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New double switching clamping sequences based ADPWM algorithm for direct torque control of induction motor drives.

Introduction

Three-phase induction motors are so common in industry that in many plants no other type of electric machine can be found. This simple and robust machine, an ingenious invention of the late nineteenth century, still maintains its unmatched popularity in industrial practice. Such a robust motor can run at high speeds and withstand heavy mechanical and electrical overloads. In adjustable-speed drives, the low electric time constant speeds up the dynamic response to control commands. Typically, induction motors have a significant torque reserve and a low dependence of speed on the load torque. Although operating principles of induction motors have remained unchanged, significant technological progress in control strategies has increased over the years, particularly in the last few decades.

Direct torque and flux control (DTC) proposed by Takahashi [1] is considered to be the next generation control strategy in the field of high performance controlled drives. Independent control of torque and flux is achieved by proper selection of appropriate voltage vector with in a sampling period. Conventional DTC (CDTC) uses hysterisis controllers as both torque and flux controllers, because of which the switching frequency of the inverter is not maintained constant [1], [2]. Also the steady state ripple in torque flux and current leads to some surplus characteristic features like increased vibrations and acoustic noise, power loss etc. Though conventional space vector pulse width modulation technique (CSVPWM) could able to make the switching frequency of the PWM inverter constant [3],[4], steady state ripple in torque, flux and current are still high predominantly when the drive is operating at high speeds. To improve the performance of the drive during high speed regions several discontinuous PWM methods (DPWM) are proposed in [5], [6]. It is shown in [5] that the harmonic distortion in line currents can be reduced significantly with the DPWM based DTC method during high modulation regions. In this paper it is shown analytically and through simulation that with the proposed DTC method harmonic distortion in line current can further be reduced to a significant value particularly when the drive is operating at near rated speeds.

SVPWM Based ADPWM Methods

The eight voltage states of a two level, three phase inverter are shown in Fig.1. Assuming the reference voltage vector [V.sub.REF] to be in sector-I making an angle [alpha] with reference to [V.sub.1], according to the CSVPWM algorithm the reference voltage vector can be synthesized by applying the two active vectors [V.sub.1], [V.sub.2] for the durations [T.sub.1], [T.sub.2] and the two zero states each of duration [T.sub.z]/2 with in a switching period, [T.sub.s]. The active vector and zero vector switching times are calculated using (1).[7]

[T.sub.1] = [M.sup.*] Sin(60[degrees] -[alpha]/Sin60[degrees] * [T.sub.s] (1.1)

[T.sub.2] = [M.sup.*] Sin[alpha]/Sin60[degrees] * [T.sub.s] (1.2)

[T.sub.z] = [T.sub.s] - [T.sub.1] - [T.sub.2] (1.3)

where 'M' is the modulation index, given by M = [3V.sub.REF]/[2V.sub.dc]

[FIGURE 1 OMITTED]

According to SVPWM algorithm desired voltage vector in a given sector can be synthesized with the two active vectors framing the sector plus a zero vector (or vectors). In the proposed DTC scheme, double switching clamping sequences that uses one zero vectors and which uses one of the active vectors twice (equally) in every switching cycle are used. The sequences of the same category are 0212, 2721. In the proposed DTC, 0121, 7212 sequences are used according to the set policy. It is clear that only one zero state is used and both are complimentary sequences [7]. Simply by changing the zero states and complimenting the two active states, results in either of the sequences. According to the proposed ADPWM algorithm changing the zero state at any spatial angle [alpha] = [gamma] where [gamma] lies between 0[degrees] and 60[degrees] an infinite number of ADPWM methods can be generated which are

[FIGURE 2 OMITTED]

further categorized into "continual clamping" and "split clamping" DPWM methods. Applying the sequence according to (2) generates continual clamping DPWM method and reversing the sequences according to (3) generates the other category of ADPWM methods, split clamping DPWM method, as shown in Fig.2. Further by changing the value of ??different ADPWM methods under each class can be obtained.

7212 for 0[degrees] [less than or equal to] [alpha] [less than or equal to] [gamma] 0121 for [[gamma].sup.0] [less than or equal to] [alpha] [less than or equal to] 60[degrees] } (2)

0121 for 0[degrees] [less than or equal to] [alpha] [less than or equal to] [gamma]} 7212 for [[gamma].sup.0] [less than or equal to] [alpha] [less than or equal to] 60[degrees]} (3)

Analysis of ADPWM Methods

A. Analysis of RMS stator flux ripple

Analysis of space vector based DPWM methods for AC drives starts with the concept of stator flux ripple. The same concept has been extended to the proposed ADPWM methods. In SVPWM strategy the reference voltage vector in a switching cycle is equals to the vector sum of the nearest two active vectors and one/two zero vectors in an average switching period. The difference between the applied voltage vector and the reference voltage vector is called the instantaneous error. Time integral of this voltage vector is called stator flux ripple, which is a measure of the line current ripple with the applied PWM strategy [7]-[9].

The d-q axes stator flux ripple components of the considered double switching clamping sequences 0121, 7212 in a synchronously rotating reference frame over a switching cycle are shown in Fig.2. [Q.sub.1], [Q.sub.2], [Q.sub.Z], D are the d and q axis components defined as in (4).

[Q.sub.1] = [2/3[V.sub.dc] cos[alpha] - [V.sub.REF]][T.sub.1] (4.1)

[Q.sub.2] = [2/3[V.sub.dc] cos(60[degrees] - [alpha]) -[V.sub.REF]][T.sub.2] (4.2)

[Q.sub.Z] = -[V.sub.REF][T.sub.Z] (4.3)

D = [2/3[V.sub.dc]sin[alpha]][T.sub.1] (4.4)

[FIGURE 3 OMITTED]

The RMS stator flux ripples over a subcycle corresponding to the above sequences are given in (5).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5.1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5.2)

+ 1/3(0.5[D.sup.2])([T.sub.1]+[T.sub.2])/[T.sub.S] (5.3)

[F.sup.2.sub.CONT](proposed) = [F.sup.2.sub.7212],0[degrees]<[alpha] [less than or equal to] [gamma] +[F.sup.2.sub.0121], [gamma]<[alpha] [less than or equal to] 60[degrees] (5.4)

[F.sup.2.sub.SPLIT] (proposed) = [F.sup.2.sub.0121],0[degrees] < [alpha] [less than or equal to] [gama] + [F.sup.2.sub.7212], [gamma] < [alpha] [less than or equal to] 60[degrees] (5.5)

The variation of RMS stator flux ripple over a sector due to CSVPWM and the considered double switching clamping sequences at low modulation of 0.45 and high modulation of 0.75 are shown in Fig.4. Also, it is clear that the sequences 0121 and 7212 can be considered as continual or split clamping methods with [gamma] = 0[degrees] or [gamma] = 60[degrees].

[FIGURE 4A OMITTED]

[FIGURE 4B OMITTED

Observations from Fig.4 leads to a conclusion that at high modulation indices the sequence that gives minimum ripple will be executed almost through out the sector in the case of split clamping ADPWM method with [gamma] = 30[degrees] whereas the sequence that gives high ripple is executed through out the sector in the case of continual clamping ADPWM method with [gamma] = 30[degrees]. Hence, the performance of split clamping ADPWM method increases with [gamma], whereas continual clamping ADPWM decreases with [gamma]. For different values of [gamma] the locus of stator flux ripple lies between AB and AD in case of the continual clamping method and with the split clamping method the locus of stator flux ripple lies between CD and CB.

B. Analysis of RMS Harmonic Distortion Factor

The RMS harmonic distortion factor (HDF) as a function of reference voltage and frequency is given by the equation (6) where [F.sub.seq.sup.2] is the RMS stator flux ripple of a particular sequence.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (6)

The harmonic distortion factor of the proposed continual and split claming sequences assuming [gamma] = 30[degrees] can be calculated using the equations (7) [9].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7.1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7.2)

Generalizing this HDF of the proposed continual or split clamping sequences for which zero vector is varied at any spatial angle [gamma] is given by the equation (8).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8.1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8.2)

[FIGURE 5 OMITTED]

Since RMS harmonic distortion factor is proportional to the RMS stator flux ripple over a sector, the proposed split clamping with [gamma] = 30[degrees] gives less compared with the remaining. The intersection of the proposed ADPWM method with the CSVPWM defines the optimal transition point. Also, it is established from the Fig 5, that the proposed split clamping method with [gamma] = 30[degrees] is the optimal ADPWM method and it is clear that at the end of the linear modulation region the harmonic distortion is still reduced. So, with the proposed optimal ADPWM method the performance of the drive operating at near rated speeds can be improved significantly.

Proposed DTC Induction Motor Drive

The block diagram of the proposed ADPWM based DTC is shown in the Fig.5. With the proposed method ripples in torque and flux at high speed operations can be reduced significantly maintaining constant inverter switching frequency. The basic principle of the Conventional Direct Torque Control (CDTC) method, proposed by Takahashi and Noguchi in 1986 is, both the magnitude of stator flux and the developed torque can be directly controlled by proper selection of space vectors of stator voltage, that is, selection of consecutive inverter states. The block diagram of the proposed DTC is shown in the Fig.6. The proposed DTC retains all the advantages of the CDTC, in addition to this gives superior performance during high speed operations which is a considerable constraint with CSVPWM based DTC drive.

The adaptive motor model estimates the torque and speed from the d-q axes voltages and currents. Actual speed and electromagnetic torque developed by the machine are estimated from the sensed voltages and currents, by the adaptive motor model. Addition of slip speed with the actual speed generates the speed of the stator flux vector. The reference d and q axis voltages are calculated by the reference voltage vector calculator using the equations given in (9). Taking these two as inputs the magnitude and position of the reference voltage vector are calculated and according to the set value of [gamma] the ADPWM block generates gating pulses to the inverter based on space vector approach. The dynamic model of the induction motor is modeled in stationary reference frame.

[V.sup.*.sub.ds] = [R.sub.s][i.sub.ds] + [DELTA][[psi].sub.ds]/[T.sub.s] (9.1)

[V.sup.*.sub.qs] = [R.sub.s][i.sub.qs] + [DELTA][[psi].sub.qs]/[T.sub.s] (9.2)

where

[DELTA][[psi].sub.ds] = [[psi].sup.*.sub.ds] - [[psi].sub.ds] (9.3)

[DELTA][[psi].sub.qs] = [[psi].sup.*.sub.qs] - [[psi].sub.qs] (9.4)

[FIGURE 6 OMITTED]

Simulation Results and Discussion

To validate the proposed scheme, simulation is done in MATLAB/SIMULINK using the Rungekutta solver, with a fixed step of 10 [micro] sec. To limit the starting transients starting torque is limited to 150% of the rated, 15N-m. Simulation is done on a 1.5KW, 1440rpm, four pole, 3-[phi] induction motor having the following parameters: Rs=7.83 [OMEGA] , Rr=7.55 [OMEGA] , Ls=0.4751H, Lr=0.4751H, Lm= 0.45351H, J=0.06Kg.[m.sup.2].

From the simulation results shown in Fig.7-Fig.8 it is clear that the proposed ADPWM based DTC method is most suitable for the drives demanding high speed operations. Simulation results showing the different conditions like starting transients, steady state performance, transients during load changes and transients during speed reversal are presented with the proposed DTC method. Also the steady state line current distortion with the proposed ADPWM method is compared with the CSVPWM based DTC and it is observed that significant improvement in the spectral performance of the drive is observed.

Fig.7a shows the no-load starting transients of stator currents, speed, torque, stator flux with the CSVPWM based DTC drive. Fig.7b shows the no-load steady state stator currents, speed, torque, stator flux. Fig.7c. shows the harmonic spectra of the no-load stator current with the CSVPWM based DTC method. Fig.8a-Fig.8b shows the starting transients, steady state ripple, in stator currents, speed, electromagnetic torque developed and stator flux. Fig.8c shows the transients during step change in load with the proposed method. When a load of 10N-m is applied at 1sec and removed at 1.4 sec corresponding dip in the rotor speed, changes in the stator currents is observed. Also it is observed that stator flux is maintained approximately equal to the reference flux, 1wb. Fig.8d shows the corresponding changes in all the mentioned parameters when a speed reversal command is issued at 1.8sec. Change in the supply frequency can be observed during speed reversal. Fig.8e shows the improved harmonic spectra with the proposed ADPWM based DTC of the IM drive operating at full rated speeds.

[FIGURE 7A OMITTED]

[FIGURE 7B OMITTED]

[FIGURE 7C OMITTED]

[FIGURE 8A OMITTED]

[FIGURE 8B OMITTED]

[FIGURE 8C OMITTED]

[FIGURE 8D OMITTED]

[FIGURE 8E OMITTED]

Conclusions

CDTC, though simple, because of the limitations like steady state ripple in torque and flux, variable switching frequency, search for PWM technique that gives an apt solution is one of the attractive areas for researchers. SVPWM based DTC though could solve some tribulations but still the search for a control technique which can reduce the steady state ripple in line current particularly during high speed operations. In this paper an ADPWM based DTC induction motor drive is proposed which can exercise a particular value of [gamma] or might select according to a set policy. It is shown that split claming DPWM with [gamma] = 30[degrees] based DTC can reduce the harmonic distortion in line current when the drive is operating at near rated speeds. Since the proposed split clamping with [gamma] = 30[degrees] gives good spectral performance, in this context it is referred as an optimal ADPWM method for drives operating at high line side voltages or near rated speeds. Simulation results conclude that with the proposed PWM method ripple in steady state line current is reduced significantly when compared with CSVPWM based DTC.
Nomenclature

[R.sub.2],[R.sub.r] stator and rotor resistances
[L.sub.s],[L.sub.r],[L.sub.m] stator and rotor self inductances,
 mutual inductance
P number of poles
[V.sub.ds],[V.sub.ds] d, q axes stator voltages
[i.sub.ds],[i.sub.ds] d, q axes stator currents
[[phi].sub.ds], [[phi].sub.ds] d, q axes stator flux linkages
[[omega].sub.r] rotor electrical speed in radians
[[omega].sub.sl] slip speed
[[omega].sub.e] synchronous speed in electrical
 radians
[T.sub.e] electromagnetic torque
J inertia constant of the induction motor


References

[1] Isao Takahashi, Toshihiko Noguchi, "A new quick-response and high efficiency control strategy of an induction motor", IEEE Trans Industrial applications, Vol IA-22,No 5, pp 820-827, Sep/Oct, 1986.

[2] P. Titinen, m. Surandra, "The next generation motor control method , DTC Direct Torque Control," IEEE proc on Power Electronics,Drives and Energy sysyems for Industrial growth, Vol 1,pp 37-43, 1996.

[3] Thomas G. Habetler, et, al, "Direct Torque control of induction Machines using space Vector Modulation", IEEE Trans Industrial Applications, Vol 28,No.5, pp 1045-1053,Sep/Oct 1992.

[4] L. Tang, L. Zhong, M.F. Rahman, Y. Hu, "An investigation of a modified direct torque control strategy for flux and torque ripple reduction for induction machine drive system with fixed switching frequency" IEEEIAS, pp. 837-844, 2002.

[5] Ahmet M. Hava, Russel J. Kerkman and Thomas A. Lipo, "A High Performance Generalized Discontinuous PWM Algorithm", IEEE Trans Ind Appl, Vol 34, No.5, pp.1059-1071September/October 1998.

[6] Ahmet M. Hava, Russel J. Kerkman and Thomas A. Lipo, "Simple Analytical and Graphical Methods for Carrier--Based PWM-VSI Drives", IEEE Trans. PowerElectronics, vol4,no.1,pp.49-61,Jan,1999.

[7] T. Brahmananda Reddy, J. Amarnath and D. Subba Rayudu, "New Hybrid SVPWM Methods for Direct Torque Controlled Induction Motor Drive for Reduced Current Ripple" IEEE Proc. Power Electronics, Drives and Energy systems for Industrial Growth, PEDES'06, New Delhi, India, Paper no. 3B-20, Dec, 2006.

[8] G. Narayanan and V. T. Ranganathan, "Analytical evaluation of harmonic distortion in PWM AC drives using the notion of stator flux ripple," IEEE Trans. Power Electron., vol. 20, no. 2, pp. 466-474, Mar.2005.

[9] G. Narayanan, Harish K. Krishnamurthy, Di Zhao and Rajapandian Ayyanar, "Advanced Bus-clamping PWM Techniques based on space vector Approach," IEEE Trans. Power Electronics, vol. 21, no.4, pp.974-984, July, 2006.

Biographies

K.Sri Gowri received the B.Tech degree from SVU college of Engineering, Tirupati in 1997, the M.Tech degree from RGM College of Engineering and Technology, Nandyal and is currently pursuing the Ph.D. in Electrical Engineering Department, JNTU, Hyderabad. She is currently an Associate Professor in the Department of EEE in RGMCET, Nandyal, A.P.

Her areas of interest include Power Electronics, pulse width modulation techniques, AC Drives and Control.

T. Brahmananda Reddy was born in 1979. He graduated from Sri Krishna Devaraya University, Anantapur in the year 2001. He received M.E degree from Osmania University, Hyderabad, India in the year 2003. He is presently Associate Professor in the Electrical and Electronics Engineering Department, G. Pulla Reddy Engineering College, Kurnool, India. He presented more than 35 research papers in various national and international conferences and journals.

His research areas include PWM techniques, DC to AC converters and induction motor drives.

Ch. Sai Babu received the B.E from Andhra University (Electrical & Electronics Engineering), M.Tech in Electrical Machines and Industrial Drives from REC, Warangal and Ph.D in Reliability Studies of HVDC Converters from JNTU, Hyderabad. Currently he is working as a Professor in Dept. of EEE in JNTUCEA, Anantapur. He has published several National and International Journals and Conferences. His areas of interest is Power Electronics and Drives, Power System Reliability, HVDC Converter Reliability, Optimization of Electrical Systems and Real Time Energy Management

(1) K. Sri Gowri, (2) T. Brahmanada Reddy and (3) Ch. Sai Babu

(1) RGMCET, Department of EEE, JNTU, Anantapur, Nandyal-518501, India E-mail: gowrivasu.3@gmail.com

(2) GPREC, Department of EEE, Kurnool, India E-mail:tbnr@rediffmail.com

(3) Department of EEE, JNTU, Kakinada, India E-mail: chs_eee@yahoo.co.in
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Title Annotation:advanced pulse width modulation
Author:Gowri, K. Sri; Reddy, T. Brahmanada; Babu, Ch. Sai
Publication:International Journal of Applied Engineering Research
Article Type:Report
Date:Nov 1, 2009
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