A high performance DTC strategy for torque ripple minimization using discrete space vector modulation techniques for SRM drive.

Jeyabharath, R. ; Veena, P. ; Rajaram, M. 等

Introduction

Switched reluctance motor, the doubly salient, singly excited motor has simple and robust construction. Although, the induction motor is still the workhorse of the industries, the promising feature of the high torque to mass ratio, high torque to inertia ratio, low maintenance, high specific output and excellent overall performance of SRM make it an efficient competitor for ac drives. The simplified converter topology and switching algorithm due to the unipolar operation avoiding shoot through faults makes SRM advantageous in applications of aerospace, which require high reliability. Also it finds wide application in automotive industries, direct drive machine tools etc [1].

However, significant torque ripple, vibration and acoustic noise are the main drawbacks of SRM to achieve high performance. As the control of SR motor is being the recent trend of research, schemes were developed involving linear and non-linear models to control torque ripple [2]. But due to inaccuracy in linear models and complexity involved in non-linear control, the Direct Torque Control (DTC) was proposed which provided simple solution to control the motor torque and speed and minimized torque ripple.

The direct torque control techniques were proposed in the middle of the 1980's for induction motor [3],[4]. The basic idea of DTC is slip control which is based on the special relationship between the slip and torque. Compared with field orientated control, the DTC has many advantages such as less machine parameter dependence, simple construction and fast dynamic torque response [5], [6]. There is no current controller needed in DTC, because it selects the voltage space vectors according to the errors of flux linkage and torque. The switching states of the inverter are updated in each sampling time. Within each sampling interval, inverter keeps the state until the output states of the hysteresis controller change. Therefore, the switching frequency is usually not fixed; it changes with the rotor speed, load and bandwidth of the flux and torque controllers.

Even though DTC is getting more popular, it also has some drawbacks, such as the torque and flux ripple. Many researchers have paid attention to this problem by now and proposed solutions for it. To increase the number of vectors to be applied to the machine, Takahashi proposed a double three phase inverter [7] and C.G. Mei used variable switching sectors to minimize the torque and flux ripple [8]. However, the researchers are not fully satisfied and the attempt to reduce the torque and flux ripple is continuing.

In classical DTC one of the six magnitude vectors of [3.sup.3] combinations is chosen to control flux and torque within the limits of hysteresis bands. Also in classical DTC the ON/OFF of SRM converter switches are determined by the errors in torque and flux but large and small errors are not distinguished. The switching vectors had chosen same for large and small errors. In order to overcome this problem, DSVMDTC methodologies were introduced.

In this paper, the primary ideas of the DSVM-DTC technique are proposed for SRM drive. The proposed method, along with its simplicity compared to classical DTC, has an improved performance in terms of torque and flux ripple and also stator current distortion. It can be easily extended to a higher numbers of vectors and it minimizes the steady state torque error.

The Classical DTC Scheme For SRM

DTC is based on theories of field oriented (FOC) control and torque vector control. Field Oriented Control uses space vector theory to optimally control magnetic field orientation. The DTC principle is to select stator voltage vectors according to the differences between the reference torque and stator flux linkage with exact value. Voltage vector are so chosen to limit the torque and flux errors within hysteresis bands. The required optimal voltage vectors are obtained from the position of the stator flux linkage space vector, the available switching vectors and the required torque and flux linkage [9].

To drive the control scheme for the SR motor, the non-uniform torque characteristics will firstly be examined. The motor torque output can be found using the motors electromagnetic equation. (1)

v = Ri + d [psi] ([theta], i)/dt (1)

The energy equation is

[dW.sub.e] = [dW.sub.m] + [dW.sub.f] (2)

Where [dW.sub.m] = differential mechanical energy, [dW.sub.f] = differential field energy. But

[dW.sub.e] = eidt (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (4)

The instantaneous torque expression is T = [dW.sub.m]/d[theta] (5)

Hence by substitutions torque expression is derived considering the variation of magnetic co-energy and is given by T [approximately equal to] i d[psi] ([theta], i)/d[theta] (6)

This approximate equation is sufficient for control purpose as it controls the general characteristics of torque production and not the magnitude of torque. The current is always positive as SRM is a unipolar drive. Hence, the sign of torque is directly related to the sign of [delta][psi]/[delta][theta]. The increase of stator flux amplitude with respect to rotor position (positive value of [delta][psi]/[delta][theta]) produce a positive torque and is called "flux acceleration". Whereas a negative value of [delta][psi]/[delta][theta]?called "flux deceleration" produce a negative torque. As this is held for both directions of rotation a four quadrant operation is achieved using unipolar currents. The DTC technique can be defined as follows.

(a) The stator flux linkage vector of the motor is kept at constant amplitude.

(b) Torque is controlled by accelerating or decelerating the stator flux vector.

Voltage Vectors For SRM

Similar to the AC drives, equivalent space vectors can be defined for SRM. The voltage space vector for each phase is defined as lying on the center axis of the stator pole because the flux linkage for a current and voltage applied to the motor phase will have phasor direction in line with the centre of the pole axis. This does not need any change in physical winding topology (Figure1).

In SRM, each motor phase can have three possible voltage states ([S.sub.q]) for a unidirectional current [10].

[FIGURE 1 OMITTED]

(i) When both devices are ON and positive voltage is applied [S.sub.q] = 1.

(ii) For [S.sub.q] = 0, one device is turned OFF and a zero voltage loop occurs.

(iii) For negative state [S.sub.q] = -1, both devices are OFF. The freewheeling current flows through the diodes.

So with each phase having three possible states (0, 1,-1) unlike conventional DTC for ac drives with two states, a total of 27 possible configuration is possible.

Figure2. shows only six equal magnitude voltage vectors separated by [pi]/6 radians is considered as DTC allows no other states to be chosen by the controller. One out of the six states is chosen to keep torque and flux within the hysteresis bands. Let the stator flux vector be located in the [K.sup.th] sector (K = 1,2,3,4,5,6). In order to increase the amplitude of the stator flux, the voltage vector [V.sub.K], [V.sub.K+1], [V.sub.K-1] can be applied and [V.sub.K+2], [V.sub.K+3], [V.sub.K-2], can be applied to decrease the flux. [V.sub.K] and [V.sub.K+3] are zero space vectors.

[FIGURE 2 OMITTED]

The control scheme of SRM is based on the results as follows.

(a) The motor is solicited only through the converter component of voltage space vectors along the same flux.

(b) The motor torque is affected by the component of the voltage space vector orthogonal to the stator flux.

(c) The zero space vectors do not affect the space vector of the stator flux.

So the stator flux when increased by [V.sub.K+1] and [V.sub.K-1] vectors and decreased by [V.sub.K+2] and [V.sub.K-2] affect the torque. As [V.sub.K+1] and [V.sub.K+2] vector advance the stator flux linkage in the direction of rotation they tend to increase the torque. But [V.sub.K-1] and [V.sub.K-2] decelerate the flux in opposite direction and decrease the torque. So the switching table becomes as Table I

The Proposed Discrete Space Vector Modulation-DTC

The functional block diagram of DSVM-DTC system is shown in Figure 3 DSVM-DTC is based on the classical direct torque control system and the differences between them are the switching table and the principles of choosing voltage vectors. Stator flux and torque are controlled respectively a two level and a five level hysteresis comparator. Their status, together with the rotor speed and the stator flux switching sector, are used to select the voltage vector to be applied to Switched reluctance motor.

[FIGURE 3 OMITTED]

Generation of Discrete space vectors and switching table

DSVM is based on this idea that new voltage vector is got by synthesizing a higher number of voltage space vectors which is used in classical DTC technique. This can be made by dividing the sampling time into N equal intervals and applying various voltage vectors in each of them. By doing this, many new equivalent voltage vectors can be synthesized. The more the voltage vectors, the more convenient is to select voltage vector according to various speed to reduce the ripples of the torque and flux. But the switching table becomes more complicated when the number of voltage vector increases. So, a good compromise between the flux and torque ripple compensation and the complexity of the switching table is achieved by choosing N = 3. By using this kind of technique we can get 19 voltage vectors as shown in Figure 4.

In classical DTC system, five voltage vectors can be used to compensate the error of the flux and torque when the flux is in sector 1 as shown in Figure 2. Under the same condition, 19 voltage vectors can be used by using DSVM with N = 3, as shown in Figure 4. Each point of intersections is the end of the new synthesized voltage vectors. Each voltage vectors occupies one third of the control cycle time.

[FIGURE 4 OMITTED]

Simulation Results

To simulate the system, a Matlab/Simulink closed loop model was constructed for the SR motor and the control system as in Figure 5. The motor parameters such as torque, phase flux and position are obtained from the 3[PI] SRM. The three phase-flux vectors are transformed on to a stationary orthogonal [alpha]-[beta] reference frame to calculate the net flux. The torque and flux errors are generated by the hysteresis comparator based on the difference between reference and actual values of torque and stator flux respectively. Based on the present position of motor, [T.sub.e] and [[psi].sub.e] the optimal selection of voltage space vector is done with the help of DSVM switching table. Thus the converter switches and hence the motor is controlled by DSVM-DTC scheme. In this simulation test, the motor reference flux and torque were maintained at a constant of 0.3Wb and 5Nm respectively. The hysteresis band limits were defined to be of [+ or -] 0.01Wb and [+ or -]0.1Nm for the flux linkages and torque respectively.

In Figure 6a and 6b, the phase flux and current values are shown. It is seen clearly that in steady state the DTC leads to regularly spaced flux linkage and currents. The individual flux linkages leads to smooth constant amplitude flux vector in the stator air gap.

The torque results in Figure 7. shows lower ripple content and constant amplitude nature. The FFT analysis in Figure 8. shows lower ripples of torque for DSVM-DTC when compared to that of classical DTC. Also at a higher frequency the magnitude of ripples is less. Further the effective control of the overlapping phase conduction attenuates the magnitude of torque ripple leading to quieter operation. The result of the torque, flux and speed control can be seen in Figure 6, and Figure 7.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

Conclusion

In the paper, a modified DTC algorithm is proposed which is based on the discrete space vector modulation theory. In DSVM voltage vectors are increased by dividing the sampling time into N equal intervals and applying various voltage vectors in each of them. Having a large number of voltage space vector, smaller torque ripple with constant switching frequency is attained. As a result, both torque and flux linkage ripples are greatly reduced, and the switching frequency is maintained constant. The use of this technique is very useful in application where the maximum sampling frequency is limited by large computational time.

References

[1] T.J.E. Miller, "Switched Reluctance Motors and their Control", Magna Physics & Oxford. 1993.

[2] P. Jinupun and P. C.-K. Luk, "Direct torque control for sensor less switched reluctance motor drives," in Proc. 7th Int. Conf. Power Electron. Variable Speed Drives, 1998, pp. 329-334

[3] M.Depenbrock, "Direct Self control of inverter fed machine" IEEE Trans. Power Elec. Vol.3. No.4 pp 420-429 Oct 1988

[4] Takahashi and T. Noguchi, "Take a look back upon the past decade of direct torque control," in Proc. IECON '97, 23rd Int. Conf. Ind. Electron.,Contr. Instrum., vol. 2, 1997, pp. 546-551.

[5] Hai-Jiao Guo "Considerations of Direct Torque Control for Switched Reluctance Motors" IEEE ISIE 2006, July 9-12,pp.2321-2325, 2006,

[6] S. K. Sahoo, S. K. Panda and J. X. Xu, "Direct Torque Controller for Switched Reluctance Motor Drive using Sliding Mode Control" IEEE Conference proceedings PEDS 2005, pp. 1129-1134, Dec 2005

[7] Takahashi and Y. Ohmori, "High Performance Direct torque control of an induction motor." IEEE Trans.Ind.Apllicant.,vol 25,no. 2,pp 257-264, March 1989.

[8] C.G. Mei, S.K .Panda, J.X. Xu and K.W. Lim "Direct Torque Control of Induction Motor-Variable switching Sectros" IEEE International Conference on Power Electronics and Drive Systems, PEDS'99, July 1999, Hongkong.

[9] Adrian David Cheok and Yusuke Fukuda "A New Torque and Flux Control Method for Switched Reluctance Motor Drives" IEEE Transaction on Power Electronics. Vol. 17, No. 4 July 2002, pp.543-557

[10] Jeyabharath R, Veena P, Rajaram M "A new scheme for Torque and Flux Control for Switched Reluctance Motor Drive" in Proc. IEEE IICPE,2006, pp. 90-94

R Jeyabharath (1), P Veena (1) and M Rajaram M (2)

(1) Department of EEE, K.S.Rangasamy College of Technology, Tiruchengode, Tamil Nadu-637 215, India. E-mail: veena_gce@yahoo.co.in. & jeya_psg@rediffmail.com

(2) Department of EEE, Thanthai Periyar Govt. Institute of Technology, Vellore, India. E-mail: rajaramgct@rediffmail.com

Table I : Stator Flux and torque variations due to applied inverter
voltage spave vector.

T [up arrow]       T [up arrow]       T [up arrow]
[PSI] [up arrow]   [PSI] [up arrow]   [PSI] [up arrow]

 [V.sub.K+1]         [V.sub.K+1]        [V.sub.K+1]

T [up arrow]
[PSI] [up arrow]

[V.sub.K+1]

Table--II: Dsvm-dtc switching tables.

                    [C.sub.T]= -2   [C.sub.T]= -1   [C.sub.T]= 0

[C.sub.[psi] = 1    (k-2,k-2,k-2)   (k+2,Z,Z)       (k+2,k+2,Z)
[C.sub.[psi] = -1   (k-1,k-1,k-1)   (k+1,Z,Z)       (k+1,k+2,Z)

(a) Sector K+

                    [C.sub.T]= +1   [C.sub.T]= +2

[C.sub.[psi] = 1    (k+2,k+2,K+1)   (k+2,k+2,k+2)
[C.sub.[psi] = -1   (k+1k+1,K+1)    (k+1,k+1,k+1)

                    [C.sub.T]= -2   [C.sub.T]= -1   [C.sub.T]= 0

[C.sub.[psi] = 1    (k-2,k-2,k2)    (k+2,Z,Z)       (k+2,k+2,Z)
[C.sub.[psi] = -1   (k-1,k-1,k1)    (k+1,Z,Z)       (k+1,k+1,Z)

(b) Sector K

                    [C.sub.T]= +1   [C.sub.T]= +2

[C.sub.[psi] = 1    (k+2,k+2,K+1)   (k+2,k+2,k+2)
[C.sub.[psi] = -1   (k+1k+1,K+1)    (k+1,k+1,k+1)