DTC Based Induction Motor Speed Control Using 10-Sector Methodology For Torque Ripple Reduction

Transcription

1 DTC Based Induction Motor Speed Control Using 10-Sector Methodology For Torque Ripple Reduction S. Pavithra, Dinesh Krishna. A. S & Shridharan. S Netaji Subhas Institute of Technology, Delhi University Department of EEE, NSIT, Salem , Tamilnadu, India. id: spavithranair@gmail.com, dinupassion7@gmail.com, shridharangokult@gamil.com Abstract - A Direct Torque Control (DTC) drive allows direct and independent control of flux linkage and electromagnetic torque by the selection of optimum inverter switching modes. It is a simple method of signal processing which gives excellent dynamic performance. Also transformation of coordinates and voltage decoupling are not required. However, the possible discrete inverter switching vectors cannot always generate exact stator voltage required, to obtain the demanded electromagnetic torque and flux linkages. This results in the production of ripples in the torque as well as flux waveforms. In the present paper a torque ripple reduction methodology is proposed. In this method the Circular locus of flux phasor is divided into 10 sector as compared to six sector divisions in conventional DTC method. The basic DTC scheme and the 10-sector method are simulated and compared for their performance. An analysis is done with sector increment so that finally the torque ripple varies slightly as the sector is increased. Keywords - Direct Torque Control (DTC), 10-Sector method, Torque ripple. I. INTRODUCTION Vector control has been a major control strategy for many years and dominated the control market of Induction motors. However, recent trends have seen the development of a new strategy called Direct Torque Control [1], a simpler and faster control technique that is advantageous in more than one way. The basic principle involves the control of both torque and flux simultaneously [2]-[4]. As compared to the indirect vector control if offers lower parameter sensitivity because the stator resistance is the only parameter used in the torque and flux estimation[5]. The number of controllers used in DTC is reduced when compared to those used in Direct Vector Control. The Direct Torque Control strategy does not require axes transformation and voltage decoupling blocks[6]. However, the generation of only six non-zero voltage vectors by the voltage source inverter is a drawback. The required torque is met only for few switching instants and most of the time the generated voltage vectors produce a torque that is either more or less than the required torque. As a result, ripples are generated in the torque as well as flux waveforms[7]. Increase of inverter switching frequency by a space vector modulation scheme is proposed for torque ripple reduction [8]-[9]. The concept of dead beat controller is used to increase the switching frequency. But this introduces complexity.in the present paper, a new DTC method, which involves 10-Sector division of the circular flux locus, is discussed. The basic induction motor model is initially presented and then the fundamentals of basic DTC are explained. The concept of new torque ripple reduction method is the discussed. A new switching table for optimum selection of voltage vctor is presented. The simulated results are then given to compare the performance of the basic scheme and the new scheme. II. INDUCTION MOTOR MODELING The dynamic analysis and description of revolving field machines is supported by well established theories[10],[11]. An Induction motor of uniform air gap, with sinusoidal distribution of mmf is considered as shown in Fig.1. the saturation effect and parameter changes are neglected. Fig. 1 : mmf distribution in induction method 1

2 The dynamic model of the Induction motor is derived by transforming the three phase quantities into two phase direct and quadrature axes quantities. The equivalence between the three-phase and two-phase machine model is derived from the concept of power invariance : the power must be equal in the three-phase macine and its equivalent two-phase model[12]. The d and q axes mmfs are found by resolving the mmfs of the three-phases along the d and q axes. The relationship between d-q and a-b-c axes currents is given by, Where ias, ibs, and ics are the three phase currents. These equations are also applicable to the voltage and flux linkage transformation. Applying this transformation to the three phase quantities the electrical model of the induction motor is expressed by the matrix equation (3) in stationary reference frame. Where vds, vqs, ids, iqsrs, Ls, Rr, Lr, Lm and θr are the d-q axes voltages and currents, stator resistance, stator inductance, rotor resistance, rotor inductance, mutual inductance between the stator and rotor windings and the rotor position respectively. The stator and rotor flux linkages in the synchronous reference frames are defined as Where Te, P, Ψds, Ψqs, Ψdr, Ψqr are the electromagnetic torque, number of poles, the stator and rotor d-q axes fluxes respectively. The electromagnetic dynamic equation describing the mechanical model of the induction motor is, Where J, T1, B, ωm are the moment of inertia, the load torque, the friction coefficient and the mechanical speed. The equations (3) and (6) form the mathematical model equations of a three phase induction motor. a) Switching Strategy III. BASIC DTC SCHEME if the stator voltage vector is applied for a short time, the stator flux linkage vector moves by a small amount in the direction of the stator voltage space vector at a speed proportional to the magnitude of the applied voltage space vector. Thus with the application of suitable voltage vector in each switching interval the stator flux can be changed in the required manner. A six pulse voltage source inverter consists of six non zero active voltage switching space vectors and two zero vectors [14] resulting in six sector formation as shown in the Fig.2. The electromagnetic torque in flux and currents is, (5) Fig. 2 : Voltage space Vector and Sector representation The stator flux linkage vector will move fast if nonzero switching vectors are applied. For a zero switching vector it will almost stop. 2

3 Assuming the stator flux linkage space vector to be in sector 1 and is rotating in anti clockwise direction, the resultant effect of generating different voltage vectors at this instant is given in the Fig.3 and Fig.4. c) Overall Operation The schematic diagram of a simple Direct Torque Controlled Induction motor Drive is shown in Fig.5. Fig. 3 : Voltage Space vector for flux variation Fig. 4 : Voltage Space vector for torque variation b) Estimation Procedure In the Direct Torque Controlled Induction motor Drive the real torque and the flux are estimated using simple estimation equations. The direct and quadrature flux components are obtained by using the voltage equations of the induction motor and are given by The real torque is obtained from equation (3). The flux angle to determine sector is obtained from, Fig.5. Block Diagram of DTC of Induction motor The Three phase AC supply is given to the rectifier. The rectifier converts from AC to DC supply. The DC supply is fed to the two Capacitors and the capacitor is reducing the voltage ripple and it s providing the constant DC supply to the Three Level Inverter. The Three level inverter converts from DC to AC supply. The feedback flux and torque are calculated from the machine terminal voltages and currents. The signal computation block also calculates the sector number θ in which the flux vector lies. The reference value of the stator flux magnitude is compared with the actual flux magnitude. The error obtained is given to a two-level hysteresis comparator. If the error is positive, it implies that the flux magnitude has to be increased and this is denoted as dψ=1. If the error is negative, it implies that the flux magnitude has to be decreased and this is denoted as dψ=0. The flux comparator conditions are given as The rotor reference speed is compared with the feedback speed and by suitable PI controller. This error is converted into reference torque. The reference torque is compared with the real torque and the error obtained is fed to a three-level hysteresis comparator. If the error is positive, it implies that the torque has to be increased and this is denoted by dte=1. If the error is negative, it implies that torque has to be reduced and this denoted by dte=(-1). If the error is zero, it implies that the torque needs to be constant and this is denoted by dte=0. The torque comparator conditions are given as 3

4 Table 2. Switching Table for Sectors 1 to 5 d) Optimum Switching Table (15) The voltage vector selection table is given in table 1. The voltage vector that is most suitable for the obtained flux and torque errors in all the sectors is given. Table 1. Optimum Switching Table Table 3. Switching Table for Sectors 6 to 10 The number in each block of the table indicates the corresponding voltage vectors designated with the same number as the subscripit as shown in Fig.3. IV. 10-SECTOR METHODOLOGY The number in each block of the table indicates the corresponding voltage vectors designed with the same number as the subscript as shown in Fig.3. V. SIMULATION RESULT The basic DTC and the new 10 sector method of DTC are simulated and the results obtained are compared for their performance in Figs. 7~12 for steady state torque, steady state current and speed. In steady state, the high magnitude ripples and the number of oscillations in current waveform during the peak value time is reduced. The 10-sector method is observed to give slightly better results. Fig. 6 : Switching vectors for 10 sectors The switching logic is similar to that of basic DTC. Thus a suitable voltage vector is selected according to the flux and torque requirements. The switching table employed for first five sectors is given in Table 2 while for the next five sectors is given in the Table 3. Fig.7 Steady State Torque in Basic DTC 4

5 Fig.12 Speed for Basic DTC Fig.8 Steady State Torque in 10-Sector DTC VI. COMPARISON TABLE The below comparison table clearly explains that the proposed method has considerably reduced the torque ripple when compared with the conventional method. Fig.9 Steady State Currents in Basic DTC Table 7.1 Comparison between Conventional DTC and Proposed DTC Table 7.2 Comparison between Conventional DTC and 12-Sector Methodology Fig.10 Steady State Currents in 10-Sector DTC Table 7.3 Comparison Table Fig.11 Speed for Basic DTC VII. CONCLUSION In the present paper a new method of torque ripple reduction based on the increased number of sectors is discussed. The induction motor drive is simulated for both basic DTC method and the modified DTC method and the results are compared. The torque and current waveforms are compared for steady state cases. It is observed that the modified DTC strategy brings about a 5

6 slight reduction in torque ripple and the results obtained support the torque ripple reduction ability. VIII. REFERENCES [1] Isao Takahashi, A New Quick-Response and High-Efficiency Control Strategy of an Induction motor, IEEE Transactions on Industry Applications, Vol.IA-22,No.5, September/October [2] M.Depenbrock, Direct Self-Control (DSC) of Inverter-Fed Induction Machine, IEEE Transactions on Power Electronics, Vol.3, No.4, October [3] T. G. Habetler et al., Sept./Oct Direct torque control of induction machines using space vector modulation, IEEE Trans. Ind. Applicat., vol. 28,pp [4] Kang, J. K. et al : 1999, Direct Torque Control of Induction Machine with Variable Amplitude Control of Flux and Torque Hysteresis Bands, Conf. Rec. IEEE-IAS, pp [5] Kyo-Beum Lee, Joong-Ho Song, Ick Choy, Joo- Yoep Choi, Jae-Hak Yoon, and Se-Hyun Lee, Torque ripple reduction in DTC of induction motor driven by 3-level inverter with low switching frequency. [6] P. A. Arias, 2000"Improvement in Direct Torque Control of Motors induction", Ph.D Thesis, University of Catalunya, Spain. [7] Kyo-Beum Lee, Joong-Ho Song, Ick Choy and Ji-Yoon Yoo, Improvement of Low-Speed Operation Performance of DTC for Three-Level Inverter-Fed Induction Motors, IEEE Transactions on Industrial Electronics, Vol.48, No.5, October [8] Domenico Casadei, Francesco Profumo, Giovanni Serra and Angelo Tani, FOC and DTC:Two Viable Schemes for Induction Motors Torque Control, IEEE Transactions an Power Electronics, Vol.17, No.5, September [9] Tang, L. et al: 2002 An Investigation of a Modified Direct Torque Control Strategy for Flux and Torque Ripple Reduction for Induction Machine Drive System with Fixed Switching Frequency, Conf. Rec. IEEE-IAS, pp [10] Giuseppe S. Buja and Marian P. Kazmierkowski, Direct Torque Control of PWM Inverter-Fed AC Motors- A Survey, IEEE Transactions on Industrial Electronics, Vol.51, No.4, August [11] Borra Suresh Kumar, R.A.Gupta and Rajesh Kumar, 12-Sector Methodology of Torque Ripple Reduction in a Direct Torque Controlled Induction Motor Drive SICE-ICASE International Joint Conference 2006, Oct 18-21, 2006 in Bexco, Busan, Korea. 6