Space Vector Modulated Direct Torque Controlled (DTC SVM) Inverter Fed Induction Motor Drive

Transcription

1 Waaw niveity of Technology Faculty of Electical Engineeing Intitute of Contol and Indutial Electonic Ph.D. Thei acin Żelechowki,. Sc. Space Vecto odulated Diect Toque Contolled (DTC SV) Invete Fed Induction oto Dive Thei upevio Pof. D Sc. aian P. Kaźmiekowki Waaw Poland, 005

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3 Acknowledgement The wok peented in the thei wa caied out duing autho Ph.D. tudie at the Intitute of Contol and Indutial Electonic in Waaw niveity of Technology, Faculty of Electical Engineeing. Some pat of the wok wee ealized in coopeation with foeign niveitie: niveity of Nevada, Reno, SA (S National Science Foundation gant Pof. Andzej Tzynadlowki), niveity of Aalbog, Denmak (Pof. Fede Blaabjeg), and company: Powe Electonic anufactue TWERD, Touń, Poland. Fit of all, I would like to expe gatitude Pof. aian P. Kaźmiekowki fo the continuou uppot and help duing wok of the thei. Hi peciou advice and numeou dicuion enhanced my knowledge and cientific inpiation. I am gateful to Pof. Andzej Sikoki fom the Białytok Technical niveity and Pof. Włodzimiez Koczaa fom the Waaw niveity of Technology fo thei inteet in thi wok and holding the pot of efeee. Specially, I am indebted to my fiend D Paweł Gabowki fo uppot and aitance. Futhemoe, I thank my colleague fom the Intelligent Contol Goup in Powe Electonic fo thei uppot and fiendly atmophee. Specially, to D Daiuz Sobczuk, D aiuz alinowki, D aiuz Cichowla, and Daiuz Świeczyńki.Sc. Finally, I would like thank to my whole family, paticulaly my paent fo thei love and patience.

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5 Content. Intoduction Page. Voltage Souce Invete Fed Induction oto Dive 6.. Intoduction 6.. athematical odel of Induction oto 6.3. Voltage Souce Invete (VSI).4. Pule Width odulation (PW) Intoduction Caie Baed PW Space Vecto odulation (SV).4.4. Relation Between Caie Baed and Space Vecto odulation Ovemodulation (O) Random odulation Technique Summay Vecto Contol ethod of Induction oto Intoduction Field Oiented Contol (FOC) Feedback ineaization Contol (FC) Diect Flux and Toque Contol (DTC) Baic of Diect Flux and Toque Contol Claical Diect Toque Contol (DTC) Cicula Flux Path Diect Self Contol (DSC) Hexagon Flux Path Summay Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) Intoduction Stuctue of DTC-SV Review DTC-SV Scheme with Cloed oop Flux Contol DTC-SV Scheme with Cloed oop Toque Contol DTC-SV Scheme with Cloe oop Toque and Flux Contol Opeating in Pola Coodinate DTC-SV Scheme with Cloe oop Toque and Flux Contol in Stato Flux Coodinate Concluion fom Review of the DTC-SV Stuctue Analyi and Contolle Deign fo DTC-SV ethod with Cloe oop Toque and Flux Contol in Stato Flux Coodinate Toque and Flux Contolle Deign Symmety Citeion ethod Toque and Flux Contolle Deign Root ocu ethod Summay of Flux and Toque Contolle Deign Speed Contolle Deign Summay 98

6 Content 5. Etimation in Induction oto Dive Intoduction Etimation of Invete Output Voltage Stato Flux Vecto Etimato Toque Etimation Roto Speed Etimation Summay 6. Configuation of the Developed I Dive Baed on DTC-SV Intoduction Block Scheme of Implemented Contol Sytem aboatoy Setup Baed on DS Dive Baed on TS30F Expeimental Reult 7.. Intoduction 7.. Pule Width odulation 7.3. Flux and Toque Contolle DTC-SV Contol Sytem 9 8. Summay and Concluion 38 Refeence 4 it of Symbol 5 Appendice 56 A.. Deivation of Fouie Seie Fomula fo Phae Voltage A.. SABER Simulation odel A.3. Data and Paamete of Induction oto A.4. Equipment A.5. dspace DS03 PPC Boad A.6. Poceo TS30F406

7 . Intoduction The Adjutable Speed Dive (ADS) ae geneally ued in induty. In mot dive AC moto ae applied. The tandad in thoe dive ae Induction oto (I) and ecently alo Pemanent agnet Synchonou oto (PS) ae offeed. Vaiable peed dive ae widely ued in application uch a pump, fan, elevato, electical vehicle, heating, ventilation and ai-conditioning (HVAC), obotic, wind geneation ytem, hip populion, etc. [6]. Peviouly, DC machine wee pefeed fo vaiable peed dive. Howeve, DC moto have diadvantage of highe cot, highe oto inetia and maintenance poblem with commutato and buhe. In addition they cannot opeate in dity and exploive envionment. The AC moto do not have the diadvantage of DC machine. Theefoe, in lat thee decade the DC moto ae pogeively eplaced by AC dive. The eponible fo thoe eult ae development of moden emiconducto device, epecially powe Inulated Gate Bipola Tanito (IGBT) and Digital Signal Poceo (DSP) technologie. The mot economical I peed contol method ae ealized by uing fequency convete. any diffeent topologie of fequency convete ae popoed and invetigated in a liteatue. Howeve, a convete coniting of a diode ectifie, a dclink and a Pule Width odulated (PW) voltage invete i the mot applied ued in induty (ee ection.3). The high-pefomance fequency contolled PW invete fed I dive hould be chaacteized by: fat flux and toque epone, available maximum output toque in wide ange of peed opeation egion, contant witching fequency, uni-pola voltage PW, low flux and toque ipple, obutne fo paamete vaiation, fou-quadant opeation,

8 . Intoduction Thee featue depend on the applied contol tategy. The main goal of the choen contol method i to povide the bet poible paamete of dive. Additionally, a vey impotant equiement egading contol method i implicity (imple algoithm, imple tuning and opeation with mall contolle dimenion lead to low pice of final poduct). A geneal claification of the vaiable fequency I contol method i peented in Fig.. [67]. Thee method can be divided into two goup: cala and vecto. Vaiable Fequency Contol Scala baed contolle Vecto baed contolle /f=cont. Volt/Hetz i = f ( ω ) Stato Cuent Field Oiented Feedback ineaization Diect Toque Contol Paivity Baed Contol Roto Flux Oiented Stato Flux Oiented Diect Toque Space - Vecto odulation Cicle flux tajectoy (Takahahi) Hexagon flux tajectoy (Takahahi) Diect (Blachke) Indiect (Hae) Open oop NFO (Jonon) & o& Cloed oop Flux & Toque Contol Fig... Geneal claification of induction moto contol method The cala contol method ae imple to implement. The mot popula in induty i contant Voltage/Fequency (V/Hz=cont.) contol. Thi i the implet, which doe not povide a high-pefomance. The vecto contol goup allow not only contol of the voltage amplitude and fequency, like in the cala contol method, but alo the intantaneou poition of the voltage, cuent and flux vecto. Thi impove ignificantly the dynamic behavio of the dive. Howeve, induction moto ha a nonlinea tuctue and a coupling exit in the moto, between flux and the poduced electomagnetic toque. Theefoe, eveal method fo decoupling toque and flux have been popoed. Thee algoithm ae baed on diffeent idea and analyi.

9 . Intoduction The fit vecto contol method of induction moto wa Field Oiented Contol (FOC) peented by K. Hae (Indiect FOC) [45] and F. Blachke (Diect FOC) [] in ealy of 70. Thoe method wee invetigated and dicued by many eeache and have now become an induty tandad. In thi method the moto equation ae tanfomed into a coodinate ytem that otate in ynchonim with the oto flux vecto. The FOC method guaantee flux and toque decoupling. Howeve, the induction moto equation ae till nonlinea fully decoupled only fo contant flux opeation. An othe method known a Feedback ineaization Contol (FC) intoduce a new nonlinea tanfomation of the I tate vaiable, o that in the new coodinate, the peed and oto flux amplitude ae decoupled by feedback [8, 83]. A method baed on the vaiation theoy and enegy haping ha been invetigated ecently, and i called Paivity Baed Contol (PBC) [88]. In thi cae the induction moto i decibed in tem of the Eule-agange equation expeed in genealized coodinate. In the middle of 80 new tategie fo the toque contol of induction moto wa peented by I. Takahahi and T. Noguchi a Diect Toque Contol (DTC) [97] and by. Depenbock a Diect Self Contol (DSC) [4, 3, 3]. Thoe method thank to the othe appoach to contol of I have become altenative fo the claical vecto contol FOC. The autho of the new contol tategie popoed to eplace moto decoupling and lineaization via coodinate tanfomation, like in FOC, by hyteei contolle, which coepond vey well to on-off opeation of the invete emiconducto powe device. Thee method ae efeed to a claical DTC. Since 985 they have been continuouly developed and impoved by many eeache. Simple tuctue and vey good dynamic behavio ae main featue of DTC. Howeve, claical DTC ha eveal diadvantage, fom which mot impotant i vaiable witching fequency. Recently, fom the claical DTC method a new contol technique called Diect Toque Contol Space Vecto odulated (DTC-SV) ha been developed. In thi new method diadvantage of the claical DTC ae eliminated. Baically, the DTC-SV tategie ae the method, which opeate with contant witching fequency. Thee method ae the main ubject of thi thei. The DTC-SV tuctue 3

10 . Intoduction ae baed on the ame fundamental and analyi of the dive a claical DTC. Howeve, fom the fomal conideation thee method can alo be viewed a tato field oiented contol (SFOC), a hown in Fig... Peented DTC-SV technique ha alo imple tuctue and povide dynamic behavio compaable with claical DTC. Howeve, DTC-SV method i chaacteized by much bette paamete in teady tate opeation. Theefoe, the following thei can be fomulated: The mot convenient indutial contol cheme fo voltage ouce invete-fed induction moto dive i diect toque contol with pace vecto modulation DTC-SV In ode to pove the above thei the autho ued an analytical and imulation baed appoach, a well a expeimental veification on the laboatoy etup with 5 kva and 8 kva IGBT invete with 3 kw and 5 kw induction moto, epectively. oeove, the contol algoithm DTC-SV ha been intoduced ued in a eial commecial poduct of Polih manufactue TWERD, Touń. In the autho opinion the following pat of the thei ae hi oiginal achievement: elaboation and expeimental veification of flux and toque contolle deign fo DTC-SV induction moto dive, development of a SABER - baed imulation algoithm fo contol and invetigation voltage ouce invete-fed induction moto, contuction and pactical veification of the expeimental etup with 5 kva and 8 kva IGBT invete, binging into poduction and teting of developed DTC-SV algoithm in Polih induty. The thei conit of eight chapte. Chapte i an intoduction. In Chapte mathematical model of I, voltage ouce invete contuction and pule width modulation technique ae peented. Chapte 3 decibe baic vecto contol method of I and give analyi of advantage and diadvantage fo all method. In thi chapte baic pinciple of diect toque contol ae alo peented. Thoe bai ae common fo claical DTC, which i peented in Chapte 3 and fo DTC-SV method. Chapte 4 i devoted to analyi and ynthei of DTC-SV contol technique. The flux, toque and peed contolle deign ae peented. In Chapte 5 the etimation 4

11 . Intoduction algoithm ae decibed and dicued. In Chapte 6 implemented DTC-SV contol algoithm and ued hadwae etup ae peented. In Chapte 7 expeimental eult ae peented and tudied. Chapte 8 include a concluion. Deciption of the imulation pogam and paamete of the equipment ued ae given in Appendixe. 5

12 . Voltage Souce Invete Fed Induction oto Dive.. Intoduction In thi chapte the model of induction moto will be peented. Thi mathematical deciption i baed on pace vecto notation. In next pat deciption of the voltage ouce invete i given. The invete i contolled in Pule Width odulation fahion. In lat pat of thi chapte eview of the modulation technique i peented... athematical odel of Induction oto When decibing a thee-phae I by a ytem of equation [66] the following implifying aumption ae made: the thee-phae moto i ymmetical, only the fundamental hamonic i conideed, while the highe hamonic of the patial field ditibution and of the magnetomotive foce (F) in the ai gap ae diegaded, the patially ditibuted tato and oto winding ae eplaced by a pecially fomed, o-called concentated coil, the effect of aniotopy, magnetic atuation, ion loe and eddy cuent ae neglected, the coil eitance and eactance ae taken to be contant, in many cae, epecially when conideing teady tate, the cuent and voltage ae taken to be inuoidal. Taking into conideation the above tated aumption the following equation of the intantaneou tato phae voltage value can be witten: d A = I AR (.a) dt A + d B = I BR (.b) dt B +

13 .. athematical odel of Induction oto d C = I C R (.c) dt C + The pace vecto method i geneally ued to decibe the model of the induction moto. The advantage of thi method ae a follow: eduction of the numbe of dynamic equation, poibility of analyi at any upply voltage wavefom, the equation can be epeented in vaiou ectangula coodinate ytem. A thee-phae ymmetic ytem epeented in a neutal coodinate ytem by phae quantitie, uch a: voltage, cuent o flux linkage, can be eplaced by one eulting pace vecto of, epectively, voltage, cuent and flux-linkage. A pace vecto i defined a: k = 3 whee: k ( t) k ( t) k ( t) A B, [ k () t + a k () t + a k () t ] A C B C (.), abitay phae quantitie in a ytem of natual coodinate, atifying the condition k ( t) + k ( t) + k ( t) = 0, a, a complex unit vecto, with a phae hift /3 nomalization facto. A B C, Im B a k 3 k a k ( t) C ak B (t) Re k A (t) A a C Fig... Contuction of pace vecto accoding to the definition (.) 7

14 . Voltage Souce Invete Fed Induction oto Dive An example of the pace vecto contuction i hown in Fig... ing the pace vecto method the I model equation can be witten a: d = IR + (.3a) dt d = IR + (.3b) dt jγ m = I + e I (.4a) jγ m = I + e I (.4b) Thee ae the voltage equation (.3) and flux-cuent equation (.4). To obtain a complete et of electic moto equation it i neceay to, fitly, tanfom the equation (.3,.4) into a common otating coodinate ytem and econdly bing the oto value into the tato ide and thidly. Thee equation ae witten in the coodinate ytem K otating with the angula peed Ω K. K K d dt K = RI K + + jωkk (.5a) d dt ( ΩK pbωm ) K K = RI K + + j (.5b) = I + I (.6a) K K K = I + I (.6b) K K K The equation of the dynamic oto otation can be expeed a: dω dt m [ BΩ ] = e m (.7) J whee: e electomagnetic toque, load toque, B vicou contant. In futhe conideation the fiction facto will be negated ( B = 0). The electomagnetic toque e can be expeed by the following fomula: 8

15 ( ).. athematical odel of Induction oto m Im I * e = pb I (.8) ( ) m Im * e = pb I (.9) Taking into conideation the fact that in the cage moto the oto voltage equal zeo and the electomagnetic toque equation (.9) a complete et of equation fo the cage induction moto can be witten a: K d dt K = RIK + + jωk K (.0a) d K 0 = RI K + + j( ΩK pbωm ) K (.0b) dt = I + I (.a) K K K = I + I (.b) K K K dω dt m p J m Im * ( ) = b I (.) Equation (.0), (.) and (.) ae the bai of futhe conideation. The applied pace vecto method a a mathematical tool fo the analyi of the electic machine a complete et equation can be epeented in vaiou ytem of coodinate. One of them i the tationay coodinate ytem (fixed to the tato) α β in thi cae angula peed of the efeence fame i zeo Ω = 0. The complex pace vecto can be eolved into component α and β. = + j (.3a) K α β K I = I + ji, I K = Iα + jiβ (.3b) K α β = + j, K = β + j β (.3c) K α β In α β coodinate ytem the moto model equation can be witten a: α = RI α + d dt α (.4a) 9

16 . Voltage Souce Invete Fed Induction oto Dive d β = RI β (.4b) dt β + d α 0 = R Iα + + pbωm β (.4c) dt d β 0 = R I β + pbωm α (.4d) α α dt = I + I (.5a) β β α = I + I (.5b) β = I + I (.5c) α β α β α = I + I (.5d) β dω dt m p J m ( I I ) = b α β β α (.6) The elation decibed above by the moto equation can be epeented a a block diagam. Thee i not jut one block diagam of an induction moto. The lay-out Contuction of a block diagam will depend on the choen coodinate ytem and input ignal. Fo intance, if it i aumed in the tationay α β coodinate ytem that the input ignal to the moto i the tato voltage, the equation (.4-.6) can be tanfomed into: d dt d dt d dt d I I dt α β α β α β = R I (.7a) α β α = R I (.7b) α β = R I p Ω (.7c) β b b m m β = R I + p Ω (.7d) α = α α (.8a) σ σ = β β (.8b) σ σ 0

17 .. athematical odel of Induction oto I I α β = α α (.8c) σ σ = β β (.8d) σ σ dω dt m p J m ( I I ) = b α β β α (.9) Thee equation can be epeented in the block diagam a hown in Fig... R α α σ I α σ σ m pb e J Ω m R I α α σ p b R β I β σ σ σ β β σ I β R Fig... Block diagam of an induction moto in the tationay coodinate ytem α β Thi epeentation of the induction moto i not good fo ue to deign a contol tuctue, becaue the output ignal flux, toque and peed depend on both input. Fom the contol point of view thi ytem i complicated. That i the eaon why thee ae a

18 . Voltage Souce Invete Fed Induction oto Dive few method popoed to decouple the flux and toque contol. It i achieved, fo example, by the oientation of the coodinate ytem to the oto o tato flux vecto. Both contol ytem ae decibed futhe in Chapte 3. The equation (.7), (.8), (.9) and the block diagam peented in the Fig.. can be ued to build a imulation model of the induction moto. It wa ued in a imulation model, which i peented in Appendix A...3. Voltage Souce Invete (VSI) The thee-phae two level VSI conit of ix active witche. The baic topology of the invete i hown in Fig..3. The convete conit of the thee leg with IGBT tanito, o (in the cae of high powe) GTO thyito and fee-wheeling diode. The invete i upplied by a voltage ouce compoed of a diode ectifie with a C filte in the dc-link. The capacito C i typically lage enough to obtain adequately low voltage ouce impedance fo the altenating cuent component in the dc-link. DC ide PW Convete T T 3 T 5 dc C S A + D S B + D 3 S C + D 5 0 T T 4 T 6 dc C S A - D S B - D 4 S C - D 6 I A I A B I C AB B C AC ide R A R B R C A A B B C C E A E B E C N I Fig..3. Topology of the voltage ouce invete

19 .3. Voltage Souce Invete (VSI) The voltage ouce invete (Fig..3) make it poible to connect each of the thee moto phae coil to a poitive o negative voltage of the dc link. Fig..4 explain the fabication of the output voltage wave in quae-wave, o ix-tep, mode of opeation. The phae voltage ae elated to the dc-link cente point 0 (ee Fig..3). a) A0 dc dc π π ωt b) B0 dc 0 dc π π ωt c) C0 dc 0 dc π π ωt d) AB dc dc 3 dc 3 0 dc 3 dc 3 π π ωt dc e) A dc 3 dc 3 0 dc 3 dc 3 π π ωt Fig..4. The output voltage wavefom in ix-tep mode The phae voltage of an invete fed moto (Fig..4e) can be expeed by Fouie eie a [6, 66]: A = π dc n= in n ( nωt) = ( ) in( nωt) m n n= (.0) whee: dc - dc upply voltage, 3

20 . Voltage Souce Invete Fed Induction oto Dive m = - peak value of the n-th hamonic, nπ ( n) dc n = +6k, k = 0, ±, ±, Deivation of the fomula (.0) i peented in Appendix A.. a) (00) b) (0) dc dc A B C A B C c) 3 (00) d) 4 (0) dc dc A B C A B C e) 5 (00) f) 6 (0) dc dc A B C A B C g) 0 (000) h) 7 () dc dc A B C A B C Fig..5. Switching tate fo the voltage ouce invete Fom the equation (.0) the fundamental peak value i given a: m () = dc (.) π 4

21 .3. Voltage Souce Invete (VSI) Thi value will be ued to define the modulation index ued in pule width modulation (PW) method (ee ection.4). Fo the ake of the invete tuctue, each invete-leg can be epeented a an ideal witch. The equivalent invete tate ae hown in Fig..5. Thee ae eight poible poition of the witche in the invete. Thee tate coepond to voltage vecto. Six of them (Fig..5 a-f) ae active vecto and the lat two (Fig..5 g-h) ae zeo vecto. The output voltage epeented by pace vecto i defined a: 3 j( v ) π dce v =...6 = 3 v (.) 0 v = 0,7 The output voltage vecto ae hown in Fig..6. Im 3 (00) (0) 4 (0) 0 (000) (00) 7 () Re 5 (00) 6 (0) Fig..6. Output voltage epeented a pace vecto Any output voltage can in aveage be geneated, of coue limited by the value of the dc voltage. In ode to ealize many diffeent pule width modulation method ae popoed [3, 7, 30, 38, 46, 47, 5, 5, 05] in hitoy. Howeve, the geneal idea i 5

22 . Voltage Souce Invete Fed Induction oto Dive baed on a equential witching of active and zeo vecto. The modulation method ae widely decibed in the next ection. Only one witch in an invete-leg (Fig..3) can be tuned on at a time, to avoid a hot cicuit in the dc-link. A delay time in the tanito witching ignal mut be ineted. Duing thi delay time, the dead-time T D tanito ceae to conduct. Two contol ignal S A +, S A - fo tanito T, T with dead-time T D ae peented in Fig..7. The duation of dead-time depend of the ued tanito. ot of them it take - 3µ. S A + S A - t T D T D t T Fig..7. Dead-time effect in a PW invete Although, thi delay time guaantee afe opeation of the invete, it caue a eiou ditotion in the output voltage. It eult in a momentay lo of contol, whee the output voltage deviate fom the efeence voltage. Since thi i epeated fo evey witching opeation, it ha ignificant influence on the contol of the invete. Thi i known a the dead-time effect. Thi i impotant in application like a enole diect toque contol of induction moto. Thee application equie feedback ignal like: tato flux, toque and mechanical peed. Typically the invete output voltage i needed to calculate it. nfotunately, the output voltage i vey difficult to meaue and it equie additional hadwae. Becaue of that fo calculation of feedback ignal the efeence voltage i ued. Howeve, the elation between the output voltage and the efeence voltage i nonlinea due to the dead-time effect [8]. It i epecially impotant 6

23 .4. Pule Width odulation (PW) fo the low peed ange when voltage i vey low. The dead-time may alo caue intability in the induction moto [5]. Theefoe, fo coect opeation of contol algoithm pope compenation of deadtime i equied. any appoache ae popoed to compenate of thi effect [, 3, 8, 9, 54, 64, 76]. The dead-time compenation i diectly connected with etimation of invete output voltage. Theefoe, compenation algoithm, which i ued in final contol tuctue of the invete i peented in Chapte Pule Width odulation (PW).4.. Intoduction In the voltage ouce invete conveion of dc powe to thee-phae ac powe i pefomed in the witched mode (Fig..3). Thi mode conit in powe emiconducto witche ae contolled in an on-off fahion. The actual powe flow in each moto phae i contolled by the duty cycle of the epective witche. To obtain a uitable duty cycle fo each witche technique pule width modulation i ued. any diffeent modulation method wee popoed and development of it i till in poge [3, 7, 30, 38, 46, 47, 5, 5, 05]. The modulation method i an impotant pat of the contol tuctue. It hould povide featue like: wide ange of linea opeation, low content of highe hamonic in voltage and cuent, low fequency hamonic, opeation in ovemodulation, eduction of common mode voltage, minimal numbe of witching to deceae witching loe in the powe component. The development of modulation method may impove convete paamete. In the caie baed PW method the Zeo Sequence Signal (ZSS) [46] ae added to extend 7

24 . Voltage Souce Invete Fed Induction oto Dive the linea opeation ange (ee ection.4.). The caie baed modulation method with ZSS coepond to pace vecto modulation. It will be widely peented in ection.4.4. All PW method have pecific featue. Howeve, thee i not jut one PW method which atifie all equiement in the whole opeating egion. Theefoe, in the liteatue ae popoed modulato, which contain fom eveal modulation method. Fo example, adaptive pace vecto modulation [79], which povide the following featue: full contol ange including ovemodulation and ix-tep mode, achieved by the ue of thee diffeent modulation algoithm, eduction of witching loe thank to an intantaneou tacking peak value of the phae cuent. The content of the highe hamonic voltage (cuent) and electomagnetic intefeence geneated in the invete fed dive depend on the modulation technique. Theefoe, PW method ae invetigated fom thi point of view. To educe thee diadvantage eveal method have been popoed. One of thee method i andom modulation (RPW). The claical caie baed method o pace vecto modulation method ae named deteminitic (DEPW), becaue thee method wok with contant witching fequency. In oppoite to the deteminitic method, the andom modulation method wok with vaiable fequency, o with andomly changed witching equence (ee ection.4.6)..4.. Caie Baed PW The mot widely ued method of pule width modulation ae caie baed. Thi method i alo known a the inuoidal (SPW), tiangulation, ubhamonic, o ubocillation method [6, 5]. Sinuoidal modulation i baed on tiangula caie ignal a hown in Fig..8. In thi method thee efeence ignal Ac, Bc, Cc ae compaed with tiangula caie ignal t, which i common to all thee phae. In thi way the logical ignal S A, S B, S C ae geneated, which define the witching intant of the powe tanito a i hown in Fig..9. 8

25 .4. Pule Width odulation (PW) dc Ac S A Bc S B Cc S C A B C t Caie N Fig..8. Block cheme of caie baed inuoidal PW dc t Ac Bc 0 dc Cc S A 0 S B 0 S C 0 A 3 dc 3 dc dc 3 dc dc AB 0 dc Fig..9. Baic wavefom of caie baed inuoidal PW 9

26 . Voltage Souce Invete Fed Induction oto Dive The modulation index m i defined a: m m = (.3) m(t) whee: m - peak value of the modulating wave, m(t) - peak value of the caie wave. The modulation index m can be vaied between 0 and to give a linea elation between the efeence and output wave. At m=, the maximum value of fundamental dc peak voltage i, which i 78.55% of the peak voltage of the quae wave (.). The maximum value in the linea ange can be inceaed to 90.7% of that of the quae wave by ineting the appopiate value of a tiple hamonic to the modulating wave. It i hown in Fig..0, which peent the whole ange chaacteitic of the modulation method [67]. Thi chaacteitic include alo the ovemodulation (O) egion, which i widely decibed in ection.4.5. π A dc [%] SVPW o SPW with ZSS O Six tep opeation SPW m Fig..0. Output voltage of VSI veu modulation index fo diffeent PW technique 0

27 .4. Pule Width odulation (PW) If the neutal point N on the AC ide of the invete i not connected with the DC ide midpoint 0 (Fig..3), phae cuent depend only on the voltage diffeence between phae. Theefoe, it i poible to inet an additional Zeo Sequence Signal (ZSS) of the 3-th hamonic fequency, which doe not poduce phae voltage ditotion and without affecting load cuent. A block cheme of the modulato baed on the additional ZSS i hown in Fig.. [46]. dc Ac Ac * S A Bc Bc * S B Cc Cc * S C A B C Calculation of ZSS Caie t N Fig... Genealized PW with additional Zeo Sequence Signal (ZSS) The type of the modulation method depend on the ZSS wavefom. The mot popula PW method ae hown in Fig.. whee unity the tiangula caie wavefom gain dc i aumed and the ignal ae nomalized to. Theefoe, ± dc atuation limit coepond to ±. In Fig.. only phae A modulation wavefom i hown a the modulation ignal of phae B and C ae identical wavefom with 0º phae hift. The modulated method illutated in Fig.. can be epaated into two goup: continuou and dicontinuou. In the continuou PW (CPW) method, the modulation wavefom ae alway within the tiangula peak boundaie and in evey caie cycle tiangle and modulation wavefom inteection. Theefoe, on and off witching occu. In the dicontinuou PW (DPW) method a modulation wavefom of a phae ha a egment which i clamped to the poitive o negative DC

28 . Voltage Souce Invete Fed Induction oto Dive bu. In thi egment ome powe convete witche do not witch. Dicontinuou modulation method give lowe (aveage 33%) witching loe. The modulation method with tiangula hape of ZSS with /4 peak value coepond to pace vecto modulation (SVPW) with ymmetical placement of the zeo vecto in a ampling peiod. It will be widely decibe in ection.4.4. In Fig.. i alo hown inuoidal PW (SPW) and thid hamonic PW (THIPW) with inuoidal ZSS with /4 peak value coeponding to a minimum of output cuent hamonic [63]. a) b) c) SPW THIPW SVPW 0.8 A = A0 0.8 A 0.8 A A A N N0-0.4 N Time Time Time d) e) f) DPW DPW DPW3 0.8 A0 0.8 A0 0.8 A A 0.4 A A N N N Time Time Time Fig... Wavefom fo PW with added Zeo Sequence Signal a) SPW, b)thipw, c) SVPW, d) DPW, e) DPW, f) DPW Space Vecto odulation (SV) The pace vecto modulation technique diffe fom the caie baed in that way, thee ae no epaate modulato ued fo each of the thee phae. Intead of them, the efeence voltage ae given by pace voltage vecto and the output voltage of the invete ae conideed a pace vecto (.). Thee ae eight poible output voltage vecto, ix active vecto - 6, and two zeo vecto 0, 7 (Fig..3). The efeence voltage vecto i ealized by the equential witching of active and zeo vecto. In the Fig..3 thee ae hown efeence voltage vecto c and eight voltage vecto, which coepond to the poible tate of invete. The ix active vecto

29 .4. Pule Width odulation (PW) divide a plane fo the ix ecto I - VI. In the each ecto the efeence voltage vecto c i obtained by witching on, fo a pope time, two adjacent vecto. Peented in Fig..3 the efeence vecto c can be implemented by the witching vecto of, and zeo vecto 0, 7. 3 (00) II (0) III I 4 (0) (t /T ) α c 0 (000) (00) 7 () (t /T ) IV VI 5 (00) V 6 (0) Fig..3. Pinciple of the pace vecto modulation The efeence voltage vecto c i ampled with the fixed clock fequency and next a ampled value ( ) T f = T, i ued fo calculation of time t, t, t 0 and t 7. The c ignal flow in pace vecto modulato i hown in Fig..4. dc f c c (T ) Secto election S A S B S C t t t 0 t 7 A B C Calculation N Fig..4. Block cheme of the pace vecto modulato 3

30 . Voltage Souce Invete Fed Induction oto Dive The time t and t ae obtained fom imple tigonometical elationhip and can be expeed in the following equation: 3 t = T in( π 3 α ) (.4a) π 3 t = T in( α ) (.4b) π Whee i a modulation index, which fo the pace vecto modulation i defined a: = c ( ix tep) c = π dc (.5) whee: c - vecto magnitude, o phae peak value, ( ix tep) - fundamental peak value ( dc π ) of the quae-phae voltage wave. The modulation index vaie fom 0 to at the quae-wave output. The length of the c vecto, which i poible to ealize in the whole ange of α i equal to 3 3 Thi i a adiu of the cicle incibed of the hexagon in Fig..3. At thi condition the modulation index i equal: dc. = 3 3 π dc dc = (.6) Thi mean that 90.7% of the fundamental at the quae wave can be obtained. It extend the linea ange of modulation in elation to 78.55% in the inuoidal modulation technique (Fig..0). Afte calculation of t and t fom equation (.4) the eidual ampling time i eeved fo zeo vecto 0 and 7. t = ( + = t + t (.7) 0,7 T t t ) 0 7 4

31 .4. Pule Width odulation (PW) The equation fo t and t ae identically fo all pace vecto modulation method. The only diffeence between the othe type of SV i the placement of zeo vecto at the ampling time. The baic SV method i the modulation method with ymmetical pacing zeo vecto (SVPW). In thi method time t 0 and t 7 ae equal: ( T t ) t = = (.8) 0 t7 t Fo the fit ecto witching equence can be witten a follow: (.9) Thi vecto witching equence in the SVPW method i hown in Fig..5a. In thi cae zeo vecto ae placed in the beginning and in the end of peiod 0, and in the cente of the peiod 7. In one ampling peiod all thee phae ae witched. To ealize the efeence vecto can alo be ued an othe witching equence, fo example: 0 0 (.30) o 7 (.3) Thee equence ae hown in Fig..5b and.5c epectively. In thee cae only two phae witch in one ampling time, and only one zeo vecto i ued 0 (Fig..5b) o 7 (Fig..5c). Thi type of modulation i called dicontinuou pule width modulation (DPW). a) b) c) S A 0 0 S A 0 0 S A S B S B S B 0 0 S C S C S C t 0 /4 t / t / t 0 /4 t 0 /4 t / t / t 0 /4 t 0 / t / t t / t 0 / t / t / t 0 t / t / T T T Fig..5. Space vecto in the ampling peiod a) SVPW, b), c) DPW The idea of dicontinuou modulation i baed on the aumption that one phae i clamped by 60 to lowe o uppe of the dc bu voltage. It give only one zeo tate pe ampling peiod (Fig..5b, c). The dicontinuou modulation povide 33% eduction 5

32 . Voltage Souce Invete Fed Induction oto Dive of the effective witching fequency and witching loe. The dicontinuou pace vecto modulation technique, like all the pace vecto method, coepond to the caie baed modulation method. It will be widely decibed in the next ection. a) DPW 3 (00) t 0 = 0 t 7 = 0 (0) 0.8 A0 t 0 = 0 t 7 = (0) t 7 = 0 t 0 = 0 0 (000) (00) 7 () A t 7 = 0 t 0 = N0 t 0 = 0 t 7 = t 0 = 0 t 7 = 0 6 (0) - 5 (00) Time b) DPW 3 (00) t 7 = 0 (0) 0.8 A0 0.6 t 0 = 0 t 0 = A 4 (0) 0 (000) (00) () -0. t 7 = 0 5 (00) t 0 = 0 t 7 = 0 6 (0) N Time c) DPW3 t 7 = 0 3 (00) t 7 = 0 t 0 = 0 t 0 = 0 (0) A0 4 (0) t 0 = 0 t 0 = 0 t 7 = 0 0 (000) (00) 7 () t 7 = A t 7 = 0 t 7 = 0 5 (00) t 0 = 0 t 0 = 0 6 (0) N Time d) DPW4 3 (00) t 0 = 0 (0) A A0 4 (0) t 7 = 0 t 7 = 0 0 (000) (00) 7 () t 0 = 0 t 0 = N0 5 (00) t 7 = 0 6 (0) Time Fig..6. The dicontinuou pace vecto modulation 6

33 .4. Pule Width odulation (PW) In the Fig..6 thee ae hown eveal diffeent kind of pace vecto dicontinue modulation. It can be een that the type of method depend on the moved do not witch ecto. Thee ecto ae adequately moved on 0, 30, 60, 90 and denoted a DPW, DPW, DPW3 and DPW4. Fig..6 alo how voltage wavefom fo each method. Fo the caie baed method with ZSS thee wavefom ae identical (Fig..). Fom the type of modulation it depend alo hamonic content, what i peented in Fig..7 fo the SVPW and DPW method. Fig..7. The output line to line voltage hamonic content a) SVPW, b) DPW In Fig..7 hamonic of output line to line voltage ae hown. The voltage fequency domain epeentation i compoed of the eie dicete hamonic component. Thee ae cluteed about multiplie of the witching fequency. In thi cae the witching fequency wa 5 khz. Spectum fo evey modulation method i diffeent. In Fig..7 the diffeence between SVPW and DPW modulation method can be een. Howeve, chaacteitic featue fo all method, which wok with contant witching fequency i cluteed highe hamonic ound multiplie of the witching fequency. Thee type of modulation method ae named deteminitic PW (DEPW). The modulation method influence alo fo cuent ditotion, toque ipple and acoutic noie emitted fom the moto. odulation technique ae till being impoved fo eduction of thee diadvantage. One of the popoed method i a andom PW (RPW) (ee ection.4.6). 7

34 . Voltage Souce Invete Fed Induction oto Dive.4.4. Relation Between Caie Baed and Space Vecto odulation All the caie baed method have equivalent to the pace vecto modulation method. The type of caie baed method depend on the added ZSS, a hown in ection.4., and type of the pace vecto modulation depending on the time of zeo vecto t 0 and t 7. A compaion of caie baed method with SV i hown in Fig.8. Thee i hown a caie baed modulation with tiangula hape of ZSS with /4 peak value. Thi method coepond to the pace vecto modulation (SVPW) with ymmetical placement of zeo vecto in ampling peiod. In Fig..8b i peented dicontinuou method DPW fo caie baed and fo SV technique. In the caie baed method thee efeence ignal * Ac, * Bc, * Cc ae compaed with tiangula caie ignal t, and in thi way logical ignal S A, S B, S C ae geneated. In the pace vecto modulation duation time of active (t, t ) and zeo (t 0, t 7 ) vecto ae calculated, and fom thee time witching ignal S A, S B, S C ae obtained. The gate pule geneated by both method ae identical. The caie baed PW method ae imple to implement in hadwae. Though the compae efeence ignal with tiangula caie ignal it eceive gate pule. Howeve, a PW invete i geneally contolled by a micopoceo/contolle nowaday. Thank to the epeentation of command voltage a pace vecto, a micopoceo uing uitable equation can calculate duation time and ealize witching equence eaily. It i poible to implement all caie baed modulation method uing the pace vecto technique. The active vecto time t and t equation ae identically fo all pace vecto modulation method. But evey method demand uitable equation fo the zeo vecto t 0 and t 7. The eight voltage vecto 0-7 coepond to the poible tate of the invete (Fig..3). Each of thee tate can be compoed by a diffeent equivalent electical cicuit. In Fig.9 the cicuit fo the vecto i peented. 8

35 .4. Pule Width odulation (PW) a) b) S A S B Cai baed PW S A S B Cai baed PW S C S C Ac * Bc * Ac * Cc * Bc * Cc * S A 0 0 S A S B S C t 0 /4 t / t / t 0 / t 0 /4 t / t / t 0 /4 Space vecto PW S B S C t 0 / t / t t / t 0 / Space vecto PW T T Fig..8. Compaion of caie baed PW with pace vecto PW a) SVPW, b) DPW A A0 dc A 0 N0 N dc B C B0 = C0 B C Fig..9. Equivalent cicuit of VSI fo the vecto 9

36 . Voltage Souce Invete Fed Induction oto Dive Taking into conideation the electical cicuit in Fig..9 the voltage ditibution can be obtained. The voltage can be witten a: A = dc ; B = dc ; C = dc (.3) A0 = dc ; B0 = dc ; C0 = dc (.33) N0 = A0 AN = dc (.34) 6 Thi analyi may be epeated fo all vecto povided to obtain voltage peented in Table.. Table.. The voltage fo the eight convete output vecto A0 dc dc dc dc dc dc dc dc B0 C0 A B C N0 dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc dc The aveage value fo ampling time of NO voltage can be witten a follow: N0 dc = t0 t + t + t7 T 3 3 fo the ecto I, III, V (.35) and N0 dc = t0 t + t + t7 T 3 3 fo the ecto II, IV, VI (.36) 30

37 .4. Pule Width odulation (PW) Fom the above equation and taking into conideation equation (.4) and (.7) the zeo vecto time fo diffeent kind of modulation can be calculated. Relation between caie baed and SV method ae peented in Table.. Thi table peent alo the zeo vecto (t 0, t 7 ) time equation fo the mot ignificant modulation method. Table.. Relation between caie baed and SV method odulation method Wavefom of the ZSS (Fig..3) Calculation of t 0 and t 7 SPW no ignal ( N0 = 0) t t 0 0 T = 4 co α π T = α π ( coα ) + 3 in fo ecto I, III, V fo ecto II, IV, VI t 7 = T t0 t t THIPW SVPW Sinuoidal with /4 amplitude Tiangula with /4 amplitude t t t 0 0 T 4 = coα co3α fo ecto I, III, V π 4 T = coα + 3 inα co3α π fo ecto II, IV, VI 7 = T t0 t t t ( T t ) 0 = t7 = t DPW Dicontinuou t 0 t = 0 7 = T t t t 7 t = 0 0 = T t t π 3 π 6 when n α < ( n + ) π 6 π 3 when ( n + ) α < ( n + ) n = 0,,, 3, 4, 5 Wavefom of the ZSS peented in Table. ae hown in Fig Ovemodulation (O) At the end of the linea ange (Fig..0) the invete output voltage i 90.7% of the maximum output peak voltage in ix-tep mode (ee equation.). The nonlinea 3

38 . Voltage Souce Invete Fed Induction oto Dive ange between thi point and ix-tep mode i called ovemodulation. Thi pat of the modulation technique i not o impotant in vecto contolled dive method fo the ake of big ditotion cuent and toque. Fo example, the ovemodulation can be applied in dive woking in open loop contol mode to inceae the value of invete output voltage. The ovemodulation ha been widely dicued in the liteatue [6, 33, 55, 75, 89]. Some of method ae popoed a extenion of the caie baed modulation and othe a extenion of pace vecto modulation. In the caie baed method ovemodulation algoithm i ealized by inceaing efeence voltage beyond the amplitude of the tiangula caie ignal. In thi cae ome witching cycle ae omitted and each phae i clamped to one of the dc bue. The ovemodulation egion fo pace vecto modulation i hown in Fig..0. The maximum length of vecto c poible to ealization in whole ange of α angle i equal 3 3 dc. It i a adiu of the cicle incibed of the hexagon. Thi value coepond to the modulation index equal to (ee equation.6). To ealize highe value a voltage ovemodulation algoithm ha to be applied. At the end of the ovemodulation egion i a ix-tep mode (at = ). 3 (00) (0) Six-tep mode = 4 (0) 0 (000) (00) 7 () (t /T ) α (t /T ) c Ovemodulation ange < < inea ange (00) 6 (0) Fig..0. Definition of the ovemodulation ange 3

39 .4. Pule Width odulation (PW) If the value of the efeence voltage beyond maximal value in the linea ange vecto c can not be ealized fo whole ange of α angle. Howeve, aveage voltage value can be obtained fo modification of the efeence voltage vecto. Becaue of the modified efeence voltage vecto ovemodulation algoithm ae not widely ued in vecto contol method of dive. To modify the efeence voltage vecto diffeent algoithm may be applied. Ovemodulation ange can be conideed a one egion [33], o it can be divided into two egion [6, 55, 75, 89]. In the algoithm whee ovemodulation egion i conideed a two egion two mode depending on the efeence voltage value wee defined. In mode I the algoithm modifie only the voltage vecto amplitude, in mode II both the amplitude and angle of the voltage vecto. Ovemodulation mode I i hown in Fig... 3 (00) (0) c 4 (0) 0 (000) α c * θ (00) 7 () 5 (00) 6 (0) Fig... Ovemodulation mode I In thi mode voltage vecto c coe the hexagon bounday at two point in each ecto. Thee i a lo of fundamental voltage in the egion whee efeence vecto exceed the hexagon bounday. To compenate fo thi lo, the efeence vecto amplitude i inceaed in the egion whee the efeence vecto i in hexagon bounday. A modified efeence voltage tajectoy poceed patly on the hexagon and patly on the cicle. Thi tajectoy i hown in Fig... 33

40 . Voltage Souce Invete Fed Induction oto Dive In the hexagon tajectoy pat only active vecto ae ued. The duation of thee vecto t and t ae obtained fom tigonometical elationhip and can be expeed in the following equation: 3 coα inα t = T (.37a) 3 coα + inα t = (.37b) T t t 0 = t 7 = 0 (.37c) The output voltage wavefom i given appoximately by linea egment fo the hexagon tajectoy and inuoidal egment fo the cicula tajectoy. Bounday of the egment i detemined by a coove angle θ which depend on the efeence voltage value. A known fom Fig.. the uppe limit in mode I i when θ = 0. Then the voltage tajectoy i fully on the hexagon. The fundamental peak value geneated in thi way voltage i 95% of the peak voltage of the quae wave [75]. It give modulation index = Fo the modulation index highe then 0.95 the ovemodulation mode II i applied. The ovemodulation mode II i hown in Fig... In thi mode not only the efeence vecto amplitude i modified but alo an angle. The efeence angle fom α to α * changed. i 3 (00) (0) α h c * c 4 (0) 0 (000) α α α h (00) 7 () 5 (00) 6 (0) Fig... Ovemodulation mode II whee both amplitude and angle i changed 34

41 .4. Pule Width odulation (PW) The tajectoy of * c i maintained on the hexagon which define amplitude of the efeence voltage vecto. The angle i calculated fom the following equation: α 0 α α h π = π 6 α h 6 π 3 fo 0 α α α < α < π 3 α h π 3 α α π 3 h h h (.38) whee: α h hold-angle. Thi angle uniquely contol the fundamental voltage. It i a nonlinea function of the modulation index [6, 55]. In Fig.. i hown the efeence vecto tajectoy geneated fo the fit ecto. Thi tajectoy i obtained in thee tep. Fit pat, if angle α i le than the epective value of α h, the algoithm hold the vecto c * at the vetex ( ). Next pat i fo α fom α h to π 3 α h. In thi angle ange the efeence vecto move along the hexagon. In the lat ange, fom π 3 α h to α h, the vecto * c i held until the next vetex ( ). The ovemodulation mode II wok up to the ix-tep mode fo α h equal zeo. The ix-tep mode chaacteized by election of the witching vecto fo one-ixth of the fundamental peiod. In thi cae the maximum poible invete output voltage i geneated Random odulation Technique The pule width modulation technique i impotant fo dive pefomance in epect to voltage and cuent hamonic, toque ipple, acoutic noie emitted fom an induction moto and alo electomagnetic intefeence (EI). Diffeent appoache wee ued in PW technique fo eduction of thee diadvantage. One of the popoed method i andom pule width modulation (RPW) [5, 7,, 4, 6, 68, 04]. Peviouly peented modulation method wee named deteminitic pule width modulation (DEPW), becaue of contant ampling and witching fequency and all 35

42 . Voltage Souce Invete Fed Induction oto Dive cycle the witching equence i deteminitic. In RPW method the witching fequency o the witching equence change andomly. One of the popoed andom modulation technique i a method with andomly vaied length of coincident witching and ampling time of the modulato. Thi method wa named RPW. The ampling and witching cycle in DEPW with RPW i compaable hown in Fig..3. The efeence voltage vecto c, which ae calculated in one ampling time T and ealized in the next witching time T w ae hown. In dive ytem the contolle motly opeate in ynchonim with modulato and in RPW aie poblem in the contol ytem, when it wok with vaiable ampling fequency. An additional contol algoithm with vaiable ampling fequency i difficult tin a digital implementation. a) () c () c (3) c (K) c ( n ) c (n) c ( n+) c ampling cycle 3... n- n... witching cycle 3... n- n... T = T w b) () c () c (3) c (K) c ( n ) c (n) c ( n+) c ampling cycle 3... n- n witching cycle 3... n- n... T = T w... Fig..3. Sampling and witching cycle a) DEPW, b) RPW Fo elimination of thee diadvantage andom modulation technique wee popoed, which opeate with a fixed witching and ampling fequency. Thee method andomly change witching equence in the inteval. Thee of thee method ae hown in Fig..4 [6]. Fit of them (Fig..4a) i andom lead-lag modulation (R). In thi method pule poition i eithe commencing at the beginning of the witching inteval (leading-edge 36

43 .4. Pule Width odulation (PW) modulation) o it tailing edge i aligned with the end of the inteval (lagging-edge modulation). A andom numbe geneato contol the choice between leading and legging edge modulation. In Fig..4b i hown a andom cente pule diplacement (RCD) method. In thi technique pule ae geneated identically a in the SVPW method (Fig..5), but common pule cente i diplaced by the amount α T fom the middle of the peiod. The paamete α i vaied andomly within a band limited by the maximum duty cycle. The lat peented method (Fig..4c) i andom ditibution of the zeo voltage vecto (RZD). Additionally ditibution of the zeo vecto can by diffeent, until only one zeo vecto in witching cycle in the dicontinuou method (Fig..5b, c). Thi fact i utilized in the andom ditibution of the zeo voltage vecto, whee the popotion between the time duation fo the two zeo vecto 0 (000) and 7 () i andomized in the witching cycle. a) ead ag ag ead S A S B S C T T T T b) αt αt αt αt S A S B S C T T T T c) S A S B S C T T T T Fig..4. Diffeent fixed witching andom modulation cheme a) Random lead-leg modulation (R), b) Random cente diplacement (RCD), c) Random zeo vecto ditibution (RZD) 37

44 . Voltage Souce Invete Fed Induction oto Dive The main diadvantage of the RPW method (Fig..3b) i vaiable witching fequency. Fo elimination of thi diadvantage RPW [9] wa popoed, which opeate with fixed ampling fequency and vaiable witching fequency. The pinciple of thi method i hown in Fig..5. T () c () c (3) c (K) c ( n ) c (n) c ( n+) c ampling cycle witching cycle t 3... n- n n- n T w... Fig..5. Sampling and witching cycle in RPW technique In thi method the tat of each witching cycle i delayed with epect to that of the coincident ampling cycle by a andom vaied time inteval t. It i given a: t = T (.39) whee denote a andom numbe between 0 and. Time inteval the ake of minimum witching time of invete. t i limited fo Fig..6. The output line to line voltage hamonic content a) RPW, b) RPW Coeponding pecta fo the RPW and RPW technique ae hown in Fig..6a and.6b epectively. It can be een that the hamonic clute typical fo the detemination modulation (compaed to Fig..7) ae pactically eliminated by the 38

45 .5. Summay andom modulation technique. Simulation eult peented in both figue (Fig..7 and Fig..6) wa done at the ame condition: ampling fequency 5 khz, output fequency 50 Hz..5. Summay In thi chapte mathematical deciption of I baed on complex pace vecto wa peented. The complete equation et i the bai of futhe conideation of contol and etimation method. The tuctue of two level voltage ouce invete wa peented. The main featue and voltage foming method wee decibed. Fo the ake of dead-time and voltage dop on the emiconducto device the invete ha nonlinea chaacteitic. Theefoe, in contol cheme compenation algoithm ae needed. The invete i contolled by pule width modulation (PW) technique. The modulation method ae divided into two goup: tiangula caie baed and pace vecto modulation. Between thoe two goup thee ae imple elation. All the caie baed method have equivalent to the pace vecto modulation method. The type of caie baed method depend on the added ZSS and type of the pace vecto modulation depend on the placement of zeo vecto in the ampling peiod. Peented modulation method will be ued in the final dive. Thi chapte contain compete eview of the modulation technique, including ome andom modulation method. Thoe method have vey inteeting advantage and can be implemented in pecial application of I dive. Cuently they have not been implemented in a peented eially poduced dive. Howeve, it will be offeed a an option in a nea futue. Some expeimental eult fo the implemented modulation method ae hown in Chapte 7. 39

46 3. Vecto Contol ethod of Induction oto 3.. Intoduction In thi chapte eview of the mot ignificant I vecto contol method i peented. Accoding to the claification peented in Chapte. The theoetical bai and hot chaacteitic fo all method ae given. The diect toque contol (DTC) method ceate a bae fo futhe analyze of DTC-SV algoithm. Theefoe, DTC i moe detailed dicued (ee ection 3.4). 3.. Field Oiented Contol (FOC) The pinciple of the field oiented contol (FOC) i baed on an analogy to the epaately excited dc moto. In thi moto flux and toque can be contolled independently. The contol algoithm can be implemented uing imple egulato, e.g. PI-egulato. In induction moto independent contol of flux and toque i poible in the cae of coodinate ytem i connected with oto flux vecto. A coodinate ytem d q i otating with the angula peed equal to oto flux vecto angula peed Ω = Ω, K which i defined a follow: dγ Ω = (3.) dt The otating coodinate ytem d q i hown in Fig. 3.. The voltage, cuent and flux complex pace vecto can be eolved into component d and q. = + j (3.a) K d q I = I + ji, I K = I d + jiq (3.b) K d q K = d + j q, K = d = (3.c)

47 3.. Field Oiented Contol (FOC) β q I β I d Ω I q δ I d γ I α α Fig. 3.. Vecto diagam of induction moto in tationay α β and otating d q coodinate In d q coodinate ytem the induction moto model equation (.0-.) can be witten a follow: d d dt d = RI d + Ω q (3.3a) d q q = RI q + + Ω d dt (3.3b) d 0 = R Id + dt (3.3c) q ( Ω p Ω ) 0 = R I + (3.3d) b m = I + I (3.4a) d q d q d = I + I (3.4b) q = I + I (3.4c) q d q d 0 = I + I (3.4d) dω dt m m = pb I q J (3.5) The equation 3.3c and 3.4c can be eay tanfomed to: 4

48 3. Vecto Contol ethod of Induction oto d dt R R = I d (3.6) The moto toque can by expeed by oto flux magnitude component I q a follow: and tato cuent e m = pb Iq (3.7) Equation (3.6) and (3.7) ae ued to contuct a block diagam of the induction moto in d q coodinate ytem, which i peented in Fig. 3.. R I d R e I q p b m e J Ω m Fig. 3.. Block diagam of induction moto in d q coodinate ytem The main featue of the field oiented contol (FOC) method i the coodinate tanfomation. The cuent vecto i meaued in tationay coodinate α β. Theefoe, cuent component I, I β mut be tanfomed to the otating ytem α d q. Similaly, the efeence tato voltage vecto component α c, β c, mut be tanfomed fom the ytem d q to α β. Thee tanfomation equie a oto flux angle γ. Depending on calculation of thi angle two diffeent kind of field oiented contol method maybe conideed. Thoe ae Diect Field Oiented Contol (DFOC) and Indiect Field Oiented Contol (IFOC) method. 4

49 3.. Field Oiented Contol (FOC) Fo DFOC an etimato o obeve calculate the oto flux angle γ. Input to the etimato o obeve ae tato voltage and cuent. An example of the DFOC ytem i peented in Fig dc c ec b p m c I dc I qc PI PI d q α β α c β c SV S A S B S C γ Flux Etimato α β Voltage Calculation I d d q I α I I q α β I β 3 oto Fig Block diagam of the Diect Field Oiented Contol (DFOC) Fo the IFOC oto flux angle γ i obtained fom efeence I dc, I qc cuent. The angula peed of the oto flux vecto peed can be calculated a follow: whee Ω = Ω + p Ω (3.8) l b m Ω l i a lip angula peed. It can be calculated fom (3.3d) and (3.4d). Ω l R = Iqc (3.9) Idc In Fig. 3.4 a block diagam of the IFOC i hown. 43

50 3. Vecto Contol ethod of Induction oto dc c ec p m b c I dc I qc PI PI d q α β α c β c SV S A S B S C γ R I dc I d d q I α I Ω I q α β I β 3 oto Ω l p b Ω m Fig Block diagam of the Indiect Field Oiented Contol (IFOC) In both peented example efeence cuent in otating coodinate ytem I dc, I qc ae calculated fom the efeence flux and toque value. Taking into conideation the equation decibing I in field oiented coodinate ytem (3.6) and (3.7) at teady tate the fomula fo the efeence cuent can be witten a follow: I I dc qc = (3.0) = ec (3.) pbm c The popety of the FOC method can be ummaized a follow: the method i baed on the analogy to contol of a DC moto, FOC method doe not guaantee an exact decoupling of the toque and flux contol in dynamic and teady tate opeation, elationhip between egulated value and contol vaiable i linea only fo contant oto flux amplitude, 44

51 3.3. Feedback ineaization Contol (FC) full infomation about moto tate vaiable and load toque i equied (the method i vey enitive to oto time contant), cuent contolle ae equied, coodinate tanfomation ae equied, a PW algoithm i equied (it guaantee contant witching fequency), in the DFOC oto flux etimato i equied, in the IFOC mechanical peed i equied, the tato cuent ae inuoidal except of high fequency witching hamonic Feedback ineaization Contol (FC) The tanfomation of the induction moto equation in the field coodinate ha a good phyical bai becaue it coepond to the decoupled toque poduction in a epaately excited DC moto. Howeve, fom the theoetical point of view, othe type of coodinate can be elected to achieve decoupling and lineaization of the induction moto equation. In [8] it i hown that a nonlinea dynamic model of I can be conideed a equivalent to two thid-ode decoupled linea ytem. In [70] a contolle baed on a multicala moto model ha been popoed. The new tate vaiable have been choen. In eult the moto peed i fully decoupled fom the oto flux. In [8] the autho popoed a nonlinea tanfomation of the moto tate vaiable, o that in the new coodinate, the peed and oto flux amplitude ae decoupled by feedback. Othe popoed alo modified method baed on Feedback ineaization Contol like in [93, 94]. In the example given new quantitie fo contol of oto flux magnitude and mechanical peed wee choen [93]. Fo thi pupoe the induction moto equation (.0-.) can be witten in the following fom: x& = f (x) + g + g (3.) α α β β whee: 45

52 3. Vecto Contol ethod of Induction oto = J I I I Ω p I Ω p I Ω p I Ω p f m b m b m b m b ) ( ) ( α β β α β β α α β α β β α α β α µ γ αβ β γ β αβ α α α α x (3.3) T g = ,,,, σ α (3.4) T g = ,,,, σ β (3.5) [ ] T x m Ω I I,,,, β α β α = (3.6) and R = α (3.7) σ β = (3.8) R R σ γ + = (3.9) J m p b = µ (3.0) Becaue β α m Ω,, ae not dependent on β α, it i poible to choe vaiable dependent on x: ) x ( = + = β α φ (3.) = Ω m (x) φ (3.) If it i aumed that ) (x φ, ) (x φ ae output vaiable, the full definition of new coodinate can be given by: φ (x) = z (3.3a) φ (x) f z = (3.3b)

53 3.3. Feedback ineaization Contol (FC) z 3 = φ (x) (3.3c) z 4 = f φ (x) (3.3d) β z = 5 actan (3.3e) α It hould be mentioned that the goal of the contol i to obtain contant flux amplitude and to follow the efeence angula peed. The fifth vaiable cannot be fully lineaized. Additionally, it i not contollable (the fifth vaiable coepond to lip in the moto). Theefoe, the lat equation i not conideed. Then the dynamic of the ytem ae given by: && z φ f = + D && z fφ 3 α β (3.4) whee gα fφ g β fφ D = (3.5) gα fφ g β fφ If φ 0 (the amplitude of flux i not zeo) then det( D) 0 and it i poible to define the lineaization feedback a: β - fφ v = D + (3.6) fφ v α Then the eulting ytem i decibed by the equation: z & = z (3.7a) z & = v (3.7b) z & 3 = z 4 (3.7c) z & 4 = v (3.7d) and the final block diagam of the induction moto with the new defined contol ignal can be hown a in Fig

54 3. Vecto Contol ethod of Induction oto ν z Ω m ν z 4 J e Fig Block diagam of the induction moto with new v and v contol ignal The contol ignal v, v ae calculated by uing linea feedback a follow: ( z z ) k v = ef (3.8) k z ( z3 z3 ) k 4 v = ef (3.9) k z whee coefficient k, k, k, k ae choen to eceive efeence cloe loop ytem dynamic. An example of a FC ytem fo PW invete-fed induction moto i peented in Fig The popety of the FC can be ummaized a follow: it guaantee exactly decoupling of the moto peed and oto flux contol in both dynamic and teady tate, the method i implemented in a tate vaiable contol fahion and need complex ignal poceing, full infomation about moto tate vaiable and load toque i equied, thee ae no cuent contolle, a PW vecto modulato i equied, what futhe guaantee contant witching fequency, 48

55 3.4. Diect Flux and Toque Contol (DTC) the tato cuent ae inuoidal except of high fequency witching hamonic. dc c Ω mc Flux Contolle Speed Contolle ν ν Contol Signal Tanfomation β c α c Vecto odulato S A S B S C Voltage Calculation z I α z z 3 z 4 z 5 Feedback Signal Tanfomation I β ˆα ˆβ Flux Etimato ˆ I oto Ω m Fig Block cheme of the feedback lineaization contol method 3.4. Diect Flux and Toque Contol (DTC) Baic of Diect Flux and Toque Contol A it wa mentioned in ection 3. in the claical vecto contol tategy (FOC) the toque i contolled by the tato cuent component I q in accodance with equation (3.7). Thi equation can alo be witten a: whee: m e = pb I inδ (3.30) δ - angle between oto flux vecto and tato cuent vecto. The fomula (3.30) can be tanfomed into the equation: e m = pb in δ (3.3) whee: δ - angle between oto and tato flux vecto. 49

56 3. Vecto Contol ethod of Induction oto It can be noticed that the toque depend on the tato and oto flux magnitude a well a the angleδ. The vecto diagam of I i peented in Fig The two angel δ and δ ae alo hown in Fig The angle δ i impotant in FOC algoithm, wheea δ in DTC technique. β I δ γ δ γ α Fig Vecto diagam of induction moto Fom the moto voltage equation (.0a), fo the omitted voltage dop on the tato eitance, the tato flux can by expeed a: d = dt (3.3) Taking into conideation the output voltage of the invete in the above equation it can be witten a: whee: t = vdt (3.33) 0 3 j( v ) π dce v =...6 = 3 v (3.34) 0 v = 0,7 Equation (3.33) decibe eight voltage vecto which coepond to poible invete tate. Thee vecto ae hown in Fig Thee ae ix active vecto - 6 and two zeo vecto 0, 7. 50

57 3.4. Diect Flux and Toque Contol (DTC) Im 3 (00) (0) 4 (0) 0 (000) (00) 7 () Re 5 (00) 6 (0) Fig Invete output voltage epeented a pace vecto It can be een fom (3.33), that the tato flux diectly depend on the invete voltage (3.34). By uing one of the active voltage vecto the tato flux vecto move to the diection and ene of the voltage vecto. It can be obeved by imulation of ix-tep mode (Fig. 3.9) and PW opeation (Fig. 3.0). In Fig. 3.9 i well hown how tato flux change diection fo the cycle equence of the active voltage vecto. Obviouly, the ame effect i fo the PW opeation (Fig. 3.0). Howeve, in thi cae the contol algoithm chooe coect voltage vecto, thank to that wavefom i cloe to be inuoidal. In thi imulation a low ampling fequency i ued (0.5kHz) fo bette peenting the effect. A zoom pat of the flux vecto tajectoy i hown in Fig. 3.. In induction moto the oto flux i lowly moving but the tato flux can be changed immediately. In diect toque contol method the angle between tato and oto flux δ can be ued a a vaiable of toque contol (3.3). oeove tato flux can be adjuted by tato voltage in imple way. Theefoe, angle δ a well a toque can be changed thank to the appopiate election of voltage vecto. Thee ae the geneal bae of the diect flux and toque contol method. Thoe conideation and above equation can be ued in analyi of the claical DTC algoithm a well a in new popoed method. It i alo bae of the DTC-SV method, which ae peented in Chapte 4. 5

58 3. Vecto Contol ethod of Induction oto a) b) Fig I unde ix-tep mode a) voltage and tato flux wavefom, b) tato flux tajectoy a) b) Fig I unde PW opeation a) voltage and tato flux wavefom, b) tato flux tajectoy 5

59 3.4. Diect Flux and Toque Contol (DTC) β voltage 4 applied voltage 3 applied voltage 4 applied voltage 3 applied voltage 4 applied 3 (00) (0) voltage 3 applied voltage applied 4 (0) 0 (000) (00) voltage 3 applied 7 () α 5 (00) 6 (0) Fig. 3.. Foming of the tato flux tajectoy by appopiate voltage vecto election Claical Diect Toque Contol (DTC) Cicula Flux Path The block diagam of claical DTC popoed by I. Takahahi and T. Nogouchi [97] i peented in Fig. 3.. c ec e e Flux Contolle d d Vecto Selection Table γ (N) S A S B S C dc Toque Contolle Secto Detection Voltage Calculation ˆ e ˆ ˆ α ˆβ Flux and Toque Etimato I oto Fig. 3.. Block cheme of the diect toque contol method 53

60 3. Vecto Contol ethod of Induction oto The tato flux amplitude ignal which ae compaed with the etimated c and the electomagnetic toque c ae the efeence ˆ and ˆ e value epectively. The flux e and toque e eo ae deliveed to the hyteei contolle. The digitized output vaiable d, d and the tato flux poition ecto ( N) γ elect the appopiate voltage vecto fom the witching table. Thu, the election table geneate pule S A, S B, S C to contol the powe witche in the invete. Fo the flux i defined two-level hyteei contolle, fo the toque thee-level, a it i hown in Fig a) b) d d e H e H Fig The hyteei contolle a) two-level, b) thee-level The output ignal d, d ae defined a: d = fo e > H (3.35a) d = 0 fo e < H (3.35b) d = fo e > H (3.36a) d = 0 fo e = 0 (3.36b) d = fo e < H (3.36c) In the claical DTC method the plane i divided fo the ix ecto (Fig. 3.4), which ae defined a: π π Secto : γ, + (3.37a) 6 6 π π Secto : γ +, 6 (3.37b) π 5π Secto 3: γ +, + (3.37c) 6 54

61 3.4. Diect Flux and Toque Contol (DTC) Secto 4: + π 5 γ, 6 6 (3.37d) Secto 5: π γ, 6 (3.37e) π π Secto 6: γ, 6 (3.37f) Secto 3 β 3 (00) Secto (0) Secto 4 4 (0) 0 (000) (00) 7 () α Secto 5 (00) 6 (0) Secto 5 Secto 6 Fig Secto in the claical DTC method Fo the tato flux vecto laying in ecto (Fig. 3.5) in ode to inceae it magnitude the voltage vecto,, 6 can be elected. Conveely, a deceae can be obtained by electing 3, 4, 5. By applying one of the zeo vecto 0 o 7 the integation in equation (3.33) i topped. The tato flux vecto i not changed. Fo the toque contol, angle between tato and oto flux δ i ued (equation 3.3). Theefoe, to inceae moto toque the voltage vecto, 3, 4 can be elected and to deceae, 5, 6. The above conideation allow contuction of the election table a peented in Table

62 3. Vecto Contol ethod of Induction oto β δ Secto α Fig Selection of the optimum voltage vecto fo the tato flux vecto in ecto Table 3.. Optimum witching table d d Secto Secto Secto 3 Secto 4 Secto 5 Secto The ignal wavefom fo teady tate opeation of claical DTC method ae hown in Fig The DTC wa popoed a an analog contol method. The implementation of the hyteei contolle in the analog etup i eay and the contol ytem wok popely. When the hyteei contolle i implemented in a digital ignal poceo (DSP), it opeation i quite diffeent fom that of the analog cheme [9]. The digital implementation of the hyteei contolle i alo called ampled hyteei. 56

63 3.4. Diect Flux and Toque Contol (DTC) a) b) Fig Steady tate opeation fo the claical DTC method ( f = 40kHz) a) ignal in time domain, b) tato flux tajectoy In Fig. 3.7 ae peented typical witching equence of the toque hyteei contolle fo the analog (Fig. 3.7a) and fo the digital (Fig. 3.7b) implementation. 57

64 3. Vecto Contol ethod of Induction oto a) b) S/H c + H m c c H m t t t 3 T T T Fig Opeating of the toque hyteei contolle a) analog, b) digital In the analog implementation the toque ipple ae kept exactly within the hyteei band and the witching intant ae not equally paced. The digital ytem opeate at fixed ampling time T and wok like analog only fo high ampling fequencie f =. T Fo the lowe apling fequency the witching intant ae not when the etimated toque coe the hyteei band but on the ampling time. Thi ituation i peented in Fig. 3.7b. The imulation eult illutated contol ytem behavio at lowe ampling fequency f = 5kHz ae given in Fig It can be een that cuent and toque ipple ae bigge compae to thi one opeate with ampling fequency f = 40kHz (ee Fig. 3.6). The influence of the toque hyteei band fo the toque eo and witching fequency at diffeent ampling fequencie i hown in Fig. 3.9 and Fig At low ampling fequency f = 0kHz (Fig. 3.9) the witching fequency and toque eo ae not enitive fo hyteei band. Howeve, at the high ampling fequency f = 80kHz (Fig. 3.0) when the hyteei band i inceaed the witching fequency deceae and the toque eo inceae. Simulated eult how that the hyteei contolle need a high ampling fequency to obtain a pope opeation. The toque and flux eo ae calculated accoding to equation: ˆ c ε ψ = 00% (3.38a) N 58

65 3.4. Diect Flux and Toque Contol (DTC) whee: ˆ e ec ε = 00% (3.38b) en N - nominal tato flux, en - nominal toque Fig Steady tate opeation fo the claical DTC method opeating with lowe f = 5kHz ampling fequency ( ) The aveage value of the flux and toque eo ae calculated in a peiod of the fundamental fequency. 59

66 3. Vecto Contol ethod of Induction oto a) f w [Hz] ,0 0,5,0,5,0,5 3,0 3,5 4,0 H m [Nm] b) ε Μ _av [%] ,06,97,00 9,43 9,93 0,68,03 9,65 0,7 0,0 0,5,0,5,0,5 3,0 3,5 4,0 H m [Nm] Fig Simulated eult fo claical DTC a) witching fequency and b) toque eo a a function of the toque hyteei band at ampling fequency f = 0kHz a) f w [Hz] ,0 0,5,0,5,0,5 3,0 3,5 4,0 H m [Nm] b) ε Μ _av [%] ,43,64 3,06 4, 5,36 6,56 7,77 8,94 0,7 0,0 0,5,0,5,0,5 3,0 3,5 4,0 H m [Nm] Fig Simulated eult fo claical DTC a) witching fequency and b) toque eo a a function of the toque hyteei band at ampling fequency f = 80kHz 60

67 3.4. Diect Flux and Toque Contol (DTC) The claical DTC method can be chaacteized a follow: Advantage: imple tuctue: o no coodinate tanfomation, o no epaate voltage modulation block, o no cuent contol loop, vey good flux and toque dynamic pefomance, Diadvantage: vaiable witching fequency, poblem duing tating and low peed opeation, high toque ipple, flux and cuent ditotion caued by tato flux vecto ecto poition change high ampling fequency i equied fo digital implementation Diect Self Contol (DSC) Hexagon Flux Path The block diagam of the diect elf contol method popoed by. Depenbock [3, 3] i peented in Fig. 3.. Thi method wa mainly applied in high powe application, which equied fat toque dynamic and low witching fequency [96]. Baed on the command tato flux C, the flux compaato geneate digital vaiable d A, c and the actual phae component A, B, d B, d C, which coepond to active voltage vecto ( 6 ). The hyteei toque contolle geneate the ignal d m, which detemine zeo tate. Fo the contant flux egion, the contol algoithm i a follow: S A = d C, B d A S =, S C = d B fo d m = (3.39a) S = 0, S = 0, S = 0 fo d = 0 (3.39b) A B C m 6

68 3. Vecto Contol ethod of Induction oto ψ c Flux Compaato d A dc S B d B S C S A ec d m Toque Contolle d C Voltage Calculation ψˆ C ψˆb ψˆ A ABC α β ψˆα ψˆβ ˆ e Flux and Toque Etimato I oto Fig. 3.. Block diagam of Diect Self Contol method The ignal wavefom fo teady tate opeation of DSC method ae hown in Fig. 3.. It can be een that the flux tajectoy i identical with that fo the ix-tep mode (Fig. 3.9). Thi follow fom the fact that the zeo voltage vecto top the flux vecto, but do not affect it tajectoy. The dynamic pefomance of toque contol fo the DSC ae imila a fo the claical DTC. The popety of the DSC can be ummaized a follow: hexagonal tajectoy of the tato flux vecto fo PW opeation, block type of PW (not inuoidal), non-inuoidal cuent wavefom, witching election table i not equied, low (minimum) invete witching fequency (depended on hyteei toque band), vey good toque and flux contol dynamic. 6

69 3.4. Diect Flux and Toque Contol (DTC) a) b) Fig. 3.. Steady tate opeation fo the DSC method a) ignal in time domain, b) tato flux tajectoy Seveal olution have been popoed to impove the conventional DSC. Fo intance, eduction of the cuent ditotion ha been achieved by intoducing tato flux ecto [0] o by poceing not only the tato flux value, but alo the tato flux 63

70 3. Vecto Contol ethod of Induction oto angle [09]. Alo olution baed on fuzzy logic and neual netwok olution wee popoed [85, 90] Summay In thi chapte eview of ignificant vecto contol method of I ha been peented. The chaacteitic featue fo all contol cheme wee decibed. The FC tuctue guaantee exact decoupling of the moto peed and oto flux contol in both dynamic and teady tate. Howeve, it i complicated and difficult to implement in pactice. Thi method equie complex computation and additionally it i enitive to change of moto paamete. Becaue of thee featue thi method wa not choen fo implementation. Advantage Table 3. Compaion of contol method FOC DTC DTC-SV odulato Contant witching fequency nipola invete output voltage ow witching loe ow ampling fequency Cuent contol loop Diadvantage Coodinate tanfomation A lot of contol loop Contol tuctue depended on oto paamete Stuctue independent on oto paamete, univeal fo I and PS Simple implementation of enole opeation No coodinate tanfomation No cuent contol loop No modulato Bipola invete output voltage Vaiable witching fequency High witching loe High ampling fequency Stuctue independent on oto paamete, univeal fo I and PS Simple implementation of enole opeation No coodinate tanfomation No cuent contol loop odulato Contant witching fequency nipola invete output voltage ow witching loe ow ampling fequency Due to above mentioned fact the FOC and DTC method wee conideed next. Analyi of advantage and diadvantage of FOC and DTC method eulted in a each fo method which will eliminate diadvantage and keep advantage of thoe 64

71 3.5. Summay method. Table 3. ummaize featue of analyzed contol method. It can be een a combination of DTC and FOC lead to the diect toque contol with pace vecto modulation (DTC-SV) method which i an effect of thi each. In Table 3. alo chaacteitic pefomance of DTC-SV wa given. The diadvantage of claical DTC ae caued by hyteei contolle and witching table ued in a tuctue. Theefoe, new DTC-SV method eplace witching table by pace vecto modulato and linea PI contolle ae ued like in the FOC cheme. Howeve, the cuent contol loop ae eliminated. The DTC-SV method ae widely dicued in the Chapte 4 whee a detailed deciption of thoe featue can be found. 65

72 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) 4.. Intoduction Diect flux and toque contol with pace vecto modulation (DTC-SV) cheme ae popoed in ode to impove the claical DTC. The DTC-SV tategie opeate at a contant witching fequency. In the contol tuctue, pace vecto modulation (SV) algoithm i ued. The type of DTC-SV tategy depend on the applied flux and toque contol algoithm. Baically, the contolle calculate the equied tato voltage vecto and then it i ealized by pace vecto modulation technique. In the DTC-SV method eveal clae have evolved: cheme with PI contolle [], cheme with pedictive/dead-beat [74], cheme baed on fuzzy logic and/o neual netwok [40], vaiable-tuctue contol (VSC) [7, 73, ]. Diffeent tuctue of DTC-SV method ae peented in the next ection. Fo each of the contol tuctue, diffeent contolle deign method ae popoed. The claical DTC algoithm i baed on the intantaneou value and diectly calculated the digital contol ignal fo the invete. The contol algoithm in DTC- SV method ae baed on aveaged value wheea the witching ignal fo the invete ae calculated by pace vecto modulato. Thi i main diffeence between claical DTC and DTC-SV contol method. 4.. Stuctue of DTC-SV Review 4... DTC-SV Scheme with Cloed oop Flux Contol In the contol tuctue of Fig. 4. the oto flux i aumed a a efeence [4]. The efeence tato flux component defined in the oto flux coodinate calculated fom the following equation: dc, qc can be

73 4.. Stuctue of DTC-SV Review d c = + dc c σ (4.a) R dt qc ec = σ (4.b) pbm c Fomula (4.) can be deived fom the equation (3.3), (3.4) and (3.7). The equation (3.3), (3.4) and (3.7) decibe the moto model in the oto flux coodinate ytem d q. The amplitude of the efeence tato flux, uing equation (4.) can by expeed a: ec = + ( ) c c σ (4.) pbm c The commanded value of tato flux dc, qc afte tanfomation to tationay coodinate ytem α β ae compaed with the etimated value ˆ α, ˆ β. c ec Eg (4.) dc qc d q α β c T c SV S A S B S C γˆ R Roto Flux Etimato ˆ Stato Flux Etimato I Voltage Calculation α β dc I A ABC I B Fig. 4.. DTC-SV cheme with cloed flux contol The efeence voltage vecto depend on the incement tato flux dop on the tato winding eitance c T + R R : = I (4.3) and voltage In thi DTC-SV tuctue the oto flux magnitude i egulated. Thank of them inceae the toque oveload capability i poible [9, 4]. Howeve, the dawback of 67

74 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) thi algoithm i that it equie all the moto paamete and moeove it i vey enitive to thei vaiation DTC-SV Scheme with Cloed oop Toque Contol The method with cloe-loop toque contol wa oiginally popoed fo the pemanent magnet ynchonou moto (PS) [35, 36, 37]. Howeve, the DTC baic fo both I and PS ae identical and theefoe the method can alo be ued fo the I [6]. The block cheme of the contol tuctue DTC-SV with cloe-loop toque contol i peented in Fig. 4.. c ec Toque Contolle PI δ ψ Eg. (4.4) c T c SV S A S B S C ˆ e γˆ ˆ Flux and Toque Etimato R I Voltage Calculation α β dc I A ABC I B Fig. 4.. DTC-SV cheme with cloed-loop toque contol Fo the toque egulation a PI contolle i applied. Output of thi PI contolle i an incement of toque angle δ (Fig. 4.3). In thi way the toque i contolled by changing the angle between tato and oto fluxe accoding to the baic of DTC (ee ection 3.4.). The efeence tato flux vecto i calculated a follow: ( ˆ γ + δ ) j = c e (4.4) c Next, efeence tato flux vecto i compaed with the etimated value. The eo of the flux equation (4.3). i ued, fo calculation of the efeence voltage vecto, accoding to the 68

75 4.. Stuctue of DTC-SV Review β δ c ˆ γˆ δˆ ˆ γˆ α Fig Vecto diagam The peented method ha imple tuctue and only one PI toque contolle. It make the tuning pocedue eaie. The flux i adjuted in open-loop fahion DTC-SV Scheme with Cloe oop Toque and Flux Contol Opeating in Pola Coodinate When both toque and flux magnitude ae contolled in a cloed-loop way, the tategie povide futhe impovement. The method opeating in pola coodinate i hown in Fig. 4.4 [49]. Flux Contolle c ec P PI γ d k γ Eg. (4.7) T c SV S A S B S C Toque Contolle γ γˆ R ˆ ˆ e Flux and Toque Etimato Voltage Calculation dc I α β I A ABC I B Fig DTC-SV cheme opeated in tato flux pola coodinate The eo of the tato flux vecto of the flux and toque contolle a follow: i calculated fom the output k and γ 69

76 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) ( k) = ( k) ( k ) j γ ( k ) ([ + k ( k) ] e ) ( ) = k (4.5) With the appoximation e j γ ( k ) + j γ ( k) (4.6) The equation (4.5) can be witten in the fom ( k) = [ k ( k) + j ( k) ] ( k ) γ (4.7) The commanded tato voltage vecto i calculated accoding to equation (4.3). To impove the dynamic pefomance of the toque contol, the angle incement compoed of two pat: the dynamic pat the tationay pat γ geneated by a feedfowad loop. γ i γ d deliveed by the toque contolle and DTC-SV Scheme with Cloe oop Toque and Flux Contol in Stato Flux Coodinate A block diagam of the method with cloe-loop toque and flux contol in tato flux coodinate ytem [] i peented in Fig The output of the PI flux and toque contolle can be intepeted a the efeence tato voltage component the tato flux oiented coodinate ( x y ). xc, yc in Flux Contolle c PI xc x y S A ec PI Toque Contolle yc ˆ ˆ e α β γˆ Flux and Toque Etimato c I SV Voltage Calculation α β S B S C dc I A ABC I B Fig DTC-SV cheme opeated in tato flux cateian coodinate 70

77 4.3. Analyi and Contolle Deign fo DTC-SV ethod Thee dc voltage command ae then tanfomed into tationay fame ( α β ), the commanded value α c, β c ae deliveed to SV Concluion fom Review of the DTC-SV Stuctue In the thee fit peented tuctue (Fig. 4., Fig. 4. and Fig. 4.4) the calculation of efeence voltage vecto i baed on demanded accoding to equation (4.3). Thi diffeentiation algoithm i vey enitive to ditubance. In cae of eo in the feedback ignal the diffeentiation algoithm may not be table. Thi i vey eiou dawback of thee method. The method peented in Fig. 4. and Fig. 4. do not have cloe-loop flux contol. In thee method tato flux magnitude i only adjuted. The lat peented method (Fig. 4.5) eliminate poblem with diffeentiation algoithm. oeove, thi method contol toque and flux in cloe-loop fahion. Theefoe, thi cheme will be elected fo expeimental ealization. In the next ubection contolle deign fo flux and toque cloed loop will be dicued Analyi and Contolle Deign fo DTC-SV ethod with Cloe oop Toque and Flux Contol in Stato Flux Coodinate The compete et of moto model equation can be witten in tato flux coodinate ytem x y. Thi ytem of coodinate x y otate with the tato flux angula peed Ω = Ω. Thi angula peed i defined a follow: K Ω dγ = (4.8) dt whee: γ i a tato flux vecto angle. The complex pace vecto can be eolved into component x and y. = + j (4.9a) K x y I = I + j I K x y, K x y I = I + ji (4.9b) 7

78 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) K = x =, K = x + j y (4.9c) The moto model equation (.0-.) in x y coodinate ytem can be witten a: d = RI x (4.0a) dt x + = R I + Ω (4.0b) y y d dt ( p Ω Ω ) x 0 = R I x + + y b m (4.a) d y 0 = R I y + + x ( Ω pbωm ) (4.b) dt = I + I (4.a) y x y x 0 = I + I (4.b) = I + I (4.c) x y x y x = I + I (4.d) y dω dt m m = pb I y J (4.3) The electomagnetic toque can be expeed by the following fomula: e m = pb I y (4.4) Baed on the equation ( ) the block diagam of induction moto can be contucted (Fig. 4.6). The block cheme peented in Fig. 4.6 i a full model of an induction moto. A can be een, thi model i quite complicated and theefoe difficult to analyze. Howeve, taking into conideation the tato voltage equation (4.0) and toque equation (4.4), the moto can be decibed a follow: d dt = R I (4.5) x x e = R p b m ( Ω ) y (4.6) 7

79 4.3. Analyi and Contolle Deign fo DTC-SV ethod R I x m x m pb e J Ω m y Ω I y R R I x σ m x p b R y I y σ Fig Complete block diagam of an induction moto in the tato flux oiented coodinate x y The block diagam of induction moto baed on equation (4.5) and (4.6) i hown in Fig R I x x Ω y p b m R e Fig Simplified (oto equation omitted) induction moto block diagam in the tato flux oiented coodinate x y 73

80 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) Diffeent contol tuctue baed on the above induction moto model ae popoed in liteatue [73,, ]. One of them i a method with two PI contolle [], which i peented in Fig Conideing a imple model of I (Fig. 4.7), Fig. 4.8 how the flux and toque contol loop fo the method hown in Fig In Fig. 4.8 the dahed line epeent the I model. R I x c PI x Ω ec PI y m pb R e Fig Contol loop with two PI contolle and implified I model of Fig. 4.7 In the next pat two appoache to a contolle deign will be peented and compaed. Both of them ae baed o the aumption that contol loop can be conideed a quai-continuou (fat ampling). The fit method i baed on imple ymmetic citeion [66], the econd one ue oot locu technique [34, 86]. PI Contolle The tanfe function of PI contolle i given a follow: whee: G R () ( ) + = K p = K p () + T i Ti = E T i (4.7) K p - contolle gain, T i - contolle integating time. The PI contolle cheme i peented in Fig

81 4.3. Analyi and Contolle Deign fo DTC-SV ethod E() K p ( ) T i Fig Block diagam of PI contolle Peented above model of the contolle wa ued in DTC-SV contol method with two PI contolle Toque and Flux Contolle Deign Symmety Citeion ethod Flux Contolle Deign The block diagam of the flux contol loop i hown in Fig Thi contol loop i baed on the model peented in Fig The voltage dop on the tato eitance i neglected. In the tato flux contol loop the invete delay i taken into conideation. c PI x + T Fig Stato flux magnitude contol loop Fo the flux contolle paamete deign the ymmety citeion can by applied [66]. In accodance with the ymmety citeion the plant tanfe function can be witten a: G () = K e T τ 0 c ( + T ) (4.8) whee: K c = i the invete gain, τ 0 i dead time of the invete ( τ 0 = 0 ideal convete), T =, and T = T i a um of mall time contant, which include tatitical delay of the PW geneation and ignal poceing delay. The optimal contolle paamete can be calculated a: 75

82 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) K p = K T T + τ = 0 T c ( ) (4.9) i ( T + ) T T = τ 4 (4.0) 4 0 = In Table 4. ae hown flux contolle paamete calculated accoding to equation (4.9) and (4.0). The conideed ange of the ampling fequency wa fom.5khz to 0kHz. In Table 4. ae alo hown paamete of the tep flux epone obtained in imulation, t n - time when the actual flux i fit time equal efeence value and p - ovehoot. The eult of imulation ae peented in Fig. 4.. Table 4.. Flux contolle paamete calculated accoding to ymmetic optimum citeion f K p T i t n p 0.0 khz % 5.0 khz %.5 khz % a) b) c) Fig. 4.. Simulated flux epone fo contolle paamete calculated accoding to ymmetic optimum citeion at diffeent ampling fequency a) f = 0kHz, b) f = 5kHz, c) f =. 5kHz 76

83 4.3. Analyi and Contolle Deign fo DTC-SV ethod Peented in Fig. 4. imulation eult confim pope opeation of the flux contolle fo the diffeent ampling fequency. The ymmetic optimum citeion can be apply to tune flux contolle in analyzed DTC-SV tuctue. Toque Contolle Deign The block diagam of the toque contol loop i hown in Fig. 4.. The ame like fo flux thi contol loop i baed on the model peented in Fig Howeve, coupling between toque and flux i omitted. Becaue of that vey imple model i obtained and fo thi model any citeion cannot be applied. ec PI y + T m pb R e Fig. 4.. Block diagam of the toque contol loop In thi cae the imple (pactical) way to deign toque contolle can be ued. Stating fom the initial value e.g. K p =, Ti = 4T the popotional gain K p i inceaing cyclically a it i hown in Fig Fom thee ocillogam the bet value of K p fo the fat toque epone without ocillation and mall ovehoot can be elected. In Fig. 4.3 the choen imulation eult fo 5kHz and 0kHz ampling fequencie ae hown. Fo the ampling fequency 5kHz the bet value of popotional gain i K = 7 and fo 0kHz K = 4. p p The finally obtained in thi way paamete of the toque contolle ae hown in Table 4.. Thee ae alo hown paamete of the tep toque epone obtained in imulation, t n - time when the actual toque achieve fit time efeence value and p - ovehoot. Table 4.. Toque contolle paamete f K p T i t n p Μ 0.0 khz % 5.0 khz % 77

84 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) a) b) K p = 4 K p = 4 K = 0 = 0 p K p K p = 7 K p = 4 Fig Toque epone fo elected contolle gain K p value, at diffeent ampling fequency a) f 5kHz T i = 800µ, b) f 0kHz T i = 400µ = ( ) = ( ) Toque and Flux Contolle Deign Root ocu ethod A oot-locu analyi i ued fo tuning the flux and toque contolle. Thi technique how how the change in the ytem open-loop chaacteitic influence the cloed-loop dynamic chaacteitic. Thi method allow to plot the locu of the cloed-loop oot in -plane a an open-loop paamete vaie, thu poducing a oot locu. The damping facto, ovehoot and ettling time [06] limit the allowable aea of exitence of the cloe-loop oot. The bode of each of thee paamete can be epeented in -plane a a taight line. The allowable aea of exitence fo the cloe-loop oot limited by dumping and ettling time i hown in Fig

85 4.3. Analyi and Contolle Deign fo DTC-SV ethod damping ettling time Im α α Re damping Fig Allowable aea of exitence fo the cloe-loop oot in -plane To plot and analyze the locu of the oot in -plane SISO Deign Tool Contol Sytem Toolbox v 5.0 the athwok, Inc. wa ued [84]. The SISO Deign Tool i a Gaphical e Inteface (GI) that allow to analyze and tune the Single Input Single Output (SISO) feedback contol ytem. ing the SISO Deign Tool, it i poible to gaphically tune the gain and dynamic of the compenato (C) and pefilte (F), uing a mix of oot locu and loop haping technique. The example window of the SISO Deign Tool i hown in Fig In the uppe ight aea of the window, the cuently teted contol tuctue i diplayed. oe on the left the value of the compenato paamete ae viible, and below them the eulting oot-locu of the ytem i hown. In the oot locu diagam, two line coeponding to the ineted value of ettling time and the ovehoot ae alo viible. 79

86 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) Fig SISO Deign Tool Configuation of the ytem tuctue i poible by impoting tanfe function of each block fom the wokpace. Thi i hown in Fig Fig Impot ytem data 80

87 4.3. Analyi and Contolle Deign fo DTC-SV ethod 8 The plant (G) i a tanfe function of the moto toque o flux and the compenato (C) i a tanfe function of the PI contolle. In the cae of flux and toque contol, the open-loop conit of a PI contolle and plant tanfe function, accoding to cheme (Fig. 4.8). The plant tanfe function fo the flux and the toque ae calculated epaately baed on the moto model equation in the tato flux efeence fame (4.0-4.). Flux Contolle Deign Baed on the moto model equation (4.0-4.), the following equation can be obtained: ( ) x dt d R R dt d R R dt d R = + σ σ ( ) m b y Ω p Ω I R + σ (4.) whee: = σ nde the aumption that the lat tem in the equation (4.) i vey mall: ( ) 0 m b y Ω p Ω I R σ (4.) the equation (4.) become: ( ) x dt d R R dt d R R dt d R = + σ σ (4.3) Baed on the equation (4.3) the open-loop flux tanfe function can be obtained a follow: () x C B A G = = (4.4) whee: R A σ = ; R R B σ + = ; R R C σ = The flux contol loop i hown in Fig. 4.7, whee ( ) G R i a tanfe function of the PI contolle given by equation (4.7).

88 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) c G R () x G ( ) Fig Flux contol loop The input data to the SISO Deign Tool ae obtained baed on equation (4.7) and (4.4). The paamete value ae calculated fo a 3 kw moto. The moto data ae given in appendix A.3. Requied contol paamete ae et a follow: ettling time < 0.003, ovehoot < 4.33%. Fo thee paamete a oot loci of the cloe-loop i obtained, ee Fig Root ocu Edito (C) Imag Axi 0 4e+003 3e+003 e+003 e Real Axi Fig Root loci of the cloe-loop tato flux contol ytem Fom the poition of the pole, the paamete of the PI flux contolle ae obtained: K = 53, T = p i The behaviou of the flux contol loop with paamete like above wa teted uing SABER imulation package. The model ceated in SABER take into account the full contol ytem, including the model of invete and induction moto (ee appendix A.). The flux tep epone i peented in Fig The imulation eult confim a good dynamic of the flux and pope opeation in the teady tate. 8

89 4.3. Analyi and Contolle Deign fo DTC-SV ethod Fig Simulated (SABER) flux epone fo contolle paamete deigned accoding to oot locu method Toque Contolle Deign Baed on moto model equation (4.0-4.), the following equation can be obtained: ( R + R ) + σ I = p Ω + I σ ( Ω p Ω ) d dt y y b m x b m whee: σ = nde the aumption that the lat tem in equation (4.5) i vey mall: x ( Ω p Ω ) 0 b m (4.5) I σ (4.6) the equation (4.5) become: d + σ dt (4.7) ( R R ) + I y = y pbωm The additional aumption i that the moto i not loaded = 0. nde thoe aumption the oto peed can be expeed: 83

90 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) dω dt m J m = pb I y (4.8) Fom equation (4.4) cuent I y can be expeed a follow: I y = e (4.9) p m b If both ide of equation (4.7) ae diffeentiated, thi equation become: ( R + R ) d dt + σ d dt I y = d dt y p b dω dt m (4.30) Baed on the equation (4.30), (4.8) and (4.9) the open-loop toque tanfe function can be obtained a follow: G () e = = (4.3) y A + B + C whee: A p m σ b = ; B R + R σ = ; C = pb m σ J The toque contol loop i hown in Fig. 4.0, whee G R ( ) i a tanfe function of the PI contolle given by equation (4.7). ec G R () y G ( ) e Fig Toque contol loop The input data to the SISO Deign Tool ae obtained in the ame way like fo the flux. The tanfe function ae calculated fo the 3 kw moto fom the equation (4.7) and (4.3). The equied contol paamete ae et a follow: ettling time < 0.005, ovehoot < %. Fo thee paamete a oot loci of the cloe-loop i obtained, ee Fig. 4.. Fom the poition of the pole (Fig. 4.), the paamete of the PI toque contolle ae obtained: K = 33., T = p i 84

91 4.3. Analyi and Contolle Deign fo DTC-SV ethod Root ocu Edito (C) Imag Axi 0 7e+003 6e+003 5e+003 4e+003 3e+003 e+003 e Real Axi Fig. 4.. Root loci of the cloe-loop toque contol ytem The tanfe function of the cloe loop toque contol hown in Fig. 4.0 i given a: G c () = e ec = + ( A K + B ) A p T K i p ( T + ) i + C + A T K i p (4.3) The SISO Deign Tool enable to obeve the tep epone of the invetigated contol ytem. In the Fig. 4. i hown the tep epone of the toque contol ytem fom Fig. 4.0 decibed by equation (4.3), with the PI contolle paamete etting a: K = 33., T = p i.4 Step Repone Fom:. Amplitude To: y Time (ec) x 0-3 Fig. 4.. Simulated (atlab) tep epone of the ytem fom Fig. 4.0 decibed by tanfe function given by equation (4.3) 85

92 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) It hould be note that moment of inetia J can change duing dive opeation (fo example in till induty ytem). Howeve, the value of coefficient (4.3) nomally i eveal ode lowe in compaion with ( A K T ) it influence on toque cloe loop dynamic can be neglected. p C i, in equation. Theefoe, Becaue of the focing element in tanfe function (4.3) the tep epone peented in Fig. 4. chaacteized much highe ovehoot then the aumed %. To compenate the focing element in the numeato (4.3) a pefilte i ineted into the efeence channel of the toque contolle. The tanfe function of the pefilte i given a: GF () = (4.33) T + F The time contant of the pefilte i equal time contant of the toque contolle T F = T i. The full contol loop of toque with pefilte i hown in Fig The tep epone of thi contol loop i peented in Fig ec G F () G R ( ) y G ( ) e Fig Toque contol loop with pefilte.4 Step Repone Fom:. Amplitude To: y Time (ec) x 0-3 Fig Simulated (atlab) tep epone of the ytem fom Fig

93 4.3. Analyi and Contolle Deign fo DTC-SV ethod Figue 4.4 how that the toque contol loop with a pefilte incopoated into the efeence channel educe conideably the ovehoot. The behaviou of the toque contol loop with the ame etting of the paamete wa alo teted in SABER imulation model. The toque tep epone i peented in Fig The eult of imulation confim a good dynamic of the toque and pope opeation in the teady tate. Fig Simulated (SABER) toque epone Toque Contolle Deign fo High Powe oto The ame method of tuning the contolle wa ued fo a 90 kw moto. The paamete of thi moto can be found in appendix A.3. The equied contol paamete ae et a follow: fo the flux ettling time < 0.003, ovehoot < 4.33% and fo the toque ettling time < 0.005, ovehoot < %. The paamete of the contolle ae obtained a follow: flux contolle K = 59, T = and toque contolle K =.849, T = p i p The imulation model of dive with a 90 kw moto wa alo build in the SABER package. The flux tep epone i peented in Fig The contol loop of the flux i identical fo both moto (Fig. 4.8) and doe not depend on the moto paamete. Theefoe, the paamete of the flux contolle and the eult of imulation (Fig. 4.6) i vey imila to the eult fo the 3 kw moto (Fig. 4.9). i 87

94 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) The toque epone fo the 90 kw moto i peented in Fig The eult of the imulation (Fig. 4.6, 4.7), imilaly like in the cae of the mall powe atting moto, confim a good dynamic of the toque and a pope opeation in the teady tate. Fig Simulated (SABER) flux epone fo 90 kw moto Fig Simulated (SABER) toque epone fo 90 kw moto Summay of Flux and Toque Contolle Deign In the Fig. 4.8 a full contol tuctue of the DTC-SV cheme i hown. Thi cheme i completed on the pefilte, compaed to the baic cheme fom Fig

95 4.3. Analyi and Contolle Deign fo DTC-SV ethod The peented above contolle tuning algoithm i baed on the open-loop tanfe function fo the flux (equation 4.4) and fo the toque (equation 4.3). Thee tanfe function ae obtained unde the aumption (4.) and (4.6) epectively. Becaue of the aumed implification, the eult of full model imulation ae lightly diffe fom the initially expected value. Flux Contolle c PI xc x y S A c SV S B ec F PI yc α β S C Pefilte Toque Contolle ˆ ˆ e γˆ Flux and Toque Etimato I Voltage Calculation α β dc I A ABC I B Fig Full cheme of the DTC-SV contol method Additional aumption fo the toque contolle analyi i that the tato flux magnitude i contant. Theefoe, decoupling between flux and toque contol loop i impotant. In Fig. 4.9 the toque tep epone (Fig. 4.9a) and magnitude tato flux tep epone (Fig. 4.9b) ae hown. Fom Fig. 4.9 can be een that both contolle ae vey fat and decoupling between flux and toque i coect. The full contol tuctue (Fig. 4.8) i diffeent fom the baic cheme, which can be een in Fig In the toque efeence channel a pefilte i incopoated. The baic tuctue aumed fou contolle paamete: K p, T i, K p and T i. The addition of the pefilte doe not intoduce any additional paamete, becaue the time contant of the pefilte i equal to the toque contolle integating time T i (ee equation 4.33). Thu the contol method need only fou paamete. Additionally, if a vey fat toque epone i not equied, the pefilte time contant can be inceaed independently fom the toque contolle paamete in ode to impove the tability of the ytem. 89

96 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) a) b) Fig Dynamic tet a) toque tep change, b) flux tep change. Fom the top: efeence and etimated toque, efeence and etimated tato flux In ection 4.3 two method of flux and toque contolle deign fo DTC-SV ae peented. The compaion of the eult obtained in two method i ummaized in Table 4.3. The ummay i done fo the 3kW moto and ampling fequency f = 0kHz. The fit method ue implified I model and i baed on ymmetic optimum citeion. Howeve, thi appoach give good eult only fo flux contol loop. The econd appoach ue dynamic model of I including oto paamete and i baed on oot locu method. The eult obtained in imulation ae good fo both flux and toque contolle. Howeve, it i much moe complicated than fit method. The dynamic of the flux contol loop i vey imila in both cae. Theefoe, to tune flux contolle ymmety citeion hould be ued becaue it i imple. 90

97 4.3. Analyi and Contolle Deign fo DTC-SV ethod Symmety Citeion ethod Table 4.3. Summay of contolle deign odel paamete Contolle paamete Flux Toque Flux Toque T T = pue integato R Root ocu A = ethod σ R B = C = R σ σ R + R T p, A B C b, m, R = = = R p p b m σ + R σ m σ b J K p T i K p T i = 5000 = = 53 = K p T i K p T i = 4.00 = = 33. = Dynamic paamete Flux Toque t n = t n = p =.6% p = 8.39% t n = t n = p =.49% p =.04% 9

98 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) All imulation eult fo oot locu method peented in ection 4.3. wee done at ampling fequency f = 0kHz. Howeve, peented contolle deign method povide to obtain contolle paamete fo diffeent ampling fequency. Thi apect will be peented fo the toque contolle. When the ampling fequency i changed the input paamete: ettling time and ovehoot mut be modified. Fo lowe ampling fequency the dynamic of contol loop i deceaing [34]. Thu, fo the continuou analyi, which i ued in oot locu method, the ettling time hould be inceaed and ovehoot educed. Table 4.4 how toque contolle paamete calculated fo thee ampling fequency value: f = 0kHz, f = 5kHz and f =. 5kHz. Table 4.4. Toque contolle paamete fo diffeent ampling fequency f ettling time ovehoot K p Μ T i Μ 0.0 khz % khz % khz % Simulated eult obtained fo paamete peented in Table 4.4 ae hown in Fig The eult of imulation confim a good behavio of the ytem fo all thee ampling fequencie. The oot locu method give pope eult fo diffeent moto type. It confim eult obtained fo the 90 kw moto. The vey impotant featue of the DTC-SV in compaion with claical DTC ae pefomance in teady tate. In the Fig. 4.3 the teady tate opeation of the DTC-SV contol ytem i hown. It can be een that the line cuent i inuoidal and voltage ha an unipola wavefom. Peented in Fig. 4.3 can be compaed with imulation eult fo claical DTC fom Fig. 3.6, whee contolle jut elect voltage vecto to educe intantaneou flux and toque eo, and doe not implement the tue PW. Theefoe, invete output voltage i not unipola. Thi inceae witching loe of the emiconducto powe device. 9

99 4.3. Analyi and Contolle Deign fo DTC-SV ethod a) b) c) Fig kw moto toque epone fo contolle paamete calculated accoding to oot locu method at diffeent ampling fequency a) f = 0kHz, b) f = 5kHz, c) f =. 5kHz 93

100 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) Fig Steady tate opeation. Fom the top: line to line voltage, line cuent The featue of the DTC-SV method can be ummaized a follow: good dynamic contol of flux and toque, contant witching fequency, unipola voltage thank to ue of PW block (SV), low flux and toque ipple, inuoidal tato cuent Speed Contolle Deign If the tato flux i aumed contant, = cont., that baed on the equation (4.3) and (4.4) dynamic of I can be decibed a: dω dt m [ ] = e (4.34) J A block diagam of the peed contol loop i hown in Fig. 4.3, whee G RS () i a ' tanfe function of PI contolle (ee equation 4.7) and G ( ) i a tanfe function of full toque contol loop. In the peed contolle deign poce the filte fo the meaued value hould be taken into conideation. T f i a time contant of the filte. The low pa filte i neceay in hadwae etup. 94

101 4.4. Speed Contolle Deign Ω mc () ec ' G RS G ( ) e J Ωm T f + Fig Block diagam of the peed contol loop The tanfe function of the full toque contol loop (Fig. 4.3) can be calculated a: G ' e () = = G () G () ec F c (4.35) whee: G c ( ) - toque contol loop tanfe function given by equation (4.3), G F () - pefilte tanfe function given by equation (4.33). ' The tanfe function G ( ) can by expeed a: whee: ' ' A G () = (4.36) ' ' B + C + A ' = C T A i K p + A K p ; B ' = C T i Ti + A K p ; C ' T = C i ( A K + B ) T i p + A K p The toque contol loop can be appoximate by fit ode integating pat, becaue of: ' B 0 (4.37) The implified tanfe function can be witten a: ' ' A G () = (4.38) ' C + Fo the toque contolle paamete K =5. 87, T = obtained in ection p at the ampling fequency f = 5kHz the tanfe function paamete have value: i 95

102 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) ' ' ' A = , B = 3.563e 007, C = Thoe paamete confim that aumption (4.37) i coect. The tep epone of the full and implified tanfe function ae hown in Fig full tanfe function implified tanfe function Time Fig Toque epone fo full and implified tanfe function Fo the peed contolle paamete deign the ymmety citeion can by applied [66]. In accodance with the ymmety citeion the plant tanfe function can be witten a: G () = K e T τ 0 c ( + T ) (4.39) whee: convete), K c = A ' i gain of the plan, τ 0 i dead time of the invete ( τ 0 = 0 ideal T = J, and T = C + Tf i a um of mall time contant. The optimal contolle paamete can be calculated a: K p = K T ( T + τ ) ( + T ) c 0 = J C ( T + ) = ( C ) i = T f f (4.40) T τ + (4.4) Fo the filte fequency f f = 5Hz whee: T f = (4.4) πf f 96

103 4.4. Speed Contolle Deign the peed contolle paamete ae obtained a follow: K =. 33; T = Fig. 4.34, 4.35 and 4.36 how imulation and expeimental eult fo the ytem opeated with peed contolle paamete obtained above. The peed eveal ae peented in Fig and 4.35 fo high and mall efeence peed diffeence epectively. The tep change of the load toque at contant peed i peented in Fig All peented in Fig. 4.34, 4.35 and 4.36 eult confim pope opeation of the peed contol loop. p i a) b) Fig Speed eveal Ω m = ±00ad / a) imulated (SABER), b) expeimental ) efeence peed (75 (ad/)/div), ) actual peed (75 (ad/)/div), 3) efeence toque (0 Nm/div) a) b) Fig Speed eveal - mall ignal Ω m = ±5ad / a) imulated (SABER), b) expeimental ) efeence peed (7.5 (ad/)/div), ) actual peed (7.5 (ad/)/div), 3) efeence toque (0 Nm/div) 97

104 4. Diect Flux and Toque Contol with Space Vecto odulation (DTC-SV) a) b) Fig oad toque tep change at Ω m = 00ad / a) imulated (SABER), b) expeimental ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 3) etimated toque (0 Nm/div) 4.5. Summay Thi chapte give eview of DTC-SV contol method. To analyi and implementation wa choen DTC-SV method with cloe-loop toque and flux contol in tato flux coodinate. Full mathematical analyi of I dive woking with thi contol method i peented. Two diffeent flux and toque contolle deign algoithm ae analyzed and dicued. Futhemoe, peed contolle tuning method i hown. The flux and toque contolle deign method fo ampling fequency change and diffeent moto powe ae dicued. The analyi peented in thi chapte give complex knowledge about contol tuctue and contolle deign method. Obtained paamete povide good dynamic and teady tate opeation of a dive. It i confimed by imulation and expeimental eult peented in thi chapte and in Chapte 7. 98

105 5. Etimation in Induction oto Dive 5.. Intoduction The vecto contol method of induction moto equie feedback ignal. Thi i an infomation about flux, toque and mechanical peed in dive opeated without mechanical eno (enole opeation mode). Thee ae many diffeent method to obtain thee tate vaiable of induction moto. Baic method can be divided into thee main goup [87]: phyical method baed on nonlinea contuction of I [60, 77, 3], mathematical model ued mathematical deciption of I and contol theoy, neual netwok method baed on the atificial intelligence technique [9, 9, 95]. The geneal claification of the tate vaiable calculation method i peented in Fig. 5. [87]. Induction moto tate vaiable calculation method Phyical method athematical model Neual netwok method Etimato of tate vaiable Obeve of tate vaiable Kalman Filte Fig. 5.. Claification of induction tate vaiable calculation method The mathematical model i baed on the pace vecto equation, which decibe induction moto. Fig. 5. how diviion of thee method into thee goup: etimato of tate vaiable, obeve of tate vaiable,

106 5. Etimation in Induction oto Dive Kalman filte. The DTC-SV method i baed on the infomation about tato flux vecto (ee ection 4.3). Theefoe, it i the mot impotant vaiable of the moto. eauement of flux in moto i difficult and demand pecial eno. Thi olution i vey expenive and complicated. Becaue of that a method of calculation moto flux wa developed. In vecto contol method thi pat of algoithm i epecially impotant. Etimation algoithm ue a input ignal value, which ae imple to meaue. Thee ae cuent and voltage ignal. Obviouly new method aim at educing numbe of eno fo moe eliable opeation and lowe pice of a dive. The moto flux i the main component to calculate toque and peed. Theefoe, accuacy of the etimation flux i vey impotant. Flux etimation i a ignificant tak in implementing of high-pefomance moto dive. The advanced tate vaiable calculation algoithm i chaacteized by: accuacy in teady and dynamic tate, obutne fo moto paamete vaiation, minimal numbe of eno, opeation in whole peed ange, low calculation demanded. All etimation algoithm baed on the moto paamete. Thee paamete change in time wok of the dive. Fo intance, with change the tempeatue. Theefoe, etimation algoithm have to be le enitive to the paamete vaiation. All peented flux etimation algoithm ae hown a tato flux etimato, becaue of thee algoithm wok with DTC-SV tuctue. In ome algoithm oto flux etimation i equied, but in thi cae it i convet on tato flux. 5.. Etimation of Invete Output Voltage Input ignal fo the etimato ae meauement of tato cuent and voltage which ae eceated fom the witching ignal. Switch ignal fo the each invete phae ae obtained by contol algoithm. The efeence voltage vecto i ealized by 00

107 5.. Etimation of Invete Output Voltage modulato (ee ection.4). Howeve, duty time ae modified by dead-time, which i equiite fo coect invete opeation (ee ection.3). Becaue of thi modification deliveed to the moto voltage i diffeent fom efeence. To eliminate dead-time effect thee i a pecial pat fo compenation of dead-time in contol algoithm. Obtained by vecto modulato duty cycle, epeented by witching ignal S A, S B, S C ae modified to S ' A, S ' ' B, S C (Fig. 5.). Thi modification depend on the phae cuent diection and i ealized fo each phae. any diffeent dead-time compenation method ae peented in liteatue [, 3, 8, 9, 64, 76]. Thank to thi modification afte change ignal by dead-time, a coect voltage vecto obtained by contolle i deliveed to the moto. Becaue of that ignal S A, S B, S C ae ued to eceate voltage value. The voltage i calculated fom the equation: α = dc A 5 B + 3 ( D 0. ( D D )) C (5.a) ( D D ) (5.b) β dc B C = 3 3 and whee D A, D B, D C ae duty cycle coeponding to the witching ignal S A, S B, S C dc i the voltage of invete dc-link. dc β c α c Vecto odulato S A S B S C Dead Time & Voltage Dop Compenation S A ' S B ' S C ' Dead Time S A + S A - S B + S B - S C + S C - α β Voltage Calculation dc I I oto Fig. 5.. Input ignal fo the etimato 0

108 5. Etimation in Induction oto Dive In Fig. 5. voltage calculation block diagam i hown. Simultaneouly with deadtime compenation a voltage dop compenation algoithm i ealized. It i epecially impotant fo low peed opeation ange, when voltage i vey low. The main aumption in voltage calculation method i that identical voltage vecto, which i calculated by a contolle i deliveed to the moto. It mean, pope infomation about voltage depend on coect implementation dead-time and voltage dop compenation algoithm. Dead Time Compenation In ode to pevent hotcicuiting an invete leg, thee hould be a dead-time (T D ) between the tun-off one witch (IGBT) and the tun-on of the next one (fom the ame leg). T D hould be lage than the maximum toage time of the witching device. The effect of the dead-time i a voltage ditotion deliveed to the moto. The voltage ditotion i depending on cuent ign, a can be een in Fig a) T b) T dc 0 C S A + A D I A > 0 dc 0 C S A + A D < 0 I A T T dc C S A - D dc C S A - D I > 0 < 0 A I A S A S A t t S A + T D S A + T D t t S A - T D S A - T D A0 t A0 t dc dc 0 t 0 t dc dc Fig Dead-time effect fo diffeent cuent ing a) I > 0, b) I < 0 A A 0

109 5.. Etimation of Invete Output Voltage So the eal voltage vecto aco the moto can be expeed a: mot = (5.) c The voltage ditotion can be witten a: ( ) = T f ign (5.3) D dc I whee: f - ampling fequency, ign ()- ignum function. The dead-time compenation can be implemented by adjuting the phae duty cycle a following: ' k D = D + T k D f ign ( I ) k (5.4) whee: k = A, B, C. Thi mean that the on-time of the uppe bidge am witch i hotened by T D and fo poitive cuent it i inceaed by the ame amount fo negative cuent. Becaue of the cuent ha ipple aound zeo-coing the algoithm hould be modified. One of the poible olution i method with cuent level. In thi method the cuent level ( I level ) i defined, which decibe zone aound the zeo cuent a: I > I > I (5.5) level k level If the condition (5.6) i pefomed the duty cycle ae modified a follow: ' k D = D + k I I k level T D f ign ( I ) k (5.6) In the othe cae the duty cycle ae modified accoding to the equation (5.4). The value of the cuent level ( I level ) depend on the moto powe and can be deducted expeimentally. Fo 3kW dive the optimal value of cuent level wa I level = 0. A. The imulated eult fo the dead-time compenation algoithm ae peented in Fig In thi tet dive opeate with cala contol (/f=cont.) algoithm at fundamental fequency f = Hz. 03

110 5. Etimation in Induction oto Dive a) b) Fig Simulated /f=cont. contol method at fequency f = Hz a) without dead-time compenation, b) with dead-time compenation Fom Fig. 5.4a it can be een that without dead-time compenation the output cuent ae conideably ditoted and ha educed value. Fig. 5.4b hown imulated eult with dead-time compenation algoithm. Thank of the compenation pope voltage i deliveed to the moto. Theefoe, cuent have coect value and cuent wavefom ae inuoidal. Peented dead-time compenation algoithm wa implemented in final contol ytem Stato Flux Vecto Etimato The flux vecto etimato algoithm can be divided into two goup in tem of the input ignal. The cuent and voltage ae the input ignal to the voltage model (V), while the cuent and peed o poition infomation ae input ignal to the cuent model (C). Obviouly, fo enole contol tuctue geneal voltage model with many diffeent modification and impovement ae ued. The tato flux can be diectly obtained fom the moto model equation (.0a) a follow: ( I ) ˆ = dt (5.7) R 04

111 5.3. Stato Flux Vecto Etimato Thi i a claical voltage model of tato flux vecto etimation, which obtain flux by integating the moto back electomagnetic foce (EF). The block diagam of thi etimato i hown in the Fig I R ˆ Fig Voltage model baed etimato with pue integato Thi method i enitive fo only one moto paamete, tato eitance. Howeve, the implementation of pue integato i difficult becaue of dc dift and initial value poblem. oeove, when etimato baed on pue integato in contol tuctue ae additional diadvantage. ing a pue integato to etimate the tato flux it i not poible to magnetize the machine if a zeo toque command i applied [5]. oeove, the dynamic pefomance i lowe and toque ocillation ae bigge than in anothe tato flux etimation method. Becaue of that many diffeent tato flux etimation algoithm baed on the voltage model wee popoed, which doe not appoach to the pue integato [5, 53, 54, 57, 58]. Voltage odel with ow Pa Filte (V-PF) The implet method, which eliminate poblem with initial condition and dc dift, which appea in pue integato, i a method with low-pa filte. In thi cae the equation (5.7) can be tanfomed a follow: dˆ dt ( ˆ R I ) ˆ = (5.8) T F The block diagam of the method with low-pa filte i peented in Fig I R T F ˆ Fig Flux etimato baed on voltage model with low-pa filte 05

112 5. Etimation in Induction oto Dive The etimato tabilization time depend on the low-pa filte time contant T F. Obviouly, the low-pa filte poduce ome eo in phae angle and a magnitude of tato flux, epecially when the moto fequency i lowe than the cutoff fequency of the filte. Theefoe, flux etimato with low-pa filte can be ued uccefully only in a limited peed ange. Voltage odel with Compenated ow Pa Filte (V-CPF) One way to ovecome the eo intoduced by low-pa filte i compenated algoithm [48]. The block diagam of flux etimato baed on a voltage model with compenated low-pa filte i peented in Fig jλign( Ωˆ ) + ˆ Ω λ ˆ ˆ γˆ ˆΩ γˆ Fig Flux etimato baed on voltage model with compenated low-pa filte In peented method the compenation i caied out befoe low-pa filteing. The tato flux i given by equation: ˆ E jλign( Ωˆ = + λ Ωˆ ) (5.9) whee: λ i a poitive contant. The complex-valued gain, intead of calculating the phae eo and the gain eo, i ued to compenation. oeove, due to hifting the pole of pue integation fom the oigin to λ Ωˆ, the dift poblem ae avoided. The λ facto can be elected in ange fom 0. to 0.5. Fo lowe λ the tanient pefomance i bette, but a highe value of λ allow bigge ytem inexactne. 06

113 5.3. Stato Flux Vecto Etimato Voltage odel with Refeence Flux (V-RF) The block diagam of the etimato baed on voltage model with efeence flux i peented in Fig. 5.8 [5]. I R σ τ + τ ˆ I σ ˆ c j e γˆ + τ γˆ Fig Flux etimato baed on voltage model with oto flux aumed a efeence Thi etimato calculate oto and tato flux vecto on the bai of tato voltage and cuent, and imultaneouly the diffeence between efeence and etimated oto flux magnitude i utilizing to coection etimated value. In thi etimato fit a oto flux vecto i calculated baed on the equation: dˆ dt E + K( ˆ = c e γ j ˆ ) (5.0) whee K i the gain facto and E i the oto back EF defined a: E di = ( RI σ ) (5.) dt m Then auming K = the equation (5.0) can be ewitten yielding: τ ˆ τ + τ + + τ j ˆ γ E c e (5.) = whee: d = (5.3) dt 07

114 5. Etimation in Induction oto Dive Fom the equation decibing the I in α β coodinate ytem (.5) fomula fo calculation tato flux vecto ae obtained. ˆ m = ˆ + σi (5.4) Thi etimato wok coectly fo a wide peed ange, enue good dynamic pefomance, eliminate influence of non coect initial value of the flux level. oeove, in thi algoithm oto flux i calculated, which i neceay fo oto peed calculation (ee ection 5.5). It i impotant advantage of thi etimato. The flux etimato baed on voltage model with efeence flux wa elected fo the implementation DTC-SV contol tuctue in enole opeation mode (ee ection 6.). Peented algoithm i compomie between peciion of oto and tato flux etimation and computing demand. Cuent odel in Roto Coodinated (C-RC) The meaued cuent and mechanical peed ae the input ignal fo the flux etimato baed on the cuent model in oto coodinate. Coodinate ytem d q otate with the angula peed of the moto haft Ω m, which can be defined a follow: dγm Ωm = (5.5) dt Taking into conideation numbe of pole pai ytem d q i equal Ω K = pbωm. p b angula peed of the coodinate The voltage, cuent and fluxe complex pace vecto can be eolved into component d and q. = j (5.6a) K d + q I = j, I K = I d + ji q (5.6b) K I d + I q K = d + j q, K = d + j q (5.6c) 08

115 5.3. Stato Flux Vecto Etimato The complete et of equation fo I (.0-.) can be tanfomed to the d q coodinate ytem. In thi coodinate ytem the moto model equation can be witten a follow: d = (5.7a) dt d d RI d + pbωm q d = (5.7b) dt q q RI q + + pbωm d d d 0 = R I d + dt (5.7c) d q 0 = R I q + dt (5.7d) d I d + I d = (5.8a) q I q + I q = (5.8b) d I d + I d = (5.8c) q I q + I q = (5.8d) dω dt m p J m ( I I ) = b d q q d (5.9) Fom the equation ( ) fomula fo the etimated oto flux can be obtained [66]. dˆ dt dˆ dt d q ( I ) = ˆ d T d ( I ) = ˆ q T q (5.0a) (5.0b) whee: T = R The cuent vecto i meaued in tationay coodinate α β. Theefoe, cuent component I α, β I mut be tanfomed to the ytem d q. Similaly, the etimated oto flux vecto, mut be tanfomed fom the ytem d q to α β. 09

116 5. Etimation in Induction oto Dive Stato flux vecto i calculated fom the equation (5.4). Block diagam of the whole tato flux etimato i hown in Fig I α σ I α α β I d T ˆ d d q ˆ α ˆ α I β I q ˆ q d q T α β ˆ β ˆ β γ m I β σ Fig Block diagam of the cuent model flux etimato in oto coodinate Thi flux etimato model enue good accuacy ove the entie fequency ange. It ha a vey good behavio in teady and dynamic tate. Alo it ha eitant to wong initial condition. It diadvantage i enitive on change moto paamete. Thi etimato wa elected fo the implementation DTC-SV contol tuctue in eno opeation mode (ee ection 6.) Toque Etimation The induction moto output toque i calculated baed on the equation (.9), which fo tationay coodinate ytem α β can be witten a follow: e m = pb Im I ( ˆ * m ) = p ( ˆ I ˆ I ) b α β β α (5.) It can be een that the calculated toque i depended on the cuent meauement accuacy and tato flux etimation method Roto Speed Etimation If a flux etimato wok popely and oto flux i accuately calculated mechanical peed can be obtained fom imple moto model equation [87]. If in contol tuctue the 0

117 5.5. Roto Speed Etimation tato flux etimato i applied oto flux can be calculated baed on the equation (5.4). In the I mechanical peed i defined a diffeence between ynchonou peed and leep fequency: Ω m b ( Ω Ω ) = l (5.) p whee: Ω - oto ynchonou peed, Ω l - lip fequency, p b - numbe of pole pai. The oto ynchonou peed i equal angula peed of the oto flux vecto and can be calculated a: Ω dγ = (5.3) dt The lip fequency of induction moto i defined a follow [66]: Ω l = Ω p Ω (5.4) b m Baed on the equation (3.3d) and (3.4d) in oto flux coodinate ytem the lip fequency can be expeed: Ω l = R Iq (5.5) Taking into conideation the toque equation (3.7) and (5.5) the etimated leep fequency can be calculated a follow: Ω l ˆ ( ˆ I ˆ I ) R = α β β α (5.6) Finally mechanical moto peed i calculated fom the equation (5.).

118 5. Etimation in Induction oto Dive 5.6. Summay In thi chapte etimation algoithm of flux, toque and oto peed ae peented. The etimato povide feedback ignal fo DTC-SV contol cheme. Algoithm elected to the implementation in final tuctue ae decibed and dicued. The peed etimato i baed on the etimated tato and oto fluxe. The mechanical peed can be calculated in a imple way if moto flux i popely etimated. Theefoe, flux etimation algoithm i the mot impotant pat of enole contol cheme. Selected flux etimato fo the enole mode i baed on the voltage model. Thu algoithm i enitive on accuacy of invete output voltage calculation. The voltage ae econtucted fom witching ignal. In thi method dead-time compenation algoithm i ignificant. The dead-time effect and compenation algoithm wa peented. The peented etimation method ae implemented in final DTC-SV contol tuctue. The expeimental eult, peented in Chapte 7 confim pope opeation of elected etimation method.

119 6. Configuation of the Developed I Dive Baed on DTC-SV 6.. Intoduction In thi chapte a whole implemented contol ytem will be peented. In the fit pat, the configuation of the ytem and opeation mode ae decibed. In the next pat, two hadwae etup, which wee ued to veify DTC-SV contol tuctue ae peented. To development wok wa ued laboatoy etup baed on dspace company contol boad DS03 PPC. Thi boad ha poweful micopoceo and pecial inputoutput inteface. The laboatoy etup and contol boad DS03 will be widely decibed in ection 6.3. The contol algoithm wa alo implemented in a etup baed on a micocontolle TS30F406 fom Texa Intument company. The TS30F406 i a 6-bit, fixed point micocontolle devoted fo dive application (ee ection 6.4). 6.. Block Scheme of Implemented Contol Sytem The I dive baed on DTC-SV contol tuctue can opeate in thee mode: cala contol, eno vecto contol, enole vecto contol. The invete opeate in a mode which i equied by application. The ytem configuation depend on the witche poition, ee Fig. 6.. The mot advanced i the enole vecto contol mode. In the cala contol mode algoithm obtain command voltage vecto baed on the efeence fequency. The command voltage vecto i ealized by pace vecto modulato (SV). The efeence peed in the command ignal in the vecto contol mode. Depending on mode the efeence peed i compaed with meaued (eno vecto contol mode) o etimated (enole vecto contol mode) peed ignal.

120 6. Configuation of the Developed I Dive Baed on DTC-SV Refeence Fequency Scala Contol Switch Refeence Speed Speed Contolle Refeence Value Toque and Flux Contolle SV eauement Signal Invete Etimation Value Switch Etimation Speed eaument Speed Toque and Flux Etimato Speed Etimato Speed Seno oto Fig. 6.. Block cheme of implemented contol algoithm Baed on the peed eo peed contolle calculate efeence toque value. The commanded flux i obtained fom the efeence peed and elected chaacteitic, which depend on the application. The efeence value of toque and flux ae compaed with etimated value. Baed on the eo flux and toque contolle calculate command voltage vecto. The command voltage vecto i ealized by the ame pace vecto modulato (SV) algoithm, which i ued in cala contol mode. Theefoe, depended on application equiement change between cala and vecto mode i imple. The meaued cuent and econtucted voltage ae input ignal fo the etimation algoithm (ee Chapte 5). An invete contol tuctue peented in Fig. 6. wa implemented fo I. Howeve, thi tuctue can be alo ued fo Pemanent agnet Synchonou oto (PS) [9]. All peented in Fig. 6. block ae decibed in peviou chapte of the thei. The toque, flux and peed contolle ae dicued in Chapte 4. The etimation algoithm ae hown in Chapte 5 and diffeent modulation technique ae peented in Chapte. The expeimental eult fo all thee opeating mode ae peented in Chapte 7. 4

121 6.3. aboatoy Setup Baed on DS aboatoy Setup Baed on DS03 The baic tuctue of the laboatoy etup i depicted in Fig. 6.. The moto etup conit of induction moto and DC moto, which i ued fo the loading. The induction moto i fed by the fequency invete contolled diectly by the DS03 boad. The dspace DS03 PPC i plugged in the hot PC. The DC moto i upplied by a toque contolled ectifie. The encode i ued fo the meaue mechanical peed. The DSP Inteface a et of euocad mounted in a 9 ack with the main pupoe to povide galvanic iolation to all ignal connected to the DS03 PPC contolle. gid 3 3 Rectifie Invete Rectifie meaued DC line voltage S A S B S C meaued phae cuent eauement PC DSP Inteface DS03 dspace ate : PowePC 604e Slave: DSP TS30F40 encode AC moto DC moto Fig. 6.. Stuctue of the laboatoy etup Fig aboatoy etup 5

122 6. Configuation of the Developed I Dive Baed on DTC-SV In Fig. 6.3 view of the laboatoy etup i hown. All pat of the laboatoy etup can be een in thi pictue. dspace DS03 PPC Boad The dspace DS03 PPC i a mixed RISC/DSP digital contolle poviding a vey poweful poceo fo floating point calculation a well a compehenive I/O capabilitie. Hee ae the mot elevant featue of the contolle: otoola PowePC 604e unning at 333 Hz, Slave DSP TI' TS30F40 Subytem, 6 channel (4 x 4ch) ADC, 6 bit, 4 µ, ±0 V, 4 channel ADC, bit, 800 n, ± 0V, 8 channel ( x 4ch) DAC, 4 bit, ±0 V,6 µ, Incemental Encode Inteface -7 channel 3 digital I/O line, pogammable in 8-bit goup, Softwae development tool (atlab/simulink, RTI, RTW, TDE, Contol Dek) The DS03 PPC cad i pluged in one of the ISA lot of the motheboad of a hot compute of the type PIII/900Hz, 5 BRA, 40GB HDD, Window 000. All the connection ae made though ix flat cable (50 wie each) available at the backide of the dektop compute. The DS03 PPC i a vey flexible and poweful ytem featuing both high computational capability and compenhenive I/O peiphey. The boad can be pogammed in C language. Additionally, it featue a oftwae SIINK inteface that allow all application to be developed in the atlab/simulink ue fiendly envionment. All compiling and downloading pocee ae caied out automatically in the backgound. An expeimenting oftwae called Contol Dek, allow eal-time management of the unning poce by poviding a vitual contol panel with intument and cope. The detailed paamete of the dspace DS03 PPC boad ae given in Appendix A5. 6

123 6.3. aboatoy Setup Baed on DS03 Expeimenting Softwae Contol Dek Contol Dek expeiment oftwae povide all the function fo contolling, monitoing, and automation of eal-time expeiment and make the development of contolle moe effective. A Contol Dek expeiment layout fo contolling an induction moto with DTC-SV contol method i hown in Fig Fig Contol Dek expeiment layout Contol Dek package conit of the following module: The Expeiment anagement - aue a conitent data management contolling all the data elevant fo an expeiment. The expeiment can be loaded a a complete et of data with a ingle opeation. The content of the expeiment can be defined by the ue. The Hadwae anagement - allow you to configue the dspace hadwae and to handle eal-time application with a gaphical ue inteface. The Intumentation Kit - offe a vaiety of vitual intument to build and configue vitual intument panel accoding to you pecial need. 7

124 6. Configuation of the Developed I Dive Baed on DTC-SV ing data acquiition intument you can captue data fom the model unning on the eal-time hadwae. Changing paamete value i pefomed by opeating input intument. The integated Paamete Edito allow you to ead the cuent paamete value fom the hadwae and to change a paamete et in one tep Dive Baed on TS30F406 DTC-SV contol algoithm wa implemented in the dive baed on micocontolle TS30F406. Setup conit of 8 kva IGBT invete and 5 kw induction moto. The view of invete i hown in Fig In thi pictue main contol boad of the invete with micopoceo module can be een. Fig kva invete contolled by TS30F406 poceo 8

125 6.4. Dive Baed on TS30F406 The moto et (Fig. 6.6), which wa ued in tet conit of 5 kw induction moto and kw DC moto. The induction moto data ae given in appendix A.3. The DC moto wok a a load and it i upply fom the contolled ectifie. Fig oto et. Fom the left kw DC moto and 5 kw I moto. Fig TS30F406 micopoceo boad 9

126 6. Configuation of the Developed I Dive Baed on DTC-SV The micopoceo boad hown in the Fig. 6.7 wa ued to contol the invete. The ize of the poceo module ae 53x56mm. Thi boad contain micocontolle TS30F406 and equied equipment. The communication with main invete boad by thee connecto (x0pin and x6pin) i povided. The TS30x40xA eie of device ae membe of the TS30 family of digital ignal poceo (DSP) deigned to meet a wide ange of digital moto contol (DC) and othe embedded contol application [99, 00]. Thi eie i baed on the CxP 6-bit, fixed-point, low-powe DSP CP, and i complemented with a wide ange of on-chip peipheal and on-chip RO o flah pogam memoy, plu on-chip dual-acce RA (DARA). The TS30 family conit of fixed-point, floating-point, multipoceo digital ignal poceo (DSP), and fixed-point DSP contolle. TS30 DSP have an achitectue deigned pecifically fo eal-time ignal poceing. The 40xA eie of DSP contolle combine thi eal-time poceing capability with contolle peipheal to ceate an ideal olution fo contol ytem application. Thee ae hot chaacteitic of the TS30 family: flexible intuction et, opeational flexibility, high-peed pefomance Innovative paallel achitectue, cot effectivene. Device within a geneation of a TS30 platfom have the ame CP tuctue but diffeent on-chip memoy and peipheal configuation. Spin-off device ue new combination of on-chip memoy and peipheal to atify a wide ange of need in the woldwide electonic maket. By integating memoy and peipheal onto a ingle chip, TS30 device educe ytem cot and ave cicuit boad pace. The detailed paamete of the TS30F406 micopoceo ae given in Appendix A6. The impotant featue of the TS30F46 micopoceo i the bootloade. Thank to that it i poible to pogam the device uing Seial Communication 0

127 6.4. Dive Baed on TS30F406 Inteface (SCI) o Seial Peipheal Inteface (SPI). Theefoe, pogam can be loaded fom the PC via tandad eial pot (RS3). Thi way of pogamming wa ued duing the implementation of DTC-SV contol algoithm. Thu it wa poible to wok with the poceo without uing the expenive tool like JTAG.

128 7. Expeimental Reult 7.. Intoduction In thi chapte elected expeimental eult obtained in the ytem decibed in Chapte 6 ae hown. All tet wa done fo 3 kw induction moto, which paamete ae given in Appendix A Pule Width odulation In Fig diffeent modulation method ae peented. All tet wa meaued at fequency f = 40 Hz. In Fig. 7. pace vecto modulation method with ymmetical zeo vecto placement SVPW i hown (ee ection.4.3). Fig. 7.. Space vecto modulation (SVPW) at fequency f = 40 Hz ) witching ignal S A, ) pole voltage A0 (50 V/div), 3) phae voltage A (50 V/div), 4) output cuent I A (5 A/div) In Fig. 7. dicontinuou pule width modulation DPW i hown (ee ection.4.3). It can be obeve diffeence in pole voltage wavefom and witching ignal in Fig. 7. and 7.. DPW modulation method ha 60º no witch ecto. Howeve, phae voltage and output cuent have inuoidal wavefom.

129 7.. Pule Width odulation Fig. 7.. Dicontinuou modulation (DPW) at fequency f = 40 Hz ) witching ignal S A, ) pole voltage A0 (50 V/div), 3) phae voltage A (50 V/div), 4) output cuent I A (5 A/div) In Fig. 7.3 and 7.4 ovemodulation (O) algoithm i hown (ee ection.4.5). Fig Ovemodulation mode I at fequency f = 40 Hz ) witching ignal S A, ) pole voltage A0 (50 V/div), 3) phae voltage A (50 V/div), 4) output cuent I A (5 A/div) 3

130 7. Expeimental Reult Fig Ovemodulation mode II at fequency f = 40 Hz ) witching ignal S A, ) pole voltage A0 (50 V/div), 3) phae voltage A (50 V/div), 4) output cuent I A (5 A/div) The eult fo ix-tep mode ae peented in Fig Fig Six-tep mode at fequency f = 40 Hz ) witching ignal S A, ) pole voltage A0 (50 V/div), 3) phae voltage A (50 V/div), 4) output cuent I A (0 A/div) Reult peented in Fig wae obtained at deceaed dc-link voltage. Theefoe, ovemodulation and ix-tep opeation mode can be hown with fequency 4

131 7.3. Flux and Toque Contolle f = 40 Hz like the othe eult. Thank to it, cuent and voltage wavefom can be bette compaed. Expeimental eult peented in Fig confim pope opeation all type modulation algoithm Flux and Toque Contolle Dynamic tet fo the flux and toque contolle wee done fo diffeent ampling fequencie value and the ame condition like fo imulation peented in ection 4.3 (moto peed Ω = 0 ). The flux contolle paamete wee calculated accoding to m ymmetic optimum citeion (ee ection 4.3.) and toque contolle paamete wee calculated accoding to oot locu method (ee ection 4.3.). In Fig ae peented tato flux tep epone at ampling fequency f = 0 khz, f = 5 khz, f =. 5 khz epectively. Thoe eult can be compaed with imulation eult peented in Fig. 4.. Fig Stato flux epone at ampling fequency f = 0 khz ) efeence flux (0.5 Wb/div), ) etimated flux (0.5 Wb/div) 5

132 7. Expeimental Reult Fig Stato flux epone at ampling fequency f = 5 khz ) efeence flux (0.5 Wb/div), ) etimated flux (0.5 Wb/div) Fig Stato flux epone at ampling fequency f =. 5 khz ) efeence flux (0.5 Wb/div), ) etimated flux (0.5 Wb/div) Peented in Fig expeimental eult confim pope opeation of the flux contol loop at diffeent ampling fequency. 6

133 7.3. Flux and Toque Contolle The expeimental eult of toque contolle dynamic tet ae hown in Fig Peented eult wee obtain at ampling fequency f = 0 khz (Fig. 7.9), f = 5 khz (Fig. 7.0), f =. 5 khz (Fig. 7.). Fig Toque epone at ampling fequency f = 0 khz ) efeence toque (4.5 Nm/div), 3) etimated toque (4.5 Nm/div) Fig Toque epone at ampling fequency f = 5 khz ) efeence toque (4.5 Nm/div), 3) etimated toque (4.5 Nm/div) 7

134 7. Expeimental Reult Fig. 7.. Toque epone at ampling fequency f =. 5 khz ) efeence toque (4.5 Nm/div), 3) etimated toque (4.5 Nm/div) The eult fom Fig can be compaed with imulation eult peented in Fig Expeimental eult peented in Fig confim pope opeation of the toque contol loop at diffeent ampling fequency. The decoupling between flux and toque contol loop i peented in Fig. 7.. The toque tep epone (Fig. 7.a) and magnitude tato flux tep epone (Fig. 7.b) ae hown. a) 8

135 7.4. DTC-SV Contol Sytem b) Fig. 7.. Dynamic tet a) toque tep change, b) flux tep change ) efeence toque (9 Nm/div), ) etimated toque (9 Nm/div), 3) efeence flux (0.3 Wb/div), 4) etimated flux (0.3 Wb/div) The eult fom Fig. 7. can be compaed with imulation eult peented in Fig Fom Fig. 7. can be een that decoupling between flux and toque i coect DTC-SV Contol Sytem In thi ection the expeimental eult fo thee poible dive opeation mode, which ae decibed in Chapte 6 ae hown. Theefoe, compaion of a ytem behavio in diffeent mode i poible. In Fig eult fo cala contol mode ae peented. Fig. 7.3 give eult fo ytem tatup to fequency f = 40Hz (moto peed Ω m = 5ad / ). 9

136 7. Expeimental Reult Fig Scala contol mode - Statup fom 0 to f = 40Hz ) efeence fequency (5 Hz/div), ) actual peed (30 (ad/)/div, 4) phae cuent (0 A/div) The load toque tep change at fequency f = 5Hz i hown in Fig Fig Scala contol mode - oad toque tep change fom 0 to = N at fequency f = 5Hz ) efeence fequency (5 Hz/div), ) actual peed (30 (ad/)/div), 3) toque (0 Nm/div), 4) phae cuent (0 A/div) In Fig. 7.5 and 7.6 eult of peed evee ae hown ( f = ± 5Hz ). The evee time i 0.5 (Fig. 7.5) and 5 (Fig. 7.6). 30

137 7.4. DTC-SV Contol Sytem Fig Scala contol mode - Speed eveal f = ± 5Hz (evee time 0.5) ) efeence fequency (5 Hz/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) Fig Scala contol mode - Speed eveal f = ± 5Hz (evee time 5) ) efeence fequency (5 Hz/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) In Fig eult fo eno vecto contol mode ae peented. Fig. 7.7 give eult fo ytem tatup to peed Ω m = 0 ad /. 3

138 7. Expeimental Reult Fig Vecto contol mode with peed eno - Statup fom 0 to Ω m = 0 ad / ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div, 4) phae cuent (0 A/div) The load toque tep change at peed Ω m = 75 ad / i hown in Fig Fig Vecto contol mode with peed eno - oad toque tep change fom 0 to = at peed Ω m = 75 ad / ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 3) toque (0 Nm/div), 4) phae cuent (0 A/div) N In Fig. 7.9 and 7.0 eult of peed evee ae hown ( Ω m = ±75ad / ). The evee time i 0.5 (Fig. 7.9) and 5 (Fig. 7.0). 3

139 7.4. DTC-SV Contol Sytem Fig Vecto contol mode with peed eno - Speed eveal Ω m = ±75ad / (evee time 0.5) ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) Fig Vecto contol mode with peed eno - Speed eveal Ω m = ±75ad / (evee time 5) ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) In enole vecto contol mode the accuacy of the peed etimation algoithm i impotant. Theefoe, tatic and dynamic eo of etimated peed wee invetigated. The eo of etimated peed can be witten a: 33

140 7. Expeimental Reult εω m Ω ˆ m Ωm = 00% (7.) Ω m whee: Ω m - actual peed, Ωˆ m - etimated peed. In Fig. 7. peed etimation eo a the function of mechanical peed in teady tate i peented. ε m [%] Ω eo_omega [%] omega_m [ad/] [ad/] Ω m Fig. 7.. Etimated peed eo a the function of mechanical peed in teady tate. The eult of peed etimato dynamic tet ae peented in Fig.. In thi tet peed contolle opeate with the eno and peed etimato wok in open loop fahion. 34

141 7.4. DTC-SV Contol Sytem Fig. 7.. Dynamic tet of the peed etimation - Speed eveal Ω m = ±50ad / ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 3) etimated peed (30 (ad/)/div), 4) eo of etimated peed (5 %/div) In Fig eult fo enole vecto contol mode ae peented. Fig. 7.3 give eult fo ytem tatup to peed Ω m = 0 ad /. Fig Senole vecto contol mode - Statup fom 0 to Ω m = 0 ad / ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div, 4) phae cuent (0 A/div) The load toque tep change at peed Ω m = 75 ad / i hown in Fig

142 7. Expeimental Reult Fig Senole vecto contol mode - oad toque tep change fom 0 to = at peed Ω m = 75 ad / ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 3) toque (0 Nm/div), 4) phae cuent (0 A/div) N In Fig. 7.5 and 7.6 eult of peed evee ae hown ( Ω m = ±75ad / ). The evee time i 0.5 (Fig. 7.5) and 5 (Fig. 7.6). Fig Senole vecto contol mode - Speed evee Ω m = ±75ad / (evee time 0.5) ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) 36

143 7.4. DTC-SV Contol Sytem Fig Senole vecto contol mode - Speed evee Ω m = ±75ad / (evee time 5) ) efeence peed (30 (ad/)/div), ) actual peed (30 (ad/)/div), 4) phae cuent (0 A/div) 37

144 8. Summay and Concluion In thi thei the mot convenient indutial contol cheme fo voltage ouce invete-fed induction moto dive wa eached fo, baed on the exiting contol method. Thi method hould povide: opeation in wide powe ange, guaantee good and epeatable paamete of dive. It i equied by a eial poduction of a dive. To achieve a low cot the contol ytem hould be implemented in imple micopoceo. The analyi of exiting method wee done in ode to choe the indutial oiented univeal cheme. The mot impotant contol technique of I wee peented in Chapte 3: Field Oiented Contol (FOC), Feedback ineaization Contol (FC) and Diect Toque Contol (DTC). The FC tuctue guaantee exact decoupling of the moto peed and oto flux contol in both dynamic and teady tate. Howeve, it i complicated and difficult to implement in pactice. Thi method equie complex computation and additionally it i enitive to change of moto paamete. Becaue of thee featue thi method wa not choen fo implementation. In next tep FOC and DTC method wee analyzed. Chaacteitic of thoe method wee done on the bai of the liteatue, imulation and expeimental invetigation. The concluion of thoe conideation wee hown in ection 3.5. Analyi of advantage and diadvantage of FOC and DTC method eulted in a each fo method which will eliminate diadvantage and keep advantage of thoe method. The diect toque contol with pace vecto modulation (DTC-SV) i an effect of thi each. The main featue of thi method can be ummaized a: Space vecto modulato, Contant witching fequency, nipola voltage thank to ue of PW block (SV), Sinuoidal wavefom of tato cuent, Algoithm opeate with toque and flux value implementation in manufactuing poce i eaie, Good dynamic contol of flux and toque. The tep epone ae lowe than in claical DTC, becaue PI contolle ae lowe than hyteei contolle,

145 8. Summay and Concluion which ae ued in claical DTC. Howeve, obtained dynamic (epone time fo the toque.5-m) i ufficient fo geneal pupoe dive. High ampling fequency i not equied. The DTC-SV algoithm wok popely at ampling fequency fequency at leat 5 40kHz. f = 5kHz wheea DTC equie ampling ow flux and toque ipple than in claical DTC. The toque ipple in DTC-SV at ampling fequency f = 5kHz ae ten time lowe than peented in ection 3.4. toque ipple fo claical DTC at ampling fequency f = 40kHz. The DTC-SV cheme i baed only on the analyi of tato equation like claical DTC, theefoe contol algoithm i not enitive to oto paamete change. Thi method can be applied alo fo uface mounted pemanent magnet (P) ynchonou moto [9]. The P ynchonou moto of thi type ae moe fequently ued in tandad peed dive a inteio P. Hence, DTC-SV method allow univeal dive building fo both type of AC moto. The vey impotant pat of DTC-SV cheme i a pace vecto modulato. The diffeent modulation technique can be applied in the ytem. Theefoe, a dive ha additional advantage. The mot impotant i full ange of voltage contol and eduction of witching loe. Fo intance, eduction of witching loe can be obtained by implementation of dicontinuou PW method. Thee modulation technique wee decibed and chaacteized in ection.4. The expeimental eult fo the implemented modulation method wee hown in Chapte 7. The hot eview of DTC-SV method popoed in liteatue wee given in ection 4.. Fo futhe conideation the DTC-SV method with cloe-loop toque and flux contol in tato flux Cateian coodinate have been choen. In autho opinion thi method i bet uited fo commecial manufactued dive. Fo choen cheme two contolle deign pocedue wee popoed. Thoe analyi wee peented in Chapte 4. Alo coection of contolle paamete fo ampling fequency change wa dicued. In adjutable peed dive upeio peed contolle i ued. The analyi of peed contol loop and contolle tuning wee peented in ection 4.4. Coectne of ued method wa confimed by imulation and expeimental eult. 39

146 8. Summay and Concluion The quality of egulation poce depend on an accuacy of feedback ignal. In the vecto contol of induction moto thoe ignal ae povided by flux and toque etimato and, in enole opeation mode, by a peed etimato. The peciion of etimated ignal depend on: exact knowledge of moto paamete, good dead-time and voltage dop compenation algoithm, well ealized meauement, implementation of on-line adaptation of moto paamete. Thoe featue ae common fo all vecto contol method. Theefoe, if feedback ignal ae etimated accuately, the contol cheme hould be a imple a poible. The DTC-SV ha a imple tuctue and it can be analyzed and implemented in a imple way. It i vey impotant featue of DTC-SV. Etimation poblem in a dive with induction moto wee dicued in Chapte 5. Following etimation algoithm, elected fo implementation, wee peented: voltage etimato with dead-time compenation algoithm, tato flux etimato, toque etimato and mechanical peed etimato. All pat of contol cheme wee veified in imulation and expeiment. The whole cheme conit of: flux and toque contolle, peed contolle, etimation of flux, toque and peed and compenation algoithm. Thoe complete tuctue wa peented in Chapte 6. Popoed olution wa implemented in 3 kw expeimental and 5 kw indutial dive. The laboatoy etup wee alo peented in Chapte 6. Peented in Chapte 7 expeimental eult confim pope opeation of developed contol ytem. Thu, thei how the poce to elect and develop the mot convenient contol cheme fo voltage ouce invete-fed induction moto dive. Whole poblem of diect flux and toque contol with pace vecto modulation (DTC-SV) wee analyzed and invetigated in imulation and expeiment. Finally, it hould be teed that the developed ytem wa bought into eial poduction. Peented algoithm ha been ued in new family of invete dive poduced by Polih company Powe Electonic anufactue TWERD, Touń. 40

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157 it of Symbol a = e j π 3 = + j 3 B - vicou contant f - fequency f - ampling fequency f w - witching fequency I - cuent, abolute value I A, I B, I C - intantaneou value of tato phae cuent I - oto cuent pace vecto I - tato cuent pace vecto I, I - tato voltage vecto component in tationay α β coodinate α β α β ytem I, I - oto voltage vecto component in tationay α β coodinate ytem k - pace vecto, geneally K p - contolle gain K p - toque contolle gain K p - flux contolle gain - inductance, abolute value - main, magnetizing inductance - tato winding elf-inductance - oto winding elf-inductance - mutual inductance, abolute value

158 it of ymbol - toque, abolute value e - electomagnetic toque - load toque, m - modulation index m - numbe of phae winding p b - numbe of pole pai S A, S B, S C - witching tate fo the voltage ouce invete R - eitance, abolute value R - oto phae winding eitance R - tato phae winding eitance T i - contolle integating time T i - toque contolle integating time Ti - flux contolle integating time T D - dead time of invete T = - oto time contant R T - ampling time T w - witching time - voltage, abolute value A, B, C - intantaneou value of the tato phae voltage - tato voltage pace vecto - oto voltage pace vecto - invete output voltage pace vecto, ν = 0,..., 7 ν c - efeence voltage vecto 5

159 it of ymbol, - tato voltage vecto component in tationay α β coodinate α β ytem α c, βc - efeence tato voltage vecto component in tationay α β coodinate ytem dc, qc - efeence tato voltage vecto component in otating d q coodinate ytem dc - invete dc link voltage - peak value of the n-th hamonic, n =,, 3, m ( n) Ac, Bc, Cc - efeence tato phae voltage t - tiangula caie ignal AB, BC, CA - line to line voltage - flux linkage, abolute value A, B, C - flux linkage of the tato phae winding - pace vecto of the tato flux linkage - pace vecto of the oto flux linkage - tato flux amplitude - oto flux amplitude, - tato flux vecto component in tationay α β coodinate ytem α β, - oto flux vecto component in tationay α β coodinate ytem β β γ m - moto haft poition angle γ - oto flux vecto angle γ - tato flux vecto angle Ω - angula peed, abolute value 53

160 it of ymbol Ω K - angula peed of the coodinate ytem Ω m - angula peed of the moto haft Ω m dγ = dt m Ω - angula peed of the oto flux vecto Ω - angula peed of the tato flux vecto Ω Ω dγ = dt dγ = dt Ω l - lip fequency σ = - total leakage facto Supecipt ^ - etimated value Subcipt..c - efeence value Rectangula coodinate ytem α β - tato oiented, tationay coodinate ytem ' ' d q - oto oiented, otated coodinate ytem x y - tato flux oiented, otated coodinate ytem d q - oto flux oiented, otated coodinate ytem Abbeviation I Induction oto F agnetomotive Foce PW Pule Width odulation 54

161 it of ymbol ZSS Zeo Sequence Signal SPW Sinuoidal (tiangulation) Pule Width odulation SVPW Space Vecto Pule Width odulation THIPW Thid Hamonic Pule Width odulation DPW Dicontinue Pule Width odulation SV Space Vecto odulation O Ovemodulation RPW Random Pule Width odulation R Random ead-ag odulation RCD Random Cente Pule Diplacement RZD Random Ditibution of the Zeo Voltage Vecto 55

162 Appendice A.. Deivation of Fouie Seie Fomula fo Phae Voltage If function f i a peiodic, piecewie continuou and an odd, then it tigonometic Fouie eie i given by [56]: ( t) b in( nωt) = f ω n (A..) n= whee, fo n =,, 3, π b n = f (A..) π 0 ( ωt) in( nωt) d( ωt) Function which decibe phae invete voltage i hown in the Fig. A.. A dc 3 dc dc dc π 3 π 3 π 4π 3 5π 3 π ωt Fig. A... Phae voltage of the invete Taking into conideation thi function coefficient b n can be witten a follow: b n = π π 0 A () t in( nωt) d( ωt) π π = 3 3 π π dc in 3 0 π 3 π = 3 co ( nωt) d( ωt) + dc in( nωt) d( ωt) + dc in( nωt) d( ωt) π π π 3 ( nωt) 3 co( nωt) ( ) π π co nωt 0 3 π n dc 3 π = co( nπ ) + co n co n π (A..3) 3π n dc 3 3

163 Appendice fo even n: π co n 3 3 ( n π ) + co n co π π π = + co n co nπ n = 0 (A..4) 3 3 and fo uneven n: π π π co π = + co n (A..5) 3 ( nπ ) + co n co n π = + + co n co π + ( n ) π n Fom above fomula the Fouie eie fo A i given by: A 4 = 3π dc n= π + co n in n 3 ( nωt) = π dc n= in n ( nωt) (A..6) whee: n=+6k, k=0, ±, ±, 57

164 Appendice A.. SABER Simulation odel The contol tuctue of I wee implemented in SABER v..4 Synopy Inc. package. SABER povide analyi behavio of the complete analog and mixed-ignal ytem including electical ubytem. SABER model cheme i peented in Fig. A... Fig. A... SABER model The SABER package include the electical and mechanical element libay. The cheme of invete (Fig. A..) i baed on the tanito and diode model fom libay. The ue of SABER package can ceate own model uing mathematical equation. In thi way i build model of induction moto. The equation (.4-.6) decibed induction moto in α β coodinate ytem ae witten in popely fom in moto.in SABER file. The content of thi file i hown in Fig. A..3 58

165 Appendice Fig. A... odel of invete The contol algoithm of induction moto ha been witten in AST SABER pogamming language. The code in AST language i connected to Contol Block, which i hown in Fig. A... The AST pogamming language i vey imila to C language. Theefoe, implementation in laboatoy etup of imulated tuctue i eaie. 59

166 Appendice #moto.in template moto t t t3 t0 =,,l,l,lm,ml,,j electical t, t, t3, t0 { <cont.in value { vt=v(t)-v(t0) vt=v(t)-v(t0) vt3=v(t3)-v(t0) va=(/3)*(*vt-vt-vt3) vb=(vt-vt3)/qt(3) fa = l*ia + lm*ia fb = l*ib + lm*ib fa = l*ia + lm*ia fb = l*ib + lm*ib } equation { ib: vb - *ib = d_by_dt(fb) ia: va - *ia = d_by_dt(fa) ib: - *ib + p*omega_m*fa = d_by_dt(fb) ia: - *ia - p*omega_m*fb = d_by_dt(fa) omega_m: (/j ) * ( te - ml )= d_by_dt(omega_m) i(t->t0)+=it it: it=ia i(t->t0)+=it it: it=0.5*(-ia + qt(3)*ib) i(t3->t0)+=it3 it3: it3=0.5*(-ia - qt(3)*ib) } } Fig. A..3. SABER file moto.in 60

167 Appendice A.3. Data and Paamete of Induction oto Table A.3.. Data of 3 kw induction moto Powe Voltage Cuent Fequency Bae peed Numbe of pole pai oment of inetia Nominal toque Nominal tato flux P N = 3 kw N = 380 V I N = 6.9 A f N = 50 Hz Ω N = 45 pm p b = J = kgm N = 0 Nm N = 0.98 Wb Table A.3.. Paamete of 3 kw induction moto Stato winding eitance Roto winding eitance Stato inductance Roto inductance utual inductance R =.85 Ω R =.84 Ω = 70 mh = 70 mh = 60 mh Table A.3.3. Data of 5 kw induction moto Powe Voltage Cuent Fequency Bae peed Numbe of pole pai oment of inetia Nominal toque Nominal tato flux P N = 5 kw N = 380 V I N = 8.9 A f N = 50 Hz Ω N = 460 pm p b = J = kgm N = 98 Nm N = 0.98 Wb 6

168 Appendice Table A.3.4. Paamete of 5 kw induction moto Stato winding eitance Roto winding eitance Stato inductance Roto inductance utual inductance R = 0.8 Ω R = 0.6 Ω = 63.5 mh = 63.5 mh = 58. mh Table A.3.5. Data of 90 kw induction moto Powe Voltage Cuent Fequency Bae peed Numbe of pole pai oment of inetia Nominal toque Nominal tato flux P N = 90 kw N = 380 V I N = 58 A f N = 50 Hz Ω N = 483 pm p b = J =.50 kgm N = 580 Nm N = 0.98 Wb Table A.3.6. Paamete of 90 kw induction moto Stato winding eitance Roto winding eitance Stato inductance Roto inductance utual inductance R = 0.00 Ω R = 0.06 Ω = 6.36 mh = 6.74 mh = 6 mh 6

169 Appendice A.4. Equipment Table A.4.. it of equipment Intument Digital ocillocope Analyze Voltage diffeential pobe Cuent pobe Simulation pogam Simulation pogam Type Tektonix TDS Hz NORA D6000 em Tektonix P500 Tektonix TCP A300 SABER 00.4 Synopy, Inc. atlab 6. athwok, Inc. 63

170 Appendice A.5. dspace DS03 PPC Boad Phyically, DS03 i built a a PC cad that can be mounted into an ISA lot of a egula PC. The I/O capability i athe impeive poviding 300 ignal. In ode to implify the inteface, 60 ignal out of 300 ae elected fo futhe poceing and then connected to the SC fo ignal conditioning. The election i caied out in the DEX cad, which wa fitted in a hielded box fo EC conideation. The DS03 i a ingle boad ytem baed on the otoola PowePC 604e/333Hz poceo (PPC), which fom the main poceing unit. I/O nit A et of on-boad peipheal fequently ued in digital contol ytem ha been added to the PPC. They include: analog-digital and digital-analog convete, digital I/O pot (Bit I/O), and a eial inteface. The PPC can alo contol up to ix incemental encode, which allow the development of advanced contolle fo obot. DSP Subytem The DSP ubytem, baed on the Texa Intument TS30F40 DSP fixed-point poceo, i epecially deigned fo the contol of electic dive. Among othe I/O capabilitie, the DSP povide 3-phae PW geneation making the ubytem ueful fo dive application. CAN Subytem A futhe ubytem, baed on Siemen 80C64 mico-contolle (C), i ued fo connection to a CAN bu. ate PPC Slave DSP Slave C The PPC ha acce to both the DSP and the CAN ubytem. Spoken in tem of inte-poceo communication, the PPC i the mate, wheea the DSP and the CAN C ae lave. Fig. A.5.4 give an oveview of the functional unit of the DS03 PPC. 64

171 Appendice Fig. A.5.. Block diagam of the dspace DS03 boad The DS03 PPC Contolle Boad povide the following featue ummaized in alphabetical ode: A/D Conveion 4 paallel A/D-convete, multiplexed to 4 channel each, 6-bit eolution, 4 µ ampling time, ± 0V input voltage ange, 4 paallel A/D-convete with channel each, -bit eolution, 800 n ampling time ± 0V input voltage ange, Slave DSP ADC nit poviding. paallel A/D convete, multiplexed to 8 channel each, 0-bit eolution, 6 µ ampling time ± 0V input voltage ange, Digital I/O 65

172 Appendice 3-bit input/output, configuation byte-wie, Slave DSP Bit I/O-nit poviding, 9-bit input/output, configuation bit-wie, CAN Suppot Slave C fulfilling CAN Specification.0 A and.0 B, and ISO/DIS 898. D/A Conveion D/A convete with 4 channel each, 4-bit eolution ±0 V voltage ange Incemental Encode Inteface analog channel with /38-bit counte ange, digital channel with 6/4/3-bit counte ange, 5 digital channel with 4-bit counte ange. Inteupt Contol - Inteupt Handling. Seial I/O tandad ART inteface, altenatively RS-3 o RS-4 mode. Time Sevice 3-bit downcounte with inteupt function (Time A), 3-bit upcounte with pe-cale and inteupt function, 3-bit downcounte with inteupt function (PPC built-in Decemente), 3/64-bit timebae egite (PPC built-in Timebae Counte). Timing I/O 4 PW output acceible fo tandad Slave DSP PW Geneation, 3 x PW output acceible fo Slave DSP PW3 Geneation and Slave DSP PW-SV Geneation, 4 paallel channel acceible fo Slave DSP Fequency Geneation, 4 paallel channel acceible fo Slave DSP Fequency eauement (FD) and Slave DSP PW Analyi (PWD). 66

173 Appendice A.6. Poceo TS30F406 Fig. A.6. give oveview of the TS30F406 tuctue. Cxx DSP Coe DARA (B0) 56 Wod DARA (B) 56 Wod DARA (B) 3 Wod 0 bit ADC P Clock SCI SPI CAN SARA (K Wod) Flah (3K Wod) Watchdog Digital I/O JTAG Pot Event anage A - Captue Input - Compae/PW Output - GP Time/ PW Event anage B - Captue Input - Compae/PW Output - GP Time/ PW Fig. A.6.. TS30F406 device oveview The featue of the TS30F406 poceo [0] can be ummaized a: High-Pefomance Static COS Technology: 5-n Intuction Cycle Time (40 Hz), 40-IPS Pefomance, ow-powe 3.3-V Deign. Baed on TS30Cxx DSP CP Coe: Code-Compatible With F43/F4/C4, Intuction Set and odule Compatible With F40/C40. On-Chip emoy: 3K Wod x 6 Bit of Flah EEPRO (4 Secto), Pogammable "Code-Secuity" Featue fo the On-Chip Flah,.5K Wod x 6 Bit of Data/Pogam RA, 67

174 Appendice 544 Wod of Dual-Acce RA, K Wod of Single-Acce RA. Boot RO: SCI/SPI Bootloade, Two Event-anage (EV) odule (EVA and EVB), Each Include: Two 6-Bit Geneal-Pupoe Time, Eight 6-Bit Pule-Width odulation (PW) Channel Which Enable: Thee-Phae Invete Contol, Cente- o Edge-Alignment of PW Channel, Emegency PW Channel Shutdown With Extenal PDPINTx\ Pin, Pogammable Deadband (Deadtime) Pevent Shoot-Though Fault, Thee Captue nit fo Time-Stamping of Extenal Event, Input Qualifie fo Select Pin, On-Chip Poition Encode Inteface Cicuity, Synchonized A-to-D Conveion. Watchdog (WD) Time odule, 0-Bit Analog-to-Digital Convete (ADC): 6 ultiplexed Input Channel, 375 n o 500 n IN Conveion Time, Selectable Twin 8-State Sequence Tiggeed by Two Event anage, Contolle Aea Netwok (CAN).0B odule, Seial Communication Inteface (SCI), 6-Bit Seial Peipheal Inteface (SPI), Phae-ocked-oop (P)-Baed Clock Geneation, 68

175 Appendice 40 Individually Pogammable, ultiplexed Geneal-Pupoe Input/Output (GPIO) Pin, Five Extenal Inteupt (Powe Dive Potection, Reet, Two akable Inteupt), Powe anagement: Thee Powe-Down ode, Ability to Powe Down Each Peipheal Independently, Real-Time JTAG-Compliant Scan-Baed Emulation, IEEE Standad 49. (JTAG), Development Tool Include: Texa Intument (TI) ANSI C Compile, Aemble/inke, and Code Compoe Studio (CCS) Debugge, Evaluation odule, Scan-Baed Self-Emulation (XDS50 ), Boad Thid-Paty Digital oto Contol Suppot, Package 00-Pin QFP PZ. 69