Direct-Torque Control of a PMSM using Four-Switch Three-Phase Inverter

Syed Abdul Rahman Kashif, Muhammad Asghar Saqib and Mustafeez ul Hassan Department of Electrical Engineering

University of Engineering and Technology Lahore 54890, Pakistan

Emails: saqib@uet.edu.pk, abdulrahman@uet.edu.pk and mustafeez18@gmail.com

Abstract—This paper presents the direct-torque control of a permanent magnet synchronous motor using four-switch three- phase inverter. The control of the four-switch inverter was developed based upon the orientation of four-switch space-vectors in the plane of six-switch inverter. The proposed inverter was successfully used in the direct-torque control of a PMSM. A dynamic model of a machine gives deep insight for designing the efficient control scheme for its control. A model based estimator was used for the sensing of currents. The control scheme was implemented using TMS320F2812 and TMS320F28835, and the results have been presented for the demonstration of efficient control of PMSMs using four-switch inverters.

Keywords—Four-switch three-phase inverter, direct-torque control, sensor-less control, surface type permanent magnet synchronous motor.

I. INTRODUCTION A four-switch three-phase inverter (FSTPI) is a cost

effective solution replacing the conventional six-switch three-phase inverter (SSTPI) because of the ease of its control structure and reduced complexity [1]. The FSTPIs are finding their applications in AC motor drives with dynamic control. References [2] and [3] have used four-switch three-phase inverters for the control of an induction motor which is the heart of majority of the industrial applications. Different inverter control strategies are being employed to improve the performance of a FSTPI in the motor control applications. References [4] and [5] have presented generalized PWM strategy for the control of a FSTPI in the AC motor drives. The authors have presented the control of a FSTPI for induction motors in reference [6] and for PMSMs in reference [7]. A PMSM is replacing an induction motor because of its high efficiency, and torque to weight and power to weight ratios. References [7] and [1] explain the control of a FSTPI in an interior permanent synchronous motor.

The vector control of AC machines provides dynamic control and usually field-oriented control (FOC) and direct-torque control (DTC) schemes are employed. The FOC treats an AC machine just like a DC machine and improves its dynamics controlling the d-axis and q-axis currents of the machine while the DTC directly updates the inverter states with reference to the command torque and flux without considering the current dynamics. In the comparison of FOC and DTC for the motor-control applications, the DTC provides

a simplified control of an inverter in motor control. References [8] and [9] discuss the direct-torque control of an induction motor using a FSTPI. An inverter’s dynamic response and control schemes affect the overall performance of a drive and should be carefully considered. The space vector pulse width modulation is considered to be the best PWM technique in the conventional SSTPI because it utilizes DC link voltage more effectively as compared to any other PWM technique and treats the three-phase bridge as a single unit. The effective use of the space vector pulse width modulation has been discussed in references [10]-[11] for a FSTPI.

This paper presents the direct-torque control of a surface type permanent magnet synchronous motor in the sensor-less control with four-switch three-phase inverter. The authors have developed the inverter control using the symmetry between the orientations of space-vectors in αβ-plane of conventional and FSTPI. The space vector pulse width modulation technique for the conventional SSTPI has been modified for a FSTPI by converting four space-vectors of the FSTPI plane into six space-vectors of the SSTPI plane. The vector control based direct-torque control has been implemented using 32-bit controllers from Texas Instruments. Experimental results validate the performance of the direct-torque control using a FSTPI.

II. PERMANENT MAGNET SYNCHRONOUS MOTOR Surface type permanent magnet synchronous motor

(SPMSM) was used in the project. The motor parameters are given in the appendix. The dynamic model of a PMSM was developed in Matlab Simulink to investigate its transient behaviour. The dynamic model was extracted from the state-space equations of a permanent magnet synchronous motor which are given below.

2

10 0 0 0

10 0 00 0

3 0 0 00 0 280 0 0 00 0 1 0

s e d PM

q q q qr rqs qs

e qr rsds ds

dd de e

PMe e

XX

BA

R LL L L L

i iL Ri id

LL LdtPP BJJ J

ω λ

ω

ω ωλθ θ

•

⎡ ⎤ ⎡ ⎤− − −⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥−⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥= +⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥− −⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦

0

rqsr

ds

L

U

VVT

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

(1)

978-1-4799-2399-1/14/$31.00 ©2014 IEEE 795

0 0 010 0 01

rqsrds

e

Ce

X

ii

Yωθ

⎡ ⎤⎢ ⎥

⎡ ⎤ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

(2)

where Rs is the stator resistance, Lq and Ld are the q-axis and d-axis inductances, ωe is the synchronous speed, P is the number of poles, B is the friction constant, J is the inertia constant, TL is the load torque,

PMλ is representing permanent magnet flux linkages, r

qsi , rdsi , r

qsV and rdsV are q- d-axis currents and

voltages respectively.

III. FOUR SWITCH INVERTER AND ITS CONTROL A conventional three-phase inverter consists of six switches

while a four-switch three-phase inverter consists of four power electronic switches with capacitors in a leg as shown in Fig. 1. Vdc represents DC link voltage; S1 and S2 are the high-side while S3 and S4 are the low-side power electronic switches respectively. There exist four possible switching combinations which are shown in Table 1; the resulting space vector in αβ-plane are also shown corresponding to the switching combinations. The space vectors, defined in Table I, are shown in Fig. 2. The control of a four-switch three-phase inverter was developed using the symmetry between the four-switch inverter and six switch inverter planes using the concept of space vector pulse width modulation. The space-vector plane of a FSTPI was rotated by 60o to match the position of space-vectors with the SSTPI plane as shown in Fig. 3. The space vector pulse modulation technique has become the standard in industrial motor control inverters. Therefore, SVPWM is being investigated currently for the control of a FSTPI exploiting the symmetry. The symmetry has been shown in Fig. 3. The symmetry generates the switching pattern, described in Table I, used in the inverter control using space vector pulse width modulation. Fig. 3 shows that the vectors Va, Vb, Vc and V4 can be generated using the vectors of the four-switch inverter plane. The vector Va is the average of V1 and V2, Vb is the average of V2 and V3, Vc is the average of V3 and V4 and V4 is the average of V4 and V1. The switching time of vectors in a switching interval for FSTPI is calculated using the equation (3). T1 represents the switching time of first vector in sector n while T2 is the switching time of the second vector. The switching time of null vector is given by To. Theta reference represents the position of the reference vector in the space vector plane.

1

2

1 2

2 3 sin( )3

2 3 1sin( )3

( )2

s ref

s ref

so

nT T

nT T

TT T T

π θπ

θ ππ

⎧= −⎪

⎪⎪ −⎪ = −⎨⎪⎪ = − +⎪⎪⎩

(3)

The switching pattern of the four-adjacent vectors in a sector using the vectors of the four-switch inverter plane is given in Table II. A detailed discussion on the derivation and

implementation of the space vector pulse width modulation for a FSTPI has been presented by authors in references [6] and [7].

Fig. 1: Four-switch three-phase inverter.

TABLE I. SWITCHING COMBINATION OF FSTPI.

Fig. 2: Space vector plane of a FSTPI.

Fig. 3: Space vector planes of the SSTPI and FSTPI.

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TABLE II. SWITCHING COMBINATIONS FOR FOUR SWITCH THREE-PHASE INVERTER USING THE SYMMETRY BETWEEN THE PLANES OF FSTPI AND SSTPI.

No. Switching vectors with SSTPI

Switching vectors with FSTPI

Switching vector timings

ON-time of a switch

Optimized switching

pattern

1 Vb, V3,

Vnull=(V0+V7)/2

Vb:(V2+V3)/2, V3,

Vnull=(V1+V3)/2

V1: T0/2=Ta V2: T1/2=Tb

V3: T0/2+T1/2+T2=Tc

S1=Tb+Tc S2=Tc

V1,V2,V3, V3,V2,V1

2 V3,

Vc, Vnull=(V0+V7)/2

V3, Vc:(V3+V4)/2,

Vnull=(V1+V3)/2

V1: T0/2=Ta V3: T0/2+T1+T2/2=Tc

V4: T2/2=Td

S1=Tc S2=Tc+Td

V1,V4,V3, V3,V4,V1

3 Vc,

Vd, Vnull=(V0+V7)/2

Vc:(V3+V4)/2, Vd:(V1+V4)/2,

Vnull=(V1+V3)/2

V1: T0/2+T2/2=Ta V3: T0/2+T1/2=Tc V4:T1/2+T2/2=Td

S1=Tc S2=Tc+Td

V1,V4,V3, V3,V4,V1

4 Vd,

V1, Vnull=(V0+V7)/2

Vd:(V1+V4)/2, V1,

Vnull=(V1+V3)/2

V1: T0/2+T1/2+T2=Ta V3: T0/2=Tc V4: T1/2=Td

S1=Tc S2=Tc+Td

V1,V4,V3, V3,V4,V1

5 V1,

Va, Vnull=(V0+V7)/2

V1, Va=(V1+V2)/2, Vnull=(V1+V3)/2

V1: T0/2+T1+T2/2=Ta V2: T2/2=Tb V3: T0/2=Tc

S1=Tb+Tc S2=Tc

V1,V2,V3, V3,V2,V1

6 Va, Vb,

Vnull=(V0+V7)/2

Va=(V1+V2)/2, Vb:(V2+V3)/2,

Vnull=(V1+V3)/2

V1: T0/2+T1/2=Ta V2: T1/2+T2/2=Tb V3: T0/2+T2/2=Tc

S1=Tb+Tc S2=Tc

V1,V2,V3, V3,V2,V1

Fig. 4: Direct-torque control loop for a PMSM using four-switch three-phase inverter.

IV. DIRECT-TORQUE CONTROL In the SVPWM based DTC space vectors are switched such

that torque and flux errors in the closed loop, shown in Fig. 4, are minimized. The DTC is optimum as compared to FOC as inverter switching states are directly updated instead of considering the stator currents regulation. The DTC is based upon the orientation of stator flux linkages and electromagnetic torque developed in the machine. In a SSTPI vectors Vb, V3, Vc, Vd, V1 and Va while in FSTPI vectors V3, V4, V1 and V2 are switched. The switching of vector is based upon the sector in which the reference vector lies. Using the symmetry between the planes of SSTPI and FSTPI the inverter switching patterns were defined for the direct-control technique and are given in Table III. To enhance the torque at any instant of time over the reference circle forward space-vector is switched while to decrease torque the reverse (previously traced vector) vector is switched. The circular trajectory of flux is ensured using the switching technique of space vector pulse width modulation.

Reference current and torque are specified and compared

with the actual values, and the flux and torque commands are generated for the four-switch three-phase modulator which in turn applies the appropriate switching combination to the inverter to realize the command torque and reference current. The actual torque is estimated using the model based estimator by processing the motor line currents as shown in Fig. 4. Fig. 5 shows the complete Simulink model that was used in generating the code for TMS320F28335 – Texas Instruments DSP microcontroller.

V. RESULTS AND DISCUSSIONS The direct-torque control was implemented with the

proposed four-switch inverter and results are shown in Figs. 6 and 7. Fig. 8 shows the photograph of the experimental setup. Fig. 6a shows the q-axis and d-axis currents in the PMSM while Fig. 6b shows the torque tracking performance of the PMSM drive with a FSTPI.

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TABLE III. SWITCHING COMBINATIONS FOR THE DTC WITH SSTPI AND FSTPI.

Six-switch three phase inverter plane for FSTPI Four-switch three-phase inverter disd dTe N=1 N=2 N=3 N=4 N=5 N=6 N=1 N=2 N=3 N=4

1 1 3V cV dV 1V aV bV 3V 4V 1V 2V

1 -1 aV bV 3V cV dV 1V 2V 3V 4V 1V

-1 1 cV dV 1V aV bV 3V 4V 1V 2V 3V

-1 -1 1V aV bV 3V cV dV 2V 3V 4V 1V

N represents the sector number

Fig. 5: Simulink model for generating code for direct-torque control with FSTPI.

Fig. 6 a) Q-axis and d-axis currents in stationary frame of reference for direct-torque control, b) Reference and actual torque with proposed FSTPI in DTC.

Fig. 7 a) Q-axis and d-axis currents in stationary frame of reference for direct-torque control, b) Reference and actual speed with proposed FSTPI in DTC.

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Fig. 8: Photograph of the experimental setup.

The digital control loop was operated at a sampling

frequency of 10 kHz. Figure 7a shows the flux trajectory with the switching sequence shown in Table III. The flux trajectory is nearly a circle and it was observed the total harmonic distortion created in the line currents with flux trajectory is 3.47% which is acceptable according to the IEEE Standard 519-1992 (Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems). It was observed that with the increase in sampling frequency the flux trajectory became smoother and the THD was further reduced. The results shown in Fig. 7a when compared with those given for a FSTPI in references [8] and [9] have reduced THD because of the use of symmetry while designing the control of a FSTPI. Figure 7b shows the performance of the overall drive system when tested with the reference speed command of 250 rpm; the rated load was applied at 0.3 s as shown in Fig. 6b. The closed loop performance of the system with FSTPI depicts the advantage of using the symmetry between the SSTPI and FSTPI planes.

VI. CONCLUSION The paper has discussed the four-switch three-phase

inverter developed based on the orientation symmetry between the planes of conventional six-switch and four-switch three-phase inverters. A FSTPI has been demonstrated to be successfully used in the DTC of a PMSM. This obviously is advantageous as a FSTPI provides the cost effective solution for the AC motor drives. A FSTPI provides high dynamic control in AC motor drives just like its counterpart, i.e. the conventional SSTPI and has the capability to replace SSTPIs in future drives. The presented results verify the performance of the proposed four-switch three-phase inverter in the direct-torque control of a PMSM.

ACKNOWLEDGMENT

The authors acknowledge the financial support of the Higher Education Commission of Pakistan in providing the funding for the implementation of this project.

REFERENCES [1] Z.M. El-Barbary, M.K. Metwally and H.Z. Azazi, “A cost effective

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[2] P.S. Phutane and S.R. Karpe, “Performance of a 4- switch, 3-phase inverter fed induction motor (IM) drive system”, International Journal of Advanced Research in Electrical, Electronics and Instrumentation Engineering, Vol. 2, No. 3, March 2013.

[3] N.K. Mohanty and R. Muthu, “Microcontroller based PWM controlled four switch three phase inverter fed induction motor drive”, Serbian Journal of Electrical Engineering, Vol. 7, No. 2, pp. 195-204, 2010.

[4] M.B.D.R. Correa, C.B. Jacobina E.R.C.D Silva, and A.M.N Lima, “A general PWM strategy for four-switch three-phase inverters”, IEEE Transactions On Power Electronics, Vol. 21, No. 6, pp. 1618-1627, 2006.

[5] M. Monfared, H. Rastegar and H.M. Kojabadi, “Overview of modulation techniques for the four-switch converter topology”, Proceedings of the 2nd IEEE International Conference on Power and Energy, December 1-3, 2008, Johor Baharu, Malaysia, pp. 803-807.

[6] S.A.R. Kashif, M.A. Saqib and S. Zia, “Implementing the induction-motor drive with four-switch inverter: an application of neural networks”, Expert Systems with Applications, Vol. 38, No. 9, pp. 11137-11148, 2011.

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[10] C.K. Lin, J.T. Yu, L.C. Fu, T.H. Liu, and C.F. Hsiao, “A sensorless position control for four-switch three-phase inverter-fed interior permanent magnet synchronous motor drive systems”, Proceedings of the IEEE International Conference on Advanced Intelligent Mechatronics, July 11-14, 2012, Kachsiung, Taiwan, pp. 1036-1041.

[11] H.H. Lee, P.Q. Dzung, L.D. Khoa and L.M. Phuong, “Dynamic adaptive space vector PWM for four switch three phase inverter fed induction motor with compensation of DC – link voltage ripple’’, Proceedings of the IEEE International Conference on Power Electronics and Drive Systems, Nov 2-5, 2009, Taipie, Taiwan, pp. 399-404.

APPENDIX The PMSM used in the project has the following parameters: 300 V (DC), 2.7 A, 660 W, 2.1 Nm, Permanent magnet flux: 0.264 Wb, No. of pole pairs: 4, 3000 rpm, J = 0.00062 kg-m2, F = 0.0003035 Nms, Rs = 4.7 Ω, Ld = Lq=13.3 mH.

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