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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 Open access under CC BY-NC-ND license. 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:
[email protected].
1877-7058 © 2011 Published by Elsevier Ltd. Open access under CC BY-NC-ND license. doi:10.1016/j.proeng.2012.01.195
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XuXing Wang et al. / Procedia Engineering 29 000–000 (2012) 1685 – 1689 Yan / Procedia Engineering 00 (2011)
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: Rs iα + Ls diα dt − ωrψ f sin θ ⎧⎪uα = (1) ⎨ Rs iβ + Ls diβ dt + ωrψ f cos θ ⎪⎩uβ = ⎧= ⎪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 ⎪⎪ = 3U α − U β ⎨U ref 2 ⎪ − 3Uα − U β ⎪⎩U ref 3 = 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 )
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
(4)
(5)
Xu Wang et al./ Procedia / ProcediaEngineering Engineering0029(2011) (2012)000–000 1685 – 1689 Yan Xing
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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
T1
-Z
Y
T2
X
Z
3
4
5
6
X
Z
-Y
-X
-Y
-X
-Z
Y
where ⎧ X = 3U β T / Vdc ⎪⎪ = ⎨Y (3Uα + 3U β )T / 2Vdc ⎪ (−3U α + 3U β )T / 2Vdc ⎪⎩ Z =
(6)
3.3. Calculation of switching point of voltage vector Defining the following variables:
⎧Ta = (T − T1 − T2 ) 4 ⎪ Ta + T1 2 ⎨ T= b ⎪ T= T + T 2 c b 2 ⎩
(7)
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 β ( k +1) ψ s * sin(θ + Δθ )
,
⎧⎪ψ α ( k ) = ψ s cos(θ ) ⎨ ⎪⎩ψ β ( k ) = ψ s sin(θ )
(8)
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XuXing Wang et al. / Procedia Engineering 29 000–000 (2012) 1685 – 1689 Yan / Procedia Engineering 00 (2011) β ψ β ( k + 1) ψ β ref
Δψ s
ψ s (k + 1)
ψ β (k )
ψ s (k ) Δθ
ψ α ref
θ
ψ α (k + 1) ψ α (k )
0
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 ref
⎧⎪ψ α= ψ α ( k +1) −ψ α= ψ s * cos(θ +Δθ ) − ψ s cos(θ ) ref (k ) ⎨ ψ β ( k +1) −ψ β= ψ s * sin(θ +Δθ ) − ψ s sin(θ ) ⎪⎩ψ β= ref (k ) can be calculated in equation (9).
(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= ψ α ref / Ts + Rs iα ( k ) α ref α (k ) ⎪⎧u= (10) ⎨ u= ψ β ref / Ts + Rs iα ( k ) ⎪⎩u= β ref β (k ) Putting equation (9) into equation (10), equation (11) can be acquired: ( ψ s * cos(θ +Δθ ) − ψ s cos(θ )) / Ts + Rs iα ( k ) ) ⎪⎧uα ref= uα ( k = (11) ⎨ ( ψ s * sin(θ +Δθ ) − ψ s sin(θ )) / Ts + Rs iα ( k ) ⎪⎩uβ ref= uβ ( 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*
T
ΔT
dθ ψs*
ψ ref
uα * uβ *
ψs θ
ψα ψβ
uα uβ iα iβ
ω
Fig.2 The system structure of SVM-DTC
Xu Wang et al./ Procedia / ProcediaEngineering Engineering0029(2011) (2012)000–000 1685 – 1689 Yan Xing
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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
1500
3 5
1
500
0
-5
-1 0
0.05
0.1
0.15
0.2
0.1 y plot
r/min
2
Te/Nm
i/A
0
0.2
1000
-0.2
0
0
0.05
0.1
0.15
0
0.2
0.05
0.1
0.15
0.2
-0.2 -0.1
t/s
t/s
t/s
0 -0.1
0 0.1 x plot
0.2
0.3
Fig.3 Performance of conventional DTC of motor 0.3
3
5
0.2
1000
1
y plot
r/min
Te/Nm
i/A
0.1
0
2
500 0
-5
-0.2
0
0
0.05
0.1
0.15
0.2
t/s
0 -0.1
0
0.05
0.1
0.15
0.2
0
0.05
t/s
0.1
0.15
0.2
t/s
-0.2
0 x plot
0.2
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. References [1] Depenbrock M. Direct self-control(DSC) of Inverter-fed Induction Machine. IEEE Transaction on Power Electronics (S0085-8993),1988,3(4):420-429. [2] Takahashi I, Naguchi T. A New Quick-response and High-efficiency Control Strategy of an Induction Motor. IEEE Transaction on Industry Applications (S0093-9994), 1986, 22(4): 820-827. [3] Mohammed Rakibul Islam. Cogging Torque, Torque Ripple and Radial force Analysis of Permanent Magnet Synchronous Machines. University of Akron, 2009. [4] Zhong L, Rahman M F, Huand W Y, Lim K W. Analysis of Direct Torque Control in Permanent Synchronous Motor Drives . IEEE Transactions on Power Electronics (S0885-8993), 1997, 12(3): 528-536. [5] Yangzhong Zhou, Yuwen Hu. Direct torque control for AC motor . Beijing: Mechanical Industry Press, 2009. [6] Chun Tian, Yuwen Hu. Study of the Scheme and Theory of the Direct Torque Control in Permanent Magnet Synchronous Motor Drives. Transactions of China Electrotechnical Society, 2002, 17(1): 7-11. [7] Yongdong Li. Digital control system of AC motor. Beijing: Mechanical Industry Press, 2003.
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