ΦAbstract -- A novel prediction technique for the direct torque control (DTC) of an induction motor is presented in the paper. The conventional DTC method selects voltage vectors from switching table. The application of these vectors does not satisfy demands for torque increase or decrease at all operating conditions and is not optimal regarding torque ripple. The novel prediction technique calculates in every sampling period the torque changes for different voltage vectors and selects discrete voltage vector which results in minimum torque deviation from the reference value. The voltage vector is selected from new switching table and applied for the whole sampling period. In comparison with the conventional DTC method, the novel technique considerable reduces torque ripple in medium and high speed region. Simulation and experimental results for 525kW motor are presented to validate the proposed technique.

Index Terms -- Induction motor drives, direct torque control, prediction method, torque ripple reduction.

I. INTRODUCTION HE direct torque control (DTC) is very simple and reliable method for the control of induction motor

drives [1], [2]. The electromagnetic torque and the stator flux are calculated from stator quantities and parameters (voltages, currents and stator resistance) and controlled by hysteresis controllers. The hysteresis controllers outputs and the stator flux vector position define which stator voltage vector will be selected from the switching table and chosen voltage vector is applied for the whole sampling period. Nevertheless, the application of voltage vectors from the conventional DTC switching table does not always result in correct torque change and therefore, high torque ripple might occur.

A DTC method presented in [3] uses a variable application time, i. e. the converter voltage vector is not applied to the motor for the whole sampling period but only for the time interval needed by the torque to reach the upper (or lower) limit of the hysteresis band. The method considerable reduces torque ripple but the improvement in the performance is obtained at the expense of the converter switching. A new DTC method proposed in [4] is based on the application of the discrete space vector modulation (SVM) and uses prefixed time intervals within a sampling period. Different switching tables are required for low, medium and high rotor speed. Compared with the conventional DTC method, the switching frequency is increased if both methods have equal sampling period. In [5], global minimum torque ripple DTC is derived. It satisfies the root-mean-square criteria of torque ripple and uses SVM in order to solve problems of varying switching frequency and torque ripple. Active and zero voltage

D. Krušelj is with KONČAR – Electrical Engineering Institute Inc.,

Fallerovo šetalište 22, HR-10000 Zagreb, Croatia (e-mail: dkruselj@koncar-institut.hr).

vectors are applied in each sampling period and the calculation of time intervals for application of these vectors requires a knowledge of induction motor stator and rotor parameters. A predictive control algorithm that uses a discrete-time state-space model is described in [6]. Cost function which inputs are the torque reference, the predicted torque, the stator flux reference and the predicted stator flux is defined and the voltage vector with smallest torque and stator flux errors is selected. The algorithm also requires all parameters of induction motor. Another prediction DTC method is presented in [7], [8]. It uses five registers to store the incremental changes in the torque, the stator flux vector magnitude and the stator flux vector angle. These changes serve as predictions and are added to the calculated values. The method reveals simplicity and robustness comparable with the conventional DTC method, but the torque ripple reduction is result of more accurate torque prediction and not of the optimal switching state application. In [9], DTC is improved with the voltage vector selection according to distances of the stator flux and torque errors from the origin of the stator flux error - torque error plane. The control strategy is not explained in details and only simulation results are given.

Aforementioned, except [7], [8], and other modified DTC methods for torque ripple reduction [10]-[13], use either some kind of the SVM or all motor parameters. In the induction motor drives where the converter switching frequency is limited (e. g. traction drives or high power drives) the use of SVM would result in a relatively large sampling period. For example, the sampling period for tram drives with SVM should be greater than 400μs and for train drives greater than 700μs, which might be too long for accurate and reliable control. Also, in traction drives is due to the reliability desirable to apply an algorithm that uses as little motor parameters as possible.

Therefore, the novel prediction technique for DTC of an induction motor is proposed in this paper. In each sampling period the electromagnetic torque and the stator flux changes are calculated using only stator quantities. The changes are computed for different voltage vectors and the discrete voltage vector that results in minimum torque deviation from the reference value is selected and applied for the whole sampling period. The voltage vector is selected from a new switching table which differs from the conventional DTC switching table and takes into account the torque changes dependence on the position of the stator flux vector in the sextant. Simulation and experimental results for 525kW traction motor used in trains show the effectiveness of the proposed technique. Compared with the conventional DTC method, the novel prediction technique in medium and high speed region reduces torque ripple and causes closer correspondence of an average torque value to the reference value.

Novel Prediction Technique for Direct Torque Control of Induction Motor

Dubravko Krušelj

T

978-1-4799-4389-0/14/$31.00 ©2014 IEEE 829

II. CONVENTIONAL DIRECT TORQUE CONTROL PERFORMANCE ANALYSIS

A. Motor Equations The stator voltage equation of an induction motor relates

the stator voltage vector su , the stator current vector si and the stator flux vector sψ

dtd

iRu ssss

ψ+= (1)

where Rs is the stator resistance. The electromagnetic torque Te can be expressed in terms

of the stator current vector and the stator flux vector

( )δψ23

= sinipT sse (2)

where p is the number of pole pairs and δ is an angle between the stator current and the stator flux vectors. The torque can also be expressed in terms of the stator flux vector and the rotor flux vector rψ

( )γψψσ2

3 sinLL

LpT rs

rs

me = (3)

where Lm, Ls and Lr are the mutual, stator and rotor inductance of the motor, respectively, σ is the motor total leakage factor and γ is an angle between the stator flux and the rotor flux vectors.

The stator flux vector and the rotor flux vector in any coordinate system are defined with the stator current vector, the rotor current vector ri and motor parameters

rmsss iLiL +=ψ (4)

.iLiL rrsmr +=ψ (5)

B. Stator Flux Changes A two-level voltage source converter can provide eight

different voltage vectors; two of them are zero-vectors. The complex plane is divided into six sextants and each discrete voltage vector lies in the center of the sextant. For one movement direction, it is useful to define a position of the stator flux vector according to the center of the sextant, i. e. when the stator flux vector crosses the sextant its position angle changes from –30º to 30º el.

Fig. 1 shows a change of the stator flux vector in sextant N.

Fig. 1. Stator flux vectors in complex plane.

The discrete voltage vector Nu is aligned with the real axis. skψ is the stator flux vector at time instant tk (beginning of the sampling period Tsp), sψΔ is the vector which represents a change of the stator flux vector during sampling period and 1+ψsk is the stator flux vector at time

instant tk+1 (end of the sampling period) .Ttt spkk +=1+ (6)

φsk is the stator flux vector angle at time instant tk defined to the center of the sextant, Δφs is the stator flux vector angle change during sampling period and λ is an angle of a triangle formed by vectors. According to (1), the stator flux change is determined by the applied voltage during sampling period and by the voltage drop on the stator resistance. If the stator resistance voltage drop is neglected, the angle λ in Fig. 1 can be calculated from the angle φsk and from the applied voltage vector position in the complex plane. Further, if converter semiconductors voltage drops and an influence of dead-time are neglected, the module of vector sψΔ is approximately

spdcs Tu32ψΔ ≈ (7)

in the case when active voltage vector is applied (udc is dc-link voltage). If zero voltage vector is applied, sψΔ is approximately zero.

The stator flux vector module at the end of the sampling period 1+ψsk and the stator flux vector angle change Δφs can be calculated using the law of cosines. A change in the stator flux vector magnitude is sksks ψψψΔ 1 −= + (8)

where skψ is the stator flux vector module at the beginning of the sampling period.

The conventional DTC method selects voltage vector from the switching table. The selection is based according to hysteresis outputs and sextant N where the stator flux vector is positioned. In this paper, an analysis is done for counterclockwise movement direction and application of active voltage vectors 1+Nu and 2+Nu for torque increasing and zero voltage vector 0u for torque decreasing (Table I). For clockwise movement direction, active vectors are 1−Nu and 2−Nu . The active and zero voltage vectors’ torque change effects are independent of movement direction.

TABLE I

CONVENTIONAL DTC METHOD, SWITCHING TABLE FOR SEXTANT N

Torque and Stator Flux Demand T ↑, ψs ↑ T ↑, ψs ↓ T ↓, ψs ↑↓

Voltage Vector 1+Nu 2+Nu 0u Fig. 2 depicts the changes of the stator flux vector

magnitude in dependence on the stator flux vector position in the sextant N for different voltage vectors ( 1+Nu , 2+Nu ,

Nu and 0u ). The changes are shown relatively to the nominal value of the stator flux vector magnitude. Motor data are given in Table II, dc-link voltage is 1500V and the sampling period is 100μs.

To ease an analysis, a value of skψ is in calculation constant and equal to the stator flux reference value. The stator flux vector magnitude changes do not depend on the stator flux angular speed and when calculated with aforementioned neglects, are not load depended. But, it is

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shown in [3] that the stator flux vector changes are very little influenced by the load.

TABLE II

MOTOR DATA

Rated power (kW) 525 Rated voltage (V) 1000 Rated current (A) 359 Rated frequency (Hz) 73 Number of pole pairs 2 Rated speed (min-1) 2172

Fig. 2. Stator flux vector magnitude changes versus stator flux vector position, sextant N (applied voltage vectors - solid line: 1+Nu ; long dash

line: 2+Nu ; round dot line: Nu ; square dot line: 0u ).

C. Torque Changes The electromagnetic torque changes are calculated from

stator quantities. The change during sampling period is ekeke TTT −= +1Δ (9) where Tek+1 and Tek are values of the torque at time instants tk+1 and tk, respectively. A relative change of the torque is

.T

TT

T

ek

ek

ek

e 1Δ 1 −= + (10)

The rotor flux vector locus is practically a circle owing to the first order, low-pass filtering action between the stator and the rotor flux vectors [14]. A sudden variation of the stator flux due to the switching processes is followed with a delay from the rotor flux. Therefore, an assumption is made that the change of the rotor flux vector magnitude during sampling period can be neglected rkrk ψψ 1 ≈+ (11)

where 1+ψrk and rkψ are the rotor flux vector modules at time instants tk+1 and tk, respectively. It is also supposed that motor parameters during sampling period are constant. Then, from (3) the following can be derived

( )( )ksk

ksk

ek

ek

sinsin

TT

γψγψ 111 +++ ≈ (12)

where γk+1 and γk are the angles between the stator and the rotor flux vectors at the end and at the beginning of the sampling period, respectively. The angle γk+1 can be expressed by a change of the angle γ in the sampling period γΔ+γ=γ 1+ kk (13) .rs φΔφΔγΔ −= (14)

Δφr is the rotor flux vector angle change during sampling period. In a stationary αβ-reference frame fixed to

the stator, both the stator and the rotor flux vectors rotate with an equal angular speed. Different from the stator flux vector angle change Δφs, which is directly influenced by the applied voltage vector (Fig. 1), the rotor flux vector angle change in the stationary αβ-reference frame is followed with some time delay. In steady state and also during speed transients, Δφr can be calculated with acceptable accuracy from the sampling period and a time period defined with the angular speed of the stator and rotor flux vectors ωs .T sspr ωφΔ ≈ (15)

The change of the angle between the stator and the rotor flux vectors Δγ (14) in the sampling period is small ( ) 1γΔ ≈cos (16) ( ) .sin γΔγΔ ≈ (17)

Finally, the torque change (9) can be calculated from (8), (12), (13), (16) and (17)

( ) ( ) .ctgTctgTTT ksk

sekkek

sk

seke γ

ψψΔ

γΔγγΔψψΔ

Δ ++≈ (18)

The angle between the stator and the rotor flux vectors γk at the beginning of the sampling period and corresponding value ctg(γk) can be derived from (2), (3), (4) and (5)

( )( )

sksks

kskk

iL

sinisin

−=

ψσ

1

δγ (19)

where ski is the module of the stator current vector and δk is the angle between the stator current and the stator flux vectors (both quantities are at time instant tk). σLs is the motor total leakage inductance

.LL

LLr

2m

ss −=σ (20)

According to Fig. 2, the stator flux magnitude changes are relatively small and therefore, the biggest influence on the torque changes has a second term in (18). Generally, the torque changes strongly depend on the motor speed and on a lesser extent, on the load. For example, at constant speed a load increase will cause an increase of the load angle γ in (3) and a decrease of ctg(γk). So, the product Tek·ctg(γk) will not change significantly. On the contrary, at constant load and with constant sampling period, a motor speed increase will cause almost proportional increase of the angle change Δφr (15). The angle change Δγ (14) will then decrease and the torque changes curves will be shifted toward smaller values.

Fig. 3 depicts the torque changes in dependence on the stator flux vector position at nominal speed nn and nominal load TLn and Fig. 4 shows the torque changes at 50%nn and TLn. The changes are shown relatively to the nominal torque value Tn. The stator flux vector lies in the sextant N and the torque changes for voltage vectors 1+Nu , 2+Nu , Nu and

0u are shown. For the sake of an easier analysis, the

changes are computed with the value of skψ equal to the reference one. Also, the values of Tek and Tek·ctg(γk) (18) are constant and equal to corresponding average values for each analyzed operating point. Although derived in a different way, calculated torque changes correspond to the changes shown in [3], [9].

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Fig. 3. Torque changes versus stator flux vector position at nominal speed and nominal load, sextant N (applied voltage vectors - solid line: 1+Nu ;

long dash line: 2+Nu ; round dot line: Nu ; square dot line: 0u ).

Fig. 4. Torque changes versus stator flux vector position at 50% nominal speed and nominal load, sextant N (applied voltage vectors - solid line:

1+Nu ; long dash line: 2+Nu ; round dot line: Nu ; square dot line: 0u ).

III. NOVEL PREDICTION TECHNIQUE The aim of the novel prediction technique is selection of

the converter discrete voltage vector which will result in minimum torque deviation from the torque reference value. In order to avoid the switching frequency increase when compared with the conventional DTC method, the selected voltage vector is applied for the whole sampling period.

A. Influence of Voltage Vectors on Torque Changes The stator flux vector lies in the sextant N and the

analysis is done regarding to the demands for the torque and the stator flux vector magnitude increase or decrease and to the position of the stator flux vector in the sextant.

The conventional DTC method selects voltage vector 1+Nu in the case when both the electromagnetic torque and

the stator flux vector magnitude should be increased. The flux will increase regardless the position of the stator flux vector in the sextant (Fig. 2). But, according to Fig. 3, the torque will increase only for angles φs<α3 (α3 is an angle of the stator flux vector at which the corresponding torque change for voltage vector 1+Nu changes sign). Namely, when the stator flux vector is leaving sextant and 1+Nu is applied, the angle change Δφs is relatively small and although the stator flux vector magnitude is increased, the torque change will be negative. It should be pointed out that for φs>α3 there is not any discrete voltage vector which would satisfy demands for both the torque and the flux increase and that only 2+Nu will increase the torque. At lower speed, the torque and the flux will also be increased

for angles φs<β1 (Fig. 4) when voltage vector Nu is used (β1 is an angle at which the torque change for Nu changes sign). The application of Nu for angles φs<β1 will result in less torque increase than the application of 1+Nu .

If the torque should be increased and the flux should be decreased, the conventional DTC method uses voltage vector 2+Nu . The flux will decrease (Fig. 2), but at higher speed the torque will increase only for angles φs>α1 (in Fig. 3 α1 is the stator flux vector angle at which the corresponding torque change for voltage vector 2+Nu changes sign). This is due to a relatively small angle change Δφs when the stator flux vector is entering sextant and due to a decrease of the stator flux vector magnitude when

2+Nu is applied. For φs<α1 there is not any discrete voltage vector that would increase the torque and decrease the flux and only 1+Nu will increase the torque. At lower speed, the application of 2+Nu increases the torque regardless the position of the stator flux vector in the sextant (Fig. 4).

Zero voltage vector 0u is applied in the conventional DTC method when the torque should be decreased. From Fig. 2, Fig. 3 and Fig. 4 one can conclude that if the flux should be increased, better solution is the application of voltage vector Nu for angles φs<α2 (Fig. 3) and β1<φs<β2 (Fig. 4) (α2 and β2 are the stator flux vector angles at which the torque changes for Nu and for 0u are equal). The application of Nu will then cause the flux increase (contrary to the application of 0u which practically will not change the stator flux magnitude), but the torque will less decrease. Also, the torque will be less decreased and the flux will be increased for angles φs>α3 (Fig. 3) if 1+Nu is applied instead of 0u .

Finally, when both the torque and the flux should be decreased, the torque will less decrease if voltage vector

2+Nu is applied for angles φs<α1 (Fig. 3) instead of zero voltage vector 0u . Otherwise, 0u is used.

It is obvious from aforementioned comments that the voltage vectors selection in the conventional DTC method (Table I) does not satisfy demands for torque increase or decrease at all operating conditions and also is not optimal regarding torque ripple.

B. Novel Prediction Algorithm The novel prediction technique uses a two-step forward

prediction algorithm. First step is the stator flux and the electromagnetic torque prediction at the end of the sampling period. The stator currents and dc-link voltage are measured at the beginning of the sampling period and the applied switching state is determined in previous sampling period. The stator voltages are computed from dc-link voltage, corresponding switching state, semiconductors voltage drops and converter dead-time. Although the stator currents are changing during sampling period, due to the fact that the stator voltage has more effect on the stator flux variation, the stator fluxes at the end of the sampling period can be calculated from the stator currents measured at the beginning of the sampling period using (1)

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( ) .TiRu spskssksksk −+=+ ψψ 1 (21) The torque calculated from the stator currents measured

at the beginning of the sampling period will differ from a value at the end of the sampling period. A simple current prediction algorithm is proposed in [15]. The stator currents are measured once again within the sampling period and their predicted values at the end of the sampling period are calculated using linear extrapolation ( ) sk

m

spskstmsk i

tT

iii +−=+1 (22) where stmi is the stator current vector calculated from measured stator currents at time instant tm.

The electromagnetic torque at the end of the sampling period is computed from predicted currents using (2)

( ).sinipT kskskek 1111 δψ23

++++ = (23)

The hysteresis controllers outputs, i. e. torque and flux demands, are then determined from 1+ψsk and Tek+1.

Second step in the prediction algorithm is calculation of the torque at the end of next sampling period, denoted by Tek+2. The torque changes ΔTe (18) for voltage vectors

1+Nu , 2+Nu , Nu and 0u are calculated from values at the end of the sampling period. If corresponding voltage vector will be applied, Tek+2 will be .TTT eekek Δ12 += ++ (24)

A deviation of Tek+2 from torque reference value Tref is .TTDT ekref 2+−= (25)

Voltage vectors that could be used in next sampling period are determined from the torque changes analysis in a previous section and a new switching table is proposed (Table III). For corresponding torque and flux demands, voltage vector which results in minimum value of DT (25) is applied in next sampling period.

TABLE III

NOVEL PREDICTION TECHNIQUE, SWITCHING TABLE FOR SEXTANT N

Torque and Stator Flux

Demand T ↑, ψs ↑ T ↑, ψs ↓ T ↓, ψs ↑ T ↓, ψs ↓

Voltage Vectors

Nu , 1+Nu ,

2+Nu 1+Nu ,

2+Nu Nu , 1+Nu ,

0u 2+Nu , 0u

Equation (25) is similar to cost functions defined in [6],

[13]. A deviation of the stator flux vector magnitude from its reference value is here not taken into account. Namely, if the stator flux vector magnitude is kept within some boundaries, the stator currents would be sinusoidal and their THD factor would be acceptable. Also, in drives where torque is directly controlled, the torque deviation is more important than the flux deviation.

All voltage vectors in Table III satisfy the stator flux vector magnitude demands except voltage vector 2+Nu in the case when both the torque and the flux should be increased and voltage vector 1+Nu in the case when the torque should be increased and the flux should be decreased. But, if the stator flux vector magnitude stays within defined boundaries when these vectors would be

applied, their application is allowed. Selected voltage vector is in the novel prediction

technique applied for the whole sampling period (like in the conventional DTC method). The novel technique also uses practically the same voltage vectors as conventional DTC method. However, it takes into account influences of voltage vectors on the torque changes and allows the application of voltage vector Nu .

IV. SIMULATION RESULTS The novel prediction technique is due to the previously

mentioned similarities compared in simulations and experiments with the conventional DTC method.

Simulations are carried out with motor data shown in Table II, dc-link voltage is 1500V and the sampling period is 100μs. Stator currents are measured at the beginning of the sampling period and second measurement is after 80μs. The described current prediction algorithm is used in both methods. The torque and the flux hysteresis bands are deliberately set to zero because then torque ripple in the conventional DTC method is smallest.

Fig. 5 shows the torque and Fig. 6 shows the stator flux vector magnitude at nominal speed and nominal load. At time instant t=4.75s control algorithm is changed from the conventional DTC method to the novel prediction technique.

Fig. 5. Torque at nominal speed and nominal load, simulation results.

Fig. 6. Stator flux at nominal speed and nominal load, simulation results.

From Fig. 5 it is clear that when the novel prediction technique is applied, torque ripple is considerably reduced and an average value of the torque is practically equal to the reference value. The stator flux ripple is increased (Fig. 6), but stator currents THD factor is not significantly deteriorated.

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V. EXPERIMENTAL RESULTS Experimental validation of the proposed technique is

carried out with 525kW traction motor feed by main propulsion converter used in trains. Control algorithms are programmed in floating-point digital signal processor TMS320F28335, hysteresis bands are zero and the sampling period is 100μs. Stator currents and dc-link voltage are measured at the beginning of the sampling period and second currents measurement is 80μs from the beginning. Time period for all calculations that use stator currents from first measurement is approximately 30μs and calculations after second measurement are executed in approximately 10μs.

A steady-state performance of the novel prediction technique is here presented and compared with the conventional DTC method. For analyzed drive, both methods are similar regarding torque ripple and correspondence of the average torque value to the reference one for speeds up to approximately 40% of the motor nominal speed. At higher speed, the novel technique reveals better performance characteristics.

Fig. 7 shows the electromagnetic torque and torque reference value at nominal speed nn and nominal load TLn.

(a)

(b)

Fig. 7. Torque at nominal speed and nominal load, experimental results: (a) conventional DTC method, (b) novel prediction technique.

Fig. 8 depicts the stator currents when the novel technique is applied and Fig. 9 shows the torque changes (18) for different voltage vectors. The changes match theoretically derived values (Fig. 3).

Fig. 8. Stator currents at nominal speed and nominal load, experimental results: novel prediction technique.

Fig. 9. Torque changes at nominal speed and nominal load, experimental results.

The torque at 75%nn and TLn is shown in Fig. 10 and at 150%nn and nominal power Pn in Fig. 11.

(a)

(b)

Fig. 10. Torque at 75% nominal speed and nominal load, experimental results: (a) conventional DTC method, (b) novel prediction technique.

(a)

(b)

Fig. 11. Torque at 150% nominal speed and nominal power, experimental results: (a) conventional DTC method, (b) novel prediction technique.

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The methods are compared regarding torque ripple Trip, rms value of torque ripple Triprms, average value of the torque Tav, converter switching frequency fsw and stator currents THD factor. Results are summarized in Table IV.

TABLE IV

COMPARISON BETWEEN CONVENTIONAL DTC METHOD AND NOVEL PREDICTION TECHNIQUE

Trip

(Nm) Triprms (Nm)

Tav/Tref

(%) fsw

(Hz) THD (%)

75%nn TLn

DTC 1361 294 94.5 1789 18.3 nov. tech. 1086 211 99.7 1980 17.2

nn TLn

DTC 1401 487 83.1 1262 20.0 nov. tech. 1095 230 99.1 1256 19.4

150%nn

Pn

DTC 942 316 83.5 1316 20.8 nov. tech. 725 156 98.8 1251 18.3

With the novel prediction technique the torque ripple is

for analyzed operating points reduced by 20.2%, 21.8% and 23.0%, respectively, and the torque average value is closer to the reference value. In the conventional DTC method the torque average value can be increased either with an increase of the reference value or by the torque hysteresis bands adjustment, which are cumbersome speed and load dependent procedures. As expected, the switching frequency is not changed significantly. Train application would require the switching frequency decrease at 75%nn for both methods (with the hysteresis bands adjustment), but here are shown results for the sake of consistency with the hysteresis bands set to zero. THD factor in Table IV is greater when the conventional DTC method is applied due to a smaller fundamental value of stator current. If the torque average values for both methods are equal, THD factor with the novel technique is greater by approximately 2%. A deterioration of THD factor is result of the stator flux ripple increase, but is not significant.

The novel technique calculates the torque changes from stator quantities. In comparison with the conventional DTC method, the only required additional parameter is the motor total leakage inductance σLs used in (19). The experiments were carried out at different speeds and loads with constant value of σLs. Therefore, it can be concluded that an approximate knowledge of it is acceptable.

VI. CONCLUSION The novel prediction technique for DTC of an induction

motor is proposed. It calculates the torque changes for different voltage vectors and selects discrete voltage vector from new switching table according to the torque deviation from the reference value. It has been shown that the conventional DTC method does not apply the voltage vector which satisfies the torque hysteresis controller demands at all operating conditions. The torque changes vary with the speed and the load and strongly depend on the position of the stator flux vector in the sextant. Therefore, when voltage vector is selected only according to the sextant, high torque ripple might occur.

The simulation and experimental results for 525kW motor show the effectiveness of the proposed technique. Compared with the conventional DTC method, torque ripple is decreased in medium and high speed region by more than 20% and the average value of the torque is

practically equal to the reference value. The switching frequency is not significantly changed because the selected voltage vector is applied for the whole sampling period. The novel technique only requires some additional calculations, which can be done easily with modern, powerful digital signal processors. It also uses the total leakage inductance of the motor but the exact knowledge of it is not critical for the effectiveness of the proposed technique.

VII. ACKNOWLEDGMENT Author would like to thank Milan Kovačević and Josip

Babić for their valuable help.

VIII. REFERENCES [1] I. Takahashi, and T. Noguchi, "A new quick-response and high-

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[3] V. Ambrožič, G. S. Buja, and R. Menis, "Band-constrained technique for direct torque control of induction motor," IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 776-784, Aug. 2004.

[4] D. Casadei, G. Serra, and A. Tani, "Implementation of a direct torque control algorithm for induction motors based on discrete space vector modulation," IEEE Trans. Power Electron., vol. 15, no. 4, pp. 769-777, July 2000.

[5] K. K. Shyu, J. K. Lin, V. T. Pham, M. J. Yang, and T. W. Wang, "Global minimum torque ripple design for direct torque control of induction motor drives," IEEE Trans. Ind. Electron., vol. 57, no. 9, pp. 3148-3156, Sept. 2010.

[6] H. Miranda, P. Cortés, J. I. Yuz, and J. Rodríguez, "Predictive torque control of induction machines based on state-space models," IEEE Trans. Ind. Electron., vol. 56, no. 6, pp. 1916-1924, June 2009.

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[13] Y. Zhang, and H. Yang, "Torque ripple reduction of model predictive torque control of induction motor drives," in Proc. IEEE ECCE 2013, Denver, Colorado, Sep. 15-19, 2013, pp. 1176-1183.

[14] D. Casadei, G. Grandi, and G. Serra, "Rotor flux oriented torque-control of induction machines based on stator flux vector control," in Proc. EPE’93, Brighton, United Kingdom, Sep. 13-16, 1993, pp. 67-72.

[15] S. Kaboli, M. R. Zolghadri, P. Eskandri, and D. Roye, "Prediction algorithm for torque ripple reduction in DTC-based drives," Iranian Journal of Science & Technology, Transaction A, vol. 31, no. A4, 2008.

IX. BIOGRAPHIE Dubravko Krušelj was born in Zagreb, Croatia in 1972. He received his B.S.E.E. and M.S.E.E. degrees from Faculty of Electrical Engineering, University of Zagreb, in 1995 and 1998, respectively.

He has been working in KONČAR – Electrical Engineering Institute since 1994. His research interests are electromotor drives with induction motors (especially traction drives), vector control and modulation techniques.

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