TORQUE RIPPLE REDUCTION IN DIRECT TORQUE CONTROLLED INDUCTION MOTOR DRIVE BY USING FUZZY CONTROLLER

Transcription

1 TORQUE RIPPLE REDUCTION IN DIRECT TORQUE CONTROLLED INDUCTION MOTOR DRIVE BY USING FUZZY CONTROLLER A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF TECHNOLOGY IN POWER CONTROL AND DRIVES By G. Venkata RamaKrihna. Department of Electrical Engineering National Intitute of Technology Rourkela

2 TORQUE RIPPLE REDUCTION IN DIRECT TORQUE CONTROLLED INDUCTION MOTOR DRIVE BY USING FUZZY CONTROLLER A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF TECHNOLOGY IN POWER CONTROL AND DRIVES By G.VENKATA RAMAKRISHNA Under the Guidance of Prof. A K PANDA Department of Electrical Engineering National Intitute of Technology Rourkela

3 National Intitute of Technology Rourkela CERTIFICATE Thi i to certify that the thei entitled, Torque ripple reduction in Direct Torque controlled Induction Motor Drive by uing Fuzzy Controller ubmitted by Mr G.Venkata RamaKrihna in partial fulfillment of the requirement for the award of MASTER of Technology Degree in Electrical Engineering with pecialization in Power Control and Drive at the National Intitute of Technology, Rourkela (Deemed Univerity) i an authentic work carried out by him/her under my/our uperviion and guidance. To the bet of my knowledge, the matter embodied in the thei ha not been ubmitted to any other Univerity/ Intitute for the award of any degree or diploma. Date: Prof A K Panda Dept of Electrical Engineering. National Intitute of Technology Rourkela

4 ACKNOWLEDGEMENT I would like to thank my upervior Prof. Dr. A. K. Panda, Department of Electrical Engineering for hi valuable guidance and contant motivation and upport during the coure of my thei work in the lat one year. I am thankful to Prof. Dr. P. K. Nanda, Head of the Electrical Engineering department for hi valuable uggetion and contant encouragement all through the thei work. I am extremely thankful to Prof. Dr. P. C. Panda, department of Electrical Engineering, who indirectly involved in my thei work by providing Power Sytem Modeling lab. I am thankful to Mr. T. Purna Chandra Rao for hi valuable help a Power Sytem modeling lab in charge. I will be failing in my duty if I do not mention the laboratory taff and adminitrative taff of thi department for their timely help. I would like to thank all whoe direct and indirect upport helped me completing my thei in time. My parent and my brother Mr. G. V. Subhah, receive my deepet gratitude and love for their dedication and the many year of upport that provided the foundation for thi work. G. Venkata. RamaKrihna M.Tech (Power Control and Drive)

5 CONTENTS Title Page no Abtract Lit of figure Lit of table iii iv vi 1 INTRODUCTION 1.1 Hitorical review 1 1. Feature of Direct Torque Control Statement of Problem Overview of thei 9 INDUCTION MOTOR MODEL AND GENERALITIES.1 Equation of the Induction Motor model Introduction Voltage equation Applying Park Tranformation Voltage Matrix Equation 13. Space Phaor Notation Introduction 15.. Current Space Phaor Flux Linkage Space Phaor Space Phaor for Stator and Rotor Voltage 18.3 Torque Expreion.3.1. Introduction i

6 .3.. Deduction of Torque equation Torque Contant 4.4 SIMULINK Model 5.5 Interim concluion 9 3 DIRECT TORQUE CONTROL OF INDUCTION MOTORS 3.1 Introduction DC Drive Analogy DTC Controller Voltage Source Inverter DTC Schematic SIMULINK Model Interim Reult 39 4 FUZZY LOGIC CONTROLLERS 4.1 Introduction to FLC Why Fuzzy Logic Controller Fuzzy Logic Controller Fuzzification Fuzzy Inference Defuzzification 44 5 TORQUE RIPPLE MINIMIZATION IN DTC DRIVES 5.1 Introduction Duty Ratio Control Deign of Duty ratio Fuzzy Controller Interim Concluion 5 ii

7 6 SIMULATION RESULTS 54 7 CONCLUSIONS AND FUTURE WORK 7.1 Concluion Direct Torque Control DTC with Duty Ratio Fuzzy Controller Future work 58 REFERENSES 60 iii

8 ABSTRACT Direct torque control (DTC) of an induction motor fed by a voltage ource inverter i a imple cheme that doe not need long computation time and can be implanted without mechanical peed enor and i inenitive to parameter variation. In principle, the motor terminal voltage and current are ampled and ued to etimate the motor flux and torque. Baed on etimate of the flux poition and the intantaneou error in torque and tator flux magnitude, a voltage vector i elected to retrict the torque and the flux error within their repective torque and flux hyterei band. In the conventional DTC, the elected voltage vector i applied for the whole witching period regardle of the magnitude of the torque error. Thi can reult in high torque ripple. A better drive performance can be achieved by varying the duty ratio of the elected voltage vector during each witching period according to the magnitude of the torque error and poition of the tator flux. A duty ratio control cheme for an inverter-fed induction machine uing DTC method i preented in thi thei. The ue of the duty ratio control reulted in improved teady tate torque repone, with le torque ripple than the conventional DTC. Fuzzy logic control wa ued to implement the duty ratio controller. The effectivene of the duty ratio method wa verified by imulation uing MATLAB/SIMULINK. iv

9 LIST OF FIGURES FIGURE PAGE NUMBER Fig 1.1 Block diagram for AC motor Drive Sytem.. 4 Fig 1. Direct Torque Control Scheme.. 6 Fig Effect of Duty Ratio Control on Torque ripple.. 7 Fig.1 Cro ection of elementary ymmetrical three Phae Induction motor.. 10 Fig. Scheme of equivalent axi Tranformation.. 1 Fig.3 Space phaor repreentation of three phae quantitie 15 Fig.4 - Cro ection of an elementary three phae machine, with Two different frame of reference 16 Fig.5 Stator current pace phaor expreed in accordance with The rotational frame fixed to the rotor and tationary frame. 1 Fixed to tator Fig.6 SIMULINK Model for induction motor.. 7 Fig.7 Induction machine ubytem model.. 7 Fig.8 - Induction motor tator current waveform in tationary Rotating reference frame... 8 Fig.9 Torque and peed waveform of induction motor 8 Fig 3.1 DC Motor model Fig 3. Voltage Source Inverter Fig 3.3 Stator flux vector locu Fig 3.4 SIMULINK Model for conventional DTC Fig 3.5 Electric Torque waveform for conventional DTC Fig 4.1 Block diagram for Mamdani type fuzzy controller.. 4 Fig 4. Memberhip function.. 43 Fig 4.3 Level of Memberhip function.. 44 Fig Block diagram for DTC with duty ratio fuzzy controller Fig 5. Memberhip function ditribution for torque error (i/p). 48 Fig 5.3 MF ditribution for flux poition (input) Fig 5.4 Mf ditribution for duty ratio (output) 49 Fig 5.5 General view of duty ratio fuzzy controller 51 v

10 Fig 5.6 Voltage and Torque witching in conventional DTC 5 Fig 5.7 Voltage and Torque witching in DTC with duty ratio fuzzy controller Fig 6.1 SIMULINK Model for DTC with duty ratio fuzzy controller 54 Fig 6. Electric torque of induction motor uing conventional DTC. 55 Fig 6.3 Electric torque of induction motor uing DTC with Duty ratio Fuzzy controller Fig 6.4 Induction motor tator current waveform Fig 6.5 Induction motor Stator and Rotor flux phaor locu. 57 LIST OF TABLES TABLE PAGE NUMBER.1 Torque contant value General election table for conventional DTC conventional DTC lookup Table Rule for duty ratio fuzzy controller Parameter of three phae induction motor ued in imulation 54 vi

11 Chapter 1 INTRODUCTION Hitorical Review Feature of Direct Torque Control Statement of Problem Overview of Thei

12 INTRODUCTION 1.1.HISTORICAL REVIEW: The hitory of electrical motor goe back a far a 180, when Han Chritian Oerted dicovered the magnetic effect of an electric current. One year later, Michael Faraday dicovered the electromagnetic rotation and built the firt primitive D.C. motor. Faraday went on to dicover electromagnetic induction in 1831, but it wa not until 1883 that Tela invented the A.C aynchronou motor []. Currently, the main type of electric motor are till the ame, DC, AC aynchronou and Synchronou, all baed on Oerted. Faraday and Tela' theorie developed and dicovered more than a hundred year ago. Before the introduction of micro-controller and high witching frequency emiconductor device, variable peed actuator were dominated by DC motor. Today, uing modern high witching frequency power converter controlled by microcontroller, the frequency, phae and magnitude of the input to an AC motor can be changed and hence the motor peed and torque can be controlled. AC motor combined with their drive have replaced DC motor in indutrial application due to their lower cot, better reliability, lower weight, and reduced maintenance requirement. Squirrel cage Induction motor are more widely ued than all the ret of the electric motor put together a they have all the advantage of AC motor and they are eay to build []. The main advantage i that induction motor do not require an electrical connection between tationary and rotating part of the motor. Therefore, they do not need any mechanical commutator (bruhe), leading to the fact that they are maintenance free motor. Induction motor alo have low weight and inertia, high efficiency and a high overload capability. Therefore, they are cheaper and more robut, and le prove to any failure at high peed. Furthermore, the motor can work in exploive environment becaue no park are produced. Taking into account all the advantage outlined above, induction motor mut be conidered the perfect electrical to mechanical energy converter. However, mechanical energy i more than often required at variable peed, where the peed control ytem i not a trivial matter. The only effective way of producing an infinitely variable induction motor peed drive i to upply the induction motor with three phae voltage of variable frequency and variable amplitude. A variable frequency i required becaue the rotor

13 peed depend on the peed of the rotating magnetic field provided by the tator. A variable voltage i required becaue the motor impedance reduce at low frequencie and conequently the current ha to be limited by mean of reducing the upply voltage [3] [4] [5]. Before the day of power electronic, a limited peed control of induction motor wa achieved by witching the three-tator winding from delta connection to tar connection, allowing the voltage at the motor winding to be reduced. Induction motor are alo available with more than three tator winding to allow a change of the number of pole pair. However, a motor with everal winding i more expenive becaue more than three connection to the motor are needed and only certain dicrete peed are available. Another alternative method of peed control can be realized by mean of a wound rotor induction motor, where the rotor winding end are brought out to lip ring. However, thi method obviouly remove mot of the advantage of induction motor and it alo introduce additional loe. By connecting reitor or reactance in erie with the tator winding of the induction motor, poor performance i achieved. With the enormou advance made in emiconductor technology during the lat 0 year, the required condition for developing a proper induction motor drive are preent. Thee condition can be divided mainly in two group: The decreaing cot and improved performance in power electronic witching device.[5] The poibility of implementing complex algorithm in the new microproceor. However, one precondition had to be made, which wa the development of uitable method to control the peed of induction motor, becaue in contrat to it mechanical implicity their complexity regarding their mathematical tructure (multivariable and non-linear) i not a trivial matter. Hitorically, everal general controller have been developed: Scalar controller: Depite the fact that "Voltage-Frequency" (V/f) i the implet controller, it i the mot widepread, being in the majority of the indutrial application. It i known a a calar control and act by impoing a contant relation between voltage and frequency. The tructure i very imple and it i normally ued without peed feedback. However, thi controller doen t achieve a good accuracy in both peed and torque repone, mainly due to the fact that the tator flux and the torque are not directly controlled. Even though, a long a the parameter are identified, the accuracy in the peed can be % (except in a very low peed), and the dynamic repone can be approximately around 50m [6]. 3

14 1.1.. Vector Controller: In thee type of controller, there are control loop for controlling both the torque and the flux [BOS 1]. The mot widepread controller of thi type are the one that ue vector tranform uch a either Park or Ku [3]. It accuracy can reach value uch a 0.5% regarding the peed and % regarding the torque, even when at tand till. The main diadvantage are the huge computational capability required and the compulory good identification of the motor parameter [7] [8] [9] Field Acceleration method: Thi method i baed on maintaining the amplitude and the phae of the tator current contant, while avoiding electromagnetic tranient. Therefore, the equation ued can be implified aving the vector tranformation, which occur in vector controller. Thi technique ha achieved ome computational reduction, thu overcoming the main problem with vector controller and allowing thi method to become an important alternative to vector controller [10] [11] [1]. Fig. 1.1 how a block diagram of an AC motor drive ytem [4]. A ingle-phae or three-phae AC power upply and an AC/DC converter provide a DC input to an inverter. A micro-controller decide the witching tate for the inverter to control the motor torque or peed. A ening unit feed back terminal value uch a motor peed, voltage and current to the micro-controller a needed for the cloed-loop control of the motor. Controller ued in AC motor drive are generally referred to a vector or field-oriented controller mentioned above. AC/DC converter INVETER AC MOTOR LOAD Control ignal µ CONTROLLER SENSING UNIT Fig 1.1.Block diagram for AC motor drive ytem The field-oriented control method are complex and enitive to inaccuracy in the motor parameter value. Therefore, in thi field, a coniderable reearch effort i devoted. The aim being to find even impler method of peed control for induction machine. One method, which i popular at the moment, i Direct Torque Control (DTC). Thi method ha emerged 4

15 over the lat decade to become one poible alternative to the well-known Vector Control of Induction Machine. It main characteritic i the good performance, obtaining reult a good a the claical vector control but with everal advantage baed on it impler tructure and control diagram FEATURES OF DIRECT TORQUE CONTROL : DTC main feature are a follow: Direct control of flux and torque. Indirect control of tator current and voltage. Approximately inuoidal tator fluxe and tator current. High dynamic performance even at tand till. The main advantage of DTC are: Abence of co-ordinate tranform. Abence of voltage modulator block, a well a other controller uch a PID for motor flux and torque. Minimal torque repone time, even better than the vector controller. However, ome diadvantage are alo preent uch a: Poible problem during tarting. Requirement of torque and flux etimator, implying the conequent parameter identification. Inherent torque and tator flux ripple. 5

16 1.3. STATEMENT OF THE PROBLEM: A implified variation of field orientation known a direct torque control (DTC) wa developed by Takahahi [1] and Depenbrock [13]. Fig. 1. how a DTC of an induction motor. In direct torque controlled induction motor drive, it i poible to control directly the tator flux linkage and the electromagnetic torque by the election of an optimum inverter witching tate. The election of the witching tate i made to retrict the flux and the torque error within their repective hyterei band and to obtain the fatet torque repone and highet efficiency at every intant. DTC i impler than field-oriented control and le dependent on the motor model, ince the tator reitance value i the only machine parameter ued to etimate the tator flux. One of the diadvantage of DTC i the high torque ripple. Under contant load in teady tate, an active witching tate caue the torque to continue to increae pat it reference value until the end of the witching period. Then a zero voltage vector i applied for the next witching period cauing the torque to continue to decreae below it reference value until the end of the witching period. That reult in high torque ψ ref ψ LOOKUP TABLE INVERTER T ref T FLUX POSITION CONTROL ESTIMATION OF TORQUE AND FLUX IM LOAD Fig 1..Direct torque control cheme ripple a hown in Fig. 1.3(a). A poible olution to reduce the torque ripple i to ue a high witching frequency; however, that require expenive proceor and witching device. A le expenive olution i to ue duty ratio control. In DTC with duty ratio control, the 6

17 elected voltage vector i applied for a part of the witching period rather than the complete witching period a in conventional DTC. (a) Conventional DTC (b) DTC with duty ratio control Fig 1.3 Effect of duty ratio control on torque ripple 7

18 By applying a nonzero voltage vector for only a portion of the witching period, and the zero voltage vector for the remainder of the period, the effective witching frequency i doubled. Therefore, over any ingle witching period, the torque variation above and below the average value are maller, a hown `in Fig. 1.3(b). Further, becaue the duty ratio i controlled, the average tator voltage i adjuted directly. There i no need to make coare correction by the ue of multiple witching period with a nonzero voltage vector or a whole witching period with a zero voltage vector. The average phae voltage i adjuted more moothly, and the overall torque ripple i reduced. The ue of a duty ratio fuzzy controller i propoed in [3][14]. The theme of thi thei i to verify by imulation that a DTC with a duty ratio fuzzy controller reduce the torque ripple compared to conventional DTC. 8

19 1.4. OVERVIEW OF THE THESIS: Chapter II give a review of the induction motor modeling, and of the field-oriented control method and their limitation. A SIMULINK model i developed for the induction machine model and imulated for three phaor to two phae tranformation of induction machine model. Chapter III cover the fundamental of the principle of DTC of induction motor and method to deal with DTC limitation on flux etimation accuracy are dicued in detail. A SIMULINK model and MATLAB iterative technique programme are ued to imulate the conventional DTC of induction motor. Chapter IV detail the theory and introduction of fuzzy logic controller ued in the duty ratio controller ued to minimize the torque ripple in DTC Chapter V detail the deign of the duty ratio fuzzy controller ued to minimize the torque ripple in DTC. The fuzzy logic controller determine the duty ratio according to torque and flux error and flux poition. SIMULINK/MATLAB i ued to imulate thi DTC with duty ratio fuzzy control. Chapter VI cover the reult and dicuion on comparion of conventional DTC and fuzzy baed DTC with duty ratio controller. The imulation reult are preented and compared to the theoretical value. Chapter VII give the ummary, concluion and direction for future work. 9

20 Chapter INDUCTION MOTOR MODEL AND GENERALITIES Equation of the Induction Motor Model Space phaor Notation Torque Expreion SIMULINK model Interim Concluion

21 INDUCTION MOTOR MODEL AND GENERALITIES.1 EQUATIONS OF THE INDUCTION MACHINE MODEL:.1.1 Introduction: A dynamic model of the machine ubjected to control mut be known in order to undertand and deign vector controlled drive. Due to the fact that every good control ha to face any poible change of the plant, it could be aid that the dynamic model of the machine could be jut a good approximation of the real plant. Neverthele, the model hould incorporate all the important dynamic effect occurring during both teady-tate and tranient operation. Furthermore, it hould be valid for any change in the inverter upply uch a voltage or current [3] [4]. Such a model can be obtained by mean of either the pace vector phaor theory or two-axi theory of electrical machine. Depite the compactne and the implicity of the pace phaor theory, both method are actually cloe and both method will be explained. For implicity, the induction motor conidered will have the following aumption: Symmetrical two-pole, three phae winding. The lotting effect are neglected. The permeability of the iron part i infinite. The flux denity i radial in the air gap. Iron loe are neglected. The tator and the rotor winding are implified a a ingle, multi-turn full pitch coil ituated on the two ide of the air gap..1. Cro ection of elementary ymmetrical three phae induction motor 10

22 .1. Voltage equation. The tator voltage will be formulated in thi ection from the motor natural frame, which i the tationary reference frame fixed to the tator. In a imilar way, the rotor voltage will be formulated to the rotating frame fixed to the rotor. In the tationary reference frame, the equation can be expreed a follow: dψ A ( t) V A = R ia ( t) (.1) dt dψ B ( t) V B = R ib ( t) (.) dt dψ C ( t) VC = RiC ( t) (.3) dt Similar expreion can be obtained for the rotor: () dψ () ra t VrA = RrirA t (.4) dt () dψ () rb t VrB = RrirB t (.5) dt () dψ () rc t VrC = RrirC t (.6) dt The intantaneou tator flux linkage value per phae can be expreed a: ψ = Li + Mi + Mi + M coθ i + M co( θ + π/ 3) i + M co( θ + 4 π/ 3) i A a B C r m ra r m rb r m rc ψ = M i + Li + Mi + M co( θ + 4 π/ 3) i + M coθ i + M co( θ + π/ 3) i A a B C r m ra r m rb r m rc ψ = M i + Mi + Li + M co( θ + π/ 3) i + M co( θ + 4 π/ 3) i + M co θ i A a B C r m ra r m rb r m rc (.7) In a imilar way, the rotor flux linkage can be expreed a follow: = ψra M co( θ ) i + M co( θ + π/ 3) i + M co( θ + 4 π/ 3) i + Li + Mi + Mi = r m A r m B r m C r ra r rb r rc ψrb M co( θ + 4 π/3) i + M co( θ ) i + M co( θ + π/3) i + Mi + Li + Mi = r m A r m B r m C r ra r rb r rc ψrc M co( θ + π/ 3) i + M co( θ + 4 π/ 3) i + M co( θ ) i + Mi + Mi + Li r m A r m B r m C r ra r rb r rc (.8) Taking into account all the previou equation, and uing the matrix notation in order to compact all the expreion, the following expreion i obtained: 11

23 V R + p pm pm pm coθ pm coθ pm coθ A L r m r ml r ml V pm R + pl pm pm co θ pm coθ pm coθ B r ml r m r ml V pm pm R + pl pm co θ pm coθ pm co θ C r ml r ml r m = V pm coθ pm co θ pm co θ R + pl pm pm V V ra r m r ml r ml r r r rb rc pm co θ pm co θ pm co θ pm R + pl pm i r ml r m r ml r r r r rb pm coθ pm co θ pm coθ pm pm R + pl i r m r ml r m r r r r rc r ia i B i C i ra (.9).1.3 Applying Park tranform: In order to reduce the expreion of the induction motor equation voltage given in equation.1 to equation.6 and obtain contant coefficient in the differential equation, the Park tranform will be applied. Phyically, it can be undertood a tranforming the three winding of the induction motor to jut two winding, a it i hown in figure. [3]... Scheme of equivalent axi tranformation In the ymmetrical three-phae machine, the direct- and the quadrature-axi tator magnitude are fictitiou. The equivalencie for thee direct (D) and quadrature (Q) magnitude with the magnitude per phae are a follow: V co co( /3) co( / 3) D θ θ π θ+ π V V = c. in θ in( θ π/ 3) in( θ+ π/3). V Q V 0 1/ 1/ 1/ V A B C (.10) 1

24 V co in 1/ A θ θ VD V = c. co( θ π/3) in( θ π /3) 1/. V B Q V C co( θ + π/ 3) in( θ + π/ 3) 1/ V (.11) Where "c" i a contant that can take either the value /3 or 1 for the o-called non-power invariant form or the value /3 for the power-invariant form a it i explained in ection.3.3. Thee previou equation can be applied a well for any other magnitude uch a current and fluxe. Notice how the expreion.9 can be implified into a much maller expreion in.1 by mean of applying the mentioned Park' tranform. VD R+ pl Lpθ plm Lm( Pw. m+ pθr i V Q Lp θ R pl Lm( Pw. m pθr) pl + + i m =. V rα plm Lm( pθ P. wm) R i r+ plr Lrp θ r Vr β Lm( pθ Pw. m) pl i m Lrpθr Rr+ plr where L =L -L m, L r =L r -L m and Lm D Q rα rβ (.1) 3 = M r (.13).1.4 Voltage matrix equation: If the matrix expreion.1 i implified, new matrixe are obtained a hown in equation Fixed to the tator. It mean that w = 0 and conequently w = -w. r m V R + pl 0 pl 0 i D D m R V 0 + pl 0 pl i Q m Q =. V pl P. w L R + pl P. w L i rd m m m r r m r rd V.. rq Pw L pl Pw L R + pl i m m m m r r r rq (.14) 13

25 .1.4. Fixed to the rotor. It mean that w r = 0 and conequently w = w m. V R + pl L Pw. pl L Pw. i D D m m m m R V LPw.. Q m + pl L mpw i m plm Q =. V pl 0 R + pl 0 i rd m r r rd V 0 pl 0 R + pl i rq m r r rq (.15) Fixed to the ynchronim. It mean that w r =.w. VD R + pl L w pl L m mw id V Lw. Q R + pl L mpw pl i m Q =. V pl L. i rd m mw R + pl L r r rw rd V L. i rq mw pl L m rw R + pl r r rq (.16) 14

26 .. SPACE PHASOR NOTATION:..1 Introduction. Space phaor notation allow the tranformation of the natural intantaneou value of a three phae ytem onto a complex plane located in the cro ection of the motor. In thi plane, the pace phaor rotate with an angular peed equal to the angular frequency of the three phae upply ytem. A pace phaor rotating with the ame angular peed, for example, can decribe the rotating magnetic field. Moreover, in the pecial cae of the teady tate, where the upply voltage i inuoidal and ymmetric, the pace phaor become equal to three-phae voltage phaor, allowing the analyi in term of complex algebra. It i hown in figure.3 the equivalent chematic for thi new model. In order to tranform the induction motor model, in natural co-ordinate, into it equivalent pace phaor form, the 10º operator i introduced: a e a e j j /3 4 /3 = π, = π (.17) Fig.3 Space phaor repreentation of three phae quantitie Thu, the current tator pace phaor can be expreed a follow: i = c. 1. ia ( t) + a. ib ( t) + a. ic ( t) (.18) The factor "c", take uually one of two different value either /3 or 3. The factor /3 make the amplitude of any pace phaor, which repreent a three phae balanced ytem, equal to the amplitude of one phae of the three-phae ytem. The factor 3 may alo be 15

27 ued to define the power invariance of a three-phae ytem with it equivalent two-phae ytem (ee ection.3.3)... Current pace phaor. During thi ection the induction machine aumption introduced in the ection.1.1 will be further conidered. It i repreented in figure.4 the model of the induction machine with two different frame, the D-Q axi which repreent the tationary frame fixed to the tator, and the α-β axi which repreent rotating frame fixed to the rotor. Fig.4.Cro-ection of an elementary ymmetrical three-phae machine, with two different frame, the D-Q axi which repreent the tationary frame fixed to the tator, and α-β axi which repreent rotating frame fixed to the rotor. The tator current pace phaor can be expreed a follow: j i = ia ( t) + a. ib ( t) + a ic ( t) = i e θ (.19) Expreed in the reference frame fixed to the tator, the real-axi of thi reference frame i denoted by D and it imaginary-axi by Q. The equivalence between the tator phaor and the D-Q two-axi component i a follow: ( ). ( ) i = i t + j i t (.0) D Q 16

28 Or: Re( i ) = Re ( i + ai. + a i 3 A B C) =i D (.1) Im( i ) = Im ( i + a. i + a i ) i 3 = A B C Q (.) The relationhip between the pace phaor current and the real tator phae current can be expreed a follow: Re( i ) = Re ( i + ai. + a i 3 A B C) Re( i ) = Re ( a. i + i + ai. 3 A B C) =i B =i A (.3) (.4) Re( i ) = Re ( ai. A + a. ib + ic) = ic (.5) In a imilar way, the pace phaor of the rotor current can be written a follow: jα ir = ira () t + ai. rb () t + a irc () t = ir e (.6) Expreed in the reference frame fixed to the rotor, the real-axi of thi reference frame i denoted by rα and it imaginary-axi by rβ. The pace phaor of the rotor current expreed in the tationary reference frame fixed to the tator can be expreed a follow: ' jθ j ( + m ) r r r i = i e = i e α θ (.7) The equivalence between the current rotor pace phaor and the α-β two-axi i a follow: i r = i ( ). ( ) r α + j i t t r β (.8) Or: Re( ir ) = Re ( ira + ai. rb + a i rc ) ir α 3 = (.9) Im( i ) Im r = ( ira + ai. rb + a irc ) ir β 3 = (.30) The relationhip between the pace phaor current and the real tator current can be expreed a follow: Re( i ) = Re ( i + ai. + a i 3 r ra rb rc ra ) = i (.31) 17

29 Re( ai) Re r = ( aira + irb + ai. rc ) irb 3 = (.3) Re( ai ) Re r = ( a. ira + a. irb + irc ) irc 3 = (.33) The magnetizing current pace-phaor expreed in the tationary reference frame fixed to the tator can be obtained a follow: N i = i + i (.34) re ' m N r e..3 Flux linkage pace phaor: In thi ection the flux linkage will be formulated in the tator phaor notation according to different reference frame Stator flux-linkage pace phaor in the tationary reference frame fixed to the tator: Similarly to the definition of the tator current and rotor current pace phaor, it i poible to define a pace phaor for the flux linkage a follow: ψ = ψ + ψ + ψ (.35) ( A a B a C ) 3 If the flux linkage equation.7 are ubtituted in equation.35, the pace phaor for the tator flux linkage can be expreed a follow: ia( L + am + a M ) + ib ( M + al + a M ) + ic ( M + am + a L ) + ( co co( 4 / 3) co( / 3) + ira Mr θm + amr θm + π + a Mr θm + π ) + ψ = (.36) 3 + irb ( Mr co( θm + π / 3) + amr coθm + a Mr co( θm + 4 π / 3) ) + + irc ( Mr co( θm + 4 π / 3) + amr co( θm + π / 3) + a Mr coθm ) Developing the previou expreion 1.33, it i obtained the following expreion: ia( L + am + am) + aib( am + al + am) + aic( M + am + al) + ( co co( 4 / 3) co( / 3) + ira Mr θm + amr θm + π + a Mr θm + π ) + ψ = 3 + ai. rb ( a Mr co( θm + π / 3) + Mr coθm + amr co( θm + 4 π / 3) ) + + a. irc ( amr co( θm + 4 π /3) + a Mr co( θm + π /3) + Mr coθm ) (.37) 18

30 And finally, expreion.37 can be repreented a follow: ( ) ψ θ θ π θ π = ( L + am + a M ) i + Mr co m + amr co( m + 4 /3) + a Mr co( m + /3) ir j m = ( L M) i + 1.5Mr co θm. ir = ( L M) i Mrire θ = ( L M) i + 1.5Mrir = Li + L i (.38) ' m r Where L i the total three-phae tator inductance and Lm i the o-called three-phae magnetizing inductance. Finally, the pace phaor of the flux linkage in the tator depend on two component, being the tator current and the rotor current. Once more, the flux linkage magnitude can be expreed in two-axi a follow: ψ = ψ + ψ (.39) D j Q Where it direct component i equal to: ψ D= Li D+ Lmir d (.40) And it quadrature component i expreed a: ψ Q = Li Q + Lmi rq (.41) The relationhip between the component i rd and i rα and i rq and i rβ may be introduced a follow: ' i i ji i e θ j m = + = (.4) r rd rq r..3.- Rotor flux-linkage pace phaor in the rotating reference frame fixed to the rotor: The rotor flux linkage pace phaor, fixed to the rotor natural frame can be defined a follow: ψ r = ( ψ ra + aψ rb + a ψ rc ) (.43) 3 If the flux linkage equation.8 are ubtituted in equation.43, the pace phaor for the rotor flux linkage can be expreed a follow: ira( Lr + amr + amr) + irb( Mr + alr + amr) + irc( Mr + amr + alr) + ( co co( / 3) co( 4 / 3) + ia Mr θm + amr θm + π + a Mr θm + π ) + ψ r = (.44) 3 + ib ( Mr co( θm + 4 π / 3) + amr coθm + a Mr co( θm + π / 3) ) + + ic ( Mr co( θm + π / 3) + amr co( θm + 4 π / 3) + a Mr coθm ) By re-arranging the previou expreion.44, it can be expreed a: ' 19

31 ira( Lr + amr + a Mr) + airb( a Mr + Lr + am ) + a irc( amr + a Mr + Lr) + ( co co( /3) co( 4 /3) + ia Mr θm + amr θm + π + a Mr θm + π ) + ψ r = --- (.45) 3 + ai. B ( a Mr co( θm + 4 π / 3) + Mr coθm + amr co( θm + π / 3) ) + + a. ic ( amr co( θm + π /3) + a Mr co( θm + 4 π /3) + Mr coθm ) And finally ( ) ψr = ( Lr+ amr+ a Mr) ir+ Mrcoθm+ amrco( θm+ π/3) + a Mrco( θm+ 4 π/3) i = ( L M) i + 1.5M co( θ ). i = ( L M) i M ie = ( L M ) i + 1.5M i jθ m ' r r r r m r r r r r r r r ' = (.46) L r ir L m i Where Lr i the total three-phae rotor inductance and Lm i the o-called three-phae magnetizing inductance. i i the tator current pace phaor expreed in the frame fixed to the rotor. ' Once more the flux linkage magnitude can be expreed in the two-axi form a follow: ψ = ψ + ψ (.47) r rα j rβ Where it direct component i equal to: ψ r α = Li r r α + Lmi α (.48) And it quadrature component i expreed a: ψ r β = Li r r β + Lmi β (.49) Rotor flux-linkage pace phaor in the tationary reference frame fixed to the tator. The rotor flux linkage can alo be expreed in the tationary reference frame uing the previouly introduced tranformation ejθm, and can be written a: ' ψ ψ ψ ψ ψ ψ r ( jθm jθm = + j = e = + j ) e (.50) rd rq r rα rβ The pace phaor of the rotor flux linkage can be expreed according to the fixed coordinate a follow: ' ' ' i ' r θ r r m r r ψ = Li + L i e = Li + Li (.51) m The relationhip between the tator current referred to the tationary frame fixed to the tator and the rotational frame fixed to the rotor i a follow: 0

32 i ' = i e jθ m ie Where ' jθ m = i ' i = i + ji D Q i = i + ji α β From figure 1.5, the following equivalencie can be deduced: i = j i e θ ' ' iα ' j( θ θm) jθm = = = i i e i e ie (.5) (.53) (.54) Fig.5.Stator-current pace phaor expreed in accordance with the rotational frame fixed to the rotor and the tationary frame fixed to the tator Stator flux-linkage pace phaor in the rotating reference frame fixed to the rotor: Similarly than..3.3 ection, it can be deduced the following expreion: ' ( ) jθ ' m jθm e Li Lmir e Li Lmir ψ = ψ = + = (.55)..4. The pace phaor of tator and rotor voltage. The pace phaor for the tator and rotor voltage can be defined in a imilar way like the one ued for other magnitude. 1

33 1 1 1 V = V t av t av t V jv V V V j ( V V = + = A() B() C () D Q A B C B C V ( 3 V t av t av t V jv V V V j V V 3 3 r = () + () + () = ra rb rc r α+ r β = + ra rb rc rb rc ) ) ---- (.56) ---- (.57) Where the tator voltage pace phaor i referred to the tator tationary frame and the rotor voltage pace phaor i referred to the rotating frame fixed to the rotor. Provided the zero component i zero [3] [4], it can alo be aid that: V V V A B C = Re( V ) = Re( a ) = Re( av ) V (.58) Equivalent expreion can alo be obtained for the rotor.

34 .3 TORQUE EXPRESSIONS: Introduction. The general expreion for the torque i a follow: e ' t = cψ i r (.59) Where the c i a contant, ψ and r ' i are the pace phaor of the tator flux and rotor current repectively, both referred to the tationary reference frame fixed to the tator. The expreion given above can alo be expreed a follow: t c ψ. i inγ = (.60) e r Where γ i the angle exiting between the tator flux linkage and the rotor current. It follow that when γ=90 o the torque obtained i the maximum and it expreion i exactly equal to the one for the DC machine. Neverthele, in DC machine the pace ditribution of both magnitude i fixed in pace, thu producing the maximum torque for all different magnitude value. Furthermore, both magnitude can be controlled independently or eparately. In an AC machine, however, it i much more difficult to realize thi principle becaue both quantitie are coupled and their poition in pace depend on both the tator and rotor poition. It i a further complication that in quirrel-cage machine, it i not poible to monitor the rotor current, unle the motor i pecially prepared for thi purpoe in a pecial laboratory. It i impoible to find them in a real application. The earch for a imple control cheme imilar to the one for DC machine ha led to the development of the o-called vector control cheme, where the point of obtaining two different current, one for controlling the flux and the other one for the rotor current, i achieved [3] [4] Deduction of the torque expreion by mean of energy conideration. conideration. Therefore, the tarting equation i a follow: Pmechanical = Pelectric Plo P field Torque equation i being deduced by mean of energy Subtituting the previou power for it value, the equation can be expreed a follow: ' 3 * dψ * * ' dψ r '* te. wr = Re( V. i ) R i Re i + Re( Vr. ir Rr Ir Re Ir dt dt --- (.61) 3

35 Since in the tationary reference frame, the tator voltage pace phaor V can only be balanced by the tator ohmic drop, plu the rate of change of the tator flux linkage, the previou expreion can be expreed a follow: ( ψ ) ( ψ ) 3 ' ' 3 ' '* 3 ' ' te. wr = Re jwr r ir = wr Re j r ir = wrψ r ir (.6) Expreing the equation in a general way for any number of pair of pole give: t e 3 ' ' = Pψ r i r (.63) If equation.38 i ubtituted in equation.63 it i obtained the following expreion for the torque: t e 3 = Pψ i (.64) If the product i developed, expreion,64 i a follow: 3 te = P( ψd. iq ψq. id ) (.65) Finally, different expreion for the torque can be obtained a follow: 3 ' ' 3 ' 3 te = P( Lrir + Lmi) ir = PLmI ir = PLmI ' i r (.66) 3 Lm ' ' 3Lm ' 3 L ' m te = P ( Lmir + Li) ir = Pψ ir = P ψ ψr L L L L L.3.3 Torque contant. r m The value of the torque contant can take two different value. Thee depend on the contant ued in the pace phaor. Both poibilitie are hown in table.1.. Table.1 Torque contant value Non power invariant Power invariant Torque contant Space phaor contant "3 " mean the change from three axi to either two axi or pace phaor notation, and " 3" either two axi or pace phaor notation to three axi. 4

36 .4 SIMULINK MODEL: Equation ued in the model. The final expreion ued in the implemented model are obtained from all the previouly introduced expreion. All equation have been re-arranged in order to ue the operator 1/ intead of the operator p becaue the Simulink deal with the integrator better than with the derivation Stator reference. Stator and rotor fluxe can be expreed a follow: 1 ψ D = ( VD Ri D) 1 ψ Q = ( VQ Ri Q) (.67) 1 1 ' ( ' ' ' ) ( ' ' ψ rd = Vrd Rr Ird Pw. mψrq = Ri r rd Pw. mψrq ) 1 1 ( ' ' ' ) ( ' ' ψ rq = Vrq Ri r rq + Pw. mψrd = Ri r rq + Pw. mψrd ) Stator and rotor current can be expreed a follow: i i i i = ψ L Lm ψ Lx = ψ Lr ' Lm ψ Lx Lx ' L Lm = ψ ψ Lx Lx (.68) ' L Lm = ψ ψ L L r ' D D rd Lx Q Q rq rd rd D rq rq Q x x Lx = LLr Lm Where Rotor reference. Stator and rotor fluxe can be expreed a follow: 1 ψ rd = ( Vrd Ri r rd ) = (.69) 1 ψ rq = ( Vrq Rrirq ) = 0 5

37 ' 1 ' ' ' 1 ' ψ (. ) (. ' d = Vd RId + Pwmψ q = Rrird Pwmψ rq ) (.70) ψ 1 1 ' ( ' '. ' ) ( ' ' q = Vq Rriq Pwm d Rrirq Pw. m rd ) ψ = + ψ Stator and rotor current can be expreed a follow: i L = ψ ψ L ' r ' m D D rd Lx Lx i L = ψ ψ L ' r ' m Q Q rq Lx Lx i L = ψ ψ ' rd rd D Lx i L = ψ ψ Where L L L L ' m rq rq Q Lx x Lx = LLr Lm Motion equation. The motion equation i a follow: m te tl J Dw m x (.71) dw = + m (.7) dt Where, te i the electromagnetic torque, tl i load torque, J i the inertia of the rotor, and finally the D i the damping contant. Uing the torque expreion.65, the previou motion equation can be expreed a follow: ( ψ D Q ψ Q D ) = L + m ( + ) Pc... i. i t w D J w r = ( ψ ψ ) Pc... i. i t D Q Q D L D + J (.73) Where P i the number of pair of pole and the torque contant take the value either 1 or /3 according to the table.1 hown in the previou ection.3.3. The SIMULINK model for induction motor i developed by uing above equation and imulated uccefully. The imulink model i given in figure.6 and induction motor ub block model alo preented in figure.7. The wave form of tator current in tationary and rotating reference frame and induction motor torque and peed waveform given in figure 6

38 variable-amplitude variable- frequency 3-phae inuoidal voltage v_abc v_ab v_dq voltage Step load pu Tl Te torque amplitude f(u) frequency w -Kwo 1 SYNCHRONOUS theta 0 w f(u) f(u) STATOR wm K*u v_abc peed ABCab wk v_ab ab thetak abdq dq REFERENCE FRAME dq v_dq v wk wm INDUCTION MOTOR pu Te i Te i_dq dq Te Tl ab i_ab MECHANICAL wm SYSTEM K*u wm i_dq i_ab i_abc peed current thetak ababc 0 ROTOR dqab Info theta angle thetak thetar 1 -K- Fig.6. SIMULINK model for induction motor to obtain current and voltage in different frame of reference K*u Te 1 Te wk rot STATOR f 1 v -K- 1 f FLUX-CURRENT RELATIONS i i fr ir ir K*u R i rot1 ROTOR fr 3 wm [0 0] vr -K- 1 Rr ir INDUCTION MACHINE SUBSYSTEM IN ARBITRARY REFERENCE FRAME Fig.7.Induction machine ubytem modeled by uing modeling equation 7

39 Fig.8 Induction motor tator current in tationary and rotating reference frame Fig.9.Torque and peed waveform of induction motor 8

40 .5 INTERIM CONCLUSIONS: In the preent chapter I have deduced the motor model. The model ha been formulated by mean of the two-axi theory equation and the pace phaor notation. Depite the fact that both nomenclature are valid, it ha been proved that the pace phaor notation i much more compact and eaier to work with. The model ha been developed in both nomenclature for the tator, rotor and ynchronou reference. In further chapter, the motor model with tator reference, introduced in ection.4.1.1, will be the one mot ued. The final concrete equation ued in the MATLAB/SIMULINK motor model have been preented by the three different reference. Some imulation are hown to prove the validity of the model, being equal for the previouly mentioned three reference. Finally the teady tate motor analyi ha been introduced. 9

41 Chapter 3 DIRECT TORQUE CONTROL OF INDUCTION MOTOR Introduction DTC controller DTC chematic SIMULINK Model Interim Concluion

42 DIRECT TORQUE CONTROL OF INDUCTION MOTORS 3.1 INTRODUCTION: DC drive analogy: In a dc machine, neglecting the armature reaction effect and field aturation, the developed torque i given by T e = K a. I a. I f (3.1) Where I a = armature current and I f = field current. ψ f Fig 3.1 DC motor model The contruction of a DC machine i uch that the field ψ f produced by the current I f i perpendicular to the armature flux ψ a, which i produced by the armature current I a. Thee pace vector, which are tationary in pace, are orthogonal or decoupled in nature a hown in figure 3.1. Thi mean that when torque i controlled by controlling the current I a, the flux ψ f i not effected and we get the fat tranient repone and high torque/ampere ratio with the rated ψ f. Becaue of the decoupling, when the field current I f i controlled, it affect the field flux ψ f only, but not the ψ a flux. The DC machine like performance i obtained in Direct Torque Controlled (DTC) drive. In DTC drive, the de-coupling of the torque and flux component i accomplihed by uing hyterei comparator which compare the actual and etimated value of the electromagnetic torque and tator flux. The DTC drive conit of DTC controller, torque and flux calculator, and a Voltage Source Inverter (VSI). 30

43 3.1. Principle of direct torque control of induction motor: Direct torque control wa developed by Takahahi [1] and Depenbrock [13] a an alternative to field-oriented control [3], [15]. In a direct torque controlled (DTC) induction motor drive upplied by a voltage ource inverter, it i poible to control directly the tator flux linkage ψ (or the rotor fluxψ or the magnetizing fluxψ ) and the electromagnetic torque by the election of an optimum inverter voltage vector. The election of the voltage vector of the voltage ource inverter i made to retrict the flux and torque error within their repective flux and torque hyterei band and to obtain the fatet torque repone and highet efficiency at every intant. DTC enable both quick torque repone in the tranient operation and reduction of the harmonic loe and acoutic noie. A it ha been introduced in expreion.64, the electromagnetic torque in the three phae induction machine can be expreed a follow [3]: t e 3 = Pψ i (3.) Where ψ i the tator flux, i i the tator current (both fixed to the tationary reference frame fixed to the tator) and P the number of pair of pole. The previou equation can be modified and expreed a follow: 3 = ψ α ρ (3.3) t P i.in( ) e Where ρ i the tator flux angle andα i the tator current one, both referred to the horizontal axi of the tationary frame fixed to the tator. If the tator flux modulu i kept contant and the angle ρ i changed quickly, then the electromagnetic torque i directly controlled. The ame concluion can be obtained uing another expreion for the electromagnetic torque. From equation 1.83, next equation can be written: 3 L ' m t = P.in( ρ ) LL L e r r m ψ ψ ρ r (3.4) Becaue of the rotor time contant i larger than the tator one, the rotor flux change lowly compared to the tator flux; in fact, the rotor flux can be aumed contant. (The fact that the rotor flux can be aumed contant i true a long a the repone time of the control i much fater than the rotor time contant). A long a the tator flux modulu i kept contant, then the electromagnetic torque can be rapidly changed and controlled by mean of changing the angle ρ ρ r [16] [3]. r m 31

44 3. - DTC CONTROLLER: The way to impoe the required tator flux i by mean of chooing the mot uitable Voltage Source Inverter tate. If the ohmic drop are neglected for implicity, then the tator voltage impree directly the tator flux in accordance with the following equation d ψ dt = V Or: (3.5) ψ = V. t Decoupled control of the tator flux modulu and torque i achieved by acting on the radial and tangential component repectively of the tator flux-linkage pace vector in it locu. Thee two component are directly proportional (R=0) to the component of the ame voltage pace vector in the ame direction. So impoing of proper voltage vector i important in direct torque control of induction motor. Thi we will obtained by uing voltage ource inverter Voltage Source Inverter There are many topologie for the voltage ource inverter ued in DTC control of induction motor that give high number of poible output voltage vector [16], [17] but the mot common one i the ix tep inverter. A ix tep voltage inverter provide the variable frequency AC voltage input to the induction motor in DTC method. The DC upply to the inverter i provided either by a DC ource like a battery, or a rectifier upplied from a three phae (or ingle phae) AC ource. Fig. 3. how a ix tep voltage ource inverter. The inductor L i inerted to limit hot through fault current. A large electrolytic capacitor C i inerted to tiffen the DC link voltage. The witching device in the voltage ource inverter bridge mut be capable of being turned off and on. Inulated gate bipolar tranitor (IGBT) are ued becaue they have thi ability in addition; they offer high witching peed with enough power rating. Each IGBT ha an invere parallel-connected diode. Thi diode provide alternate path for the motor current after the IGBT, i turned off [5]. 3

45 Fig 3. Voltage Source Inverter Each leg of the inverter ha two witche one connected to the high ide (+) of the DC link and the other to the low ide (-); only one of the two can be on at any intant. When the high ide gate ignal i on the phae i aigned the binary number 1, and aigned the binary number 0 when the low ide gate ignal i on. Conidering the combination of tatu of phae a, b and c the inverter ha eight witching mode (V a V b V c = ) two are zero voltage vector V 0 (000) and V 7 (111) where the motor terminal i hort circuited and the other are nonzero voltage vector V 1 to V 6 The dq model for the voltage ource inverter in the tationary reference frame i obtained by applying the dq tranformation Equation to the inverter witching mode. The ix nonzero voltage pace vector will have the orientation hown in Fig..6, and alo how the poible dynamic locu of the tator flux, and it different variation depending on the VSI tate choen. The poible global locu i divided into ix different ector ignaled by the dicontinuou line. Each vector lie in the center of a ector of 60 o width named S1 to S6 according to the voltage vector it contain. From Equation 3.5 it can be een that the inverter voltage directly force the tator flux, the required tator flux locu will be obtained by chooing the appropriate inverter witching tate. Thu the tator flux linkage move in pace in the direction of the tator voltage pace vector at a peed that i proportional to the magnitude of the tator voltage pace vector. By electing tep by tep the appropriate tator voltage vector, it i then poible to change the tator flux in the required way. If an increae of the torque i required then the torque i controlled by applying voltage vector that advance the flux linkage pace vector in the direction of rotation. If a decreae in torque i required then zero witching vector i applied, the zero vector that minimize inverter witching i elected. In ummary if the tator flux vector lie in the k-th ector and the motor i running anticlockwie 33

46 Fig 3.3.Stator flux vector locu and different poible witching Voltage vector. FD: flux decreae. FI: flux increae. TD: torque decreae. TI: torque increae. then torque can be increaed by applying tator voltage vector V k+1 or V k+, and decreaed by applying a zero voltage vector V 0 or V 7. Decoupled control of the torque and tator flux i achieved by acting on the radial and tangential component of the tator voltage pace vector in the ame direction, and thu can be controlled by the appropriate inverter witching. In general, if the tator flux linkage vector lie in the k-th ector it magnitude can be increaed by uing witching vector V k-1 (for clockwie rotation) or V k+1 (for anticlockwie rotation), and can be decreaed by applying voltage vector V k- (for clockwie rotation) or V k+ (for anticlockwie rotation). In Accordance with figure.1, the general table II.I can be written. It can be een from table II.I, that the tate Vk and Vk+3, are not conidered in the torque becaue they can both increae (firt 30 degree) or decreae (econd 30 degree) the torque at the ame ector depending on the tator flux poition. Table3.1.General Selection Table for Direct Torque Control, "k" being the ector number. 34

47 Thi can be tabulated in the look-up Table.1 (Takahahi look-up table). Finally, the DTC claical look up table i a follow: Flux Error dψ 1 Torque Error dt S1 S S3 S4 S5 S6 1 0 v v 3 v 4 v 5 v 6 V1 V 0 v 7 V 0 v 7 V 0 v v 6 Vi v v 3 v 4 v 5 v 3 v 4 v 5 v 6 V1 v V 0 v 7 V 0 v 7 V 0 v 7 v 5 v 6 V1 v v 3 v 4 Table3. conventional DTC look up table 3.3 DTC SCHEMATIC: In figure 1. a poible chematic of Direct Torque Control i hown. A it can be een, there are two different loop correponding to the magnitude of the tator flux and torque. The reference value for the flux tator modulu and the torque are compared with the actual value, and the reulting error value are fed into the twolevel and three-level hyterei block repectively. The output of the tator flux error and torque error hyterei block, together with the poition of the tator flux are ued a input of the look up table (ee table II.II). The input to the look up table are given in term of +1,0,-1 depend on weather the torque and flux error within or beyond hyterei band and the ector number in which the flux ector preent at that particular intant. In accordance with the figure 1., the tator flux modulu and torque error tend to be retricted within it repective hyterei band. From the chematic of DTC it i cleared that, for the proper election of voltage ector from lookup table, the DTC cheme require the flux and torque etimation Method for Etimation of Stator Flux in DTC: Accurate flux etimation in Direct Torque controlled induction motor drive i important to enure proper drive operation and tability. Mot of the flux etimation technique propoed i baed on voltage model, current model, or the combination of both [18]. The etimation baed on current model normally applied at low frequency, and 35

48 it require the knowledge of the tator current and rotor mechanical peed or poition. In ome indutrial application, the ue of incremental encoder to get the peed or poition of the rotor i undeirable ince it reduce the robutne and reliability of the drive. It ha been widely known that even though the current model ha managed to eliminate the enitivity to the tator reitance variation. The ue of rotor parameter in the etimation introduced error at high rotor peed due to the rotor parameter variation. So in thi preent DTC control cheme the flux and torque are etimated by uing voltage model decribed by equation , which doe not need a poition enor and the only motor parameter ued i the tator reitance. ψ ψ Lx ' L = ( V R I ) dt = i. + ψ. L L m D D D D rd (3.6) m r Lx ' L = ( V R I ) dt = i. + ψ. L L m Q Q Q Q rq (3.7) m r Where Lx LLr Lm = and D And torque can be etimated by equation i, i Q are calculated by uing equation.. 3 te = P( ψ D. iq ψq. id ) (3.8) By uing thee etimated value from voltage model we proceed to the lookup table to elect the proper voltage vector The voltage model give accurate etimation at high peed however, at low peed, ome problem arie. In practical implementation, even a mall DC off-et preent in the back emf due to noie or meaurement error inherently preent in the current enor, can caue the integrator to aturate [3]. 3.4 SIMULINK MODEL FOR CONVENTIONAL DTC: A SIMULINK model i developed by uing the induction motor model preented in figure 3.3 and alo MATLAB programme i developed for the implementation of conventional DTC. The imulink model for the conventional DTC i developed and i imulated. The waveform for induction motor torque, which i obtained from imulation of MATLAB programme i preented and verified with SIMULINK waveform. 36

49 qrt(u(1)^+u()^) Bf 0 tate 0 1 f_ref Bf 3-D T[k] -D T[k] T_er numbin1 numbin 0 ector # ector f ector elector 3 f Stator voltage elector Fig 3.4 SIMULINK model for conventional DTC A three dimenional matrix i developed by MATLAB programme which i called by imulink model during the imulation and i given by %witching table for DTC clc,clear a(:,:,1) =[1 0 ;5 7 6]; a(:,:,) =[5 7 3;4 0 ]; a(:,:,3) =[4 0 1;6 7 3]; a(:,:,4) =[6 7 5; 0 1]; a(:,:,5) =[ 0 4;3 7 5]; a(:,:,6) =[3 7 6;1 0 4]; a 37

50 The waveform for torque of the induction motor with the application of load torque of 1.5N.m i given in figure 3.4, which i obtained from imulation of MATLAB programme with a ampling time of It indirectly mean that the drive output i updated at a rate of 5 KHz. Fig 3.5 Electric torque waveform for conventional DTC 38

51 3.5 INTERIM CONCLUSIONS: From the torque waveform obtained from imulation of conventional DTC, it i cleared that the torque ripple i 0.6 Nm (approximately Nm maximum and minimum value repectively) with the conventional DTC. Thi high magnitude of torque ripple i the main drawback of conventional DTC. The other drawback alo ummarized a follow: Large and mall error in flux and torque are not ditinguihed. In other word, the ame vector are ued during tart up and tep change and during teady tate. Sluggih repone (low repone) in both tart up and change in either flux or torque. In order to overcome the mentioned drawback, there are different olution, like Non artificial intelligence method, mainly "ophiticated table" and fuzzy logic baed ytem. In the next ection of my thei work deal with DTC with the duty ratio fuzzy control to minimize torque ripple and realized the bet DTC improvement. 39

52 Chapter 4 FUZZY LOGIC CONTROLLERS Introduction to FLC Why Fuzzy Logic Controller Fuzzy Logic Controller

53 FUZZYLOGIC CONTROLLERS 4.1 Introduction to FLC Fuzzy logic ha rapidly become one of the mot ucceful of today technology for developing ophiticated control ytem. With it aid complex requirement o may be implemented in amazingly imple, eaily minted and inexpenive controller. The pat few year have witneed a rapid growth in number and variety of application of fuzzy logic. The application range from conumer product uch a camera,camcorder,wahing machine and microwave oven to indutrial proce control,medical intrumentation,and deciionupport ytem.many deciion-making and problem olving tak are too complex to be undertand quantitatively however,people ucceed by uing knowledge that i imprecie rather than precie. fuzzy logic i all about the relative importance of preciion.fuzzy logic ha two different meaning.in a narrow ene,fuzzy logic i a logical ytem which i an extenion of multi valued logic.but in wider ene fuzzy logic i ynonymou with the theory of fuzzy et. Fuzzy et theory i originally introduced by Lotfi Zadeh in the 1960, reemble approximate reaoning in it ue of approximate information and uncertainty to generate deciion. Several tudie how, both in imulation and experimental reult, that Fuzzy Logic control yield uperior reult with repect to thoe obtained by conventional control algorithm thu, in indutrial electronic the FLC control ha become an attractive olution in controlling the electrical motor drive with large parameter variation like machine tool and robot. However, the FL Controller deign and tuning proce i often complex becaue everal quantitie, uch a memberhip function, control rule, input and output gain, etc mut be adjuted. The deign proce of a FLC can be implified if ome of the mentioned quantitie are obtained from the parameter of a given Proportional-Integral controller (PIC) for the ame application. 4. Why fuzzy logic controller (FLC) Fuzzy logic controller i ued to deign nonlinear ytem in control application. The deign of conventional control ytem eential i normally baed on the mathematical model of plant.if an accurate mathematical model i available with known parameter it can be analyzed., for example by bode plot or nyquit plot, and controller can be deigned for pecific performance.uch procedure i time conuming[18]. Fuzzy logic controller ha adaptive characteritic. 40

54 The adaptive characteritic can achieve robut performance to ytem with uncertainty parameter variation and load diturbance Fuzzy logic controller (FLC) Fuzzy logic expreed operational law in linguitic term intead of mathematical equation. Many ytem are too complex to model accurately, even with complex mathematical equation; therefore traditional method become infeaible in thee ytem. However fuzzy logic linguitic term provide a feaible method for defining the operational characteritic of uch ytem [18]. Fuzzy logic controller can be conidered a a pecial cla of ymbolic controller. The configuration of fuzzy logic controller block diagram i hown in Fig.4.1 Fig 4.1 Block diagram for Mamdani type Fuzzy Logic Controller The fuzzy logic controller ha three main component 1. Fuzzification.. Fuzzy inference. 3. Defuzzification Fuzzification The following function: 41

55 1. Multiple meaured crip input firt mut be mapped into fuzzy memberhip function thi proce i called fuzzification.. Perform a cale mapping that tranfer the range of value of input variable into correponding univere of dicoure. 3. Perform the function of fuzzification that convert input data into uitable linguitic value which may be viewed a label of fuzzy et. Fuzzy logic linguitic term are often expreed in the form of logical implication, uch a if-then rule. Thee rule define a range of value known a fuzzy member hip function. Fuzzy memberhip function may be in the form of a triangle, a trapezoidal, a bell (a hown in Fig.4.) or another appropriate from [18]. The triangle memberhip function i defined in (4.1).Triangle memberhip function limit defined byv al1, V al andv al3. ui Val1, Val1 ui Val Val Val1 Val3 ui µ ( ui ) =, Val ui Val (4.1) Val3 Val 0, othetrwie Trapezoid memberhip function defined in (4.).Trapezoid memberhip function limit are defined byv al1, V al, V al3 and V al 4. ui Val V al V 1, µ i ( ui ) = Val 4 u Val 4 V 0 1 al1 i al 3, V, V, V al1 al al 3 u u u V V V, otherwie i i i al al 3 al 4 (4.) The bell memberhip function are defined by parameter X p, w and m a follow: 1 µ ( ui ) = (4.3) m ui X P 1+ w Where X the midpoint and w i the width of bell function. m 1, and decribe the convexity of the bell function. p 4

56 µ 1 µ 1 Val1 Val V al 3 (a) u Val1 Val Val3 V al 4 (b) u (c) Fig.4.. (a) Triangle, (b) Trapezoid, and (c) Gauian memberhip function. The input of the fuzzy controller are expreed in everal linguit level. A hown in Fig.4.3 thee level can be decribed a poitive big (PB), poitive medium (PM), poitive mall (PS) negative mall (NS), negative medium (NM), negative big(nb) or in other level. Each level i decribed by fuzzy et [18]. NB NM NS Z PS PM PB Figure.4.3.Seven level of fuzzy memberhip function 43

57 4.3.. Fuzzy inference Fuzzy inference i the proce of formulating the mapping from a given input to an output uing fuzzy logic. The mapping then provide a bai from which deciion can be made, or pattern dicerned. There are two type of fuzzy inference ytem that can be implemented in the Fuzzy Logic Toolbox: Mamdani-type and Sugeno-type. Thee two type of inference ytem vary omewhat in the way output are determined. Fuzzy inference ytem have been uccefully applied in field uch a automatic control, data claification, deciion analyi, expert ytem, and computer viion. Becaue of it multidiciplinary nature, fuzzy inference ytem are aociated with a number of name, uch a fuzzy-rule-baed ytem, fuzzy expert ytem, fuzzy modeling, fuzzy aociative memory, fuzzy logic controller, and imply (and ambiguouly) fuzzy Mamdani fuzzy inference method i the mot commonly een fuzzy methodology. Mamdani method wa among the firt control ytem built uing fuzzy et theory. It wa propoed in 1975 by Ebrahim M amdani [18] a an attempt to control a team engine and boiler combination by yntheizing a et of linguitic control rule obtained from experienced human operator. Mamdani effort wa baed on Lotfi Zadeh 1973 paper on fuzzy algorithm for complex ytem and deciion procee [18]. The econd phae of the fuzzy logic controller i it fuzzy inference where the knowledge bae and deciion making logic reide.the rule bae and data bae from the knowledge bae. The data bae contain the decription of the input and output variable. The deciion making logic evaluate the control rule.the control-rule bae can be developed to relate the output action of the controller to the obtained input Defuzzification The output of the inference mechanim i fuzzy output variable. The fuzzy logic controller mut convert it internal fuzzy output variable into crip value o that the actual ytem can ue thee variable [18]. Thi converion i called defuzzification. One may perform thi operation in everal way. The commonly ued control defuzzification trategie are (a).the max criterion method (MAX) The max criterion produce the point at which the memberhip function of fuzzy control action reache a maximum value. (b) The height method 44

58 The centroid of each memberhip function for each rule i firt evaluated. The final outputu 0 i then calculated a the average of the individual centroid, weighted by their height a follow: U O n uiµ ( ui ) i= 1 = (4.4) n µ ( u ) i= 1 i (c).the centroid method or center of area method (COA) The widely ued centroid trategy generate the center of gravity of area bounded by the y = µ ( y). ydy ( y) dy memberhip function cure. Y µ Y (4.5) 45

59 Chapter 5 TORQUE RIPPLE MINIMIZATION IN DTC DRIVES Introduction Duty Ratio Control Deign of Duty Ratio Fuzzy Controller Interim Concluion

60 TORQUE RIPPLE MINIMIZATION IN DTC DRIVES 5.1 Introduction: Direct torque control ha many promiing feature and advantage uch a abence of peed and poition enor, abence of coordinate tranformation, reduced number of controller and minimal torque repone time. In addition, there are many limitation that need to be invetigated. A major concern in direct torque control of induction motor drive i torque and flux ripple, ince none of the inverter witching vector i able to generate the exact tator voltage required to produce the deired change in torque and flux. Poible olution involve the ue of high witching frequency or alternative inverter topologie. Increaed witching frequency i deirable ince it reduce the harmonic content of the tator current, and reduce torque ripple. However, high witching frequency reult in ignificantly increaed witching loe leading to reduced efficiency and increaed tre on the inverter emiconductor device. Furthermore, in the cae of high witching frequency, a fat proceor i required ince the control proceing time become mall. When an alternative inverter topology i ued [16], it i poible to ue an increaed number of witche, but thi alo increae the cot. However, if intead of applying a voltage vector for the entire witching period, it i applied for a portion of the witching period, then the ripple can be reduced. Thi i defined a duty ratio control in which the ratio of the portion of the witching period for which a non-zero voltage vector i applied to the complete witching period i known a the duty ratio (δ). 5. Duty Ratio Control: In the conventional DTC a voltage vector i applied for the entire witching period, and thi caue the tator current and electromagnetic torque to increae over the whole witching period. Thu for mall error, the electromagnetic torque exceed it reference value early during the witching period, and continue to increae, cauing a high torque ripple. Thi i then followed by witching cycle in which the zero witching vector are applied in order to reduce the electromagnetic torque to it reference value. The ripple in the torque and flux can be reduced by applying the elected inverter vector not for the entire witching period, a in the conventional DTC induction motor drive, but only for part of the witching period. The time for which a non- 46

61 Fig 5.1 Block diagram for DTC with duty ratio fuzzy controller -zero voltage vector ha to be applied i choen jut to increae the electromagnetic torque to it reference value and the zero voltage vector i applied for the ret of the witching period a in Fig. 1.3(b). During the application of the zero voltage vector no power i aborbed by the machine, and thu the electromagnetic flux i almot contant; it only decreae lightly. Fig. 5.1 how a DTC induction motor drive with a duty ratio fuzzy logic controller. The average input DC voltage to the motor during the application of each witching vector i δv dc. By varying the duty ratio between zero and one, it i poible to apply voltage to the motor with an average value between 0 and V dc during each witching period. Thu, the torque ripple will be le compared to applying the full DC link voltage for the complete witching period. Thi increae the choice of the voltage vector, without an increae in the number of emiconductor witche in the inverter. The duty ratio of each witching period i a non-linear function of the electromagnetic torque error, tator flux-linkage error, and the poition of the tator fluxlinkage pace vector. Thu, it i difficult to model thi non-linear function. However, by uing a fuzzy-logic-baed DTC ytem, it i poible to perform fuzzy-logic-baed duty-ratio control, where the duty ratio i determined during every witching cycle. In uch a fuzzy- 47

62 logic ytem, there are three input, the electromagnetic torque error (E te =T ref -T), the tator flux-linkage pace vector poition ( θ ψ ) within each ector aociated with the voltage vector a in Fig. 3.3 and the ign of the flux error (ign( E ψ )) where ( E ψ = ψ the fuzzy-logic controller i the duty ratio (δ). ref ψ ). The output of 5.3 Deign of the Duty Ratio Fuzzy Controller There are many type of fuzzy logic controller for thi particular application. A Mamdani-type fuzzy logic controller, which contain a rule bae, a fuzzifier, and a defuzzifier, i choen. Fuzzification i performed uing memberhip function. The input and the output of the fuzzy controller are aigned Gauian memberhip function a hown in Fig The univere of dicoure for the torque error and the duty ratio i adjuted uing imulation to get optimal torque ripple reduction. There are three group of memberhip function depicted in Figure correponding to three input variable. Fig 5. Memberhip function ditribution for the torque error (input) 48

63 Fig 5.3 Memberhip function ditribution of the flux poition (input) Fig 5.4 Memberhip function ditribution for duty ratio (output) For the purpoe of reducing the total rule number the fuzzy ubet correponding to the input ' θ only cover the partial univere (0-П/3) not like that of [19][1][] which cover the whole univere. In [19][1][] there are 180 rule altogether, which i too much to be incorporated into Fuzzy Logic Toolbox and i difficult to implement with hardware a well. 49

64 Baed on the ymmetry of impreed PWM voltage vector and flux angle in d-q coordinate, we define a mapping to convert the 8' in the range of (0-.П) into a ector with range of 0- π /3 [0]. ' π θ ' π + θ θ 6 = 3 π 3 Where θ ', the original angle of the tator i i i flux ector and θ i the actual angle that goe into fuzzy logic controller. The emphai in the fuzzy rule i to reduce the torque ripple. Generally the duty ratio i proportional to the torque error, ince the torque rate of change i proportional to the angle between the tator flux and the applied voltage vector, the duty ratio depend alo on the flux poition within each ector. The ue of two fuzzy et i due to the fact that when the tator flux i greater than it reference value a voltage vector that advance the tator flux vector by two ector i applied which reult in a higher rate of change for the torque compared to the application of a voltage vector that advance the tator flux vector by one ector when the tator flux linkage i le than it reference value. The duty ratio i elected proportional to the magnitude of the torque error o if the torque error i mall, medium or large then the duty ratio i mall, medium or large repectively. The fuzzy rule are then adjuted and tuned to reflect the effect of the flux error and poition. If the torque error i medium and the tator flux lie in ector k with a magnitude greater than it reference value (negative flux error) then the voltage vector V k+ i elected. If the flux poition i mall that mean there i a large angle between the flux and the elected voltage vector that make the elected vector more effective in increaing the toque o the duty ratio i et a mall rather than medium, the fuzzy rule i tated a If (torque error i medium) and (flux poition i mall) then (duty ratio i mall) If (torque error i large) and (flux poition i mall) then (duty ratio i medium) Uing the above reaoning and imulation to find the fuzzy rule, the two et of fuzzy rule are ummarized in Table

65 flux Negative dλ=0 Poitive dλ=1 Torque error dt=±1 Small Medium Large Fluxangle Small Small Small Medium Medium Small Medium Large Large Small Medium Large Small Small Medium Large Medium Small Medium Large Large Medium Large Large Table 5.1Rule for the duty ratio fuzzy controller MATLAB fuzzy logic toolbox wa ued in the implementation of the duty ratio fuzzy controller. The Graphic Uer Interface (GUI) included in the toolbox wa ued to edit the memberhip function for the input (the torque error and the flux poition), the output (the duty ratio) a hown in Fig and the two et of fuzzy rule ummarized in Table 4.1. A Mamdani type fuzzy inference engine (a decribed in Chapter IV) wa ued in the imulation. The memberhip function and the fuzzy rule were adjuted uing the imulation until an optimal torque ripple reduction wa achieved. Fig. 4.8 how the general view of the fuzzy controller when the tator flux i greater than it reference value. Fig 5.5 general view of duty ratio fuzzy controller 51

66 5.4 INTERIM CONCLUSIONS: To examine the performance of the duty ratio controller the imulation wa run at witching frequency 5 khz. The difference between the conventional DTC and DTC with the duty ratio fuzzy control i clearly realized by examining the witching behavior of the tator voltage and the electric torque. Figure 5.6 contain voltage and torque witching in conventional DTC, where the drive output i updated at a rate of 5 khz. The dotted vertical line mark the beginning of the ampling period. It can be een that the elected voltage vector i applied for the complete ampling period and the torque keep increaing for the complete period; then a zero voltage i applied and the torque keep decreaing for the complete ampling period and thi reult in high torque ripple. Fig 5.6 Voltage and torque witching in conventional DTC 5

67 In the DTC with the duty ratio fuzzy control a hown in Fig. 5.7, contain voltage and torque witching, where the drive output i updated at a rate of 5 khz. The elected voltage vector i applied for part of the ampling period and removed for the ret of the period. A a reult, the electric torque increae for part of the ampling period and then tart to decreae, thi reult in le torque ripple. By adjutment of the duty ratio, the deired average torque may be continuouly maintained. The duty ratio controller moothly adjut the average tator voltage. There i no need to make coare correction by the ue of multiple witching period with a nonzero voltage vector or a whole witching period with a zero voltage vector a in the conventional DTC. Fig 5.7 Voltage and torque witching in DTC with duty ratio fuzzy controller 53

68 Chapter 6 SIMULATION RESULTS

69 SIMULATION RESULTS A MATLAB programme i developed to tudy the performance of the conventional DTC and DTC with duty ratio fuzzy controller for 4 pole Induction Motor torque control, and alo a SIMULINK model i developed and imulated for the ame and verified. Contant torque and flux command of 1.5 Nm and 0.16Wb were ued. The imulation wa run at witching frequency of 5 khz with a 110-V DC bu voltage. The parameter for the induction motor are R Rr Lr L Lm 1.7Ω 4.3 Ω 0.084H 0.084H 0.08H Table 6.1 Parameter of three phae induction motor The induction motor wa imulated uing a tate pace model which i developed in chapter II. The SIMULINK model for DTC with duty ratio fuzzy controller i a hown in figure 6.1 Fig 6.1 SIMULINK model for DTC with duty ratio fuzzy controller 54

70 Fig. 6. and 6.3 how the torque repone of the motor uing conventional DTC and DTC with the duty ratio fuzzy control repectively for a tep torque command of 1.5 Nm with the drive output updated at a rate of 5 khz. The torque ripple i 0.6 Nm (approximately Nm maximum and minimum value repectively) with the conventional DTC while with DTC with the duty ratio fuzzy control the ripple i reduced to 0.3 Nm (approximately Nm maximum and minimum value repectively, neglecting the underhoot in the torque value at the beginning of each voltage ector) Fig 6. Electric torque of induction motor uing conventional DTC Fig 6.3 Electric torque of induction motor uing DTC with duty ratio fuzzy controller 55

71 The waveform of tator current for both conventional DTC and DTC with fuzzy duty ratio controller are hown in figure a) Uing conventional DTC b) Uing DTC with duty ratio fuzzy controller Fig 6.4 Induction motor tator current waveform Fig 6.5 how the tator flux vector locu of the motor uing conventional DTC and DTC with the duty ratio fuzzy control, repectively with the controller output updated at a rate of 5 khz. The duty ratio fuzzy control reduce the tator flux ripple, 56

72 a) uing conventional DTC b) Uing DTC with duty ratio fuzzy controller Fig 6.5 tator and rotor flux phaor locu of induction motor 57