A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BARIŞ TUĞRUL ERTUĞRUL

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1 SENSORESS VECTOR CONTRO OF INDUCTION MOTOR BASED ON FUX AND SPEED ESTIMATION A THESIS SUBMITTED TO THE GRADUATE SCHOO OF NATURA AND APPIED SCIENCES OF MIDDE EAST TECHNICA UNIVERSITY BY BARIŞ TUĞRU ERTUĞRU IN PARTIA FUFIMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN EECTRICA AND EECTRONICS ENGINEERING DECEMBER 8

2 Appoval of the thei: SENSORESS VECTOR CONTRO OF INDUCTION MOTOR BASED ON FUX AND SPEED ESTIMATION ubmitted by BARIŞ TUĞRU ERTUĞRU in patial fulfilment of the equiement fo the degee of Mate of Science in Electical and Electonic Engineeing, Middle Eat Technical Univeity by, Pof. D. Canan ÖZGEN Dean, Gaduate School of Natual and Applied Science Pof. D. İmet ERKMEN Head of Depatment, Electical and Electonic Engineeing Pof. D. Aydın ERSAK Supevio, Electical and Electonic Engineeing, METU Examining Committee Membe: Pof. D. Muamme ERMİŞ Electical and Electonic Engineeing, METU Pof. D. Aydın ERSAK Electical and Electonic Engineeing, METU Pof. D. Işık ÇADIRCI Electical and Electonic Engineeing, Hacettepe Univ. Ait. Pof. D. Ahmet M. HAVA Electical and Electonic Engineeing, METU Ait. Pof. D. M. Timu AYDEMİR Electical and Electonic Engineeing, Gazi Univeity Date:.1.8

3 I heeby declae that all infomation in thi document ha been obtained and peented in accodance with academic ule and ethical conduct. I alo declae that, a equied by thee ule and conduct, I have fully cited and efeenced all mateial and eult that ae not oiginal to thi wok. Name, at name : Baış Tuğul ERTUĞRU Signatue : iii

4 ABSTRACT SENSORESS VECTOR CONTRO OF INDUCTION MOTOR BASED ON FUX AND SPEED ESTIMATION ERTUĞRU, Baış Tuğul M. Sc. Depatment of Electical and Electonic Engineeing Supevio: Pof. D. Aydın Eak Decembe 8, 148 page The main focu of the tudy i the implementation of technique egading flux etimation and oto peed etimation by the ue of enole cloed-loop obeve. Within thi famewok, the infomation about the mathematical epeentation of the induction moto, pule width modulation technique and flux oiented vecto contol technique togethe with peed adaptive flux etimation a kind of enole cloed loop etimation technique- and Kalman filte i given. With the compaion of enole cloed-loop peed etimation technique, it ha been attempted to identify thei upeioity and infeioity to each othe by the ue of imulation model and eal-time expeiment. In the expeiment, the pefomance of the technique developed and ued in the thei ha been examined unde extenively changing peed and load condition. The eal-time expeiment have been caied out by the ue of TI TMS3F81 digital ignal poceo, XIINX XCSS15E Field Pogammable Gate Aay (FPGA), contol cad and the iv

5 moto dive cad Futhemoe, Matlab Embedded Taget fo the TI C DSP and Code Compoe Studio oftwae tool have been ued. The imulation and expeiment conducted in the tudy have illutated that it i poible to inceae the pefomance at low peed at the expene of inceaed computational buden on the poceo. Howeve, in ode to contol the moto at zeo peed, high fequency ignal implementation hould be ued a well a a diffeent electonic hadwae. Key wod: Speed contol of induction machine, enole cloed loop field oiented contol, flux obeve, peed obeve v

6 ÖZ HIZ DUYAÇSIZ ENDÜKSİYON MOTORUNUN AKI VE HIZ KESTİRİM YÖNTEMERİNE DAYAI VEKTÖR DENETİMİ ERTUĞRU, Baış Tuğul Yükek ian, Elektik ve Elektonik Mühendiliği Bölümü Tez Yöneticii: Pof. D. Aydın Eak Aalık 8, 148 ayfa Bu çalışma enükiyon motolaını ea alan hız kontollü moto üücü taaımını ve uygulamalaını kapamaktadı. Bu çalışmanın temel olaak yoğunlaştığı alan hızduyaçız kapalı döngü gözleyicile kullanılaak manyetik akı ketiimi ve oto hızı ketiim teknikleinin uygulanmaıdı. Bu çeçevede tezde endükiyon motounun matematikel modellenmei, dabe genliği modülayonu tekniği ve akı yönlendimeli vektö kontol teknikleiyle beabe duyaçız kapalı döngü ketiim teknikleinden hız uyalamalı manyetik akı ketiim metodu ile Kalman filtele hakkında bilgi veilmişti. Duyaçız kapalı döngü hız ketiim yöntemleinin bibileine göe olan ütünlüklei ile zayıflıklaı benzetim modellei ve geçek zamanlı deneylele otaya konmaya çalışılmıştı. Deneylede yöntemlein geniş bi hız bandında ve yük altındaki pefomanı incelenmişti. vi

7 Geçek zamanlı deneyle TI TMS3F81 ayıal işaet işlemcii, XIINX XCSS15E alanda pogamlanabili kapı dizilei (FPGA) ile bilikte çeşitli analogdan ayıala, ayıaldan analoga çeviimlei ağlayan yongala ve çeve elemanladan oluşan kontol katı ile bilikte temel olaak güç anahtalama, işaet aayüz uyumlama, geilim ve akım ölçme develeini içeen moto üücü katı vaıtaıyla yapılmıştı. Ayıca, yazılım aayüzü olaak Matlab Embedded Taget fo the TI C DSP ve Code Compoe Studio yazılım aaçlaı kullanılmıştı. Çalışma üeince otaya konan benzetim ve deneyle götemişti ki işlemci yükünü attımak uetiyle düşük hızlada pefomanı attımak mümkün olmaktadı ancak ıfı hızda moto kontolünü geçekleştimek için faklı bi elektonik donanımla bilikte yükek fekan işaet uygulama yöntemlei kullanılmalıdı. Anahta Kelimele: Endükiyon makineleinin hız denetimi, duyaçız kapalıdöngü alan yönlendimeli denetim, akı gözleyici, hız gözleyici vii

8 ACKNOWEDGEMENTS I would like to expe my incee gatitude to my upevio Pof. D. Aydın Eak fo hi encouagement and valuable upeviion thoughout the tudy. I would like to thank to ASESAN Inc. fo the facilitie povided and my colleague fo thei uppot duing the coue of the thei. Thank a lot to my fiend, Öme GÖKSU, Evim Onu ARI, Muat ERTEK, Günay ŞİMŞEK and Doğan YIDIRIM fo thei help duing the expeimental tage of thi wok. I appeciate my family due to thei geat tut. The lat but not leat acknowledgment i to my peciou fiancée Didem SÜÜKÇÜ fo he encouagement and continuou emotional uppot. viii

9 TABE OF CONTENTS ABSTRACT......iv ÖZ... vi ACKNOWEDGEMENTS... viii TABE OF CONTENTS... ix IST OF TABES... xi IST OF FIGURES.....xii IST OF SYMBOS.....xviii CHAPTERS 1 INTRODUCTION INDUCTION MACHINE DRIVES THE FIED ORIENTED CONTRO (VECTOR CONTRO) OF INDUCTION MACHINES INDUCTION MACHINE FUX OBSERVATION SENSORESS VECTOR CONTRO OF INDUCTION MACHINE STRUCTURE OF THE CHAPTERS... 7 INDUCTION MACHINE MODEING, FIED ORIENTED CONTRO AND PWM WITH SPACE VECTOR THEORY SYSTEM EQUATIONS IN THE STATIONARY A,B,C REFERENCE FRAME Detemination of Induction Machine Inductance [1] Thee-Phae to Two-Phae Tanfomation The Clake Tanfomation [1] The Pak Tanfomation [1] REFERENCE FRAMES Induction Moto Model in the Abitay dq Refeence Fame Induction Moto Model in dq Stationay and Synchonou Refeence Fame....3 FIED ORIENTED CONTRO (FOC) SPACE VECTOR PUSE WIDTH MODUATION (SVPWM) Voltage Fed Invete (VSI) Voltage Space Vecto SVPWM Application to the Static Powe Bidge OBSERVERS FOR SENSORESS FIED ORIENTED CONTRO OF INDUCTION MACHINE SPEED ADAPTIVE FUX OBSERVER FOR INDUCTION MOTOR Flux Etimation Baed on the Induction Moto Model Etimation of Roto Flux Angle Adaptive Scheme fo Speed Etimation KAMAN FITER FOR SPEED ESTIMATION Dicete Kalman Filte Obtaining Synchonou Speed, w Speed Data though the ue of Roto Flux Angle Extended Kalman Filte (EKF) Selection of the Time-Domain Machine Model Dicetization of the Induction Moto Model ix

10 Detemination of the Noie and State Covaiance Matice Q, R, P Implementation of the Dicetized EKF Algoithm; Tuning SIMUATIONS AND EXPERIMENTA WORK EXPERIMENTA WORK Induction Moto Data Expeimental Set-up Expeimental Reult of Speed Adaptive Flux Obeve No-oad Expeiment of Speed Adaptive Flux Obeve The Speed Etimato Pefomance unde Switched oading The Speed Etimato Pefomance unde Acceleating oad The Speed Etimato Pefomance unde No-oad Speed Reveal Expeimental Reult of Kalman Filte fo Speed Etimation No-oad Expeiment of Kalman Filte fo Speed Etimation The Kalman Filte fo Speed Etimation Pefomance unde Switched oading The Kalman Filte fo Speed Etimation Pefomance unde Acceleating oad The Kalman Filte fo Speed Etimation Pefomance unde No-oad Speed Reveal Expeimental Reult of Paallel Run of Speed Adaptive Flux Obeve and Kalman Filte fo Speed Etimation No-oad Expeiment of Paallel Run of Speed Adaptive Flux Obeve and Kalman Filte fo Speed Etimation Paallel Run of Speed Adaptive Flux Obeve and Kalman Filte fo Speed Etimation unde Switched oading Paallel Run of Speed Adaptive Flux Obeve and Kalman Filte fo Speed Etimation unde Acceleating oad Paallel Run of Speed Adaptive Flux Obeve and Kalman Filte fo Speed Etimation unde No-load Speed Reveal SIMUATIONS OF EXTENDED KAMAN FITER Tuning of EKF Covaiance Matice Simulation at owe Speed CONCUSION REFERENCES x

11 IST OF TABES Table -1 Intantaneou Baic Voltage Vecto [5] Table - Powe bidge output voltage (V an, V bn, V cn ) Table -3 Stato voltage in (d q ) fame and elated voltage vecto Table -4 Duation of ecto bounday... 4 Table -5 Aigned duty cycle to the PWM output Table 4-1 Induction moto electical data Table 4- Induction moto paamete Table 4-3 Diect on-line tating pe unit definition Table 4-4 Contol paamete ued at the peed adaptive flux obeve expeiment84 Table 4-5 oading meauement... 9 Table 4-6 Contol paamete ued at Kalman filte fo peed etimation expeiment xi

12 IST OF FIGURES Figue 1-1 Input and output of the voltage model flux obeve (VMFO)... 3 Figue 1- Input and output of the cuent model flux obeve... 4 Figue 1-3 Input and output of the peed adaptive flux obeve... 5 Figue -1 Axial view of an induction machine... 9 Figue - Magnetic axe of thee phae induction machine... 9 Figue -3 Relationhip between the α, β and the abc quantitie [3] Figue -4 Relationhip between the dq and the abc quantitie [3] Figue -5 The Pak and the Clake tanfomation at the machine ide [1]... 7 Figue -6 Vaiable tanfomation in the field oiented contol [1]... 8 Figue -7 Phao diagam of the field oiented dive ytem... 9 Figue -8 Indiect field oiented dive ytem... 9 Figue -9 Diect field oiented dive ytem... 3 Figue -1 Indiect field oiented induction moto dive ytem with eno [1]... 3 Figue -11 The block diagam of VSI upplied fom a diode ectifie... 3 Figue -1 Thee phae voltage ouce invete upplying induction moto [1]... 3 Figue -13 Baic pace vecto [5] Figue -14 Pojection of the efeence voltage vecto Figue 3-1 The block diagam of oto flux angle etimation Figue 3- Adaptive tate obeve... 5 Figue 3-3 Dicete Kalman filte algoithm Figue 3-4 The tuctue of EKF algoithm... 7 Figue 4-1 The diect on-line tating moment v moto peed gaph Figue 4- The diect on-line tating moto cuent v moto peed gaph Figue 4-3 The diect on-line tating time v moto peed gaph Figue 4-4 The chematic block diagam of expeimental et-up Figue 4-5 The Magtol tet bench load epone... 8 Figue 4-6 The expeimental et-up xii

13 Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto quadatue encode poition Figue pm peed efeence, moto phae cuent Figue pm peed efeence, moto phae voltage Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue 4-5 pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue 4-1 pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm to 5 pm peed efeence, moto peed etimate unde acceleating load xiii

14 Figue pm to 5 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 75 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 75 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue 4-31 The peed efeence, moto peed etimate unde no-load peed eveal fo the peed ange 5 pm to -5 pm Figue 4-3 The peed efeence, moto peed etimate unde no-load peed eveal fo the peed ange 5 pm to -5 pm Figue 4-33 The peed efeence, moto peed etimate unde no-load peed eveal fo the peed ange 1 pm to -1 pm... 1 Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue 4-4 5pm peed efeence, moto quadatue encode poition Figue pm peed efeence, moto phae cuent Figue pm peed efeence, moto phae voltage Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading xiv

15 Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm to 5 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 5 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 75 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 75pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue pm to -1 pm peed efeence, moto peed etimate unde noload peed eveal xv

16 Figue pm to - 5 pm peed efeence, moto peed etimate unde noload peed eveal Figue pm to -1 pm peed efeence, moto peed etimate unde noload peed eveal... 1 Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, moto peed etimate unde witched loading Figue pm to 75 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 75 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue pm to 15 pm peed efeence, moto peed etimate unde acceleating load Figue pm to -5 pm peed efeence, moto peed etimate unde noload peed eveal xvi

17 Figue pm to -1 pm peed efeence, moto peed etimate unde noload peed eveal Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, tationay efeence fame i d cuent Figue pm peed efeence, tationay efeence fame, i q cuent Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, tationay efeence fame, i d cuent Figue pm peed efeence, tationay efeence fame, i q cuent Figue pm peed efeence, moto peed etimate unde witched loading Figue pm peed efeence, tationay efeence fame, i d cuent Figue pm peed efeence, tationay efeence fame, i q cuent xvii

18 IST OF SYMBOS SYMBO e md e mq i e d i e q i i d i q i a i b i c i a i b i c m l l K k P k q md q mq R R T em τ Back emf d-axi component Back emf q-axi component d-axi tato cuent in ynchonou fame q-axi tato cuent in ynchonou fame Stato cuent in tationay fame d-axi tato cuent in tationay fame q-axi tato cuent in tationay fame Phae-a oto cuent Phae-b oto cuent Phae-c oto cuent Phae-a tato cuent Phae-b tato cuent Phae-c tato cuent Magnetizing inductance Stato leakage inductance Roto leakage inductance Stato elf inductance Roto elf inductance Kalman gain Kalman filte eo covaiance matix Reactive powe d-axi component Reactive powe q-axi component Stato eitance Refeed oto eitance Electomechanical toque Roto time-contant xviii

19 V a V b V c V a V b V c V V d V q V e d V e q V dc w e w w l x k xˆ k z k θ e θ d θ q θ ψ ψ ψ d ψ q ψ e d ψ e q ψ a Phae-a tato voltage Phae-b tato voltage Phae-c tato voltage Phae-a oto voltage Phae-b oto voltage Phae-c oto voltage Stato voltage in tationay fame d-axi tato voltage in tationay fame q-axi tato voltage in tationay fame d-axi tato voltage in ynchonou fame q-axi tato voltage in ynchonou fame DC-link voltage Angula ynchonou peed Angula oto peed Angula lip peed Kalman filte a pioi tate etimate Kalman filte a poteioi tate etimate Kalman filte meauement Angle between the ynchonou fame and the tationay fame Angle between the ynchonou fame and the tationay fame when d-axi i leading Angle between the ynchonou fame and the tationay fame when q-axi i leading Roto flux angle Stato flux linkage in tationay fame d-axi tato flux linkage in tationay fame q-axi tato flux linkage in tationay fame d-axi tato flux linkage in ynchonou fame q-axi tato flux linkage in ynchonou fame Phae-a tato flux linkage xix

20 ψ b ψ c ψ a ψ b ψ c σ Phae-b tato flux linkage Phae-c tato flux linkage Phae-a oto flux linkage Phae-b oto flux linkage Phae-c oto flux linkage eakage coefficient xx

21 CHAPTER 1 1 INTRODUCTION 1.1 Induction Machine Dive Due to non-linea and complex mathematical model of induction moto, it equie moe ophiticated contol technique compaed to DC moto. The cala V/f method i able to povide peed contol, but thi method cannot povide eal-time contol. In othe wod, the ytem epone i only atifactoy at teady tate and not duing tanient condition. Dynamic pefomance of thi type of contol method wa unatifactoy becaue of atuation effect and the electical paamete vaiation with tempeatue. Thi eult in exceive cuent and ove-heating, which neceitate the dive to be oveized. Thi ove-deign no longe make the moto cot effective due to high cot of the dive cicuity [1]. Recent impovement with educed lo and fat witching emiconducto powe witche on powe electonic, fat and poweful digital ignal poceo on contolle technology have made advanced contol technique of induction machine dive feaible and applicable. Thank to field-oiented contol (FOC) cheme []- [3] induction moto can be made to opeate with popetie imila to thoe of a epaately excited DC moto. 1. The Field Oiented Contol (Vecto Contol) of Induction Machine Baically, field oiented contol (FOC) i a method baed on vecto coodinate. The tem vecto efe to the contol technique that contol both the amplitude and the phae of AC excitation voltage. Vecto contol i ued fo contolle that 1

22 maintain 9 patial oientation between the two field component which ae d and q co-odinate of a time invaiant ytem. In a field oiented induction moto dive, the field flux and amatue mmf ae epaately ceated and contolled baed on the vecto coodinate tanfomation. Thee pojection lead to a tuctue imila to that of a DC machine contol. The field oiented contol i ued in mot of the induction moto dive application in ode to obtain high contol pefomance, but it need moto flux poition (oto flux angle) infomation and utilize AC excitation voltage fo the cuent egulation. Cuent egulation i povided with advanced feedback contol method baed on the cuent meauement taken at the output of excitation voltage upplied fom voltage ouce invete (VSI). The oto flux angle can be meaued by uing haft eno and that infomation i utilized by field oientation cheme. Howeve, a dicued in the cuent tudy, enole contol algoithm eliminate the need fo a haft eno. The induction machine dive without the peed eno ae attactive due to low cot and high eliability. Theefoe, flux and peed etimation have become paticula iue of the field oiented contol in the ecent yea. The main advantage of peed enole induction moto dive ae lowe cot, educed ize of the dive machine, elimination of eno cable and inceaed eliability. A it i tated, fo implementing vecto contol, the detemination of the oto flux poition i equied. Two baic appoache to detemine the oto flux poition angle have evolved. One of them i the diect field oientation which depend on diect meauement o etimation of oto flux magnitude and angle. Fom the feaibility point of view, implementation of the diect method i difficult. The othe one i the indiect field oientation which make ue of lip elation in computing the angle of the oto flux elative to oto axi. 1.3 Induction Machine Flux Obevation The oto flux poition could be etimated fom the teminal quantitie (tato voltage and cuent). Thi technique equie the knowledge of the tato eitance

23 along with the tato-leakage, and oto-leakage inductance and the magnetizing inductance. The flux obevation though diect integation of tato voltage i called Voltage Model Flux Obeve (VMFO) which utilize the meaued tato voltage and cuent. Diect integation bing about eo due to the tato eitance voltage dop and integato bia. Since the voltage dop on tato eito at high peed i le ignificant compaed to tato voltage dop at lowe peed, the eo at low peed dominate. In addition, the leakage inductance can ignificantly affect the ytem pefomance in tem of tability and dynamic epone. i d i q θ ψ Figue 1-1 Input and output of the voltage model flux obeve (VMFO) Cuent Model Flux Obeve (CMFO) i intoduced a an altenative appoach in ode to ovecome the poblem caued by the change in leakage inductance and tato eitance at low peed. Cuent model baed obeve ue the meaued tato cuent and oto velocity. The velocity dependency of the cuent model i a dawback ince thi mean that even though uing the etimated flux eliminate the flux eno, poition eno i till equied. 3

24 i d i q θ ψ w Figue 1- Input and output of the cuent model flux obeve Seveal method ae uggeted which povide a mooth tanition between cuent and voltage flux obeve model. They combine two tato flux model via a fit ode lag-umming netwok [4]. The mooth tanition between cuent and voltage model i govened by the oto flux egulato which make ue of CMFO at low peed and VMFO at high peed. The obeve tuctue VMFO and CMFO ae open-loop cheme, baed on the induction machine model and they do not ue any feedback fo coecting output. Theefoe, they ae quite enitive to paamete vaiation. Flux etimation though cloed-loop tate obeve i alo poible. The obutne againt paamete mimatche and ignal noie can be impoved by employing cloed-loop obeve fo the etimation of tate vaiable. State obeve i dependent on induction machine model and machine paamete. Baically, the obeved tate ae oto flux, tato cuent and oto peed. Full tate obeve could be utilized by uing adaptive etimation technique which make etimation accuacy impoved. Speed adaptive flux obeve i a cloed-loop flux obeve which i intoduced by Kubota [5]. Adding an eo compenato to the model etablihe the cloed-loop obeve. The eo between induction moto model cuent and meaued cuent i ued to geneate coective input to dynamic ubytem of the tato and the oto. 4

25 The oto peed i alo equied fo adaptive obeve; the oto peed i obtained though a PI contolle, pimaily fom the cuent eo. V d V q i d Speed Adaptive Flux Obeve ψ d ψ q î d î q tan 1 ( ψ d / ψ ) q θ ψ i q w Figue 1-3 Input and output of the peed adaptive flux obeve Cloed-loop Kalman filteing technique can be baed on the complete machine model. The oto peed i conideed a a tate vaiable and induction moto model become non-linea, o the extended Kalman filte mut be applied. The coective input to the dynamic ubytem of the tato, oto and mechanical model ae deived o that the eo function i minimized. The eo function i evaluated on the bai of the pedicted tate vaiable, taking the noie in the meaued ignal and paamete deviation into account. The tatitical appoach educe the eo enitivity of the obeve. 1.4 Senole Vecto Contol of Induction Machine To implement vecto contol, detemination of the oto flux poition i equied. Roto peed o poition could be meaued by a haft eno. Moeove, oto flux poition could be taken by ening the ai-gap flux with the flux ening coil. 5

26 The main dawback of uing peed/poition eno ae high cot, lowe ytem eliability and pecial attention to noie. Such poblem make enole dive popula. The ecent tend in field-oiented contol i towad avoiding the ue of peed eno and uing algoithm baed on the teminal quantitie of the machine fo the etimation of the fluxe. Diffeent olution fo enole dive have been popoed in the pat few yea. Saliency baed fundamental o high fequency ignal injection i one of the flux and peed etimation technique. A method involving modulation of the oto lot [6] eult in a alient oto, and the aliency can be tacked by impoing a balanced, thee-phae, high-fequency et of hamonic fom the invete. An altenative method i to ue aliency caued by magnetic atuation [7]. A cloely elated method i peented in [8]. The main benefit of the method in [6], [7] and [8] i that the abolute oto poition can be detected. The advantage of the aliency technique i that the aliency i not enitive to actual moto paamete. The method in [6], [7] and [8] wok alo at zeo oto peed. Howeve, exta hadwae i equied and high fequency ignal injection may caue toque ipple, vibation and audible noie [9]. The oto peed can be etimated though nonlinea obeve, e.g. [1]-[18]. Altenatively, the oto peed can be conideed a a paamete and etimated uing ecuive identification, e.g. [19], [] and [5]. The latte method can alo be augmented to include machine paamete etimation (inductance, eitance, and time contant). Thee method do not need to ely on hamonic o aliency, and the hadwae equiement ae the ame a fo the digital implementation of vecto contol, given that the etimation algoithm i not too complex. Thei dawback i that the oto peed etimate will be inaccuate if the non-etimated machine paamete ae not known. 6

27 1.5 Stuctue of the Chapte Chapte include mathematical model of induction machine in tem of efeence fame notation. Field oiented contol (FOC), pace vecto pule width modulation technique ae alo intoduced at chapte. Chapte 3 cove obeve fo enole field oiented contol of induction moto. Chapte 4 include implementation of technique egading magnetic flux etimation and oto peed etimation by the ue of enole cloed loop obeve. Such that adaptive magnetic flux etimato a kind of enole cloed loop etimation technique- and Kalman filte. Chapte 5 conclude the oveall thei wok of the cloed peed loop vecto contolled induction moto. 7

28 CHAPTER INDUCTION MACHINE MODEING, FIED ORIENTED CONTRO and PWM with SPACE VECTOR THEORY.1 Sytem Equation in the Stationay a,b,c Refeence Fame The induction machine ha two electically active element: a oto and a tato hown in Figue -1. In nomal opeation, the tato i excited by altenating voltage. The tato excitation ceate a magnetic field in the fom of a otating, o taveling wave, which induce cuent in the cicuit of the oto. Thoe cuent, in tun, inteact with the taveling wave to poduce toque. To tat the analyi of induction machine, aume that both the oto and the tato can be decibed by the balanced thee phae winding. The two et ae, of coue, coupled by mutual inductance which ae dependent on oto poition. It i aumed that the winding configuation i a in the Figue -. Stato winding ae indicated a a, b and c. The a, b and c ae uppoed to have the ame numbe of effective tun, N. The b and c ae ymmetically diplaced fom the a by ±1 o. The ubcipt i ued to denote that thee winding ae tato o tationay winding. The oto winding ae imilaly aanged but have N tun. Thee winding ae deignated by a, b and c in which econd ubcipt emind u that thee thee winding ae oto o otating winding. [1] 8

29 Figue -1 Axial view of an induction machine Figue - Magnetic axe of thee phae induction machine 9

30 The voltage equation (-1) - (-8) decibing the tato and oto cicuit ae well known and widely efeed equation in the liteatue [1]. Phae voltage equation can be epeented in matix fom. v v abc abc = i = i abc abc dψ + dt dψ + dt abc abc (-1) v abc, i abc and ψ abc ae 3x1 column vecto defined by v abc v = v v a b c ia ψ a = ; iabc = ib ; ψ abc ψ b (-) i c ψ c Simila definition apply fo the oto vaiable v abc, i abc and ψ abc. vabc va ia ψ a = = vb ; iabc = ib ; ψ abc ψ b (-3) vc ic ψ c Coupling between tato and oto phae ae given in matix fom a follow. The flux linkage ae, theefoe, elated to the machine cuent. ψ ψ abc abc = ψ = ψ abc( ) abc( ) + ψ + ψ abc( ) abc( ) (-4) whee a ab ac ψ abc ab b ( ) = bc iabc (-5) ac bc c 1

31 a, a a, b a, c ψ abc( ) = b, a b, b b, c iabc (-6) c a c b,, c, c a ab ac ψ abc ab b ( ) = bc iabc (-7) ac bc c a, a a, b a, c ψ abc ( ) = b, a b, b b, c iabc (-8) c a c b,, c, c Note that a a eult of ecipocity, the inductance matix in (-7), i imply the tanpoe of the inductance matix of (-6), becaue mutual inductance ae equal. (i.e., a b b, a, = ).1.1. Detemination of Induction Machine Inductance [1] The mutual inductance between a winding x and a winding y i detemined by: l π xy = μn xn y coα (-9) g 4 whee i the adiu, l i the length of the axial length of tato and g i the length of aigap. N x i the numbe of effective tun of the winding x and N y i the numbe of effective tun of the winding y. Finally, let α be the angle between magnetic axe of the phae x and y. The elf inductance of tato phae a winding i obtained by imply etting α=, and by etting both N x and N y in (-9) to N a l π am = μn (-1) g 4 11

32 The ubcipt m i ued to denote the fact that thi inductance i magnetizing inductance. That i, it i aociated with flux line which co the ai gap and link oto a well a tato winding. In geneal, it i neceay to add a elatively malle, but moe impotant leakage tem to (-1) to account fo leakage flux. Thi tem account fo flux line which do not co the gap but intead cloe to the tato lot itelf (lot leakage) in the ai gap (belt and hamonic leakage) and at the end of the machine (end winding leakage). Hence, the total elf inductance of phae a can be expeed. = + (-11) a l am whee l epeent the leakage tem. Since the winding of the b and the c phae ae identical to phae a, it i clea that the magnetizing inductance of thee winding ae the ame a phae a o that b c = = l l + + bm cm (-1) It i appaent that am, bm, cm ae equal making the elf inductance alo equal. It i, theefoe, ueful to define tato magnetizing inductance l π m = μn (-13) g 4 o that = = = + (-14) a b c l m The mutual inductance between phae a and b, b and c, and c and a i deived by imply etting α=π/3 and N x =N y =N in (-9). The eult i 1

33 l π ab = bc = ca = μn (-15) g 8 o, in tem of (-13), ab m = bc = ca = (-16) The flux linkage of phae a, b and c eulting fom cuent flowing in the tato winding can be now expeed in matix fom a l + m m m m m ψ abc( ) = l + m iabc (-17) m m + l m et u now tun ou attention to the mutual coupling between the tato and oto winding. Refeing to Figue -, we can ee that the oto phae a i diplaced by tato phae a by the electical angle θ whee θ in thi cae i a vaiable. Similaly, the oto phae b and c ae diplaced fom tato phae b and c by θ epectively. Hence, the coeponding mutual inductance can be obtained by etting N x =N, N y =N, and α= θ in (-9). a, a = b, b = c, c l π = μnn coθ g 4 N = m coθ N (-18) The angle between the a and b phae i θ +π/3, o that N a, b = b, c = c, a = m co( θ + π / 3) (-19) N 13

34 Finally, the tato phae a i diplaced fom the oto c phae by angleθ π / 3 Theefoe,. N a, c = b, a = c, b = m co( θ π / 3) (-) N The above inductance can now be ued to etablih the flux linking the tato phae due to cuent in the oto cicuit. In matix fom, ψ N coθ co( θ + π / 3) co( θ π / 3) ( θ π / 3) coθ co( θ + π / 3) ( θ + π / 3) co( θ π / 3) coθ abc( ) = m iabc N co (-1) co The total flux linking the tato winding i clealy the um of the contibution fom the tato and the oto cicuit, (-17) and (-1), ψ = ψ + ψ (-) abc abc( ) abc( ) It i not difficult to continue the poce to detemine the oto flux linkage. In tem of peviouly defined quantitie, the flux linking the oto cicuit due to oto cuent i N + l m m m N N N 1 N N 1 N ψ abc = m l + m m iabc N N N ( ) (-3) 1 N N m 1 N 1 N N m 1 N l N + N m whee l i the oto leakage inductance. The flux linking the oto winding due to cuent in the tato cicuit i 14

35 ψ N coθ co( θ π / 3) co( θ + π / 3) ( θ + π / 3) coθ co( θ π / 3) ( θ π / 3) co( θ + π / 3) coθ abc( ) = m iabc N co (-4) co Note that the matix of (-4) i the tanpoe of (-1).The total flux linkage of the oto winding ae again the um of the two component defined by (-3) and (-4), that i ψ = ψ + ψ (-5) abc abc( ) abc( ).1.. Thee-Phae to Two-Phae Tanfomation The pefomance of thee-phae AC machine i decibed by thei voltage equation and flux linkage. Some machine inductance ae alo function of oto poition. The coefficient of the diffeential equation, which decibe the behavio of thee machine, ae time-vaying except when the oto i talled. A change of vaiable i often ued to educe the complexity of thee diffeential equation. Uing tanfomation, many popetie of electic machine can be tudied without complexitie in the voltage equation. Thee tanfomation make it poible fo contol algoithm to be implemented on the DSP. Fo thi pupoe, the method of ymmetical component ue a complex tanfomation to decouple the abc phae vaiable. By thi appoach, many of the baic concept and intepetation of thi geneal tanfomation ae conciely etablihed The Clake Tanfomation [1] The tanfomation of tationay cicuit to a tationay efeence fame wa developed by E. Clake []. The tationay two-phae vaiable of Clake tanfomation ae denoted a α and β. A hown in Figue -3, α-axi and β-axi ae othogonal. 15

36 Figue -3 Relationhip between the α, β and the abc quantitie [3] The ymbol f i ued to epeent any of the thee phae tato cicuit vaiable uch a voltage, cuent o flux linkage, vaiable along a, b and c axe ( f a, f b and f c ) can be effeed to the tationay two-phae vaiable α, β and zeo equence ( fα, f β and f ) by, [ fαβ ] = [ Tαβ ][ f abc ] (-6) whee [ f αβ ] = [ fα fβ f ] [ f ] = [ f f f ] abc a b c T T The tanfomation matix i defined a 16

37 T = αβ (-7) [ ] And invee tanfomation matix i peented by T αβ = 1 (-8) [ ].1... The Pak Tanfomation [1] In the late 19, R.H. Pak [4] intoduced a new appoach to electic machine analyi. He fomulated a change of vaiable which eplaced vaiable uch a voltage, cuent, and flux linkage aociated with fictitiou winding otating with the oto. He efeed the tato and oto vaiable to a efeence fame fixed on the oto. Fom the oto point of view, all the vaiable can be obeved a contant value. Pak tanfomation, a evolution in machine analyi, ha the unique popety of eliminating all time vaying inductance fom the voltage equation of thee-phae ac machine due to the oto pinning. Although change of vaiable ae ued in the analyi of AC machine to eliminate time-vaying inductance, change of vaiable ae alo employed in the analyi of vaiou tatic and contant paamete in powe ytem component. Fotunately, all known eal tanfomation fo thee component ae alo contained in the tanfomation to the abitay efeence fame. The ame geneal tanfomation ued fo the tato vaiable of ac machine eve a the oto 17

38 vaiable of induction machine. Pak tanfomation i a well-known thee-phae to two-phae tanfomation in machine analyi. Pak tanfomation peented in Figue -4 tanfom thee-phae quantitie f abc into two-phae quantitie developed on a otating dq axe ytem, whoe peed i w. Figue -4 Relationhip between the dq and the abc quantitie [3] f ] = [ T ( θ )][ f ] (-9) [ dq dq abc whee [ dq ] = [ fd fq f f ] T [ f ] = [ f f f ] abc a b c T whee the dq tanfomation matix i defined a: 18

39 = in 3 in in 3 co 3 co co 3 )] [ ( π θ π θ θ π θ π θ θ θ dq T (-3) and the invee i given by: + + = 1 3 in 3 co 1 3 in 3 co 1 in co )] ( [ 1 π θ π θ π θ π θ θ θ θ dq T (-31) whee θ i the angle between the phae a- axi and d - axi. and can be calculated by = + t d w () ) ( θ τ τ θ (-3) whee τ i the dummy vaiable of integation.. Refeence Fame..1. Induction Moto Model in the Abitay dq Refeence Fame The coupling between the tato and oto cicuit can be eliminated if the tato and the oto equation ae efeed to a common fame of efeence. The efeence fame ae uually elected on the bai of convenience o computational eduction. A common fame of efeence can be non-otating (i.e. w = ) which it i aociated with the tato and it i, theefoe, called a the tato o tationay efeence fame

40 with a fame notation d q. Altenatively, dq axe (i.e. the common fame) can be taken to otate with the ame angula velocity (i.e. w = w, ynchonou peed), a the oto cicuit, and i temed a the oto efeence fame with a fame notation d e q e. It may even be ueful to elect thee axe ynchonouly otating at w with one of the complex vecto denoting tato o oto voltage, cuent o even flux a abitay efeence fame. Each efeence fame ha appealing advantage. Fo example, tationay efeence fame, the d q vaiable of the machine ae in the ame fame a thoe nomally ued fo the upply netwok. Futhemoe, at the ynchonouly otating fame, the d e q e vaiable ae DC in teady tate. Once the equation of the induction machine ae deived in the abitay efeence fame, which i otating at a peed w, in the diection of the oto otation, the tanfomation between efeence fame could be obtained eaily. When the induction machine un in the tationay fame, thee equation of the induction machine can then be achieved by etting w =. Thee equation can alo be obtained in the ynchonouly otating fame by etting w = w e. In matix notation, the tato winding abc voltage equation can be expeed a: v abc dψ abc = iabc + (-33) dt Applying tanfomation to the tato winding abc voltage, the tato winding qd voltage in abitay efeence fame ae obtained. 1 dψ ψ (-34) dt dq vdq = w 1 dq + + dqidq whee

41 1 = = dq and dt d w θ (-35) ikewie, the oto voltage equation become: dq dq dq dq dq i dt d w w v 1 1 ) ( + + = ψ ψ (-36) Stato and oto flux linkage equation ae given a; = d q d q l m m l m m d q d q i i i i i i ψ ψ ψ ψ ψ ψ (-37) whee pimed quantitie denote efeed value to the tato ide. m l m l + = + = (-38) And l l m m N N g l N ) (, = = = π μ (-39) Electomagnetic toque, T em equation i given a, [ ] Nm i i w w i i w w p T d q q d d q q d em ) )( ( ) ( 3 + = ψ ψ ψ ψ (-4)

42 Uing the flux linkage elationhip fom (.37), (-4) can be implified a, T em = 3 p ( ψ qi d ψ i ) d q Nm = 3 p ( ψ di q ψ i q d ) Nm (-41) = 3 p m ( i i d q i i q d ) Nm... Induction Moto Model in dq Stationay and Synchonou Refeence Fame Once the induction moto model in the abitay dq efeence fame i etablihed, dq tationay (denoted a d q ) and ynchonou (denoted a d e q e ) efeence fame equation can be deived. To ditinguih thee two fame fom each othe, an additional upecipt will be ued, fo tationay fame vaiable and e fo ynchonouly otating fame vaiable. i. dq tationay fame induction moto equation ae given a (-4) - (-45). Stato q d voltage equation: v q = dψ dt q + i q (-4) v d = dψ dt d + i d Roto q d voltage equation:

43 3 d q d d q d q q i w dt d v i w dt d v + + = + + = ψ ψ ψ ψ ) ( ) ( (-43) whee = d q d q m m m m d q d q i i i i ψ ψ ψ ψ (-44) Toque Equation: Nm i i i i p Nm i i p Nm i i p T d q q d m d q q d q d d q em ) ( 3 ) ( 3 ) ( 3 = = = ψ ψ ψ ψ (-45) ii. dq ynchonou fame induction moto equation ae given a (-46) - (-49). Stato q e d e voltage equation:

44 4 d e q e e d e d e q e d e e q e q e i w dt d v i w dt d v + = + + = ψ ψ ψ ψ (-46) Roto q e d e voltage equation: d e q e e d e d e q e d e e q e q e i w w dt d v i w w dt d v + = + + = ψ ψ ψ ψ ) ( ) ( (-47) whee = d e q e d e q e m m m m d e q e d e q e i i i i ψ ψ ψ ψ (-48) Toque Equation: Nm i i p Nm i i p T d e q e q e d e q e d e d e q e em ) ( 3 ) ( 3 ψ ψ ψ ψ = = (-49)

45 .3 Field Oiented Contol (FOC) Following the concept outlined fo the DC machine, the equiement ae fo toque and flux contol which ha to be alo atified fo ac machine in ode to implement ucceful field oientation contol [1]. They can be baically tated a: Independent contol of the amatue cuent to ovecome the effect of amatue winding eitance, leakage inductance and induced voltage. Independent contol of flux at a contant value. Independent contol of othogonality between the flux and magnetomotive foce (MMF) axe to avoid inteaction of MMF and flux. If all of thee thee equiement ae met at all time, the toque will follow the cuent, which will allow an intantaneou toque contol and decoupled flux and toque egulation. In the DC machine, fit and econd equiement ae aued by the peence of the commutato and the epaate field excitation ytem. In AC machine, thee two equiement ae achieved by extenal contol. Next, a two phae dq model of an induction machine otating at the ynchonou peed i intoduced which will help to cay out thi decoupled contol concept to the induction machine. Thi model can be ummaized by the following equation: dψ dt e d v e d = w e eψ q + i e d (-5) dψ e q v e q = + w e eψ d + dt i e q (-51) e dψ q e = + ( w ) e e w ψ d + i q (-5) dt e dψ d e = ( w ) e e w ψ q + i d (-53) dt 5

46 e e e ψ q = iq + mi q (-54) ψ e d = i + i e d m e d (-55) e e e ψ q = miq + i q (-56) e e e ψ d = mid + i d (-57) T em 3p = m e e e e ( ψ i ψ i ) d q q d (-58) dw = Bw T (-59) dt T em J + + In thi model, it can be een fom the toque expeion (-58) that if the oto flux along the q-axi i zeo, then all the flux i aligned along the d-axi and theefoe, the toque can be intantaneouly contolled by contolling the cuent along q-axi. The q e -axi i et pependicula to the d e -axi. The flux along the q e -axi in that cae will obviouly be zeo. The phao diagam Figue -7 how thee axe. The angle θ e keep changing a the machine input cuent change. The angle θ e accuately known, d-axi of the d e q e fame can be locked to the flux vecto. The Pak and the Clake tanfomation at the machine ide i epeented in Figue -5. 6

47 Figue -5 The Pak and the Clake tanfomation at the machine ide [1] The contol input at field oiented contol can be pecified in tem of two-phae ynchonou fame i e d and i e q vaiable. i e d i aligned along the d e -axi i.e. the flux vecto, o doe i e q with the q e -axi. Thee two-phae ynchonou contol input ae fit conveted into two-phae tationay one and then to thee-phae tationay contol input. Thi can be achieved by taking the invee tanfomation of vaiable fom the abitay otating efeence fame to the tationay efeence fame and then to the abc ytem. To accomplih thi, the flux angle θ e mut be known peciely. The block diagam of thi pocedue i hown in Figue -6. In thi block diagam, * i a epeentation of commanded o deied value of vaiable. The angle θe can be found eithe by Indiect Field Oiented Contol (IFOC) o by Diect Field Oiented Contol (DFOC). The contolle implemented in thi fahion that can achieve a decoupled contol of the flux and the toque i known a field oiented contolle. The block diagam i a in Figue -1. 7

48 Figue -6 Vaiable tanfomation in the field oiented contol [1] The abence of the field angle eno, along with the eae of opeation at low peed, ha inceaed the populaity of the indiect vecto contol tategy. While the diect method i inheently the mot deiable cheme, it uffe fom the uneliability in meauing the flux. Although the indiect method can appoach the pefomance of the diect meauement cheme, it majo weakne i the accuacy of the contol gain, which heavily depend on the moto paamete. The block diagam of indiect field oiented contol and diect field oiented contol ae illutated at Figue -8 and Figue -9 epectively. 8

49 Figue -7 Phao diagam of the field oiented dive ytem Figue -8 Indiect field oiented dive ytem A it can be een fom Figue -8, indiect field oientation dive ytem need the oto eitance o oto time-contant a a paamete. Accuate knowledge of the oto eitance i eential to achieve the highet poible efficiency fom the contol tuctue. ack of thi knowledge eult in detuning of the FOC. 9

50 Figue -9 Diect field oiented dive ytem Figue -1 how the block diagam of indiect field oientation contol tategy with eno in which peed egulation i poible uing a contol loop. Figue -1 Indiect field oiented induction moto dive ytem with eno [1] 3

51 A hown in Figue -1, two-phae cuent feed the Clake tanfomation block. Thee pojection output ae indicated a i d and i q. Thee two component of the cuent povide the input to Pak tanfomation, which give the cuent in qd e the excitation efeence fame. The i e d and i e q component, which ae output of the Pak tanfomation block, ae compaed to thei efeence value i e* d, the flux efeence, and i e* q, the toque efeence. The toque command, i e* q, come fom the output of the peed contolle. The flux command, i e* d, i the output of the flux contolle which indicate the ight oto flux command fo evey peed efeence. Magnetizing cuent i e* d i uually between 4 and 6% of the nominal cuent []. Fo opeating in peed above the nominal peed, a field weakening ection hould be ued in the flux contolle ection. The cuent egulato output, v e* d and v e* q ae applied to the invee Pak tanfomation. The output of thi pojection ae v d and v q, which ae the component of the tato voltage vecto in d q the othogonal efeence fame. They fom the input of the SVPWM block. The output of thi block ae the ignal that dive the invete..4 Space Vecto Pule Width Modulation (SVPWM).4.1. Voltage Fed Invete (VSI) The voltage ouce invete (VSI) ae the mot common powe electonic convete. The block diagam of the voltage ouce invete upplied fom the uncontolled ectifie i hown in Figue -11. The DC link capacito contitute the actual voltage ouce, ince voltage aco it cannot change intantly. Since the output voltage of the diode bidge ectifie i not a pue DC, a filte inducto i included to abob ipple component. 31

52 Figue -11 The block diagam of VSI upplied fom a diode ectifie A diagam of a thee phae VSI i hown in the Figue -1. Figue -1 Thee phae voltage ouce invete upplying induction moto [1] A it can be een fom Figue -11 and Figue -1, voltage ouce invete ha bidge topology with thee banche (phae), each coniting of two powe witche 3

53 and two feewheeling diode. The invete hee i upplied fom an uncontolled, diode-baed ectifie, via DC link which contain an C filte in the inveted configuation. The uncontolled ectifie allow the powe flow fom the upply to the load only..4.. Voltage Space Vecto In tem of the deied phae voltage, the voltage pace vecto can be witten by multiplying phae voltage by thei phae oientation. V ( t) _ j j π / 3 j 4π / 3 = V an e + V bn e + V cn e (-6) A witch in a VSI i eithe up o down, with the intantaneou output voltage eithe 1 o time of Vdc. With thee banch, eight witch-tatu combination ae poible.the voltage pace vecto can intantly take on one of the following even ditinct intantaneou value a hown in Table -1. Table -1 Intantaneou Baic Voltage Vecto [5] Switching State S5 S3 S Baic Vecto v () v 1(1) v (1) v (11) 3 Value V e dc V e dc V e dc j jπ / 3 jπ / 3 33

54 1 Table -1 (Cont d) v 4 (1) V e dc j 4π / v (11) 5 v (11) 6 V e dc V e dc j5π / 3 jπ v 7 (111) In Table -1, v1 and v 7 ae the zeo vecto. The eulting intantaneou voltage vecto, which ae called the baic vecto, ae hown in Figue -13. The baic vecto fom ix ecto in Figue -13. Figue -13 Baic pace vecto [5] 34

55 .4.3. SVPWM Application to the Static Powe Bidge Space Vecto PWM (SVPWM) efe to a pecial technique of detemining the witching equence of the uppe thee powe tanito of a thee-phae voltage ouce invete (VSI). It ha been hown to geneate le hamonic ditotion in the output voltage o cuent in the winding of the moto. SVPWM povide moe efficient ue of the DC bu voltage compaed to the diect inuoidal modulation technique. In AC dive application, voltage ouce ae not inuoidal. Intead, they ae eplaced by 6 powe witche which act a on/off to the ectified DC bu voltage. The aim i to ceate inuoidal cuent in the winding to geneate otating field. Owing to the inductive natue of the phae, a peudo inuoidal cuent i ceated by modulating the duty-cycle of the powe witche. The witche hown in the Figue -1 ae activated by ignal a, b, c and thei complement value. Eight diffeent combination ae available with thi thee phae voltage ouce invete including two zeo tate. It i poible to expe each phae to neutal voltage in tem of DC upply voltage Vdc, fo each witching combination of witche a lited in Table -. The voltage, V an, V bn, and V cn ae the output voltage applied to the winding of a moto. The ix powe tanito which ae contolled by a, a, b, b, c and c gating ignal and hape the output voltage. When an uppe tanito i witched on, i.e., when a, b, and c ae 1, the coeponding lowe tanito i witched off, i.e., the coeponding a, b o c i. The on and off tate of the uppe tanito S 1, S 3, and S 5, o the tate of a, b, and c ae ufficient to evaluate the output voltage. Table - Powe bidge output voltage (V an, V bn, V cn ) Switch Poition Phae Voltage S 5 S 3 S 1 V an V bn V cn 35

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