Vector Control

VECTOR CONTROL AND RELIAl3ILITY IMPROVEMENT FOR A SWITCHED RELUCTANCE MOTOR Tian-€ha Liu, Yung-Ju Chen, and Ming-Tzan Lin Department of Electrical Engineering National Taiwan Institute of Technology Taipei, Taiwan 106,

ABSTRACT This paper presents a vector control for a switched reluctance motor. The design, and implementation of a three phase, eight-pole, 10 IIP switched reluctance mot,or with a. vector control is described. Two different control algorithms which consist of a field oriented control, and a maximum torque control are discussed. Performa.nce of the switched reluctance niotor system is improved. In order to improve the reliability of the system, some control strategies are proposed. These strategies result, in the torqiie of the motor being held constant while one leg of the inverter is opened or shorted. A theoretical analysis, and experimental results follow. INTRODUCTION

A number of studies have been published recently [1]-[3] on switched reluctance motors as they are simple i n construction, and economical in comparison with synchronous and induction motors. These studies have just focused simply on the analysis and design of the motor and the drive circuit configuration where the winding ciirrents have constant amplitudes and are injected into the motor in accordance with the rotor position. Many disadvantages exist with the traditional method. For example, a huge torqiie pulsation is produced during the period of phase current switching. As a, result of this pulsation, the speed range is not wide enough. Unlike papers [1]-[3], this paper presents a vector control for a switched reluctance motor of large horsepower. Based on the vector control principle, t,wo different control algorithms are proposed. One consists of a field orient,ed control, and the other, a maximum torque control. In accordance with these control algorithms, the current commands are sinusoidal

538

waveforms. The input currents can thus be decoupled as flux and torque currents, and the speed-loop controller design easily achieved. I n addition, this paper studies the improvement i n reliability of the switched reluctance system. Strategies have also been proposed to solve the problems arising from one phase of the inverter being opened or shorted. Recently, T. H. Liu , J. R. Fu, and T. A. Lip0 proposed some strategies to improve the reliability of an induction motor drive system. However, to the authors' best knowledge, prior to the study described herein, the strategy of the reliability improvement for a switched reluctance motor system had not been studied. The proposed block diagram of vector control for a switched reluctance motor is shown in Fig. 1. The system consists of four major elements: a switched reluctance motor, a current regulated inverter, a digital controller implemented by a microcomputer, and some sensors. A 32-bit 16.7-MHz Motorola MC68020 monoboard microprocessor (VME-110) serves as the speed-loop controller. The microprocessor-based controller is connected to various peripheral devices such as the D/A conversion modules, and a parallel 1/0 module via the VME bus. The controller determines the reference stator current magnitude * command is and current phase angle 6. Then, the three-phase sinusoidal wave generator, implemented by the microprocessor, provides three-phase currents to the current-regulated inverter. The three-phase motor line currents are measured by hall-effect current sensors. These measured currents we fed back to the current controller to execute the current regulated algorithm and then to the microprocessor to execute the strategies of reliability improvement. The other feedback quantity is the absolute rotor position, measured by the absolute encoder mounted on the motor shaft,.

(2) Maximum Torque Control Snitched Regulated

eluctonce

Inverter

Hcroprocessor

m

The phase angle 6 is changed in the fieid oriented control; however, it is kept constant in the maximum torque control. The electromagnetic torque is Te = 0.5 i, 2 (Ld - L9) sin 26. (6) From ( 6 ) , the maximum torque is obtained when 6 is 45'. The torque Te being proportional to i s 2 implies that the

Absdute

relationship between the torque and the current magnitude is nonlinear.

Encoder

Fig. 1 Block diagram of proposed system.

RELIABILITY IMPROVEMENT

CONTROL ALGORITHM

A. Simplified Mathematical Model In this paper, a simplified model of the switched reluctance motor is used. Based on the vector control with a d-q synchronous reference frame, the torque equation of the simplified model can be described as

Te = ( L d - L 9 ) 9i i d and the speed of the motor is

(1)

1

ITe-T1 - B m u r 1. (2) m where Te is the electromagnetic torque, Ld and L are the dQ and q- axes inductances, id and i are the d- and q- axes Pur = -J--

9

currents, p is the differential operator d/dt, wr is the rotor shaft speed, Jm is the inertia constant, T, is the load torque,

and Bm is the coefficient of viscous of the motor. B:Torque Control Methods (1) Field Oriented Control In this method, the d- axis current is fixed at a constant value to produce flux. The q- axis current, which is called "torque current", is determined by the speed-loop controller and the speed error. A fast response to the torque can thus be achieved. The torque of the motor can be expressed as Te=(Ld-L ) i i q d q = K t iq (3)

There are many cases where one phase of the inverter is opened or shorted because a solid-state device is easily opened or shorted under abnormal operation. Friction braking or magnetic braking are usually to be used to avoid an accident. However, those methods require expensive mechanical devices such ad friction brakes or mechanical contactors. Strategies are herein proposed where by this can be avoided simply adjusting the current commands of the drive system. Modification of the hardware is minimal. In addition, regardless of faults, the motor can be operated continuously. A. ONE PHASE OPENED When one phase of the motor is opened while running, the torque is abruptly reduced. In order to maintain constant torque and speed while one phase of the motor is opened, a control strategy has been derived. By suitably adjusting the other two phase current commands, the torque can be kept at a constant. The coordinate system of the paper is shown in Fig. 2 . According to the figure, the current commands of stationary a-b-c frame can be expressed as * * i a = I cos 4 (7)

*

*

2p) ib = I cos (4 - * * 2 ic = I cos (4 -p)

+

(8) (9)

P

a t

where Kt is the constant coefficient of torque. The current maenitude and Dhase are i = ( i 2d + i 2 ) 112

-

S

-

9

(4)

Fig. 2 Coordination System

539

* * *

*

where ia, ib, ic are a-b-c

three phase current commands, I

*

is current vector comm&d, 4 is the current vector angle. The stationary:a - P current commands are * 2 * : 1 * 1 * i, = -5- ( i a - T i b -Tic) (10)

*

*

' P* =-8 (ib - i c )

(11)

s

After a- hase is opened, its current is equal to zero. This implies i, is equal to zero also. Then, from (lO)-(ll), we can obtain the a

-

-p

mea current commands, after a-phase

omned. are

'* 2 1 'b*f - -21 icf) * id=3-(-T' * I * * ( ibf - i,f)

%=-8

It is apparent to understand that if the torque remains constant, then, the efiaxes current commands should also * * * * remain constant, i. e., i, = id and ib = ip So, from equatioy (7)-(13), it is not difficult to derive f!i = 81* cos ( 4 - T r2 - + r )

*

icf = 8 I cos (4

+ -p+ -p) 2

1

(14) (15)

After the a-phase is opened, the b-phase current command ibf has to increase its amplitude to fi,and lags phase angle 1 -6" rad/sec; the c-phase current command iif, however,

has to increase its amplitude to +r.

a,and leads its phase angle

Gimilarly, when the b-phase is opened, the a-phase and c-phase current commands are adjusted as 1 f:i = P I* cos (4 -p) (16)

+ iSf = 8 I* cos (4 + T2= - T r ) 1

(17)

When the c-phase is opened, the other two phase current commands are i> = 8 I* cos (4 --r (18) 2 1 i t = $S I* cos (4 - -p+ T r ) (19) Fig. 3 shows the main circuit of the proposed system. In order to implement the system, a neutral line is connected between the neutral point of the motor and the neutral point of the DC voltage source. While one phase of the inverter is opened, the neutral current increases abruptly. So, an R - C network is used to keep the average voltage of the plus half and minus half voltages equal. The value of the resistance and the capacitor is selected according to the trade off between the transient response of the voltages and power losses of the resistances.

540

Fig. 3 Main circuit configuration. B. ONE PHASE SHORTED Short circuits usr;ally occur when a solidstate device is shot through, whereby, the current is increased abiuptly. Therefore, we recommend a fast action fuse in series with each winding of the motor. When a solid-state device is shorted, the fuse forces the leg of the inverter open. The system then becomes one phase open, and the strategy discussed in part A of this section can be effectively applied. The fuses used here should be fast enough to interrupt the shorting current. If the fuses are too slow, the three-phase currents of the motor become unbalanced, and the torque seriously altered. Fig. 4 shows the influence of the interruption time for different fuses. In this proposed system, if the fuses can be broken in 13 ms, the speed of the motor can be kept near a constant. If the breaking time of the fuse is over 13 ms, the speed of the motor is seriously altered. 220

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zoo.

> -.I $

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EXPERIMENTAL RESULTS

The implementation of the system is shown in Fig. 1, where the microprocessor system consists of a MC 68020 CPU, a MC 68881 coprocessor, and some peripheral devices

such as D/A converter, A/D converter, and parallel 1/0 1x)rl.s. Tlic microprocessor syskni cxcci~tc~ I.hc vccl.or con1 rol algorithm and thc strategies o l reliability improvrmcnt. The sampling period of the microprocessor is 1 111s. The parameters o l the R-C network are choscn as: R , = 500R, and C1 = 2200pl. The motor is tlir_ce-phasc, eight-pole, IOIIP, and is made by Allenwest Company. The parainet.er,s of the switched reluctance motor are sliown in Table I.

\

Fig. 6. Spccd responses at 400 r/min.

Table I Parameters of the Switched nelrictaiice Motor 0.13II Ld 0.06511

Lq

20

R.9

2

J

0.0222 N-msec

Dm

0.00028 N-m-sec/rad

/rad

The concepts behind this paper ha.vc bwn validat.cd i n the laboratory. The system has very low torque pulsation and can reduce the noise of motor opcra.t,ion. 'The implemcnt.cd system ca.n be operated at as low as 15 r/min. Fig. 5 show the torque to ccirrent curves of dircrcni coiif.rol mcthotls. Fig. G to Fig. 8 show the results ohtained when the motor was operated at, a 1 N.m load. The measured spcctl rcspnnscs arc shown i n Fig. G. The figure clearly intlicat,cs that the maximum torque cont,rol has a hcl,ter response I.lian the field oriented control although they operate rinrlcr the same conditions and the same parameters of thc cont.roller. Fig. i shows the currents and speccl of the motor whcii ~h I)-phasc is opened. According t,o these cxpc.rimcnl,al results, I hc spcctl can be kept at, a constant,. Fig. 8 shows the spcetl a n d currents o l the motor. Although one solid+ta!,e device of the I>-phase of the invcrter is xliorled, the slwctl o l I.hr nio1.or is still close to constant. ..

-

nu**n nw

-

hldakmd rmrnl

*

,I

.-/I

1

I

If (Amp)

4

Fig. 5 Torque to current curves of different, mntrol.

. . I

(dl Fig. 7. The wavclorms or a motor when the b-phase is op"A.(a) a-phase current (b) 1)-phase current (c) c-phase current (d) speed.

CONCLUSION

In this paper, the design and implementation of a switched reluctance motor system are proposed. Based on the vector control formulation, this study has developed two different algorithm of vector control, and some strategies to improve reliability. Experimental results validate the theoretical analysis, and show the applicability of vector control in switched reluctance drive. In comparison with the conventional desjgn method, this drive system has lower noise, lower harmonics, and better performance at low speed. Moreover, from the simplified model, a systematic controller design procedure can be easily derived. The results presented herein represent a first step toward the vector control and reliability improvement for a switched reluctance motor. ACKNOWLEDGEMENT

The authors are grateful for the financial support of the National Science Council, Republic of China, under the Grant NSC-83-0404-E-011-032. REFERENCES

R. Krishnan and P. N. Materu, "Design of a single-switch-per-phase converter for switched reluctance motor drives," IEEE Trans. Ind. Electron. ,vol. 37, 110.6, pp.469-476, Dec. 1990. L. H. Hoang, K. Slimani, and P. Viarouge, "A current-controlled quasi-resonant converter for switched-reluctance motor," IEEE Trans. Ind. Electron. , vol. 38, no.5, pp. 355-362, Oct. 1991.

M. Ehsani, I. Husain, and A. B. Kulkami, "Elimination of discrete position sensor and current sensor in switched reluctance motor drives," IEEE Trans. Ind. Appl., vol. 28, no. 1, pp. 128-135, Jan./Feb. 1992.

,,

T. H. Liu, J. R. Fu, and T. A. Lipo, " A strategy for improving reliability ,,of field-oriented controlled induction motor drives, IEEE Trans. Ind. Appl., vol. 29, no.5, pp. 910418, Sep./Oct. 1993. I,

I,

I,

1w

I*

( 4

11

(4 Fig. 8. The waveforms of a motor when the b-phase is shorted. (a) a-phase current (b) b-phase current (c) c-phase current (d) speed.