVM-DTC. Hence torque ripple would Te ↓ψs ↓
decrease effectively and system performance would be
improved apparently. The key issue is how to calculate the
amplitude an angle of reference voltage vector without accurate Fig.1 Schematic diagram of improved voltage vector
calculation to maintain robustness and simplicity of conventional
DTC system. Tab.1 Relationship between voltage area and torque & flux

Area of voltage vector torque flux

III. IMPROVED SVM-DTC OF PMSM θs~θs+900 + +
A. Reference voltage vector amplitude calculation θs+900~θs+1800 + -
To avoid complicated calculation and maintain θs+1800~θs+2700 - -
robustness, the magnitude coefficient of voltage vector is θs+2700~θs+3600 - +
determined according to the flux error and torque error and is The angle increment of voltage vector by toque error is
expressed as
expressed as
π π
d =KT ET + Kψ Eψ =KT Te*−Te + Kψ ψ s*−ψ s (7) ΔϕT =KT ET × =KT Te* − Te × (9)
2 2
The angle increment of voltage vector which is
Where ET , Eψ are errors of torque and stator negatively proportional to the stator flux change is expressed
as
flux, T
*
e ,ψ *
s are reference values of torque and stator flux, Te
 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia)

Stator flux ψ s can be expressed as (15) when stator flux

'
π π
Δϕψ =(1-Kψ Eψ ) × =(1-Kψ ψ s* − ψ s ) × (10)
is estimated with first order filter cascaded with high pass
2 2
From the (9) and (10), the final angle increment of filter
voltage vector is Es jωe
ψ s′ = (15)
 K ΔϕT + (1 − K )Δϕψ area 1 jωe + kLωe jωe + kH ωe
 K (π −Δϕ ) + (1−K )(π −Δϕ ) area 2
 T ψ (11)
Δϕ= 
 K ( −π +Δϕ T ) + (1−K )( −π +Δ ϕψ ) area 3 Comparing (14) and (15), and expanding in αβ
− K ΔϕT − (1 − K )Δϕψ area 4 coordinates, we can get the compensation relation [14]:

The final angle of voltage vector is expressed as
ϕ = θ s + Δϕ (12) ψ sα = ψ s′α (1 − k L k H ) + ψ s′β ( k L + k H )
Where K is the weighting factor, in usual, torque has higher  (16)
priority than flux, so K is chosen to be greater than 0.5[8]. ψ sβ = ψ s′β (1 − k L k H ) −ψ s′α ( k L + k H )
The proposed improved SVM-DTC of PMSM system
diagram is shown as Fig.2. The torque and stator flux are Simulation studies have shown: the HPF has ability to
estimated with the DC bus voltage, two phase current and eliminate the influence of the DC bias and the initial position
switch status. The amplitude and angle increments of the deviation and the observations with HPF scheme are closest to
expected voltage vector are respectively calculated by (8) and real steady state.
(11). After that, the voltage vector composed by SVM module
could be expressed as [9][10] IV. EXPERIMENTAL RESULTS

U ref = U s ⋅ e jϕ (13) The proposed SVM-DTC scheme was further
 experimentally tested in a two-level inverter-fed PMSM motor
Where U ref is the output voltage vector. drive. The control and motor parameters are the same as
introduced in Tab.2.The hardware of the PMSM control
system is designed based on the DSP TMS320F28335. The
Te* ET
speed of PMSM is obtained through a 2500-pulse incremental
encoder.Fig.4a shows the transient waveforms of speed,
ψ s* Eψ
torque and flux when reference speed suddenly changes from
θs 300rpm to the final speed of 1200rpm without load.
Te
ψs Tab.2 Motor and system parameters
Number of pole pairs p 4
Fig.2 Block diagram of improved SVM-DTC system Permanent magnet flux ψf 0.0658Wb
Stator resistance Rs 1.6Ω
We can see that only the torque and flux errors are used to
d- and q-axis inductance Ld Lq 4mH
calculate output voltage vector in the proposed method. No
other motor parameters are required. Hence it is robust [11] [12] . Rated speed nN 3000rpm
Rated torque TN 2.39 Nm
C. Stator flux observer with first order filter cascaded with Rated power 750W
PN
HPF Moment of inertia J 1.03kg ⋅ cm2
In order to eliminate DC bias, first order filter cascaded Sampling period Ts 50 μ s
with HPF is adopted to estimate stator flux linkage. From the Fig.4, it has been observed the speed, torque
Furthermore amplitude and phase deviation are compensated. and flux waveforms of the conventional DTC and proposed
The implement of stator flux estimate compensation scheme is SVM-DTC. The range of torque ripple for DTC is ±0.6N·m,
shown as Fig.3 [13] while that for the SVM-DTC is ±0.15N·m. and the range of
flux ripple for DTC is ±0.02Wb, while that for the SVM-DTC
esα 1 s ψ s′α ψ sα
is ±0.004Wb. On the other hand, the dynamic responses of the
s + k L ωe s + k H ωe
proposed SVM-DTC are similar to those of the conventional
DTC. The speed overshoot and speed fluctuation at steady
esβ s ψ s′β ψ sβ state are slightly reduced for proposed SVM-DTC.
1
s + k L ωe s + k H ωe By comparing the data analysis above can clearly find
that the torque and flux ripples of proposed SVM-DTC are
Fig.3 voltage model stator flux estimation scheme schematic
also much smaller than those of conventional DTC. It is
Stator flux ψ s can be expressed as (14) when pure proved that the proposed method has strong robustness and
integration is adopted to estimate stator flux, can effectively reduce the torque and flux ripples. Similarly,
ψ s = Es / jωe the waveform distortion rate of the three phase currents are
(14)
 2016 IEEE 8th International Power Electronics and Motion Control Conference (IPEMC-ECCE Asia)

significantly lower for the SVM-DTC, the sinusoidal phase voltage vector is adopted in SVM-DTC. It requires only the
current waveforms are significantly better. torque and flux errors. The simulation and experimental
results show that the proposed SVM-DTC scheme has
ψs excellent steady-state performance while retaining the merits
of the quick dynamic responses, simplicity and robustness as
in conventional DTC.
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V. CONCLUSIONS 2011,35(2):94-9
Available voltage vector has only six which mainly causes
high ripple of torque in conventional DTC. To maintain
robustness and simplicity of conventional DTC system, a
simple method of calculating amplitude and angle of the