A Novel Direct Torque Control Scheme for Induction Machines With Space Vector Modulation

Transcription

1 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, 24 A Novel Direct Torque Control Scheme for Induction Machine With Space Vector Modulation Joé Rodríguez, Jorge Pontt, Céar Silva, Samir Kouro and Hernán Miranda Departamento de Electrónica, Univeridad Técnica Federico Santa María, Valparaío, CHILE hernan.miranda@elo.utfm.cl Abtract In thi paper a new method for Direct Torque Control (DTC) baed on load angle control i developed. The ue of imple equation to obtain the control algorithm make it eay to undertand and implement. Fixed witching frequency and low torque ripple are obtained uing pace vector modulation. Thi control trategy overcome the mot important drawback of claic DTC. Reult how the feaibility of the propoed method, obtaining good peed control bandwidth while overcoming claic DTC drawback. Index Term Electric Drive, AC Machine, Direct Torque Control, Space Vector Modulation. I. INTRODUCTION In recent year much reearch ha been developed in order to find impler control cheme for induction motor that meet the mot demanding requirement, uch a low torque ripple, low harmonic ditortion or quick dynamic repone. Today Field Oriented Control (FOC) [] and Direct Torque Control (DTC) [2],[3] are conidered the mot important technique to achieve high dynamic performance in AC machine. The ue of current control loop in a rotating reference frame to decouple torque and flux control i the main characteritic of FOC. The ue of thee controller add an additional time delay making torque dynamic repone lower. Space vector modulation (SVM) ha been frequently ued in FOC to generate the gate pule for the inverter emiconductor. Claic DTC make ue of hyterei comparator with torque and tator flux magnitud error a input to decide which tator voltage vector i applied to motor terminal. The complex plane i divided in ix ector, and a witching table i deigned to obtain the required vector baed on the hyterei comparator output. Due to fat time contant of tator dynamic it i very difficult to keep machine torque between the hyterei band. Thi can be done either by increaing the ampling frequency a in [4], thu increaing witching frequency, commutation loe and computation requirement, or uing multilevel power converter [5],[6]. The ue of hyterei comparator in claic DTC implementation give rie to variable witching frequency, which depend on rotor peed, load, ample frequency, etc. Thi variable witching frequency may excite reonant dynamic in the load and hence contitute a eriou drawback of DTC. The ue pace vector modulation in conjunction with DTC ha been propoed a a olution to overcome the above mentioned problem [7]-[7]. In [7],[8] and [9] a econd degree equation with parameter depending on machine operating point mut be olved to obtain the tator vector reference. In [] and [] an invere machine model i ued for tator flux (ψ ) calculation. The ue of PI controller for torque and tator flux in a rotating reference frame i propoed in [2], leading to a control cheme that i imilar to field oriented control. The technique propoed in thi paper i imilar to that ued in [3],[4] for permanent magnet ynchronou motor and i not clearly explained in [5], and[6]. The main contribution of thi work i to ue a new and very imple one tep flux control algorithm for induction machine control uing DTC and SVM (DTC-SVM) and few controller, avoiding coordinate rotation and complicated predictive controller. Reult for the propoed trategy are preented for a 5.5 [kw] induction motor and are compared with FOC and claic DTC in term of torque tranient repone, torque ripple and witching frequency. Finally it i concluded that improved reult are obtained with a imple algorithm baed on an eay to undertand theoretical principle. II. THEORETICAL BACKGROUND Applying the uual pace vector tranformation to a three phae voltage ytem, a ingle pace vector i defined by v = 3 ( va av b a 2 ) v c, () 2 where a = /2j 3/2, and v a, v b and v c are tator phae voltage, it i poible to obtain a imple equation et that decribe the AC machine dynamic behavior in a tator fixed coordinate ytem [8]. Thee equation are: v = R i dψ (2) dt = R r i r dψ r jω m ψ r (3) dt ψ = L i L m i r (4) ψ r = L m i L r i r, (5) where R and R r are the tator and rotor reitance, L, L r and L m are the tator, rotor and mutual inductance and ω m i the rotor peed. The baic relation between torque and machine fluxe i: /4/$2. 24 IEEE. 392

2 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, 24 in( ± ) D Fig.. i x i y Fig. 2. Fig. 3. ± co(±) µ v Rotor flux ψ r, reference and etimated tator flux ψ relation. PI u x Current Controller u y PI (x,y) (, ) r Field Oriented Control block diagram. Claic DTC control block diagram. u u Switching Table SVM r Inverter IM Inverter IM k r = L m /L, and σ = L 2 m/(l L r ). Baed on (6) it i clear that it i poible to achieve machine peed and torque control directly by actuating over the load angle. III. FIELD ORIENTED AND CLASSIC DIRECT TORQUE CONTROL A. Field Oriented Control Field Oriented Control i baed on the decompoition of the intantaneou tator current i into two orthogonal component in rotor flux oriented coordinate: one proportional to the flux (i x ) and the other proportional to the torque (i y ). Since both current vector are perpendicular to each other, a decoupled dynamic ytem i obtained o that both variable can be controlled eparately, achieving a imilar operation principle a in DC-drive. Fig. 2 illutrate a implified control diagram of FOC. Both current component are controlled by individual PI controller, which compute the correponding tator voltage vector (v x,v y ) that will generate the deired correction in the current control loop. Then a coordinate rotation i performed to orient the variable repect the tator (α, β). Finally the deired tator voltage vector i generated uing pace vector modulation. B. Direct Torque Control Due to low rotor flux dynamic, the eaiet way to change the load angle i to force a change in the tator flux vector by the application of the appropriate tator voltage vector v. Neglecting the effect of the voltage drop on the tator reitance in (2), the tator flux vector i the time integral of the tator voltage vector. For ampling time t ufficiently mall, (2) can be approximated by (7). ψ t v (7) In claic DTC the tator voltage election i made by hyterei comparator a hown in Fig. 3, with torque and flux magnitude error a input and a predeigned gate-pule lookup table that elect the tator voltage vector correponding to the deired action. Thi control trategy lead to change from full negative torque to full poitive cauing high torque ripple. A demontrated in [4], the capability to actuate on torque greatly depend on the emf ω m ψ. Thi mean that ripple frequency varie with rotor peed obtaining variable witching frequency and a wide pectrum for torque and tator current. = 3 2 p k r σl ψ ψ r (6) = 3 2 p k r σl ψ ψ r in(δ), where δ, known a load angle, i the angle between tator and rotor fluxe a hown in Fig., p i the number of pole pair, IV. PROPOSED CONTROL STRATEGY In the propoed method, the control objective i to elect the exact tator voltage vector (v ) that change ψ to meet the load angle reference, and o the deired torque while keeping flux amplitude contant. A pace vector modulation algorithm i ued to apply the required tator voltage vector. It i expected that torque ripple i almot eliminated, while zero teady tate error i achieved with fixed witching frequency. 393

3 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, 24 T e ± Flux Calculator D Dt v SVM IM r Torque and Flux Etimator i! m Fig. 4. Propoed DTC-SVM control cheme. f (t) t L i m r r d. ψ r = τ r ( L m i ( τ r jω m ) ψ r ) dt, (9) and the tator flux derived from. j r L r L m K ψ = σl i L r ψr. () L m From thee equation the flux etimator block give the required rotor flux angle to be added to the reference tator flux ignal. And the etimated tator flux needed to calculate ψ. Torque etimation i made from (6). Where the cro product can alo be written a! m Fig. 5. Torque and Flux Etimator Flux etimator block diagram. ¾L The preented trategy ue one PI torque regulator, a imple flux calculation block and no rotating coordinate tranformation making the control trategy a traightforward application of (6). Thi i illutrated by the control block diagram of Fig. 4. Here torque controller actuate over the load angle δ to meet torque reference tracking. The tator flux calculator block output i given by ψ = ψ co (δ ψ r )j ψ in (δ ψ r ), (8) where ψ i an arbitrary reference value. The ue of rotor flux angle to obtain tator flux reference mean that the propoed method i rotor oriented. The ue of a rotatory reference frame aligned with rotor flux allow better torqueflux decoupling, leading to fater tranient repone. According to the flux calculator output, the tator flux reference ignal i compared with the etimated flux obtaining ψ, that i needed to follow the torque reference, a it can be een in Fig.. Thi value i divided by t to calculate v a in (7). The SVM block perform the claical pace vector modulation of v to obtain the gate drive pule for the power circuit. V. FLUX AND TORQUE ESTIMATOR To implement the tator and torque etimator block hown in Fig. 5 a rotor flux etimator baed on the rotor model i implemented in tator coordinate by {ψ ψ r } = ψ α ψ rβ ψ β ψ rα. () Flux and torque etimator block diagram i hown in Fig. 5, where K =3/2p. The feedback loop in the integration of the rotor model can compenate for finite time diturbance in the input i and unknown initial condition. VI. RESULTS Cloed loop performance of the propoed method i teted and compared to claic direct torque control and field oriented control by mean of peed reference tracking, torque dynamic repone, flux control and ignal pectrum. A 5.5[kW], 38[V l l ], two pole pair induction machine i conidered with [khz] ampling frequency and 5[V ] DC link voltage. A tep change up to rated peed on the reference ignal i applied in t = 2[m] at rotor peed ω m = 5[rad/ec]. The reult are hown in Fig. 6. In Fig. 6(a) the dynamic repone uing claic field oriented control i hown. Similarly, Fig. 6(b) how the repone with claic DTC. At the top of each figure the peed tracking reference i hown, torque repone in the middle and tator flux magnitude at the bottom. Finally, imilar reult are preented for the propoed method in Fig. 6(c). Figure 6 illutrate that field oriented control and the propoed method have imilar dynamic repone, good peed reference tracking while keeping contant rotor flux amplitude for FOC and tator flux amplitude for the propoed DTC-SVM 394

4 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, 24 peed [rad/ec] Ψ r [Wb] peed [rad/ec] Ψ [Wb] peed [rad/ec] (a) (b) Ψ [Wb] (c) Fig. 6. Comparion of dynamic repone between DTC-SVM, Field Oriented Control and Claic DTC. (a) Field Oriented Control, (b) Claic Direct Torque Control, (c) Propoed Method (a) (b) (c) Fig. 7. Torque repone comparion between DTC-SVM and claic DTC. (a) Field Oriented Control, (b) Claic Direct Torque Control, (c) Propoed Method. method. Claic DTC how high torque and flux ripple and imilar rotor peed dynamic repone a DTC-SVM and FOC. To compare the fat dynamic torque repone between the propoed method, FOC and claic DTC, the torque repone to a tep change in peed demand from negative to poitive rated peed i analyzed. The reult are hown in Fig. 7. It i clear that the DTC-SVM improve claic DTC torque reference tracking, reducing torque ripple, achieving zero teady tate error and obtaining a torque repone almot a fat a claic DTC. In Fig. 7(a) FOC torque tep repone i hown. It can be een that the inner current loop dynamic have an important role in the torque repone. It i important to remark that in claic DTC torque ripple a big a in Fig. 7(b) can not be reduced by imply reducing torque hyterei band. The high torque change rate hinder the detection of the hyterei band croing unle high ample frequency i ued. The effect of a reduced hyterei band in the torque ripple can be oberved in Fig. 8 top, where a 395

5 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, H t F S = % r = [khz] H t = 5% r 4 F S = [khz] Fig. 8. Size of hyterei band and ampling frequency effect on torque ripple for claic DTC. Spectral Content Frequency [Hz] (a).6 band of % rated torque ha been ued maintaining the ame ample frequency a before. It can be een that there are not important difference with figure 7(b). On the other hand, in Fig. 8 bottom increaed ampling frequency wa ued while keeping the band to it original 5% value, effectively reducing the torque ripple. It may be concluded then, that the only way to improve claic DTC performance i to increae ampling frequency, thi i normally not poible due to contraint on the witching frequency and minimum computational time requirement. A major advantage of the propoed DTC-SVM method over claic DTC i that the ue of a voltage modulator lead to fixed witching frequency, equal to ample frequency. Fig. 9(a) how torque pectral analyi with the propoed method and Fig. 9(b) how a typical pectral content uing claic DTC. The energy of torque harmonic in claic DTC i ditributed in a wide range of frequencie. Thi can generate reonance and undeirable acoutic noie. In the propoed method the pectral energy i concentrated at ample frequency harmonic. Although, the propoed method control tator flux, Figure how three-phae tator current repone during the peed change, here the inuoidal current waveform i clear, howing that good current control i inherent to the algorithm. VII. CONCLUSIONS The DTC-SVM trategy propoed in thi work to control flux and torque i baed on few induction machine fundamental equation. Conequently, the control method i imple and eay to implement. No coordinate rotation and le PI controller than in field oriented control are needed. In addition, the propoed DTC trategy i well uited for ue in conjunction with pace vector modulation reulting in a powerful alternative to overcome the well known drawback of the original DTC olution: variable witching frequency and high torque ripple. Spectral Content Frequency [Hz] (b) Fig. 9. Torque pectral analyi comparion. (a) DTC-SVM torque pectrum, (b) Claic DTC torque pectrum. Stator Current [A] Fig Stator Current during peed reveral. 396

6 24 35th Annual IEEE Power Electronic Specialit Conference Aachen, Germany, 24 APPENDIX Motor parameter ued to tet and compare the propoed control trategy are given in table I. TABLE I MOTOR PARAMETERS Parameter Value R [Ω] 3.2 R r [Ω] 4.46 L [Hy].337 L r [Hy].337 L m [Hy].322 p 2 J [rad/nm].6 power [KW] 5.5 V RMS 38 [4] L. Tang, L. Zhong, M. Rahman, Y. Hu. A Novel Direct Torque Control for Interior Permanent-Magnet Synchronou Machine Drive With Low Ripple in Torque and Flux - A Speed-Senerole Approach. IEEE Tran. on Indutry Application, 39(6): , Nov/Dec 23. [5] L. Tang, L. Zhong, F. Rahman. Modeling and Experimental Approach of a Novel Direct Torque Control Scheme for Interior Permanent Magnet Synchronou Machine Drive. IECON 2, Indutrial Application Society, :235 24, 5-8 November 22. [6] L. Tang, M.F. Rahman. A New Direct Torque Control Strategy for Flux and Torque Ripple Reduction for Induction Motor Drive by Uing Space Vector Modulation. IEEE PESC 32 nd International Conference, page , 2. [7] C. Lacu, I. Boldea, F. Blaabjerg. A Modified Direct Torque Control for Induction Motor Senorle Drive. IEEE Tran. on Indutry Application, 36():22 3, January/Frebruary 2. [8] I. Boldea, S.A. Naar. Electric Drive. CRC Pre LLC, 999. ACKNOWLEDGMENT The author gratefully acknowledge the financial upport provided, under grant n 483, by Fondo Nacional de Dearrollo Científico y Tecnológico (FONDECYT) of the Chilean Government. REFERENCES [] F. Blachke. A New Method for the Etructural Decoupling of AC Induction Machine. Conf. Rec. IFAC, Dueeldorf, Germany, page 5, Oct. 97. [2] I. Takahahi, Y. Ohmori. High-Performance Direct Torque Control of an Induction Motor. IEEE Tran. on Indutrial Application, 25(2): , March/April 989. [3] M. Depenbrock. Direct Self-Control (DSC) of Inverter-Fed Induction Machine. IEEE Tran. on Power Electronic, 3(4):42 429, October 988. [4] D. Caadei, G. Serra, A. Tani. Implementation of a Direct Torque Control Algorithm for Induction Motor Baed on Dicrete Space Vector Modulation. IEEE Tran. on Power Electronic, 5(4): , July 2. [5] C. Martin, X. Roboam, T.A. Meynard, A. Carvalho. Switching Frequency Impoition and Ripple Reduction in DTC Drive by Uing a Multilevel Converter. IEEE Tran. on Power Electronic, 7(2): , March 22. [6] Z. Tan, Y. Li, M. Li. A Direct Torque Control of Induction Motor Baed on Three-level NPC Inverter. IEEE 32 nd PESC, Vancouver, Canada, June 2. [7] T. Habetler, F. Profumo, M. Patorelli, L. Tolbert. Direct Torque Control of Induction Machine Uing Space Vector Modulation. IEEE Tran. on Indutry Application, 28(5):45 53, September/October 992. [8] J. Mae, J. Melkebeek. Dicrete Time Direct Torque Control of Iduction Motor uing Back-EMF Meaurement. IEEE IAS 33 rd Annual Meeting, October 998. [9] B. Kenny, R. Lorenz. Stator- and Rotor-Flux-Baed Deadbeat Direct Torque Control of Induction Machine. IEEE Tran. on Indutry Application, 39(4):93, July/Augut 23. [] D. Caadei, G. Grandi, G. Serra. Rotor Flux Oriented Torque-Control of Induction Machine Baed on Stator Flux Vector Control. in Proc. EPE 93, Brighton, UK, 5:67 72, Sept [] D. Caadei, G. Serra, A. Tani, L. Zarri, F. Profumo. Performance Analyi of a Speed-Senorle Induction Motor Drive Baed on a Contant-Switching-Frequency DTC Scheme. IEEE Tran. on Indutry Application, 39(2): , Marhc/April 23. [2] Y.S. Lai, J.H. Chen. A New Approach to Direct Torque Control of Induction Motor Drive for Contant Inverter Switching Frequency and Torque Ripple Reduction. IEEE Tran. on Energy Converion, 6(3):22 227, September 2. [3] D. Swierczynki, M. Kazmierkowki. Direct Torque Control of Permanent Magnet Synchronou Motor (PMSM) Uing Space Vector Modulation (DTC-SVM) - Simulation and Experimental Reult. IECON 2, Indutrial Application Society, :75 755, 5-8 November