Improved Selective Harmonic Elimination for Reducing Torque Harmonics of Induction Motors in Wide DC Bus Voltage Variations

Transcription

1 Improved Selective Harmonic Elimination for Reducing Torque Harmonic of Induction Motor in Wide DC Bu Voltage Variation Hoein Valiyan Holagh, Tooraj Abbaian Najafabadi School of Electrical and Computer Engineering College of Engineering, Univerity of Tehran Tehran, Iran Mohen Mahoor Dept. of Electrical and Computer Engineering Univerity of Denver Denver, CO, USA Abtract Conventionally, Selective Harmonic Elimination (SHE) method in 2-level inverter, find bet witching angle to reach firt voltage harmonic to reference level and eliminate other harmonic, imultaneouly. Conidering Induction Motor (IM) a the inverter load, and wide DC bu voltage variation, the inverter mut operate in both over-modulation and linear modulation region. Main objective of the modified SHE i to reduce harmonic torque through finding the bet witching angle. In thi paper, optimization i baed on optimizing phaor equation in which harmonic torque are calculated. The procedure of thi method i that, firt, the ratio of the ame torque harmonic i etimated, econdly, by uing that etimation, the ratio of voltage harmonic that generate homogeneou torque i calculated. For the etimation and the calculation of the ratio motor parameter, mechanical peed of the rotor, the applied frequency, and the concept of lip are ued. The advantage of thi approach i highlighted when mechanical load and DC bu voltage variation are taken into conideration. Simulation reult are preented under a wide range of working condition in an induction motor to demontrate the effectivene of the propoed method. Index Term--Induction motor drive, torque harmonic reduction, modified SHE PWM, variou dc bu voltage, low witching frequency. I. INTRODUCTION AC motor drive, operated with PWM inverter, produce pulating torque due to non-inuoidal nature of the inverter output voltage [], [2]. Modulation method have been dicued to reduce the pulating torque in induction motor drive uch a pace-vector modulation [3], [4], Advanced PWM technique [5], [6] and vector-control [6]. The fundamental of the voltage applied by inverter generate the average output torque, and the harmonic voltage generate increaed loe and torque pulation. The contribution of the harmonic to the average torque i not ignificant [7], [8]. There are different method to calculate or etimate the harmonic current, torque, and loe. Thee method are preented in [7] []. The loe are eparated into variou component and it i hown that the larget lo i uually happening in the rotor bar [7]. Harmonic loe are hown to be nearly independent of motor load and the fundamental magnetizing current i found to increae over that. In [], the machine d-q model have been ued to calculate the torque wherea the ingle-phae equivalent circuit i alo ued for tudying the teady-tate behavior of the machine [7] [0]. Reference [8] how that torque fluctuation are due mainly to the interaction of fundamental flux in the air gap at rotor current harmonic. In [0], the major torque ripple in the induction motor that i the 6th harmonic component ha been etimated baed on the fundamental harmonic and other harmonic of the rotor current. In megawatt-rated inverter-fed induction motor drive ytem, the witching frequency mut be kept at a low value of only a few hundred hertz. Not only low witching frequency operation reduce the device witching loe, but alo bring down the device dv/dt requirement. Thi iue lead to improve the inverter efficiency, and leer Electro Magnetic Interference (EMI) generation from the inverter [8]. The reduction of witching frequency generally reult in increaing current ditortion, and conequently undeirable machine torque harmonic and higher machine loe. Compromie between exceive witching loe and undeirable harmonic can be achieved by employing optimal witching trategie for the inverter control. Off-line optimization method hown in [2] are limited to drive ytem with low dynamic requirement, and on-line optimized pule control hown in [3] i uitable for high dynamic performance. The work in [4] how the practical realization of a high dynamic performance and on-line

2 optimized pule control cheme baed on field-orientation uing a rectangular error boundary. Another PWM method by uperpoing a rectangular wave on the pecific trapezoidal wave i preented to reduce torque ripple in induction motor [5]. Direct Self-Control (DSC) wa mainly applied in high power application, which required fat torque dynamic and low witching frequency. The tudy in [6] compare the tationary operational behavior of inverter-fed induction motor traction drive with high power and/or high dc-link voltage. Reference [7] propoed a new DTC method to reduce the torque ripple in five-phae IM. In [8], two optimal PWM cheme are propoed to minimize the loworder harmonic torque. The firt approach which i independent of machine parameter and mechanical load i baed on Frequency-Domain (FD), that i called claic SHE in thi paper. The econd approach conidering the motor parameter and load torque i baed on Synchronou Reference Frame (SRF). In thi paper, a new control method i propoed to reduce the torque ripple in three-phae induction motor in low witching frequency. Thi approach introduced an on-line optimization method baed on the parameter and the data of IM. Therefore, thi approach contantly etimated the ituation of the generated torque harmonic and determined the bet witching angle to control. The effectivene of the propoed approach i verified through MATLAB/SIMULINK imulation with an induction motor drive with a power equal to 3 kw. The ret of thi paper i organized a follow. In Section II, the ummary of the torque harmonic calculation are provided and alo their eparation are accomplihed. The propoed approach and the etimation of the phae difference and the amplitude ratio for the ame torque harmonic are hown in ection III. The calculation way of the witching angle and the evaluation of the maximum poible modulation index are preented in ection IV. Section V provide the imulation reult. The concluion i preented in ection VI. II. REVIEW AND ANALYSIS OF THE TORQUE HARMONICS The effective voltage harmonic by witching in the threephae induction motor are the fundamental voltage harmonic and the voltage harmonic of order (±). Each of thee harmonic produce a rotating magnetic field in the tator and the rotor of the induction machine. The fundamental voltage harmonic generate magnetic field with rotational peed ω, the voltage harmonic of the order (-) generate magnetic field with rotational peed (-+)ω, and the voltage harmonic of the order(+) generate magnetic field with rotational peed (+)ω. The interaction between generated magnetic field in the rotor and generated magnetic field in the tator produce fixed and fluctuating electromagnetic torque. Thee fluctuating electromagnetic torque only included torque harmonic of the order. In other word, the voltage harmonic of the order (±) manufacture the torque harmonic of the order [7], [8], [9]. In thi paper, ingle-phae equivalent circuit i ued to calculate the ratio of amplitude and phae difference in the ame torque harmonic. The effect of harmonic in the applied voltage into induction motor on the ingle-phae equivalent circuit parameter have been tudied by in [7]. Single phae equivalent circuit i hown in Fig.. Figure. Single-phae equivalent circuit for induction motor. A method for calculating the torque harmonic baed on the ingle-phae equivalent circuit i hown in [7] [0]. According to the method, torque fluctuation are engendered baed on the interaction between fundamental air-gap flux harmonic and (±) th current harmonic of the rotor in addition to the interaction between the fundamental current harmonic of the rotor and (±) th air-gap flux harmonic. The torque harmonic generated baed on input voltage harmonic can be ditinguihed a following: τ Ψ m I r( ) in(6 kωt) +Ψ m( ) I r co(6 kωt) A co(6 kωt + θ ) () + τ Ψ I in(6 kω t) +Ψ I co(6 kω t) m r(+ ) m(+ ) r A co(6 kω t + θ ) + + Where Ψ m(-) and Ψ m(+) are the (-) th and (+) th airgap flux harmonic, repectively; I' r(-) and I' r(+) are the (-) th, and (+) th current harmonic of the rotor; ω i the applied frequency to the tator; τ - and τ + are the torque harmonic generated from the (-) th and (+) th voltage harmonic repectively; A ± and θ ± are the amplitude and the phae of the torque harmonic. According to (), torque harmonic can be formulated a following: τ A co(6 kωt+ θ ) + A+ co(6 kωt+ θ+ ) (2) A co(6 kωt+ θ) where τ i th torque harmonic, and A and θ are their correponding amplitude and phae, repectively. Another method for calculating torque harmonic i preented in [4] which i baed on the ingle-phae equivalent circuit. Thi method unlike the former ha been preented approximately and only ue the rotor current harmonic for the etimation a following: 3Rr τ * I r ( I r(+ ) I r( ) )in(6 ω t ) (3) 2ω where k, 2,, S denote the fundamental lip of the induction motor, and R r i the rotor reitance. The torque harmonic generated by fundamental and (±) th harmonic of the current can be eparated a following: τ I I in(6 ω t ) A co(6 k ω t + θ ) (4a) r r( ) ω

3 τ I I in(6 ω t ) A co(6 k ω t + θ ) (4b) + r r(+ ) + + ω According to the above equation, the amplitude and the phae of th harmonic of the torque are proportional with the amplitude and phae of the fundamental and (+) th harmonic of the rotor current. The ingle-phae equivalent circuit i ued to calculate the amplitude and phae difference of the rotor current. The current amplitude i proportional with applied voltage, frequency, and mechanical load, but the current phae i proportional only with applied voltage and frequency. According to fig. current phae are calculated a following: L + L r I r Vph ϕ actan Lm 2 Rr ( ) R + Lm LS + (± )*( L + L ) r I r(± ) V(± ) ph ϕ± actan Lm 2 Rr ( ) R + Lm LS + ± (5a) (5b) Where L, L r, and L m are tator, rotor and mutual inductance, repectively; R i tator reitance, S ±are harmonic lip of the induction motor, and φ i the phae difference between the rotor current and the correponding voltage in every frequency. To implify the calculation in (5a) and (5b), the voltage angle can be aumed equal to zero. harmonic are further than the amplitude of the (-) th harmonic. To achieve the propoed method, the phae difference and the amplitude of the ame torque harmonic mut be etimated or calculated. A. Etimation of the phae difference of the ame torque harmonic The expreed approximate equation in (3) i ued to etimate the phae difference. According to (4a) and (4b), the phae of the ame torque harmonic are equivalent with the correponding current harmonic phae and the fundamental current harmonic phae. In thi cae, the phae difference of the ame torque harmonic will be equal to the difference of two determined phae. Δ θ θ θ+ 2ϕ + ϕ ϕ (8) + According to (5b), the φ ± amount are almot fixed for the certain ω when IM work from no-load to full load, however φ i variou and the φ variation caue the variation of the phae difference of the ame torque harmonic. The φ variation i hown in Fig.2. It hould be mentioned that the etimated relation are indefeaible with changing ω. III. THE PROPOSED METHOD FOR MINIMIZING TORQUE HARMONICS In ection II, in order to reduce the torque fluctuation, we eparated the amplitude and the phae of the ame generated torque harmonic. The phaor relationhip of the equation are ued to eliminate and minimize thee fluctuation. To calculate the um of two or more inuoidal ignal with the ame frequency we can ue their correponding phaor intead of trigonometric expanion a following: Bco( ωt+δ θ) + B2co( ωt+ π) B3co( ωt+ θ3) (6a) where ( B3) ( Bco( Δθ) B2) + ( Bin( Δ θ)) f( B, B2, Δ θ) (6b) B in( Δθ ) θ3 arctan( ) (6c) Bco( Δθ ) B2 To minimize the phaor phrae, (6b) hould be minimized. For thi purpoe, (7) i ued to reduce the amplitude of two ignal of the ame frequency. min( B, B2) co( Δ θ) (7) max( B, B2) According to the expreed relationhip in term of the phaor, two general method are propoed to decreae the amplitude of the torque harmonic. Two method expre that the poible minimum of the torque harmonic can be reached if the ratio of the ame torque harmonic correpond the coine of their frequency difference. In the firt method, we have aumed that the amplitude of the (-) th harmonic are alway further than the amplitude of the (+) th harmonic, but in the econd method the amplitude of the (+) th Figure 2. The variation of the fundamental current harmonic phae with changing the mechanical load from no-load to full load at the fixed ynchronou peed. B. Etimation of the ratio of the ame torque harmonic To etimate the ratio of the ame torque harmonic, we ue the concept of lip. Harmonic lip in the induction motor are defined a following: ( ± ) ω ± pωm ± (9) ( ± ) ω where ω m and P are mechanical angular peed and number of pole pair repectively. With changing the induction motor operation from no-load to full load, harmonic lip change correpondingly. Thi lip expree the impact of voltage harmonic on their correponding torque harmonic. According to (9) having two velocitie, the mechanical peed and the ynchronou peed, we can obtain the impact of the voltage harmonic on their correponding torque harmonic.

4 The ratio of the ame torque harmonic have the direct relation with the ratio of the voltage harmonic and the invere relation have with the ratio of their correponding harmonic lip. A( ) V( ) ph + * (0) A(6 k+ ) V(6 k+ ) ph With conidering (7), (8), and (0), the ratio of two voltage harmonic which generate the ame torque harmonic i defined in accordance with () to both propoed method. Thi relation alo for all the input frequency from no-load to maximum torque are confirmed, and a condition of uing the expreed relation i that the IM work in it table area. V( ) ph co( Δ θ ) (a) V V V (+ ) ph + (+ ) ph + ( ) ph co( Δ θ ) (b) IV. CALCULATION OF THE BEST SWITCHING ANGLES The propoed approach i uitable to control the induction motor torque when the number of the witching angle are very few, ay k. However, in thi paper we focu on two witching angle in each cycle. In the elective harmonic elimination method which employe two witching angle, the amplitude of fundamental harmonic i controlled and the 5 th harmonic i eliminated. However, in thi method the amplitude of the fundamental, 5 th, and 7 th harmonic i controlled altogether. A a reult of uing two witching angle, the main torque i controlled and the 6 th torque harmonic i minimized. On the other hand, when three witching angle are employed, the main torque i alo controlled and the 6 th and 2 th torque harmonic are minimized. Fig. 3 illutrate the output voltage waveform of voltage ource inverter in which two witching angle are applied. 2V dc 5 2 V ( )( 2co(5 α ) + 2co(5 α )) (2) 5π 2V V7 ( dc )( 2co(7 α) + 2co(7 α2)) 7π where α and α 2 are the witching angle, MI i the modulation index, and V dc i the dc bu voltage. Baed on (2), the witching angle are obtained from olving the following equation: MI 2co( α) + 2co( α2) V5 7 ( 2 co(5 α) + 2 co(5 α2)) 5 ( ) co( Δθ6 ) (I) V7 5 ( 2co(7 α) + 2co(7 α2)) 7 V7 5 ( 2 co(7 α) + 2 co(7 α2)) 7 ( ) co( Δθ6 ) (II) V 7 ( 2co(5 α ) + 2co(5 α )) α < α2 π (3) The lip i variable from zero to maximum torque lip. According to thee change range, witching angle i calculated. B. Evaluation of the maximum modulation index in the change range At thi tage, due to the importance of the modulation index, we are urveying the maximum of modulation index that can be reached againt the change of the ratio of the voltage harmonic. Behavior of the modulation index changing i different in the two uggeted method. The curve of the maximum of modulation index extracted from (3) i hown in Fig.4. According to thi curve, in the method (a). The maximum poible amount of MI i 0.955, in the operation of maximum torque. On the other hand, in the method (b), the maximum poible amount of modulation index i approximately equal to, in the operation of intermediate load. A a reult, to reach the maximum modulation index uing two witching angle, the ratio of the 7 th voltage harmonic per the 5 th voltage harmonic mut be approached to about 0.7. Figure 3. The output voltage waveform of a voltage ource inverter with two witching angle. A. Calculating the witching angle to minimize the 6 th torque harmonic In both propoed method uing two witching angle, the fundamental, 5 th, and 7 th harmonic are controlled with the purpoe of minimizing the 6 th torque harmonic. According to Fig. 3, for the voltage waveform generated by voltage ource inverter, the harmonic amplitude on Fourier coefficient are calculated a following: 2 V /( Vdc ) MI 2co( α) + 2co( α2) π Figure 4. The curve of the maximum modulation index againt the change of the voltage harmonic ratio in the method (a) and (b). V. SIMULATION RESULTS For imulation, the three-phae quirrel-cage induction motor i ued with the nominal information 3 kw, 380 V, and 45 rpm. The parameter of thi induction motor are lited in Table I. The induction motor i connected to a voltage ource inverter that feed from a dc bu voltage that i equal to 560 V. In thi paper, open loop control i conidered a the type of control trategy. In imulation, our method compare with two other method. Thee method are elective harmonic elimination (SHE-PWM), claic method, and two

5 propoed method. The uggeted method for the torque harmonic reduction are online. In other word, the preented method need the ratio of voltage harmonic of the ame torque baed on the function of IM to calculate witching angle, furthermore the need to the modulation index. However, two firt method, SHE and claic SHE, uing only the modulation index are able to calculate the witching angle. TABLE I. INDOCTION MOTOR PARAMETERS. Parameter Rotor Reitance(R ) Rotor Reitance(R r) Stator Self Inductance(L ) Rotor Self Inductance(L r) Magnetizing Inductance (L m) Moment of Inertia Number of Pole Pair Value.85 Ω.84 Ω 70mH 70mH 60mH kg.m 2 2 To evaluate the mentioned method, three different working condition for the induction motor torque are conidered. In the firt condition, the motor work under noload, and the applied frequency to the IM i contant and equal to 50Hz. In the econd condition, the IM i applied the linear load changing according to the mechanical peed of the rotor, and the frequency with which the motor work i equal to 50Hz. In the third condition, in addition to changing the applied linear mechanical load, the applied frequency i propounded equal to 45Hz until we can evaluate the propoed method in the other applied frequency and the variable mechanical load. A. Evaluation of the Sixth Torque Harmonic Reduction in the Firt Condition The imulation reult for four mentioned method are hown in Fig. 5 when the IM work under no-load. Fig. 5 portray the curve of the ixth torque harmonic amplitude veru the modulation index in the four mentioned method. In all method, for each modulation index value, the motor lip i about zero. Figure 5. The amplitude of the ixth torque harmonic in the four mentioned method under no-load in term of the MI. According to the curve of the elective harmonic elimination method in the firt condition, we can conclude that the ixth harmonic amplitude firtly increaed and econdly decreaed with increaing the modulation index. In the other method thi reult i indefeaible, but their variation are le. According to the numerical amount, the torque harmonic amplitude for the all modulation range in the claic, (a), and (b) method are leer than SHE- PWM method. And the numerical value of the torque in three method, claic, (a), and (b), are almot equal becaue the ratio the fifth voltage harmonic per the eventh voltage harmonic i contant in the whole range of modulation. In the firt Condition for reducing the ixth torque harmonic, the claic method i uperior to the other method becaue that need le memory than two method (a) and (b) wherea thee two method due to being online need more memory. B. Evaluation of the Sixth Torque Harmonic Reduction in the econd Condition In the econd condition, the linear load in term of the mechanical peed and the frequency equal to 50Hz applied to the IM. Fig. 6 how the imulation reult for the econd condition. Figure 6. The amplitude of the ixth torque harmonic in the four mentioned method under linear load in term of the MI at the applied frequency equal to 50Hz. According to the obtained amount, the ixth torque harmonic i firtly increaed and econdly decreaed with increaing the modulation index in four mentioned method. In the econd condition, becaue the IM i under linear load, the motor lip i changing from pecified amount to about zero with increaing the modulation index. The motor lip change conclude the phaor ituation variation of ixth torque harmonic produced with the 5 th and 7 th voltage harmonic. According to the numerical value of the torque harmonic amplitude, the appropriate method election for reducing the torque fluctuation i different with changing the modulation index or the motor lip. In the firt condition, becaue the motor lip i about zero, the claic approach i more appropriate than the other technique. In thi cae, when the motor lip i cloe to zero, the claic method and two method (a) and (b) have better performance like the firt condition. Moreover, when the motor lip amount reache the maximum value which maximum electromagnetic torque i produced, SHE-PWM method and method (a) are appropriate approache for reducing torque fluctuation. Finally, the propoed method (a) i uitable when the IM work in the middle of the lip, between the maximum lip and about zero. It hould be noted that motor operation area i more in the middle area of the motor lip, which depend on the mechanical load. Thu method (a) i uitable way in the whole motor operation area uch a under no-load, middle-

6 load, and full-load. Furthermore, the operation of method (b) in the middle area of the lip i better than SHE-PWM method, and another advantage of thi method compared to other method i that it can be reached the maximum modulation index. C. Evaluation of the Sixth Torque Harmonic Reduction in the third Condition In the third condition, in line with changing the applied linear load, we conider the applied frequency equal to 45Hz until we can evaluate the propoed method in the variable frequency and load. Due to the applied linear load, the modulation index can change from a pecified value to a peak value. The imulation reult for four mentioned method are hown in fig. 7. According to the obtained numerical reult, all the reult expreed in the econd condition can alo be concluded. In thi condition with changing the applied frequency, the propoed method till have their previou performance. Figure 7. The amplitude of the ixth torque harmonic in the four mentioned method under linear load in term of the MI at the applied frequency equal to 45Hz. VI. CONCLUSION The claic method for the torque fluctuate reduction i uitable when either the IM i under no-load or the motor lip i negligible. In fact, thi method i not proper when the motor lip i at it middle area or at it maximum value. SHE- PWM approach operate better only when the IM work at the maximum poible lip. Accordingly, each of the available approache only operate at the pecific area of working range. Wherea, the propoed approach in thi paper provided the bet function in the entire working range of the IM a thi method contantly detect the poition of the generated torque harmonic, and then elect the bet witching angle, in order to minimize the fluctuation. Thi approach wa divided into the two method. In the firt method, It wa aumed that the amplitude of the (-) th torque harmonic were alway further than the amplitude of the (+) th torque harmonic, but thi wa converely in the econd method The conidered aumption wa compatible with the inverter operation, o that the firt method preented the bet function among other method. In addition, the econd method can only be reached the maximum modulation index. Finally, a an extenion of the approach, we uggeted implementation of the preented approach on SVM-PWM working in over- modulation region. REFERENCES [] W. Liang, W. Fei, and P. C.-K. Luk, "Analytical invetigation of ideband torque ripple in induction machine drive with SPWM and SVPWM technique," International Conference on Electrical Machine and Sytem (ICEMS), 204 7th, 204, pp [2] J. Song-Manguelle, G. Ekemb, S. Schröder, T. Geyer, J.-M. Nyobe- Yome, and R. Wamkeue, "Analytical expreion of pulating torque harmonic due to PWM drive," Energy Converion Congre and Expoition (ECCE), 203 IEEE, 203, pp [3] B. Singh, S. Jain, and S. Dwivedi, "Torque ripple reduction technique with improved flux repone for a direct torque control induction motor drive," IET Power Electronic, vol. 6, pp , 203. [4] U. V. Patil, H. M. Suryawanhi, and M. M. Renge, "Cloed-loop hybrid direct torque control for medium voltage induction motor drive for performance improvement," IET Power Electronic, vol. 7, pp. 3-40, 204. [5] K. Bau, J. S. Praad, G. Narayanan, H. K. Krihnamurthy, and R. Ayyanar, "Reduction of torque ripple in induction motor drive uing an advanced hybrid PWM technique," IEEE Tranaction on Indutrial Electronic, vol. 57, pp , 200. [6] V. P. K. Hari and G. Narayanan, "Space-vector-baed hybrid PWM technique to reduce peak-to-peak torque ripple in induction motor drive," IEEE Tranaction on Indutry Application, vol. 52, pp , 206. [7] E. A. Klinghirn and H. E. Jordan, Poly-phae induction motor performance and loe on noninuoidal voltage ource, IEEE Tran. on power apparatu and ytem, vol. PAS-87, pp , Mar [8] S. D. Roberton and K. Hebbar, Torque pulation in induction motor with inverter drive, IEEE Tran. on Indutry and General Application, vol. IGA-7, pp , Mar./Appr. 97. [9] G. Jainy, The effect of voltage wavehape on the performance of a 3-phae induction motor, IEEE Tran. on Power Apparatu and Sytem, vol. 83, pp , 964. [0] B. K. Boe, Power Electronic and AC Drive. Englewood Cliff, NJ: Prentice-Hall, 986. [] P. C. Kraue, Method of multiple reference frame applied to the analyi of ymmetrical induction machinery, IEEE Tran. on Power Apparatu and Sytem, pp , Jan [2] G. S. Buja and G. B. Indri, Optimal pulewidth modulation for feeding AC motor, IEEE Tran. Ind. Appl., Vol. A-3, pp , Jan./Febr [3] J. Holtz and S. Stadtfeld, A predictive controller for the tator current vector of ac machine fed from a witched voltage ource, in JIEE IPEC-Tokyo Conf, 983, pp [4] A. Khambadkone and J. Holtz, Low witching frequency and high dynamic pulewidth modulation baed on field-orientation for highpower inverter drive, IEEE tran. power elec., vol. 7, pp , Oct [5] K. Taniguchi, M. Inoue, Y. Takeda, and S. Morimoto, A PWM trategy for reducing torque-ripple in inverter-fed induction motor, IEEE tran. Ind. Appl., Vol. 30, pp. 7-77, Jan./Febr [6] A. Steimel, Direct elf-control and ynchronou pule technique for high-power traction inverter in comparion, IEEE Tran. on Ind. Elec., vol. 5, pp , Aug [7] Y. N. Tatte and M. V. Aware, Torque ripple reduction in five-phae direct torque controlled induction motor, in Power Electronic, Drive and Energy Sytem (PEDES), 204 IEEE International Conference on, 204, pp. -5 [8] A. Tripathi and G. Narayanan, Evaluation and Minimization of Low-Order Harmonic Torque in Low-Switching-Frequency Inverter- Fed Induction Motor Drive, IEEE Tran. Ind. Appl., vol. 52, pp , 206.