Open Access Study of Direct Torque Control Scheme for Induction Motor Based on Torque Angle Closed-Loop Control. Xuande Ji *, Daqing He and Yunwang Ge

Transcription

1 Send Order for Reprint to 6 The Open Electrical & Electronic Engineering Journal, 25, 9, 669 Open Acce Study of Direct Torque Control Scheme for Induction Motor Baed on Torque Angle CloedLoop Control Xuande Ji, Daqing He and Yunwang Ge College of Electrical Engineering and Automation Luoyang Intitute of Science and Technology, No.8 XueZi Street Luolong Ditrict Luoyang HeNan, 4723, China Abtract: For diadvantage of the large flux and torque ripple and current waveform ditortion of Direct Torque Control (BASICDTC), the DTC cheme for induction motor baed on torque angle cloedloop control wa preented and the propoed cheme wa realized with three method of torque angle cloedloop control. The main characteritic of three method of torque angle cloedloop control for the propoed cheme wa analyzed, emphaizing their advantage and diadvantage. The performance of three method of torque angle cloedloop control for the propoed cheme wa tudied in term of flux and torque ripple, current waveform ditortion and tranient repone. Simulation reult howed that the propoed cheme improve the performance of induction motor BASICDTC by combining low flux ripple, low torque ripple and low current waveform ditortion characteritic with fat dynamic. Keyword: BASICDTC, CloedLoop, Induction Motor, SVM, Torque Angle Control.. INTRODUCTION The adjutable peed drive (ASD) i generally ued in elevator, electric vehicle, hybrid electric vehicle, pump, robotic, wind power generation and hip propulion ytem etc. DC motor i mainly ued in DCASD, and induction motor i mainly ued for ACASD []. The natural decoupling between flux and torque i achieved due to DC motor unique internal tructure, thu DCASD ha a good and fat dynamic repone. DC motor ha been dominant in indutrial application over the pat few decade. However, DC motor ha the diadvantage of higher cot, higher rotor inertia and maintenance difficultie with bruhe and commutator. In addition, DC motor cannot operate in dirty and exploive environment. Induction motor ha not the diadvantage of DC motor. Therefore, DC motor will be gradually ubtituted with induction motor. Induction motor control i much more complex than DC motor becaue of it mathematical model that ha the nature of nonlinear, multivariable and trong couple. Field Oriented Control [2] (FOC) wa propoed by F. Blahke in early 97. FOC make induction motor have a imilar performance to the DC motor in tatic and dynamic characteritic. An accurate flux etimator had to be employed to enure the etimated value ued in calculation doe not deviate from the actual value. Beide, the coordinate tranformation had increaed the complexity of thi control method. Addre correpondence to thi author at the College of Electrical Engineering and Automation Luoyang Intitute of Science and Technology, No.8 XueZi Street Luolong Ditrict Luoyang HeNan, 4723, China; Tel: ; litdqx@ohu.com BASICDTC wa firt introduced by M. Depenbrock in 986 [3, 6]. A new direction had opened up for a highperformance control of induction motor. Shortcoming of FOC control algorithm complexity and rotor parameter dependence were largely overcome by BASICDTC. However, BASICDTC alo ha it own diadvantage uch a difficulty to control torque and flux at lowpeed, high flux and torque ripple, high current waveform ditortion and variable witching frequency. A large number of technical paper appear in the literature mainly to improve the performance of Induction Motor. SVMDTC cheme [4] that combined Space Vector Modulation (SVM) and Direct Torque Control (DTC) wa widely ued in many cheme. SVMDTC cheme ued the PI controller intead of the hyterei comparator, ued the SVM intead of the voltage vector election table and ued the flux oberver intead of the pure integrator to olve the problem uch a the difficulty to control torque and flux at lowpeed, high flux and torque ripple, high current waveform ditortion and variable witching frequency. However, due to the three PI controller of cloedloop flux, peed cloedloop and torque cloedloop, the controller parameter deign become difficult, and the rotate invere tranform make the ytem tructure complex. Thu SVMDTC cheme lot the advantage of the imple tructure of the BASICDTC ytem. The DTC cheme for induction motor baed on torque angle cloedloop control wa preented in thi paper. According to the approximate linear relationhip between electromagnetic torque and torque angle, the torque angle cloedloop control intead of the cloedloop torque control, the flux tracking control intead of the flux cloedloop control and the flux etimator intead of the pure integrator were ued to achieve the control of the flux and torque. Three method were ued for torque angle cloedloop control: 87429/5 25 Bentham Open

2 Study of Direct Torque Control Scheme for Induction Motor The Open Electrical & Electronic Engineering Journal, 25, Volume 9 6 () Torque angle difference cloedloop control; (MethodFirt). (2) Torque angle PI controller cloedloop control; (Method Second). (3) Torque angle compenation cloedloop control; (Method Third). Three method of torque angle cloedloop control for the new control cheme were imulated by imulation tool. The imulation reult were given. Three method were compared and analyzed, and finally concluion were drawn. 2. INDUCTION MOTOR MODEL AND FLUX OB SERVER The following tate equation written in a tationary reference frame decribe the dynamic behavior of an induction motor [7]. d dt #!! r ' ' = A A 2 A & 2 A # 22 ' ' & #!! r ' ' + & # I ' u () & The output equation i! i = C! (2)! Where I = #! u = # u! u! = L L r L m 2, T & '( C = (/! )# L r I L m I & J = #!, i = # i! i T &, '(! = &, A =!(R L r / )I,!!! # r ', & T,! i = C!ˆ! (6)! A Where A 2 A = # & # A 2 A 22 &, B =! I # &,!ˆ!!ˆ! = '!!ˆ '. # r & i the etimated value of the oberver. K i the gain matrix of the oberver. The parameter configuration of the oberver gain matrix can be configured according to the method of Ref [5]. 3. PRINCIPLES OF BASICDTC The BASICDTC principle i to ue the deviation of torque amplitude and tator flux amplitude repectively to produce the torque witching ignal L T and the flux witching ignal L! through the hyterei torque comparator and the flux hyterei comparator. And the appropriate voltage vector wa elected with the voltage vector election table according to the current poition of the tator flux vector!ˆ! to achieve the control of the torque and flux [4]. Fig. () i a block diagram of the induction motor BASICDTC. BASICDTC only realized the qualitative control of torque and flux due to not only the limited number of the voltage vector, but alo the nature of the torque bia and flux bia that were only repreented by L T and L!. Thu the ripple of torque and flux wa too high. The application of torque and flux hyterei comparator led to the variable witching frequency of the inverter, and then led to the higher current waveform ditortion. While the pure integrator with oberving flux made the performance of control ytem be woren at low peed [, 2]. A 2 = (R r L m /! )I, A 2 = (R L m /! )I, A 22 =!(R r L / )I + # r J. The electromagnetic torque equation i: = 3 2 P n! L m!! #! # r (3) d! r dt Where P n i number of pole pair. The motor mechanical equation i: = P n T l J Where ω i motor angular peed. r The flux oberver tate equation and output equation are: d!!ˆ = dt Â!!ˆ + B u! + K # i! î! & (4) (5) 4. DTC SCHEME FOR INDUCTION MOTOR BASED ON TORQUE ANGLE CLOSEDLOOP CONTROL DTC cheme for induction motor baed on torque angle cloedloop control i that the traight axi component u! quadrature axi component u! u u and of the Voltage Space Vector in the! coordinate ytem were calculated with the calculation formula through the increment! of the phae angle! of the tator flux by cloedloop control torque, the tator flux reference magnitude! and the tator flux oberving magnitude!. And then the PWM ignal driving the inverter were generated with uing the SVM algorithm to achieve the quantitative control of the torque and flux, thereby reducing the flux and torque ripple, reducing the current waveform ditortion, and o that the witching frequency i contant. The key to generating inverter drive ignal i the calculation of u.

3 62 The Open Electrical & Electronic Engineering Journal, 25, Volume 9 Ji et al. Speed ψ Hyterei L T L ψ Vector Selection Table S a S b S c V dc VOLTAGE SOURCE INVERTER Hyterei Sector Detection Voltage ψ ψ Flux and Torque Etimator u i 2 3 i a i b i c M Fig. (). Block diagram of BASICDTC. β Δ = Δ ( k + ) ( k + ) ψ ( k +) Δ ( k +) Δψ k = u ( + ) ( k + ) T ψ ( k ) ( k ) O ( k ) r ( k ) ψ r ( k ) α Fig. (2). Stator flux vector in the teady tate proce. β Δ = Δ + Δ ( k + ) ( k + ) d ( k + ) ψ ( k +) Δ d ( k +) Δ ( k +) Δψ k = u ( + ) ( k + ) T ψ ( k ) ( k ) O ( k ) r ( k ) ψ r ( k ) α Fig. (3). Stator flux vector in the dynamic proce. Fig. (2 and 3) are repectively the reference tator flux vector! for calculating u in the proce of the teadytate and dynamic proce [35]. In Fig. (2 and 3),! r(k ) i the k hot of the rotor flux vector! r.! (k ) i the k hot of the tator flux vector!.! (k+) i the k+ hot of!.! (k+) i the increment of

4 Study of Direct Torque Control Scheme for Induction Motor The Open Electrical & Electronic Engineering Journal, 25, Volume 9 63 V dc Speed = f ( ) ψ Δ U u α u β SVM S a S b S c VOLTAGE SOURCE INVERTER ψ i u Voltage Flux and Angle Etimator i 2 3 i a i b i c M Fig. (4). Block diagram of DTC with cloedloop control of torque angle difference.! from k hot to k+ hot.! (k ) i the phae angle of! (k ) in the! coordinate ytem.! r(k ) i the phae angle of! r(k ) in the! coordinate ytem.! (k ) i the k hot of torque angle!, that i the phae difference between! (k ) and! r(k ) that repreent the ize of the k hot torque.! (k+) i the increment of! (k ), that i the increment of torque from k hot to k+ hot. ω i the ynchronou peed of induction motor, T i the control period of the ytem. The increment of! (k+) conit of two part: dynamic phae angle increment! d (k+) and teadytate phae angle increment! (k+). When the ytem i in the teadytate proce, due to the balance between the electromagnetic torque and load torque,! d (k+) =, and then the increment of! (k+) i:! (k+) =! (k+) = # T (7) A hown in Fig. (2). When the ytem i in the dynamic proce, due to the imbalance between the electromagnetic torque and load torque,! d (k+) #, and then the increment of! (k+) i:! (k+) =! d (k+) +! (k+) (8) A hown in Fig. (3). In order to arbitrarily control the electromagnetic torque within a control period T, the phae angle of the tator flux! require to be increaed from! (k ) to! (k ) +! (k+). Fig. (3) how:! (k+) =! e j( ( k ) +# ( k+) ) (9)! (k ) =! e j ( k ) then! (k+) = e j(# ( k ) +!# ( k+) ) e j# ( k ) and o u (k+) () () =! (k+) / T (2) Conidering the voltage drop of the tator reitance, then the required voltage pace vector u (k+) u (k+) then U = u (k+) =! (k+) / T + i R equation [6]: (3) 4.. Torque Angle Difference CloedLoop Control (MethodFirt) To improve the performance of BASICDTC and not to loe the advantage of tructure imple of the BASICDTC ytem, the method of torque angle difference cloedloop control ignore the increment! (k+) of the teadytate phae angle of the tator flux, and then! (k+) i gotten with the method of torque angle difference cloedloop control to realize the control of torque and flux. Block diagram of DTC with cloedloop control of torque angle difference i hown in Fig. (4). Compared with the method of BASICDTC, the ytem tructure of the method of torque angle difference cloedloop control i further implified due to omitting the rotation invere tranformation and the hyterei comparator of torque and flux.

5 64 The Open Electrical & Electronic Engineering Journal, 25, Volume 9 Ji et al. V dc Speed = f ( ) Torque Angle ψ Δ U u α u β SVM S a S b S c VOLTAGE SOURCE INVERTER ψ i u Voltage Flux and Angle Etimator i 2 3 i a i b i c M Fig. (5). Block diagram of DTC with cloedloop control of torque angle controller Torque Angle PI CloedLoop Control (MethodSecond) The method of torque angle difference cloedloop control ha little effect on the torque in the ytem teadytate proce, although ignoring the increment! (k+) of the teadytate phae angle of the tator flux. But there i a large impact on the torque in the ytem dynamic proce. The torque cannot maintain a contant maximum in the ytem dynamic proce due to ignoring! (k+), thereby reducing the dynamic repone of the ytem. In order to maintain the inherent advantage of the BASICDTC fat dynamic repone, the increment! (k+) of the teadytate phae angle of the tator flux i gotten to control torque and flux uing the method of torque angle PI controller cloedloop control. Block diagram of DTC with the method of torque angle PI controller cloedloop control i hown in Fig. (5). The torque angle controller hown in Fig. (5) i the PI controller. The method of torque angle PI controller cloedloop control make the torque maintain at the maximum contant in a dynamic proce, and then to maintain a rapid ytem dynamic repone. However, the advantage of the ytem imple tructure i lot becaue of the uage of the torque angle PI controller Torque Angle Compenation CloedLoop Control (Method Third) In order to overcome the hortcoming of the method of torque angle difference cloedloop control and torque angle PI controller cloedloop control,! (k+) i gotten with the method of torque angle compenation cloedloop control to realize the control of torque and flux. The method of torque angle compenation cloedloop control not only allow the torque to maintain a contant maximum in the dynamic proce, and then to get a rapid dynamic repone, but alo can reduce the uage of PI controller, and then ha a advantage of imple tructure of the BASICDTC ytem. Block diagram of DTC with the method of torque angle compenation cloedloop control i hown in Fig. (6). 5. CALCULATION OF GIVEN TORQUE ANGLE AND FEEDBACK TORQUE ANGLE Another form of electromagnetic torque equation by formula (3) i: = 3 2 P! L m n! #! # in (4) r Where! i the angle between the tator flux vector and the rotor flux vector, i.e., the torque angle. The relationhip between the torque and the torque angle! i nonlinear from formula (4). But and in! i directly a proportional relationhip when the amplitude of the tator flux, the rotor flux and torque i known. The cope of the torque angle i far le thanπ/2 under normal circumtance. The angle range of the Induction motor torque i generally between [.2,+.2]. The relationhip between the torque angle! and in! i hown in Fig. (7). From Fig. (7), the relationhip between! and in! i approximately linear in the cae of the mall torque angle, and o the relationhip between! and i approximately linear.

6 Study of Direct Torque Control Scheme for Induction Motor The Open Electrical & Electronic Engineering Journal, 25, Volume 9 65 V dc Speed = f ( ) Δ d Δ + ψ Δ U u α u β SVM S a S b S c VOLTAGE SOURCE INVERTER ψ i u Voltage Flux and Angle Etimator i 2 3 i a i b i c M Fig. (6). Block diagram of DTC with cloedloop control of torque angle compenation. Fig. (7). Relationhip between! and in!. In the condition of ignoring electromagnetic inertia of the tator and rotor, knowing the tator and rotor flux amplitude and torque,! can be approximated by:! in! = / C m Where C m = (.5! P n! L m! #! # ) i contant. r (5) A can be een from formula (5), a long a the torque i known,! will be obtained uing the torque coefficient C m. Arcine calculation i omitted, o that the calculation become imple. The given torque angle! can be calculated directly by equation (5):! in! = / C m Where C m = (.5! P n! L m! #!! #! r ) i contant. The feedback torque angle! can be very imply obtained baed on taking full advantage of the flux oberver. By the two component of the tator and rotor flux, the following equation are obtained: co! = a / in! = # /, co! r = ra / r in! r = r# / r. Therefore! in! = in(! #! r )! in! co! r # co! in! r (6)

7 66 The Open Electrical & Electronic Engineering Journal, 25, Volume 9 Ji et al. 6. SIMULATION RESULTS AND ANALYSIS To compare the performance of the BASICDTC program and the propoed control cheme in thi paper, and in order to analyze their own characteritic of the three torque angle cloedloop control method of the propoed control cheme, the imulation model of BASICDTC and the three torque angle cloedloop control method of the propoed control cheme were etablihed, and then imulation wa carried out. The ame motor parameter were ued in both ytem. (a) tator flux amplitude of BASICDTC (b) tator flux amplitude of MethodFirt (c) tator flux amplitude of MethodSecond (d) tator flux amplitude of MethodThird The length of imulation time i 6 econd, and the given rotor mechanical angle peed are repectively 6rad/ and 6rad/. The ytem tart up when Load torque i 5N.m, and Load Torque i 2N.m when the time i 4 econd. The imulation reult were hown in Fig. (8) when the given rotor mechanical angle peed are repectively 6rad/. ʌ /Wb ʌ /Wb t/ (a) Stator flux amplitude of BASICDTC t/ (b) Stator flux amplitude of MethodFirt ʌ /Wb ʌ /Wb t/ (c) Stator flux amplitude of MethodSecond t/ (d) Stator flux amplitude of MethodThird Fig. (8). Waveform of tator flux amplitude when the rotor angular peed i 6rad per econd. A can be een from Fig. (8): compared with BASIC DTC, the three torque angle cloedloop control method of the propoed control cheme make the flux ripple ignificantly reduced, epecially at low peed. The flux ripple ha no ignificant difference when three torque angle cloedloop control method are compared with each other. And it wa indicated that the effect on reducing flux ripple of the three torque angle cloedloop control method i imilar. A can be een from Fig. (9): compared with BASIC DTC, the three torque angle cloedloop control method of the propoed control cheme make the torque ripple ignificantly reduced, epecially at low peed. The torque ripple ha no ignificant difference when three torque angle cloedloop control method are compared with each other. And it wa indicated that the effect on reducing the torque ripple of the three torque angle cloedloop control method i imilar. A can be een from Fig. (): compared with BASIC DTC, the three torque angle cloedloop control method of the propoed control cheme make the current waveform ditortion ignificantly reduced, epecially at low peed.

8 Study of Direct Torque Control Scheme for Induction Motor The Open Electrical & Electronic Engineering Journal, 25, Volume 9 67 The current waveform ditortion ha no ignificant difference when three torque angle cloedloop control method are compared with each other. And it wa indicated that the effect on reducing the current waveform ditortion of the three torque angle cloedloop control method i imilar ʌ /Wb ʌ /Wb t/ (a) Torque of BASICDTC t/ (d) Torque of MethodThird Fig. (9). Waveform of torque when the rotor angular peed i 6rad per econd. ʌ /Wb t/ (b) Torque of MethodFirt Ia/A t/ (a) Stator current of BASICDTC ʌ /Wb Ia/A t/ (c) Torque of MethodSecond t/ Fig. (). Contd (b) Stator current of MethodFirt

9 68 The Open Electrical & Electronic Engineering Journal, 25, Volume 9 Ji et al Ia/A 2 2 ʍr/rad t/ t/ (c) Stator current of MethodSecond (b) Speed of MethodFirt Ia/A 2 2 ʍr/rad t/ (d) Stator current of MethodThird Fig. (). Waveform of tator current when the rotor angular peed i 6rad per econd. A can be een from Fig. (): torque angle PI controller cloedloop control and torque angle compenation cloedloop control can be obtained at the ame peed dynamic repone a BASICDTC. The dynamic peed repone of torque angle difference cloedloop control i lower than BASICDTC, becaue it torque in the dynamic proce cannot maintain a contant maximum ʍr/rad t/ (c) Speed of MethodSecond ʍr/rad t/ (a) Speed of BASICDTC t/ (d) Speed of MethodThird Fig. (). Speed waveform when the rotor angular peed i 6rad per econd. CONCLUSION The DTC Scheme for induction motor baed on torque angle cloedloop control wa preented in thi paper. The control of induction motor wa realized uing three method

10 Study of Direct Torque Control Scheme for Induction Motor The Open Electrical & Electronic Engineering Journal, 25, Volume 9 69 of torque angle cloedloop control. The principle of three method of torque angle cloedloop control for the propoed cheme wa analyzed. Three method of torque angle cloedloop control improved the performance of the ytem in three area uch a flux ripple, torque ripple and current waveform ditortion. Three method of torque angle cloedloop control have their own characteritic: Torque angle difference cloedloop control ha a more imple ytem configuration, but it dynamic repone wa affected. Torque angle PI controller cloedloop control maintain the inherent advantage of the fat ytem dynamic repone, but the uage of PI regulator increae the difficulty of the ytem parameter deign. Torque angle compenation cloedloop control not only overcome the hortcoming of the other two method, while maintaining the fat dynamic repone, but alo it ha a imple ytem architecture. CONFLICT OF INTEREST The author confirm that thi article content ha no conflict of interet. ACKNOWLEDGEMENTS Declared none. REFERENCES [] B.K. Boe, Modern Power Electronic and AC drive. Prentice Hall, Upper Saddle River, 22. [2] F. Blachke, The principle of fieldorientation a applied to the Tranvector cloedloop control ytem for rotatingfield machine, Siemen Review, vol. 34, pp. 2722, 972. [3] M. Depenbrock, Direct elfcontrol (DSC) of inverterfed induction machine, IEEE Tranaction on Power Electronic, vol. 3, pp , 988. [4] Y. Xue, X. Xu, T.G. Habetler, and D.M. Divan, A low cot tator flux oriented voltage ource variable peed drive, In: Conference Record of the 99 IEEE Indutry Application Society Annual Meeting, vol., pp. 445, 99. [5] H.M. Kojabadi, and L. Chang, Comparative tudy of pole placement method in adaptive flux oberver, Control Engineering Practice, vol. 3, pp , 25. [6] I. Takahahi, and T. Noguchi, A new quickrepone and high efficiency control trategy of an induction machine, IEEE Tranaction on Indutry Application, vol. 22, pp ,986. [7] M. H. Toodehki, S. Hoeinnia, and J. Akari, Adaptive robut control of uncertain ytem with tate and input delay, International Journal of Control, Automation, and Sytem, vol. 8, pp.2222, 2. [8] A. Sivaubramanian, and B. Jayanand, Application of neural network tructure in voltage vector election of direct torque control induction motor, International Journal of Mechanic and Thermodynamic, vol., pp. 78, 2. [9] V. Kumar, Modified direct torque control of threephae induction motor drive with low ripple in flux and torque, Leonardo Journal of Science, vol. 8, pp. 2744, 2. [] S. Belkacem, F. Naceri, and R. Abdeemed, Improvement in DTCSVM of AC drive uing a new robut adaptive control algorithm, International Journal of Control, Automation, and Sytem, vol. 9, pp , 2. [] Y. Zhang, J. Zhu, Z. Zhao, W. Xu, and D. G. Dorrell, An improved direct torque control for threelevel inverterfed induction motor enorle drive, IEEE Tranaction on Power Electronic, vol. 27, pp. 5253, 22. [2] R. Rajendran, and Dr. N. devarajan, A comparative performance analyi of direct torque control cheme for induction motor drive, International Journal of Power Electronic and Drive Sytem, vol. 2, pp. 779, 22. [3] C.H. Krihna, J. Amarnath, and S. Kamakhiah, A implified SVPWM algorithm for multilevel inverter fed DTC of induction motor drive, International Journal of Engineering and Innovative Technology, vol., pp. 667, 22. [4] F.R. Haan, Modified direct torque control uing algorithm control of tator flux etimation and pace vector modulation baed on fuzzy logic control for achieving high performance from induction motor, IEEE Tranaction on Power Electronic, vol. 3, pp , 23. [5] F.R. Haan, and N.M.L. Tan, DTCSVM baed on pi torque and pi flux controller to achieve high performance of induction motor, Reearch Journal of Applied Science, vol. 7, pp , 24. [6] F.B. Salemand and N. Derbel, Performance analyi of DTCSVM liding mode controllerbaed parameter etimator of electric motor peed drive, Mathematical Problem in Engineering, vol. 24, pp., 24. Received: July 5, 25 Revied: Augut 5, 25 Accepted: September, 25 Ji et al.; Licenee Bentham Open. Thi i an open acce article licened under the term of the Creative Common Attribution NonCommercial Licene ( which permit unretricted, noncommercial ue, ditribution and reproduction in any medium, provided the work i properly cited.