UKSim 2009: 11th International Conference on Computer Modelling and Simulation

A Direct Torque Controlled Induction Motor with Variable Hysteresis Band

Kanungo Barada Mohanty
Electrical Engineering Department, National Institute of Technology, Rourkela, India
AbstractAn improved direct torque controlled induction motor drive is reported in this paper. It is established that the conventional direct torque controlled drive has more torque and flux ripples in steady state, which result in poor torque response, acoustic noise and incorrect speed estimations. Hysteresis controllers also make the switching frequency of voltage source inverter a variable quantity. A strategy of variable duty ratio control scheme is proposed to increase switching frequency, and adjust the width of hysteresis bands according to the switching frequency. This technique minimizes torque and current ripples, improves torque response, and reduces switching losses in spite of its simplicity. Simulation results establish the improved performance of the proposed direct torque control method compared to conventional methods. KeywordsDirect Torque Control, Hysteresis controllers, Switching Frequency, Torque Ripple, Induction Motor Drive

NOMENCLATURE

s , is s , r
s,ref s,k s Te Tref T sr

stator voltage vector and current vector stator and rotor flux linkage vectors reference stator flux linkage vector stator voltage vector in k-th sector of flux plane change in stator flux linkage vector in time t developed torque of machine reference torque half the width of torque hysteresis band angle between stator and rotor flux vectors flux and torque error status dc link voltage input to inverter stator resistance per phase stator (self), rotor (self) and mutual inductances stator flux leakage coefficient number of poles

d , dTe Vdc Rs Ls ,Lr, Lm P

I. INTRODUCTION Many adjustable speed drive applications require instantaneous electromagnetic torque control, instead of precise, closed loop speed control. The advantages of torque control in this type of application include greatly improved transient response, avoidance of over-current trips, and the elimination of load dependent controller parameters. An example of an application where torque is to be controlled, without precise speed control, is traction drives for electric vehicles. There are basically two types of instantaneous torque controlled a.c. drives used for high performance

applications: vector controlled, and direct torque controlled drives. Vector controlled drives [1], were introduced more than 30 years ago. They have achieved a high degree of maturity and have become increasingly popular in a wide range of applications. However, complexity of coordinate transformation, inclusion of shaft encoder, and parameter dependency are well known disadvantages of vector controlled drives [1]. To overcome these problems, direct torque control (DTC) [2], or direct self control (DSC) [3], [4] technique was introduced. In this method the inverter is switched so as to keep stator flux and torque within the limits of two hysteresis bands. This method allows a decoupled control of flux and torque without the need of coordinate transformation, PWM pulse generation and current regulation but results in a variable switching frequency. At steady state current, flux and torque pulsates, which result in inaccurate flux and speed estimation, and increased acoustical noise. Several solutions with improved DTC are presented in the literature. To improve torque and flux response and reduce inverter switching frequency of a high power drive, two inverters with DTC is implemented in [5]. In [6,7], techniques have been presented which allow constant switching frequency operation. Over a fixed switching period, inverter switching pattern or duty cycle is calculated in [6] directly in order to control the torque and flux in a deadbeat fashion. Reduction of current and torque ripple is obtained in [7] by calculating the required variation of stator flux vector, and exactly compensating the flux and torque errors. To apply this technique, the control system should be capable of generating any voltage vector at each sampling period. This concept is applied in [5] to generate a number of voltage vectors higher than that used in basic DTC, by using a double three phase inverter. Direct torque and flux control (DTFC) based on space vector modulated (SVM) inverter for sensorless induction motor drive is implemented in [8]. Constant and controllable switching frequency is achieved, and steady state torque ripple is reduced. Discrete space vector modulation (DSVM) technique is used in [9] to increase the number of voltage vectors. Voltage vectors are selected in [9] from switching tables according to rotor speed, flux error and torque error. This reduces flux and torque ripples, and current distortion. In [10], a comparative study of classical DTC, space vector modulated (SVM) DTC and discrete space vector modulated (DSVM) DTC is done with emphasis on stator current distortion and torque ripple. In this paper, the principle of direct torque and flux control is discussed in section II. The improved DTC technique is presented in section III. The strategy for

978-0-7695-3593-7/09 $25.00 2009 IEEE DOI 10.1109/UKSIM.2009.24

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adjusting the width of hysteresis band to reduce torque and flux ripples is also reported in section III. Test results are presented in section IV. II. DIRECT TORQUE AND FLUX CONTROL The scheme of conventional direct torque controlled induction motor drive is shown in Fig. 1. It consists of a pair of hysteresis comparator, torque and flux estimators, voltage vector selector and a voltage source inverter. The schematic diagram of 3-phase voltage source inverter is shown in Fig. 2. It has eight possible voltage space vectors, as shown in Fig. 3, according to the combination of the switching modes: k = [Sa Sb Sc] where each of Sa, Sb, Sc takes the value 1 or 0 independent of others. There are six active voltage vectors: s,1 to s,6 and two zero voltage vectors: s,0 , s,7 corresponding to [0 0 0] and [1 1 1], respectively. It can be shown that the voltage vector is given by (1). 2 s, k = Vdc S a + S b e j.2 / 3 + S c e j.4 / 3 (1) 3 DTC performs separate control of the stator flux and torque, which is also known as decoupled control. Direct flux control and direct torque control are discussed in the following sections.
Vdc/2 Vdc/2
Figure 2. Schematic diagram of voltage source inverter

1 Sa 0

1 Sb 0

1 Sc 0

IM

s,4 s ,5
[ 0 1 1]

[ 0 1 0]

s,3 [ 1 1 0] s ,7 s , 2 s,0 [ 1 0 0]
[ 1 0 1]

[ 0 0 1]

s ,6

s,1

Figure 3. Voltage space vectors

A. Direct Flux Control A dynamic model of the machine is considered to design and simulate the direct torque control technique. The machine model in stator reference frame [1], is used for simulation. The stator flux linkage vector is given as [1],

s = ( s R s i s ) dt (2) Neglecting the voltage drop in stator resistance, the flux change over a small period of time can be written as s = s t (3)
In (3), s is the voltage vector, which may occupy any of the eight space positions as shown in Fig. 3.

The magnitude and orientation of the stator flux must be known in order to directly control the stator flux by selecting appropriate voltage vector. The stator flux plane is divided into six sectors as shown in Fig. 4. Each sector has a different set of voltage vectors to increase (voltage vector highlighted in gray) or decrease (voltage vector highlighted in black) the stator flux as illustrated in Fig. 4. The stator flux is forced to follow the reference value within a hysteresis band by using a 2-level hysteresis comparator. If the stator flux lies in sector k, then the voltage vector s,k +1 is selected to increase the stator flux, and s,k + 2 selected to decrease the stator flux.

ref

Vdc
+-

Tref

Voltage vector selector

+ -

Sa Sb Sc

Voltage Source Inverter v

IM

Stator flux and torque estimator

Figure 1. Schematic diagram of direct torque controlled induction motor drive

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d = 0 if s s,ref + s

(5)

The performance of the control system is directly dependent on the estimation of stator flux and torque. Stator flux is estimated using the voltage model, as in (2).
B. Direct Torque Control The instantaneous torque in terms of stator and rotor flux linkages is given by (6). 3 Lm 3 Lm Te = s r = s r sin sr (6) 2 LsLr 2 LsLr In order to obtain instantaneous torque control, it is necessary to vary sr quickly. Variation of sr and electromagnetic torque with the application of different voltage vectors are given in Table I. Two assumptions are motor rotates in counterclockwise rotation, and load torque remains constant. It can be summarized that, the stator flux which lies in sector k, plays an important role in controlling sr by applying an appropriate voltage vector as tabulated in Table I.
TABLE I. VARIATION OF sr AND TE WITH DIFFERENT VOLTAGE VECTORS Voltage vector Active forward ( s , k +1 and s , k + 2 ) Zero ( s, 0 and Effect on stator flux Stator flux advances forward Stator flux weakens only due to stator resistance drop Stator flux magnitude increases or reduces rapidly Stator flux rotates in reverse direction

Figure 4. Control of voltage space vectors in six sectors of flux plane

The radial voltage vectors s,k and s,k + 3 , which can be used to quickly affect the flux, are generally avoided. The estimated stator flux error is fed to the hysteresis comparator as shown in Fig. 5, which produces the flux error status d . It can be either 1 or 0. Typical waveforms of stator flux, stator flux error and stator flux error status are shown in Fig. 6.

sr , and Te
Increase Decrease Decrease Decrease rapidly

s, 7 )

Radial ( s, k and s , k + 3 ) Reverse active ( s , k 1 and s , k 2 ) Figure 5. Block diagram of the stator flux hysteresis comparator

In DTC, the torque is controlled within its hysteresis band similar to the stator flux. Three-level hysteresis controller as shown in Fig. 7 is employed because the machine may operate in motoring mode as well as braking mode as shown in Fig. 8. Waveforms of the torque, torque error, speed and torque error status are shown in Fig. 8. Torque error status, dTe=1, 1 or 0, if the torque is to be increased, decreased or not to be changed, respectively. 2T 1 +_ -1
T
Figure 7. Block diagram of 3-level torque hysteresis comparator

Tref
Figure 6. Waveforms of stator flux, flux error and flux error status

dT

If stator flux is to be increased d = 1 , and if stator flux is to be decreased d = 0 .

d = 1 if s s,ref s

(4)

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TABLE III . VOLTAGE VECTOR SELECTION FOR CLOCKWISE ROTATION Flux error stats 0 1 Torq Sector Sector error 1 2 status 1 011 001 0 111 000 -1 110 010 1 001 101 0 000 111 100 110 -1 Sector Sector Sector Sector 3 4 5 6 101 111 011 100 000 010 100 000 001 110 111 011 110 111 101 010 000 001 010 000 100 011 111 101

Figure 8. Waveforms of torque, torque error and torque error status

When a negative reference torque is applied, motor enters to braking mode, and the torque error status alternates between 1 and 0. When the reference torque is positive, the torque error status switches between 1 and 0, indicating motoring mode operation. The developed torque is estimated from the stator flux and the stator current space vectors, using (7). 3P Te = s is (7) 2 2 III. CONTROL TECHNIQUE
A. Voltage Vector Selection Due to the decoupled control of torque and stator flux in DTC, a high performance torque control can be established. If stator flux lies in sector k with motor rotating in counter clockwise, active voltage vector s,k +1 is used to increase

B. Switching Frequency The variable switching frequency may produce significant acoustic noise of variable intensity, a non-uniform distribution of switching losses for each semiconductor switch in the power inverter, and currents that have nondeterministic harmonic content. Many techniques are proposed and implemented to produce constant switching frequency for DTC. Basically, they can be divided into hysteresis based, and non-hysteresis based solutions. A variable hysteresis band comparator is proposed in this paper, where the band is adjusted according to the switching frequency. C. Torque Ripple With a larger sampling time, the possibility of torque overshoot and undershoot is higher. By reducing the sampling period, a better torque trajectory is obtained. Switching frequency is increased by changing the duty ratio of the selected voltage vector during each switching period according to the magnitude of the torque error and position of the stator flux. Here a zero voltage vector is chosen to reduce the torque.

both stator flux and torque, where as s,k + 2 is selected to increase torque but decrease stator flux. The two zero voltage vectors ( s,0 and s,7 ) are used to reduce the torque and freeze the stator flux. In this case stator flux weakens only due to stator resistance drop. In forward braking mode, reverse voltage vector s,k 2 is used to decrease both torque and flux, where as s,k 1 is selected to reduce the torque and increase the flux. The optimum selection of switching vectors in all sectors of stator flux plane is tabulated in Table II for counterclockwise rotation, and in Table III for clockwise rotation.
TABLE II. VOLTAGE VECTOR SELECTION FOR COUNTERCLOCKWISE ROTATION Flux error stats 0 1 Torq Sector Sector error 1 2 status 1 110 010 0 111 000 -1 011 001 1 100 110 0 000 111 001 101 -1 Sector Sector Sector Sector 3 4 5 6 011 111 101 010 000 100 001 000 100 011 111 110 101 111 110 001 000 010 100 000 010 101 111 011

Figure 9. Two trajectories of torque with (a) large sampling time, (b) small sampling time

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IV. TEST RESULTS For the simulation, the induction motor whose specifications and parameters are given in Table-IV is used. The reference flux linkage is taken as 1V.s and starting torque is limited to 15 N-m. The SIMULINK block diagram for the proposed drive system is shown in Fig. 10. The model is run for typical conditions of reference speed and applied torque values. The simulation results of the starting transients for the DTC drive at no load condition are shown in Fig. 11. The simulation results of the DTC drive for load variations are shown in Fig. 12. The hexagonal flux plot of stator flux linkage is shown in Fig. 13. Fig. 14 shows the locus diagram of stator flux linkage vector with load variation. Time variations of flux and torque are shown in Fig. 15 and Fig. 16, respectively. Fig. 17 and Fig. 18 show the time variation of q-axis stator flux and d-axis stator flux, respectively.
TABLE IV. SPECIFICATION AND PARAMETERS OF THE INDUCTION MOTOR Specifications Parameters Rs Rr Ls Lr Lm J B 1.5kW, 1440 r.p.m., 4 pole, 3 phase, 50Hz Nominal values 7.83 7.55 0.4751H 0.4751H 0.4535H 0.06 Kg m2 0.01 N m/rad/s Figure 11. No-load starting transients

Figure 12. Starting transients with load variations

Flux linkage (V.s)

Flux linkage (V.s)

Figure 10. SIMULINK block diagram of the drive system Figure 13. Hexagonal plot of stator flux linkage vector tip at no load

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Flux linkage (V.s)

Flux linkage (V.s)

Flux linkage (V.s)

Figure 14. Locus of tip of stator flux linkage vector with load

Time (s) Figure 18. d-axis flux linkage versus time

V. CONCLUSIONS The conventional direct torque control (DTC) strategy with fixed hysteresis band is simpler to implement than vector control, but it has high torque ripple and poor torque response. The proposed scheme uses a variable hysteresis band comparator, where the band is adjusted according to the switching frequency. Switching frequency is also increased significantly by varying the duty ratio of the selected voltage vector according to the magnitude of the torque error and position of the stator flux. Simulation results establish that the proposed technique has improved the torque response, and reduced the torque ripple. This DTC method also allows the decoupled control of torque and stator flux. So, a better drive performance is achieved. REFERENCES
P. Vas, Sensorless Vector and Direct torque control, Oxford University Press, 1998. [2] I. Takahashi and T. Noguchi, A new quick response and high efficiency control strategy of an induction motor, IEEE Trans. Ind. Appl., vol. 22, no. 5, pp. 820-827, 1986. [3] M. Depenbrock, Direct self control (DSC) of inverter-fed induction machines, IEEE Trans. Power Electronics, vol. 3, no. 4, pp. 420-429, 1988. [4] U. Badder and M. Depenbrock, Direct self control (DSC) of inverterfed induction machines: A basic for speed control without speed measurement, IEEE Trans. Ind. Appl., vol. 28, no. 3, pp. 581-588, 1992. [5] I. Takahashi and Y. Ohmori, High-performance direct torque control of induction motor, IEEE Trans. Ind. Appl., vol. 25, no. 2, pp. 257264, 1989. [6] T. G. Habetler, F. Profumo, M. Pastorelli, and L. M. Tolbert, Direct torque control of induction machines using space vector modulation, IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1045-1053, 1992. [7] D. Casadei, G. Sera, and A. Tani, Stator flux vector control for high performance induction motor drives using space vector modulation, Electromotion, vol. 2, no. 2, pp. 79-86. [8] C. Lascu, I. Boldea, and F. Blaabjerg, A modified direct torque control for induction motor sensorless drive, IEEE Trans. Industry Applications, vol. 36, no. 1, pp. 122-130, 2000. [9] D. Casadei, G. Sera, and A. Tani, Implementation of a direct torque control algorithm for induction motors based on discrete space vector modulation, IEEE Trans. Power Electronics, vol.15, no.4, pp. 769777, 2000. [10] P. Marino, M. DIncecco and N. Visciano, A comparison of direct torque control methodologies for induction motor, Procc. IEEE Porto Power Tech Conference, Portugal, Sept. 2001. [1]

Flux linkage (V.s)

Time (s) Figure 15. Flux linkage versus time

Torque (N.m)

Time (s) Figure 16. Torque versus time

Flux linkage (V.s)

Time (s) Figure 17. q-axis flux linkage versus time

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