Simulink Implementation of Induction Machine Model A Modular Approach

Transcription

1 Simulink Implementation of Induction Machine Model A Modular Approach Burak Ozpineci burak@ieee.org Oak Ridge National Laboratory P.O. Box 9 Oak Ridge, TN Abtract - In thi paper, a modular Simulink implementation of an induction machine model i decred in a tep-by-tep approach. With the modular ytem, each block olve one of the model equation; therefore, unlike black box model, all of the machine parameter are accele for control and verification purpoe. After the implementation, example are given with the model ued in different drive application, uch a open-loop contant V/Hz control and indirect vector control are given. Finally, the ue of the model a an induction generator i demontrated. I. INTRODUCTION Uually, when an electrical machine i imulated in circuit imulator like PSpice, it teady tate model i ued, but for electrical drive tudie, the tranient behavior i alo important. One advantage of Simulink over circuit imulator i the eae in modeling the tranient of electrical machine and drive and to include drive control in the imulation. A long a the equation are known, any drive or control algorithm can be modeled in Simulink. Hover, the equation by themelve are not alway enough; ome experience with differential equation olving i required. Simulink induction machine model are available in the literature [-], but they appear to be black-boxe with no internal detail. Some of them [-] recommend uing S- function, which are oftware ource code for Simulink block. Thi technique doe not fully utilize the por and eae of Simulink becaue S-function programming knowledge i required to acce the model variable. S- function run fater than dicrete Simulink block, but Simulink model can be made to run fater uing accelerator function or producing tand-alone Simulink model. Both of thee require additional expene and can be avoided if the imulation peed i not that critical. Another approach i uing the Simulink Por Sytem Blocket [] that can be purchaed with Simulink. Thi blocket alo make ue of S-function and i not a eay to work with a the ret of the Simulink block. Reference [5] refer to an implementation approach imilar to the one in thi paper but fail to give any detail. In thi paper, a modular, eay to undertand Simulink induction motor model i decred. With the modular ytem, each block olve one of the model equation; therefore, unlike black box model, all of the machine Leon M. Tolbert, tolbert@utk.edu Department of Electrical and Computer Engineering The Univerity of nneee Knoxville, TN parameter are accele for control and verification purpoe. Simulink induction machine model dicued in thi paper ha been featured in a recent graduate level text book [6], and it alo ha been ued by different cholar in the US [7-9], Korea, and Brazil [-] in their reearch. II. INDUCTION MOTOR MODEL The induction machine d-q or dynamic equivalent circuit i hown in Fig.. One of the mot popular induction motor model derived from thi equivalent circuit i Kraue model detailed in []. According to hi model, the modeling equation in flux linkage form are a follow: q ω e R = ω b vq Fd + ( + Fq ( ωb xl ω e R ω b vd + Fq + ( + F ( ωb xl d = d qr dr v q v d ( F F ω b vqr + mq ( ω b = qr ω b vdr + + md ( ω b ( F F = dr i q R L l =L -L m L lr =L r -L m R r ω e Ψ d i d L m i qr (ω e -ω r Ψ dr R L l =L -L m L lr =L r -L m R r ω e Ψ q Ψ q =F q Ψ d =F d (a (b L m Ψ qr =F qr Ψ dr =F dr i dr (ω e -ω r Ψ qr Fig.. Dynamic or d-q equivalent circuit of an induction machine. v qr v dr

2 Fq F qr = + xl (5 F d = + xl (6 iq = ( Fq xl (7 id = ( Fd xl (8 = ( (9 = ( ( p = ( Fdiq Fqid ωb ( dωr TL = J p ( where d : direct axi, q : quadrature axi, : tator variable, r : rotor variable, F ij i the flux linkage (i=q or d and j= or r, v q, v d : q and d axi tator voltage, v qr, v dr : q and d axi rotor voltage, F mq,f md : q and d axi magnetizing flux linkage, Rr : rotor reitance, R : tator reitance, X l : tator leakage reactance (ω e L l, X lr : rotor leakage reactance (ω e L lr, X ml : + +, xm xl i q, i d : q and d axi tator current, i qr, i dr : q and d axi rotor current, p : number of pole, J : moment of inertia, T e : electrical output torque, T L (or T l : load torque, ω e : tator angular electrical frequency, ω b : motor angular electrical bae frequency, and ω r : rotor angular electrical peed. For a quirrel cage induction machine a in the cae of thi paper, v qr and v dr in ( and ( are et to zero. An induction machine model can be repreented with five differential equation a een above. To olve thee equation, they have to be rearranged in the tate-pace form, x & = Ax + b where x = [ F ] T q Fd ωr i the tate vector. Note that Fij = ψ ij ωb, where F ij i the flux linkage (i=q or d and j= or r and ψ ij i the flux. In thi cae, tate-pace form can be achieved by inerting (5 and (6 in (- and collecting the imilar term together o that each tate derivative i a function of only other tate variable and model input. Then, the modeling equation (- and of a quirrel cage induction motor in tate-pace become q ω e R = ω + + b vq Fd F q ( ω b xl xl ω e R ω b vd + Fq + + F ( ω b xl xl d = d ω b + Fq + F (5 ω b xl qr = qr dr = ω + + b Fd F dr (6 ω b xl dωr p = ( TL (7 J III. SIMULINK IMPLEMENTATION The input of a quirrel cage induction machine are the three-phae voltage, their fundamental frequency, and the load torque. The output, on the other hand, are the threephae current, the electrical torque, and the rotor peed. The d-q model require that all the three-phae variable have to be tranformed to the two-phae ynchronouly rotating frame. Conequently, the induction machine model will have block tranforming the three-phae voltage to the d-q frame and the d-q current back to three-phae. The induction machine model implemented in thi paper i hown in Fig.. It conit of five major block: the o-n converion, abc-yn converion, yn-abc converion, unit vector calculation, and the induction machine d-q model block. The following ubection will explain each block. A. o-n converion block Thi block i required for an iolated neutral ytem, otherwie it can be bypaed. The tranformation done by thi block can be repreented a follow: 5 vao vbo theta-e theta-e vco vao van vbo vbn vco vcn o-to-n in(theta-e theta-e co(theta-e unit vector van vbn vcn co(theta-e in(theta-e abc-yn vq vd vq vd iq id Induction Motor d-q- model 5 iq ia id co(theta-e in(theta-e ic yn-abc Fig.. The complete induction machine Simulink model. ia ic

3 v v v an bn cn + = + v v v + ao bo co (8 Thi i implemented in Simulink by paing the input voltage through a Simulink Matrix Gain block, which contain the above tranformation matrix. B. Unit vector calculation block Unit vector coθ e and inθ e are ued in vector rotation block, abc-yn converion block and yn-abc converion block. The angle, θ e i calculated directly by integrating the frequency of the input three-phae voltage, ω e. θ e = ω e (9 The unit vector are obtained imply by taking the ine and coine of θ e. Thi block i alo where the initial rotor poition can be inerted, if needed, by adding an initial condition to the Simulink Integrator block. Note that the reult of the integration in (9 i reet to zero each time it reache π radian o that the angle alway varie beten and π. C. abc-yn converion block To convert three-phae voltage to voltage in the twophae ynchronouly rotating frame, they are firt converted to two-phae tationary frame uing ( and then from the tationary frame to the ynchronouly rotating frame uing (. v an v q = vbn ( vd v cn v q = vq coθe vd inθe ( vd = vq inθe + vd coθe where the upercript refer to tationary frame. Equation ( i implemented imilar to (8 becaue it i a imple matrix tranformation. Equation (, hover, contain the unit vector; therefore, a imple matrix tranformation cannot be ued. Intead, vq and vd are calculated uing baic Simulink Sum and Product block. D. yn-abc converion block Thi block doe the oppoite of the abc-yn converion block for the current variable uing ( and ( following the ame implementation technique a before. i i q d = v q coθe + vd inθe = vq inθe + vd coθe i a = ic i i q d ( ( E. Induction machine d-q model block Fig. how the inide of thi block where each equation from the induction machine model i implemented in a different block. Firt conider the flux linkage tate equation becaue flux linkage are required to calculate all the other variable. Thee equation could be implemented uing Simulink State-pace block, but to have acce to each point of the model, implementation uing dicrete block i preferred. Fig. how what i inide of the block olving (. All the other block in Column are imilar to thi block. Simulation Tip : Do not ue derivative. Some ignal will have dicontinuitie and/or ripple that would reult in pike when differentiated. Intead try to ue integral and baic arithmetic. Simulation Tip : Beware of the algebraic loop. Algebraic loop might appear when there i a feedback loop in your ytem, i.e. when the calculation of the preent value of a variable require it preent value. When Simulink notice an algebraic loop, it will try to olve it. If not, it will top the imulation. An algebraic loop can be broken by adding a Simulink Memory block, which delay it input ignal by one ampling time; hover, thi might affect the operation of the ytem. If pole, avoid algebraic loop. Once the flux linkage are calculated, the ret of the equation can be implemented without any difficulty. The block olving the ret of the equation are alo organized in column. The block in Column olve (5 and (6. Equation (7- ue the flux linkage to olve for the tator and rotor d and q current. The fourth and the lat column include the electrical torque calculation from ( and the rotor peed calculation uing the lat tate equation (; the implementation of which i hown in Fig. 5. The rotor peed information i required for the calculation of the rotor flux linkage in Column ; therefore, it i fed back to two block in thi column.

4 Column Column Column Column Fig. Fq iq Fd id vq vd Fd Vq Fq Fq Fq Vd Fd Fd Fq Fd Fq Fd Fq iq iq Fd id id iq id 6 5 The reulting model i modular and eay to follow. Any variable can be eaily traced uing the Simulink Scope block. The block in the firt two column calculate the flux linkage, which can be ued in vector control ytem in a flux loop. The block in Column calculate all the current variable, which can be ued in the current loop of any current control ytem and to calculate the three-phae current. The two block of Column, on the other hand, calculate the torque and the peed of the induction machine, which again can be ued in torque control or peed control loop. Thee two variable can alo be ued to calculate the Vq Fd /wb Xmtar/Xlr /wb Xml/Xlr Sum Product R/Xl R/Xl Sum Fig.. Induction machine dynamic model implementation in Simulink. wb wb (Xmtar/Xl- (Xml/Xl- / Integrator Fig.. Implementation of ( in Simulink. Fq output por of the machine. IV. SIMULATION RESULTS A. Initialization To imulate the machine in Simulink, the Simulink model ha to be initialized firt o that it will know all the machine parameter. For thi reaon, an initialization file containing all the machine parameter i formed. Thi file aign value to the machine parameter variable in the Simulink model. For example, Figure 6 how the initialization file for a kw induction machine. Before the imulation, thi file ha to be executed at the Matlab prompt, otherwie Simulink will diplay an error meage. Note that thi initialization file i the only machine pecific part of the Simulink model that need to be changed when the machine being imulated i changed. B. Direct ac tart-up To tet the model, the induction machine with the parameter given in Fig. 6 i imulated by applying V three-phae ac voltage at 6Hz with jut an inertia load. Sum7 p/(j p/(j / Integrator Fig. 5. Implementation of ( in Simulink.

5 To Initialize Double-click /wb vq vao vao vao vao ia Gain vd vbo vbo vbo vbo i Contant vco vco vco vco ic Command Voltage Generator -phae PWM Inverter Mux6 Subytem Induction Machine Model Mux5 T iemdc.mat To File Mux7 Fig. 8. Open loop contant V/Hz control Simulink model. load diturbance can be oberved. Fig. 6. Induction machine model initialization file. Fig. 7 how the three-phae current, torque, and peed of the machine. The machine accelerate and come to teady tate at. with a mall lip becaue of the inertia load. C. Open-loop contant V/Hz operation Fig. 8 how the implementation of open-loop contant V/Hz control of an induction machine. Thi figure ha two new block: command voltage generator and -phae PWM inverter block. The firt one generate the three-phae voltage command, and it i nothing more than a yn-abc block explained earlier. The latter firt compare the reference voltage, v ref to the command voltage to generate PWM ignal for each phae, then ue thee ignal to drive three Simulink Switch block witching beten +V d / and V d / (V d : dc link voltage. The open-loop contant V/Hz operation i imulated for. ramping up and down the peed command and applying tep load torque. The reult are plotted in Fig. 9 where the repone of the drive to change in the peed command and ia,, and ic, A T e and, N.m T l T e Simulation Tip : Do not elect a large ampling time. A a rule of thumb, the ampling time hould be elected no larger than one-tenth of the mallet time contant in the model. For example, for a khz witching frequency, the witching period i m; then, a ampling time of.m would do the job. Do not elect a maller ampling time than required, either. A maller ampling time doe not necearily increae accuracy but the imulation time increae. D. Indirect Vector Control operation By adding a vector control block to Fig. 8 and d-q current feedback, the induction machine can be imulated under indirect vector control. The reulting block diagram i hown in Fig.. Fig., on the other hand, how the vector control block. Note that, the current feedback for the current controller come directly from the induction machine d-q model through Simulink Goto and From block. The reaon for uing thee block i to reduce the clutter of ignal line. The reult of the vector control imulation are hown in Fig. where the peed command and load torque profile are imilar to the one decred earlier. A een in thi figure, the peed tracking and the repone to the torque diturbance i a,, and ic, A - and, N.m T l T e ω eand ωr, rad/ec 6 ω e ω r Time, Fig. 7. Simulation reult direct ac tartup. ω r and ω r, rad/ec ω r ω r Time, Fig. 9. Simulation reult - open loop contant V/Hz control.

6 To Initializ e Double-c lick vq vd wl Torque and Flux Control vao vao vq vao vao vbo vbo vd vbo vbo vco vco vco vco Sum Command Voltage - phae PWM Inverter Generator Sub y tem ia ic Mux 6 Mux5 ia iemdc.mat To File i a, i b, and i c, A Induction Machine Model are excellent. E. Induction generator operation Recently, with increaing importance of ditruted energy reource uch a wind turbine and microturbine, there i rened attention to induction generator. The model decred in thi paper can alo be ued to model an induction generator. The only change compared to motoring operation i that an external mover rotate the motor at a peed higher than the ynchronou peed. Thi can be implemented in Simulink by uing a negative load torque intead of a poitive one ued for motoring. Fig. how the torque-peed curve of the induction machine in both motoring and generating region. The machine accelerate freely to almot the ynchronou peed with direct ac tart-up, and then a large negative torque i applied o that the machine tart generating. V. CONCLUSIONS In thi paper, implementation of a modular Simulink model for induction machine imulation ha been introduced. Unlike mot other induction machine model implementation, with thi model, the uer ha acce to all the internal variable for getting an inight into the machine operation. Any machine control algorithm can be imulated in the Simulink environment with thi model without actually uing etimator. If need be, when the etimator are developed, they can be verified uing the ignal in the machine model. The eae of implementing control with thi model i alo demontrated with everal example. Finally, the operation of the model to imulate both induction motor and generator ha been hown o that there i no need for different model for different application. Mux7 Fig.. Indirect vector control Simulink model. and, N.m. ω r and ωr, rad/ec REFERENCES: [] M. L. de Aguiar, M. M. Cad, The concept of complex tranfer function applied to the modeling of induction motor, Por engineering Society Winter Meeting,, pp [] A. Dumitrecu, D. Fodor, T. Jokinen, M. Rou, S. Bucurencio, Modeling and imulation of electric drive ytem uing Matlab/Simulink environment, International Conference on Electric Machine and Drive (IEMD, 999, pp [] S. Wade, M. W. Dunnigan, B. W. William, Modeling and imulation of induction machine vector control with rotor reitance identification, IEEE Tranaction on Por Electronic, vol., no., May 997, pp [] H. Le-Huy, Modeling and imulation of electrical drive uing Matlab/Simulink and Por Sytem Blocket, The 7th Annual Conference of the IEEE Indutrial Electronic Society (IECON', Denver/Colorado, pp [5] L. Tang, M. F. Rahman, A new direct torque control trategy for flux and torque ripple reduction for induction motor drive a Matlab/Simulink model, IEEE International Electric Machine and Drive Conference,, pp [6] Bimal K. Boe, Modern Por Electronic and AC Drive, Prentice Time, Fig.. Simulation reult indirect vector control. Motoring T e Generating 5 PI Sum PI Controller Saturation [iq] From Sum PI PI Controller Saturation vq T e, N.m. -5 [id] From Id id Sum PI PI Controller Saturation vd - Lm/(Tr -5 fluxr abolute peak rotor flux Gain u u Ab Math Function Fig.. Vector control block in Simulink. Product wl ω r, rad/ec Fig.. Torque-peed curve in motoring and generation mode.

7 Hall,. [7] B. Ozpineci, B.K. Boe, "A oft-witched performance enhanced high frequency non-reonant link phae-controlled converter for ac motor drive," The th Annual Conference of the IEEE Indutrial Electronic Society (IECON'98, Aachen/Germany, 998, vol., pp [8] H. Li, B.Ozpineci and B.K.Boe, "A oft-witched high frequency nonreonant link integral pule modulated dc-dc converter for ac motor drive," The th Annual Conference of the IEEE Indutrial Electronic Society (IECON'98, Aachen/Germany, 998, vol., pp [9] Burak Ozpineci, Leon M. Tolbert, Syed K. Ilam, Md. Haanuzzaman, "Effect of ilicon carbide (SiC por device on pwm inverter loe," The 7th Annual Conference of the IEEE Indutrial Electronic Society (IECON', Denver/Colorado,,pp [] J. O. P. Pinto, B. K. Boe, L. E. B. Silva, M. P. Kazmierkowki, "A neural-network-baed pace-vector PWM controller for voltage-fed inverter induction motor drive," IEEE Tranaction on Indutry Application, vol. 6, no. 6, Nov./Dec., pp [] J. O. P. Pinto, B. K. Boe, L. E. B. Silva, "A tator flux oriented vectorcontrolled induction motor drive with pace vector PWM and flux vector ynthei by neural network," IEEE Indutry Application Society Annual Meeting, Rome/Italy,, pp [] J. O. P. Pinto, B. K. Boe, L. E. Borge, M. P. Kazmierkowki, "A neural-network-baed pace-vector PWM controller for voltage-fed inverter induction motor drive," IEEE Indutry Application Society Annual Meeting, Phoenix/Arizona, 999, pp [] P. C. Kraue, Analyi of Electric Machinery, McGraw-Hill Book Company, 986.