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

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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

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