Performance Analysis of Direct Torque Control of PMSM Drive using SVPWM - Inverter

Narayan Prasad Gupta

Electrical and Electronics Engg. Deptt. Oriental Institute of Science and Technology,

Bhopal, India- 462021 narayan. irig@gmail.com

Abstract-Permanent magnet synchronous motors (PMSM)

have been universally used as variable speed drives due to its

characteristics such as small volume, light weight, high efficiency,

small inertia and hence high torque / inertia ratio, maintenance

free and ease of control, high steady state torque density create

possibility of replacing induction machines with PMSMs in

industrial drive applications. PMSM are now widely accepted as

high performance drives such as industrial robots and machine

tools. A novel direct torque control (DTC) scheme incorporating

space vector pulse width modulated (SVPWM) inverter, for

speed control of PMSM drive has been presented in this paper,

which has advantage of fast dynamic response with low ripples in

torque and speed response, elimination of current controllers and

least dependency on motor parameters. According to the

differences in estimated value of torque and stator flux linkage

with actual reference value; the stator voltage vectors are directly

selected, in DTC to control the speed of motor. Mathematical

model of PMSM and proposed DTC scheme is presented here. A

simulation model is developed in MATLAB / SIMULINK to

judge the various performance parameters.

Keywords- Direct torque control; permanent magnet synchronous motor; space vector pulse width inverter; flux and torque estimation;

I. INTRODUCTION

Permanent Magnet Synchronous Motor (PMSM) has gained popularity especially in the automation industry, because of its compact size, high efficiency, and faster response, simple control technique makes it comparable with induction motor drive [1,4], As reliability and cost of modern PMSM drives are of importance, advanced control techniques have been developed. The PMSM is very similar to the standard wound rotor synchronous machine except that the PMSM has no damper windings and excitation is provided by a permanent magnet instead of a dc field winding. The elimination of field coil, dc supply and slip rings reduces the motor loss and complexity [4]. In general there are two high­performance control strategies for PMSM e.g. field-oriented control (FOC) and direct torque control (DTC). These control strategies are different in their operating principles but their aim is same; control effectively the motor torque and flux in order to force the motor to accurately track the speed and torque references regardless of the machine and load parameter variation or any disturbances [8]. In field oriented control rotor flux space vector is calculated and controlled by using the

978-1-4673-0934-9/12/$31.00 ©2012 IEEE

Preeti Gupta

Electrical and Electronics Engg. Deptt., Thakral College of Technology,

Bhopal, India- 462021 preetigupta@oriental.ac.in

angular velocity which is derived from the speed feedback and the stator current vector which can be done by tachogenerator or any speed / torque sensor.

With the improvement in power electronics technology, direct torque control (DTC) technique is proving best optimized method for speed control of PMSM drive. faster torque control, high torque at low speeds, and high speed sensitivity are some of the attribute of DTC. The main idea in DTC is to use the motor stator flux linkage and torque as basic control variables. In conventional method of speed control the rotor speed and angular position are sensed and feed back to control the speed of motor. In PMSM increase of electromagnetic torque is directly proportional to the increase of the angle between the stator and rotor flux linkages, consequently fast torque response can be achievable by adjusting the rotating speed of the stator flux linkage. This is achieved by using direct torque control (DTC) technique. The proposed system of DTC includes a flux and torque estimator which involves three phase voltage measurement at input terminal of motor. In DTC the stator voltage vectors are selected according to the difference between the reference value and actual value of torque and stator flux linkages in order to reduce the torque and flux errors within the specified hysteresis band [4,15].

Space Vector Pulse Width Modulation (SVPWM) control technique has been used in this paper, due to its potential advantages, such as small current waveform distortion (low THD), high utilization of DC voltage, easy-to-digital implementation, low switching and noise losses, constant switching frequency of inverter, effectively to reduce pulsation of the motor torque and flux linkage. The simulation result shows that the system has the advantage of fast response, good dynamic performance, and low speed and torque ripples [3,6].

II. MATHEMATICAL MODELLING OF PMSM

Permanent Magnet Synchronous Motor (PMSM) has a sinusoidal back emf which requires sinusoidal stator currents to produce constant torque. The PMSM is different from wound rotor synchronous machine as it has no damper and dc excitation winding. Different mathematical models viz. abc­model, two axis dq-model have been proposed for different applications, the two axis dq-model is simple and is widely

used. The dynamic model of PMSM is derived from two phase synchronous (stator) reference frame. For dynamic model of PMSM, the assumptions made are - spatial distribution of magnetic flux in air gap should be sinusoidal, and magnetic circuit should be linear (hysteresis and eddy current losses are negligible) [1, 4, 13].

j3

Fig. 1. Stator and rotor flux linkage in coordinate system

The stator flux reference frame in D axis is in phase with stator flux linkage space vector 'Ps. Q axis (of SRF) leads 90° to D axis in CCW direction as depicted in Fig 1.

(1)

Where, 9s= rotational angle of stator flux vector 9r=rotational electric angle of rotor 9s =9r+o Stator flux linkage is given by

(2)

Where Ls is stator self inductance and 'Paf is the rotor permanent magnet flux linkage. The stator voltage equation in rotor reference frame (dq reference frame) are given as

. d\Pd Vd = Rsld + dt - wr\Pq (3)

(4)

Where 'I' q= Lqiq and 'I'd = Ldid+'I'af, Vd and Vq are d-q axis stator voltages, id and iq are d-q axis stator currents, Ld and Lq are d-q axis inductances. Rs is stator winding resistance per phase, 'I'd, 'l'q are stator flux linkage in d-q axis & (Or is rotor speed in (rad/sec) electrical. The developed electromagnetic torque is given by

3 Te = 2" P[\Pdiq - \Pqid] (5)

Where P = No. of pole pair = p/2, and p = Total No. of poles Based on theory of dynamics the motion equation of PMSM is given by

(6)

Where T L is load torque, J is moment of inertia, B is (viscous friction) damping coefficient. For simplifying modeling of PMSM; three phase system can be transformed to an orthogonal (dq) reference frame with direct axis (d) and quadrature axis (q), for rotor position 9.

cos e [Vq] 2 Vd = "3 sine Vo 1

2rr cos(e --)

3 2rr

sinCe --) 3

1

2rr cos(e + 3)

2rr [Va]

sinCe -3) Vb

1 Vc

2 2 2

(7)

The simulink model of PMSM based on above equation is shown in Fig 2.

Fig. 2. Simulink model of PMSM

Tef----.(: Te

r--�2 we

id

iq

theta III. DIRECT TORQUE CONTROL FOR PMSM

iab<:

Direct torque control and vector control are two popular methods for speed control of ac drives. In DTC method the control of electromagnetic torque and flux linkage is done directly and independently by using space vectors. In a PMSM, if we neglect voltage drop due to stator resistance, variation of stator flux is directly proportional to applied stator voltage. Thus control of torque in PMSM can be achieved quickly by varying the stator flux position (change in applied voltage to motor. DTC calculate and control stator flux linkages and torque of PMSM directly to achieve excellent transient performance [4].

A. Torque andflux linkage estimator

Simulink block diagram of of PMSM with direct torque control is shown in Fig.13. The d-q axis component of current can be derived from sampling of the three phase voltages at SVPWM output, using abc to dq transform. Then after electromagnetic torque Te will be estimated by "(5)" and d, q axis stator flux 'Pd, 'Pq are given by

(8)

(9)

(10)

(11)

B. Optimal voltage Estimator

This proposed DTC scheme uses three path closed loop control of speed, torque and flux linkage. PI controller is used to reduce steady state errors in all the three closed loop paths. The optimal voltage estimator has advantage of flux weakening control to reduce the ripples in torque and flux waves. In closed loop system sensed speed is compared with reference speed, and error L1ffir is fed to PI controller, its output Te which is again compared with estimated Te in another closed loop [4]. The torque error L1Te is processed in a PI controller give output as () which is angle between 'I' afand 'I's. The d-axis and q-axis voltage component of stator voltage in stator reference frame are calculated in optimal voltage estimator, by "(3)" and "(4)". The stator voltage component Ua, Up is expressed in tenns of Ud, Uq as-

- sin 8 ] [Ud] cos 8 Uq (12)

After dq8/a.p transformation, the a.-axis, p-axis voltage component of stator voltage (Ua. Up) will be input of SVPWM to generate three phase sinusoidal voltages fed to PMSM.

C. Space Vector PWM-Inverter

Space Vector PWM Inverter refers to a sequential switching of six switches (lGBT transistors) of a three-phase three leg bridge inverter which generate less harmonic distortion in the output voltages and currents, which provides more efficient use of supply voltage as compared to sinusoidal modulation technique. The circuit model of a three-phase voltage source PWM inverter is shown in Fig. 3. SI to S6 are the six power switches, when any upper switch is on (a, b or c is 1), the corresponding lower switches is turned off, (a', b' or c' is 0). Therefore, the on and off states of the upper switches S 1, S3 and S5 can be used to detennine the output voltage [3, 6].

+ Vdc

Fig. 3. Three phase voltage source PWM Inverter with PMSM

The relationship between the switching variable vector [a, b, cr and the line-to-line voltage vector [Vab Vbc Vcar is given by

[Vab ] [1-1 Vbe = Vde.!! 1 Vea 1 0

(13)

There are eight possible combinations of on and off patterns for the three upper power switches, as shown in table I [9].

TABLE I. SWITCHING VECTORS AND LINE VOLTAGES

Voltage

Vectors

Vo

VI

V,

V3

V4

V5

V6

V7

V4

Switching Vectors

a b

0 0

I 0

\ \

0 \

0 1

0 0

\ 0

1 1

q axis

c

0

0

0

0

I

\

\

I

Vl (100)

(011) t------'=-iF---r----t---.

Vl V6 (001) (101)

Fig. 4. Basic switching voltage vectors and sectors

Li ne to Ii ne voltage

Vab Vbc Vca

0 0 0

1 0 -I

0 \ -\

-\ \ 0

-I 0 1

0 -\ \

\ -\ 0

0 0 0

Fig. 4 shows the switching voltage vectors and sectors where Tl and Tm refers to the operation times of two adjacent non­zero voltage space vectors in the same zone [7]. Both Vo (000) and V7 (111) are called the zero voltage space vector, and the other six vectors are called the effective vector with a magnitude of 2Vdc/3.

Based on the principle of SVPWM, the simulink model of SVPWM is shown in Fig. 5, which primarily include the sector judgment model, operation, time calculation model for fundamental vectors, calculation model of switching time, and generation model of SVPWM waveforms [3,6,7].

)-----r---flUah IJaIa Nsedorf-----.-------,

}--"f4---+1Ubela

H--+\wc

XYl

Fig. 5. Simulink model of SVPWM inverter

1) Sector Judgement Model Using the expression of voltage vector in the a-� coordinate

for control implementation, the following procedure is used for determining the sector. If

V� > 0, A = 1;

3Va-V� > 0, B = 1;

--J3Va+V� < 0, C = l .

(14)

(15)

(16)

Then, the sector containing the voltage vector can be decided according to N = A+2B+4C, listed in Table II.

TABLE IT. THE SECTOR CONTAINING THE VOLTAGE VECTOR VERSUS N

SECTOR I II III IV V VI

N 3 I 5 4 6

2) Calculation a/ Operation Time a/Fundamental Vectors

Table III lists the operation times of fundamental vectors against sector N, where Tl and Tm refer to the operation times of two adjacent non-zero voltage space vectors in the same zone. X, Y, Z can be calculated by

Z = T(---J3Va+V�)/(--J2Vdc)

Y = T(--J3Va+V�)/(--J2Vdc)

X = 2T [VW(--J2Vdc)]

(17)

(18)

(19)

The sum of Tl and Tm must be smaller than or equal to T (PWM modulation period). The over saturation state must be judged; if Tl +Tm > T, take Tl = Tl [T/(Tl +Tm)] and Tm = Tm[T/(Tl + Tm)].

TABLE Ill. OPERATION TIMES OF FUNDAMENTAL VECTOR

N 1 2 3 4 5

T, Z Y -z -x x

Tm y -x X z -y

3) Generation 0/ SVPWM Voltage Wave/arms

6

-y

-z

The relation between N and switch operation times IS

shown in Table IV, where

Ta = (T-Tl -Tm)/4 (20)

Tb = Ta+Tl /2 (21)

Tc = Tb+Tm/2 (22)

Where Tcml , Tcm2 and Tcm3 are the operation times of the three phases respectively, and is calculated from Ta, Tb, Tc.

TABLE IV. RELATION BETWEEN N, TCM, T A, TB, AND Tc

N 1 2 3 4 5 6

Teml Tb Ta Ta Tc Tc Tb

Tem2 Ta Tc Tb Tb Ta Tc

Tcm3 Tc Tb Tc Ta Tb Ta

By comparing the computed Tcml , Tcm2 and Tcm3 with the carrier signal having 20 KHz, a symmetrical space vector PWM pulses for three phase bridge inverter willn be generated.

IV. SIMULATION RESULT AND ANALYSIS

The simulink model of proposed DTC for PMSM drive based on SVPWM is shown in Fig 13. The Results are taken for specific value of PMSM parameters given in Table V

TABLE V. SPECIFICATION OF PMSM

SNo. PMSM Parameters Values

I Stator Resistance Rs l.4n

2 d-axis Inductance Ld 0.0066 H

3 q-axis Inductance Lq 0.0066 H

4 Permanent Magnet Flux 'Par 0.1546

5 Rated Speed Wr 1050 rpm

6 No of Poles p 6

7 Moment of Inertia J 0.00176

8 Damping Coefficient B 0.0003881

The starting characteristics of PMSM drive with a speed reference of (Or = 600 rpm, and load torque T L = 3 N-m with a step change to 8 N-m at 0.1 sec. Fig 6 and Fig 7 shows the Speed and torque response of PMSM along with d-q axis stator current for speed reference of 600 rpm and 900 rpm respectively.

Fig. 6. Speed, Torque response and id -iq stator current waveform for DTC (wr=600rpm)

Ijf�·ir�!;�i'i�!i\� o 0,05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

.� {±;±1:i+:2 o 005 0.1 0.15 0.2 0.25 0.3 0.35 04 0.45

Fig. 7. Speed, Torque response and id -iq stator current waveform for DTC (ffir = 900rpm)

As seen from torque response curve, at starting of PMSM, torque ripple is larger, because initially electromechanical time constant is much larger than electromagnetic time constant, instantaneous rate of change of stator flux linkage is larger than that of rotor flux linkage. When the actual motor torque becomes less than the given value, the angle between the stator and rotor flux linkage increases, that leads torque growing fast; and vice versa, after a exact equilibrium state; the torque as well as speed settles very fast to final value.

Fig. 8. Three phase stator current waveform (ffir = 600rpm and 900 rpm)

The three phase stator current is shown in fig 8, will remains same for all values of speed (O)r = 600rpm and 900 rpm) only it changes with dynamic loading (value of load torque), it may increase or decrease with value, as in this case increasing with increase in load torque as applied at 0.1 sec. The stator current settles to a steady state value very fast within two cycle.

The flux linkage response curves are shown in Fig 9 and Fig.l 0 for speed reference of 600 rpm and 900 rpm respectively

0.2 0.15

0.1 O.OS ."

il 0 -0.05

-0.1 -0.15

-0.2

Flux Tfaje<:tOfY

·0.2 ·0.15 ·0. 1 -0.05 0 0.05 0.1 0.15 0.2 XAlo:is Fig. 9. Flux Trajectory (ffir = 600rpm)

XVPlot

0.15

o X Ale,.

Fig. 10. Flux Trajectory (ffir = 900rpm)

The estimated flux linkage and estimated torque for DTC is shown in Fig 11 and Fig 12, for O)r = 600rpm and 900 rpm respectively. A close observation of these two wavefonns indicates that value of estimated Electromagnetic torque Te, remains same for all values of speed and is only a function of electromechnical torque TL, as motor have to balance load torque. These estimated flux curve shows that it is increasing a little bit with increase in speed reference and also with load torque.

Estim'">t .. d Flu>< d 0,18

���'H" Estim",ted Flu .. q

��rti:,lftLl o 0.05 0.' 0,15 0.2 0.25 0.3 0,35 0.4 0.45 Estim .. tedT ..

Fig. II. Estimated flux and torque waveforms (ffir = 600rpm)

J;:� a 0.05 D.' 0.15 0.2 0.25 0.3 0,35 0.4 0.45 :J j [: T"O'"'!" Ii ,:j o 0,05 0,' 0.15 0.2 0.25 0.3 0,35 0,4 0,45 l' , " ,t." i Co'_o"o : ,:1 : ' - " - ' - " - " - " - ' - " - ' - " -f- " - " - '- " - '- " - " - " - ' - " - " ,'-"-" -'"-"-'-"-"-" f"-'-"-' " -"-'-"-'-"-' "-"-i-"-" -' -"-"-'-"-"-"-'_ T _ " - "-"-'-"-" -" -"-'-"i"-"-'-"-'-"-'·-"-'-"-'- i .'·-"-'-·- ' ·-"-'-"-'·-'J."-'-"-'·-··-"-'-· 2 ' - - - - , - - - - - ; - - - - - , - - - - - - , .' - - - - - , - - - - , - -� - - - - , - - - - , - , - : - - , - - - - - - , - - - � , - - - - - - , - - - - -� - , - - - - , - , - - - - ; o ..... , .... ,: ...... , ...... ,; .... , ...... , . : .... , .... , ... � .. , ...... , ... :. , ...... , .... ;. , .... , ...... [ ...... , .... , .: ..... , ..... . o O,OS 0,1 0.15 0.2 0.25 0,4 0,45

Fig. 12. Estimated flux and torque waveforms (wr = 600rpm)

Optimal Voltage Estimator

Aux-Torque .----___ -"Est:!!limator

V. CONCLUSION

The simulink model of proposed Direct Torque Control for PMSM drive has been developed and analyzed. With sensing of three phase stator voltages, this technique will be most reliable and promising with reduced cost. Space vector pulse width modulation technique have been used for six gate pulse generation of three phase bridge inverter. A number of simulation results shows that DTC scheme has fast and smooth dynamic response of torque and stator flux linkage followed by excellent performance against sudden change in speed and torque. In DTC scheme, the need of speed/Torque sensors may also be eliminated; making it more reliable and robust. In order to reduce harmonic content in stator current three level H­bridge inverter topology based on SVPWM will be proposed. The excellent dynamic performance of DTC for PMSM will make it more feasible for industrial implementation.

xv Graph

Fig. 13. Simulink Model of Proposed DTC scheme for PMSM drive

REFERENCES

[I] P. Vas, "Sensorless Vector and Direct Torque Control", Oxford University Press, 1998

[2] G. Mino-Aguilar. Etal, "A Direct Torque Control for a PMSM", proc. IEEE, pp.260-264, 2010

[3] Xiaoting Ye, Tao Zhang, "Direct Torque Control of Permanent Magnet Synchronous Motor Using Space Vector Modulation", Proc. IEEE Chinese Control and Decision Conference pp. 1450-1453, 2010

[4] Sanjeet Dwivedi, Bhim Singh, " Vector Control Vs Direct Torque Control Comparative Evaluation for PMSM Drive", IEEE proc. PEDES, pp. 1-8, 2010.

[5] Sanda Victorinne Paturca," Direct Torque Control of Permanent Magnet Synchronous Motor (PMSM) - an approach by using Space Vector Modulation (SVM)", Proc. of the 6th WSEAS/IASME In!. Conf. on Electric Power Systems, High Voltages, Electric Machines, 16-18, 2006

[6] Thomas J. Vyncke, Rene K Boel, Jan A.A. Melkebeek , "Direct torque control of Permanent magnet synchronous motors - an overview", 3rd IEEE Benelux young researchers symposium in Electrical Power Engineering, 2006

[7] LT Yaohua, Yu Qiang, Zhang Depeng, Guan Jiawu, Cai Hongmin , " Study on the use of zero voltage vectors in the PMSM DTC Systems", Proc. 0f 30th Chinese control conf., pp. 3559-3564, 2011

[8] T.Rekioua, D.Rekioua, " Direct Torque Control Strategy of Permanent Magnet Synchronous Machines", IEEE Power Tech. Conf. 2003

[9] Ahmed A. Mahfouz, Wael Mohd. Mamdouh, "Intelligent DTC for PMSM Drive using ANFIS Technique", International Journal of Engineering Science and Technology, Vol. 4 No.03 March 2012

[10] Antoni Arias, Luis Romeral, Emiliano, Marcel Jayne, " Stator flux optimized Direct Torque Control system for Induction motors", Electric Power Systems Research 2005, pp.257-265

[11] Pragasan Pillay, Krishnan, R., " Modelling of Permanent Magnet Motor Drives", IEEE trans. Industrial electronics. Vol. 35, NO. 4, Nov. 1988

[12] N. Bianchi, S. Boloqnani, M. D. Pre, G.Grezzani,. "Design considerations of fractional-slot winding configuration of synchronous machines," IEEE Transactions on Industry App, pp. 997-1006 ,2006

[13] Kurihara, K., Rahman, M.A., "High-efficiency line-start interior permanent-magnet synchronous motors," IEEE Trans. Industry Applications, vol. 40, March. 2004, pp.789-796.

[14] Zhen Chen, XiangDong Liu, DaPeng Yang , " Dynamic Sliding Model Control for Direct Torque Control of PMSM based on Expected Space Vector Modulation", 2nd International Conference on Industrial and Information Systems, IEEE 2010

[15] Yukinori Inoue, Morimoto, S., Sanada, M .. , "Comparative Study of PMSM Drive Systems Based on Current Control and Direct Torque Control in Flux-weakening Control Region", IEEE International Elec. Machines & Drives Conf. 2011, pp. 1094-109