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


 Harvey Maxwell
 1 years ago
 Views:
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
2
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.
4
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 (DTCSV) Intoduction Stuctue of DTCSV Review DTCSV Scheme with Cloed oop Flux Contol DTCSV Scheme with Cloed oop Toque Contol DTCSV Scheme with Cloe oop Toque and Flux Contol Opeating in Pola Coodinate DTCSV Scheme with Cloe oop Toque and Flux Contol in Stato Flux Coodinate Concluion fom Review of the DTCSV Stuctue Analyi and Contolle Deign fo DTCSV 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 DTCSV 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 DTCSV 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 aiconditioning (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 highpefomance 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, unipola voltage PW, low flux and toque ipple, obutne fo paamete vaiation, fouquadant 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 highpefomance. 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 Euleagange 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 onoff 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 (DTCSV) ha been developed. In thi new method diadvantage of the claical DTC ae eliminated. Baically, the DTCSV tategie ae the method, which opeate with contant witching fequency. Thee method ae the main ubject of thi thei. The DTCSV 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 DTCSV technique ha alo imple tuctue and povide dynamic behavio compaable with claical DTC. Howeve, DTCSV 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 invetefed induction moto dive i diect toque contol with pace vecto modulation DTCSV 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 DTCSV 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 DTCSV induction moto dive, development of a SABER  baed imulation algoithm fo contol and invetigation voltage ouce invetefed 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 DTCSV 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 DTCSV method. Chapte 4 i devoted to analyi and ynthei of DTCSV 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 DTCSV 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 theephae I by a ytem of equation [66] the following implifying aumption ae made: the theephae 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, ocalled 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 theephae 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 fluxlinkage. 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 fluxcuent 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 layout 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 theephae 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 feewheeling diode. The invete i upplied by a voltage ouce compoed of a diode ectifie with a C filte in the dclink. The capacito C i typically lage enough to obtain adequately low voltage ouce impedance fo the altenating cuent component in the dclink. 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 quaewave, o ixtep, mode of opeation. The phae voltage ae elated to the dclink 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 ixtep 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 nth 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 inveteleg 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 af) ae active vecto and the lat two (Fig..5 gh) 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 inveteleg (Fig..3) can be tuned on at a time, to avoid a hot cicuit in the dclink. A delay time in the tanito witching ignal mut be ineted. Duing thi delay time, the deadtime T D tanito ceae to conduct. Two contol ignal S A +, S A  fo tanito T, T with deadtime T D ae peented in Fig..7. The duation of deadtime depend of the ued tanito. ot of them it take  3µ. S A + S A  t T D T D t T Fig..7. Deadtime 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 deadtime 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 deadtime effect [8]. It i epecially impotant 6
23 .4. Pule Width odulation (PW) fo the low peed ange when voltage i vey low. The deadtime 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 deadtime 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 theephae ac powe i pefomed in the witched mode (Fig..3). Thi mode conit in powe emiconducto witche ae contolled in an onoff 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 ixtep 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 3th 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 N00.4 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 quaephae voltage wave. The modulation index vaie fom 0 to at the quaewave 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
Small Hydropower Plant with variable speed PM generator
Witold MAZGAJ, Zbigniew SZULAR, Tomaz WĘGEL, Tadeuz SOBCZYK Politechnika Kakowka, ntytut Elektomechanicznych Pzemian Enegii Small Hydopowe Plant with vaiable peed PM geneato Abtact. Thi pape peent a new
More informationChapter 30: Magnetic Fields Due to Currents
d Chapte 3: Magnetic Field Due to Cuent A moving electic chage ceate a magnetic field. One of the moe pactical way of geneating a lage magnetic field (.11 T) i to ue a lage cuent flowing though a wie.
More informationExperimental DTC of an Induction Motor Applied to Optimize a Tracking System
Euopean Aociation fo the Development of Renewable Enegie, Envionment and Powe Quality (EA4EPQ) Intenational Confeence on Renewable Enegie and Powe Quality (ICREPQ 2) Santiago de Compotela (Spain), 28th
More informationModelling and simulation of a signal injection selfsensored drive
Modelling and imulation o a ignal injection elenoed dive Alen Poljugan Faculty o Electical Engineeing and Computing, Depatment o electic machine, dive and automation, Univeity o Zageb Unka, Zageb, Coatia,
More informationEffect of Unemployment Insurance Tax On Wages and Employment: A Partial Equilibrium Analysis
Effect of Unemployment nuance Tax On Wage and Employment: atial Equilibium nalyi Deegha Raj dhikai, Oklahoma Employment Secuity Commiion ynn Gay, Oklahoma Employment Secuity Commiion Jackie Bun, Texa &
More informationSolutions to Problems: Chapter 7
Solution to Poblem: Chapte 7 P71. P72. P73. P74. Authoized and available hae LG 2; Baic a. Maximum hae available fo ale Authoized hae 2,000,000 Le: Shae outtanding 1,400,000 Available hae 600,000 b.
More informationSECTION 53 Angles and Their Measure
53 Angle and Thei Meaue 357 APPLICATIONS Appoximating. Poblem 93 and 9 efe to a equence of numbe geneated a follow: If an nd egula polygon i incibed in a cicle of adiu, then it can be hown that the aea
More informationDSC Baseline Improvements Obtained by a New Heat Flow Measurement Technique
DS Baeline Impovement Obtained by a New Heat Flow Meauement Technique obet L. Danley, Pete A. aulfield TA Intument, 109 Luken Dive, New atle DE 19720 ABSTAT Nealy all diffeential canning caloimety (DS)
More informationThe Essence of the Electromagnetic Wave is Not Energy
The Eence of the Electomagnetic Wave i Not Enegy Zeng Qingping Ai Foce Rada Academy Pofeo cienceum@yahoocn Abtact The cutomay opinion i: electic ave o light ave i enegy, TYang expeiment i the intefeence
More informationParameter Identification of DC Motors
Paamete dentification of DC Moto utho: Dipl.ng. ngo öllmecke dvantage of the Paamete dentification Method Saving time and money in the teting poce: no anical coupling neceay Full infomation: Entie chaacteitic
More informationStandardized Coefficients
Standadized Coefficient Ta. How do ou decide which of the X ae mot impotant fo detemining? In thi handout, we dicu one poile (and contoveial) anwe to thi quetion  the tandadized egeion coefficient. Fomula.
More informationOptimizing Supply Chain Collaboration Based on Negotiation and Bargain Power for Single Retailer And Single Supplier
Poceeding of the Intenational MultiConfeence of Enginee and Compute Scientit 20 Vol II,, Mach , 20, Hong Kong Optimizing Supply Chain Collaboation Baed on Negotiation and Bagain Powe fo Single Retaile
More informationApplication Note, V1.0, July 2006 AP16097 XC164. Different PWM Waveforms Generation for 3Phase AC Induction Motor with XC164CS.
Application Note, V1.0, July 006 AP16097 XC164 Diffeent PWM Wavefom Geneation fo 3Phae AC Induction Moto with XC164CS Micocontolle Edition 0060804 Publihed by Infineon echnologie AG 8176 München, Gemany
More informationCOMPARISON OF SCALAR AND VECTOR CONTROL STRATEGIES OF INDUCTION MOTORS
HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. 9() pp. 6570 (0) COMPARISON OF SCALAR AND VECTOR CONTROL STRATEGIES OF INDUCTION MOTORS G. KOHLRUSZ, D. FODOR Univeity of Pannonia, Faculty of Engineeing,
More informationPurchase and rental subsidies in durablegood oligopolies* 1
Hacienda Pública Epañola / Review of Public Economic, 3(/05): 40 05, Intituto de Etudio Ficale DOI: 0.7866/HPERPE.5.. Puchae and ental ubidie in duablegood oligopolie* AMAGOIA SAGASTA JOSÉ M. USATEGUI
More informationVector Calculus: Are you ready? Vectors in 2D and 3D Space: Review
Vecto Calculus: Ae you eady? Vectos in D and 3D Space: Review Pupose: Make cetain that you can define, and use in context, vecto tems, concepts and fomulas listed below: Section 7.7. find the vecto defined
More informationUsing Model Checking to Analyze Network Vulnerabilities
Uing Model Checking to Analyze Netwok Vulneabilitie Ronald W. Ritchey Paul Ammann * National Secuity Team Infomation and Softwae Engineeing Depatment Booz Allen & Hamilton Geoge Maon Univeity Fall Chuch,
More information1D STEADY STATE HEAT
D SEADY SAE HEA CONDUCION () Pabal alukda Aociate Pofeo Depatment of Mecanical Engineeing II Deli Email: pabal@mec.iitd.ac.in Palukda/MecIID emal Contact eitance empeatue ditibution and eat flow line
More informationDeflection of Electrons by Electric and Magnetic Fields
Physics 233 Expeiment 42 Deflection of Electons by Electic and Magnetic Fields Refeences Loain, P. and D.R. Coson, Electomagnetism, Pinciples and Applications, 2nd ed., W.H. Feeman, 199. Intoduction An
More informationScal abil it y of ANSYS 16 applicat ions and Hardware select ion.
Technical white pape Scal abil it y of ANSYS 16 applicat ion and Hadwae elect ion. On multicoe and floating point acceleato poceo ytem Table of Content Ab t a ct... 2 Tet configuation detail... 2 Meage
More informationA THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BARIŞ TUĞRUL ERTUĞRUL
SENSORESS VECTOR CONTRO OF INDUCTION MOTOR BASED ON FUX AND SPEED ESTIMATION A THESIS SUBMITTED TO THE GRADUATE SCHOO OF NATURA AND APPIED SCIENCES OF MIDDE EAST TECHNICA UNIVERSITY BY BARIŞ TUĞRU ERTUĞRU
More informationForces & Magnetic Dipoles. r r τ = μ B r
Foces & Magnetic Dipoles x θ F θ F. = AI τ = U = Fist electic moto invented by Faaday, 1821 Wie with cuent flow (in cup of Hg) otates aound a a magnet Faaday s moto Wie with cuent otates aound a Pemanent
More informationCoordination and Risk Sharing with Considering Supply Chain External Quality Fault
COMPUTER MODELLING & NEW TECHNOLOGIES 14 18(1C) 44545 Abtact Coodination and Rik Shaing with Conideing Supply Chain Extenal Quality Fault Li Yongfei 1,* 1 School of Economic and Management, Xian Univeity
More informationAdvanced Control of Active Filters. in a Battery Charger Application. Martin Bojrup
Advanced Contol of Active Filtes in a Battey Chage Application Matin Bojup Lund 999 ii Cove pictue Measuement on the dynamic esponse of the MRI hamonic filte contolle: load cuent (top), esulting line cuent
More information4a 4ab b 4 2 4 2 5 5 16 40 25. 5.6 10 6 (count number of places from first nonzero digit to
. Simplify: 0 4 ( 8) 0 64 ( 8) 0 ( 8) = (Ode of opeations fom left to ight: Paenthesis, Exponents, Multiplication, Division, Addition Subtaction). Simplify: (a 4) + (a ) (a+) = a 4 + a 0 a = a 7. Evaluate
More information2 r2 θ = r2 t. (3.59) The equal area law is the statement that the term in parentheses,
3.4. KEPLER S LAWS 145 3.4 Keple s laws You ae familia with the idea that one can solve some mechanics poblems using only consevation of enegy and (linea) momentum. Thus, some of what we see as objects
More informationAN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM
AN IMPLEMENTATION OF BINARY AND FLOATING POINT CHROMOSOME REPRESENTATION IN GENETIC ALGORITHM Main Golub Faculty of Electical Engineeing and Computing, Univesity of Zageb Depatment of Electonics, Micoelectonics,
More informationINITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS
INITIAL MARGIN CALCULATION ON DERIVATIVE MARKETS OPTION VALUATION FORMULAS Vesion:.0 Date: June 0 Disclaime This document is solely intended as infomation fo cleaing membes and othes who ae inteested in
More informationThe transport performance evaluation system building of logistics enterprises
Jounal of Industial Engineeing and Management JIEM, 213 6(4): 194114 Online ISSN: 213953 Pint ISSN: 2138423 http://dx.doi.og/1.3926/jiem.784 The tanspot pefomance evaluation system building of logistics
More informationEthernetbased and functionindependent vehicle controlplatform
Ethenetbaed and independent vehicle contolplatfom motivation, idea and technical concept fulfilling quantitative afetyequiement fom ISO26262 Andea Zikle, Michael Ambute, Ludge Fiege, Gunte Feitag,
More informationPAN STABILITY TESTING OF DC CIRCUITS USING VARIATIONAL METHODS XVIII  SPETO  1995. pod patronatem. Summary
PCE SEMINIUM Z PODSTW ELEKTOTECHNIKI I TEOII OBWODÓW 8  TH SEMIN ON FUNDMENTLS OF ELECTOTECHNICS ND CICUIT THEOY ZDENĚK BIOLEK SPŠE OŽNO P.., CZECH EPUBLIC DLIBO BIOLEK MILITY CDEMY, BNO, CZECH EPUBLIC
More informationInternational Journal of Pure and Applied Sciences and Technology
Int. J. Pue App. Sci. Techno., 4(1) (211), pp. 4148 Intenationa Jouna of Pue and Appied Science and Technoogy ISSN 2229617 Avaiabe onine at www.ijopaaat.in Reeach Pape Effect of Roto Reitance Vaue of
More informationQuestions & Answers Chapter 10 Software Reliability Prediction, Allocation and Demonstration Testing
M13914 Questions & Answes Chapte 10 Softwae Reliability Pediction, Allocation and Demonstation Testing 1. Homewok: How to deive the fomula of failue ate estimate. λ = χ α,+ t When the failue times follow
More informationTHE PRINCIPLE OF THE ACTIVE JMC SCATTERER. Seppo Uosukainen
THE PRINCIPLE OF THE ACTIVE JC SCATTERER Seppo Uoukaie VTT Buildig ad Tapot Ai Hadlig Techology ad Acoutic P. O. Bo 1803, FIN 02044 VTT, Filad Seppo.Uoukaie@vtt.fi ABSTRACT The piciple of fomulatig the
More informationDIRECT TORQUE CONTROL FOR INDUCTION MOTOR DRIVES MAIN FEATURES OF DTC
DIRECT TORQUE CONTROL FOR INDUCTION MOTOR DRIVES MAIN FEATURES OF DTC Decoupled control of torque and flux Abence of mechanical tranducer Current regulator, PWM pule generation, PI control of flux and
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations By Victo Avela White Pape #48 Executive Summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance the availability
More informationApplication Note. 8bit Microcontrollers. AVR494: AC Induction Motor Control Using the constant V/f Principle and a Natural PWM Algorithm
AVR494: AC Induction Moto Contol Uing the contant V/f Pinciple and a Natual PWM Algoithm Featue Coteffective and flexible phae induction moto dive Inteupt diven Low memoy and computing equiement 8bit
More informationPhysics 235 Chapter 5. Chapter 5 Gravitation
Chapte 5 Gavitation In this Chapte we will eview the popeties of the gavitational foce. The gavitational foce has been discussed in geat detail in you intoductoy physics couses, and we will pimaily focus
More informationSTUDENT RESPONSE TO ANNUITY FORMULA DERIVATION
Page 1 STUDENT RESPONSE TO ANNUITY FORMULA DERIVATION C. Alan Blaylock, Hendeson State Univesity ABSTRACT This pape pesents an intuitive appoach to deiving annuity fomulas fo classoom use and attempts
More informationDecisionDriven Fixed Income Attribution
Reeach am (Yanqiu) Zhong +44 (0)20 3134 7577 yanqiu.zhong@baclay.com Diecto, Index, otfolio & Rik Solution DeciionDiven Fixed Income Attibution  Match Attibution ith Invetment DeciionMaking oce Octobe
More informationUNIT CIRCLE TRIGONOMETRY
UNIT CIRCLE TRIGONOMETRY The Unit Cicle is the cicle centeed at the oigin with adius unit (hence, the unit cicle. The equation of this cicle is + =. A diagam of the unit cicle is shown below: + =   
More informationStrength Analysis and Optimization Design about the key parts of the Robot
Intenational Jounal of Reseach in Engineeing and Science (IJRES) ISSN (Online): 23209364, ISSN (Pint): 23209356 www.ijes.og Volume 3 Issue 3 ǁ Mach 2015 ǁ PP.2529 Stength Analysis and Optimization Design
More informationMechanics 1: Work, Power and Kinetic Energy
Mechanics 1: Wok, Powe and Kinetic Eneg We fist intoduce the ideas of wok and powe. The notion of wok can be viewed as the bidge between Newton s second law, and eneg (which we have et to define and discuss).
More informationNUCLEAR MAGNETIC RESONANCE
19 Jul 04 NMR.1 NUCLEAR MAGNETIC RESONANCE In this expeiment the phenomenon of nuclea magnetic esonance will be used as the basis fo a method to accuately measue magnetic field stength, and to study magnetic
More informationTwo Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL
Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy
More informationVoltage ( = Electric Potential )
V1 of 9 Voltage ( = lectic Potential ) An electic chage altes the space aound it. Thoughout the space aound evey chage is a vecto thing called the electic field. Also filling the space aound evey chage
More informationComparing Availability of Various Rack Power Redundancy Configurations
Compaing Availability of Vaious Rack Powe Redundancy Configuations White Pape 48 Revision by Victo Avela > Executive summay Tansfe switches and dualpath powe distibution to IT equipment ae used to enhance
More informationON THE (Q, R) POLICY IN PRODUCTIONINVENTORY SYSTEMS
ON THE R POLICY IN PRODUCTIONINVENTORY SYSTEMS Saifallah Benjaafa and JoonSeok Kim Depatment of Mechanical Engineeing Univesity of Minnesota Minneapolis MN 55455 Abstact We conside a poductioninventoy
More informationHour Exam No.1. p 1 v. p = e 0 + v^b. Note that the probe is moving in the direction of the unit vector ^b so the velocity vector is just ~v = v^b and
Hou Exam No. Please attempt all of the following poblems befoe the due date. All poblems count the same even though some ae moe complex than othes. Assume that c units ae used thoughout. Poblem A photon
More informationMagnetic Bearing with Radial Magnetized Permanent Magnets
Wold Applied Sciences Jounal 23 (4): 495499, 2013 ISSN 18184952 IDOSI Publications, 2013 DOI: 10.5829/idosi.wasj.2013.23.04.23080 Magnetic eaing with Radial Magnetized Pemanent Magnets Vyacheslav Evgenevich
More informationCoordinate Systems L. M. Kalnins, March 2009
Coodinate Sstems L. M. Kalnins, Mach 2009 Pupose of a Coodinate Sstem The pupose of a coodinate sstem is to uniquel detemine the position of an object o data point in space. B space we ma liteall mean
More informationCarterPenrose diagrams and black holes
CatePenose diagams and black holes Ewa Felinska The basic intoduction to the method of building Penose diagams has been pesented, stating with obtaining a Penose diagam fom Minkowski space. An example
More informationPredictive Control of Permanent Magnet Synchronous Motor Based on Optimization Model Algorithmic Control
Pedictive Contol of Pemanent Magnet Synchonous Moto Based on Optimization Model Algoithmic Contol 1 Chen Junshuo, 2 Liu Jinglin, 3 Zhang Ying *1, Chen Junshuo School of Automation, Nothwesten Ploytechnical
More informationELECTRİC DRİVE SYSTEMS AND MATLAB APPLICATIONS
EECTRİC DRİVE SYSTEMS AND MATAB Assist. Pof. D. H. İbahim OKUMUŞ Engineeing Faculty Electical & Electonics Engineeing Depatment (D. Nik Rumzi Nik Idis in des notlaından alınmıştı) 1 Contents 1. Intoduction
More informationChapter 4: Fluid Kinematics
Oveview Fluid kinematics deals with the motion of fluids without consideing the foces and moments which ceate the motion. Items discussed in this Chapte. Mateial deivative and its elationship to Lagangian
More informationTracking/Fusion and Deghosting with Doppler Frequency from Two Passive Acoustic Sensors
Tacking/Fusion and Deghosting with Dopple Fequency fom Two Passive Acoustic Sensos Rong Yang, Gee Wah Ng DSO National Laboatoies 2 Science Pak Dive Singapoe 11823 Emails: yong@dso.og.sg, ngeewah@dso.og.sg
More informationMagnetic Field and Magnetic Forces. Young and Freedman Chapter 27
Magnetic Field and Magnetic Foces Young and Feedman Chapte 27 Intoduction Reiew  electic fields 1) A chage (o collection of chages) poduces an electic field in the space aound it. 2) The electic field
More informationChapter 3 Savings, Present Value and Ricardian Equivalence
Chapte 3 Savings, Pesent Value and Ricadian Equivalence Chapte Oveview In the pevious chapte we studied the decision of households to supply hous to the labo maket. This decision was a static decision,
More informationExperiment 6: Centripetal Force
Name Section Date Intoduction Expeiment 6: Centipetal oce This expeiment is concened with the foce necessay to keep an object moving in a constant cicula path. Accoding to Newton s fist law of motion thee
More informationInterface Design for Rationally Clocked GALS Systems
Intefae Deign fo Rationally Cloked GALS Sytem Joyee Mekie, Supatik Chakaboty, Giih Venkataamani,.S. Thiagaajan, D.K. Shama Mah 15, 2006 Motivation SoC : integation of pedeigned I oe Rationally loked ytem
More informationYARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH
nd INTERNATIONAL TEXTILE, CLOTHING & ESIGN CONFERENCE Magic Wold of Textiles Octobe 03 d to 06 th 004, UBROVNIK, CROATIA YARN PROPERTIES MEASUREMENT: AN OPTICAL APPROACH Jana VOBOROVA; Ashish GARG; Bohuslav
More informationSimulation of Sensorless Speed Control of Induction Motor Using APFO Technique
International Journal of Computer and Electrical Engineering, Vol. 4, No. 4, Augut 2012 Simulation of Senorle Speed Control of Induction Motor Uing APFO Technique T. Raghu, J. Sriniva Rao, and S. Chandra
More informationA framework for the selection of enterprise resource planning (ERP) system based on fuzzy decision making methods
A famewok fo the selection of entepise esouce planning (ERP) system based on fuzzy decision making methods Omid Golshan Tafti M.s student in Industial Management, Univesity of Yazd Omidgolshan87@yahoo.com
More informationAP Physics Electromagnetic Wrap Up
AP Physics Electomagnetic Wap Up Hee ae the gloious equations fo this wondeful section. F qsin This is the equation fo the magnetic foce acting on a moing chaged paticle in a magnetic field. The angle
More informationUNIVERSIDAD DE CANTABRIA TESIS DOCTORAL
UNIVERSIDAD DE CANABRIA Depatamento de Ingenieía de Comunicaciones ESIS DOCORAL Cyogenic echnology in the Micowave Engineeing: Application to MIC and MMIC Vey Low Noise Amplifie Design Juan Luis Cano de
More informationSpirotechnics! September 7, 2011. Amanda Zeringue, Michael Spannuth and Amanda Zeringue Dierential Geometry Project
Spiotechnics! Septembe 7, 2011 Amanda Zeingue, Michael Spannuth and Amanda Zeingue Dieential Geomety Poject 1 The Beginning The geneal consensus of ou goup began with one thought: Spiogaphs ae awesome.
More informationest using the formula I = Prt, where I is the interest earned, P is the principal, r is the interest rate, and t is the time in years.
9.2 Inteest Objectives 1. Undestand the simple inteest fomula. 2. Use the compound inteest fomula to find futue value. 3. Solve the compound inteest fomula fo diffeent unknowns, such as the pesent value,
More informationGravitational Mechanics of the MarsPhobos System: Comparing Methods of Orbital Dynamics Modeling for Exploratory Mission Planning
Gavitational Mechanics of the MasPhobos System: Compaing Methods of Obital Dynamics Modeling fo Exploatoy Mission Planning Alfedo C. Itualde The Pennsylvania State Univesity, Univesity Pak, PA, 6802 This
More informationDetermining solar characteristics using planetary data
Detemining sola chaacteistics using planetay data Intoduction The Sun is a G type main sequence sta at the cente of the Sola System aound which the planets, including ou Eath, obit. In this inestigation
More informationAn Introduction to Omega
An Intoduction to Omega Con Keating and William F. Shadwick These distibutions have the same mean and vaiance. Ae you indiffeent to thei iskewad chaacteistics? The Finance Development Cente 2002 1 Fom
More informationAn Analysis of Manufacturer Benefits under Vendor Managed Systems
An Analysis of Manufactue Benefits unde Vendo Managed Systems Seçil Savaşaneil Depatment of Industial Engineeing, Middle East Technical Univesity, 06531, Ankaa, TURKEY secil@ie.metu.edu.t Nesim Ekip 1
More informationWorked Examples. v max =?
Exaple iction + Unifo Cicula Motion Cicula Hill A ca i diing oe a eicicula hill of adiu. What i the fatet the ca can die oe the top of the hill without it tie lifting off of the gound? ax? (1) Copehend
More informationMULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION
MULTIPLE SOLUTIONS OF THE PRESCRIBED MEAN CURVATURE EQUATION K.C. CHANG AND TAN ZHANG In memoy of Pofesso S.S. Chen Abstact. We combine heat flow method with Mose theoy, supe and subsolution method with
More informationLab M4: The Torsional Pendulum and Moment of Inertia
M4.1 Lab M4: The Tosional Pendulum and Moment of netia ntoduction A tosional pendulum, o tosional oscillato, consists of a disklike mass suspended fom a thin od o wie. When the mass is twisted about the
More informationSoftware Engineering and Development
I T H E A 67 Softwae Engineeing and Development SOFTWARE DEVELOPMENT PROCESS DYNAMICS MODELING AS STATE MACHINE Leonid Lyubchyk, Vasyl Soloshchuk Abstact: Softwae development pocess modeling is gaining
More informationRevision Guide for Chapter 11
Revision Guide fo Chapte 11 Contents Student s Checklist Revision Notes Momentum... 4 Newton's laws of motion... 4 Gavitational field... 5 Gavitational potential... 6 Motion in a cicle... 7 Summay Diagams
More informationInstituto Superior Técnico Av. Rovisco Pais, 1 1049001 Lisboa Email: virginia.infante@ist.utl.pt
FATIGUE LIFE TIME PREDICTIO OF POAF EPSILO TB30 AIRCRAFT  PART I: IMPLEMETATIO OF DIFERET CYCLE COUTIG METHODS TO PREDICT THE ACCUMULATED DAMAGE B. A. S. Seano 1, V. I. M.. Infante 2, B. S. D. Maado
More informationEpisode 401: Newton s law of universal gravitation
Episode 401: Newton s law of univesal gavitation This episode intoduces Newton s law of univesal gavitation fo point masses, and fo spheical masses, and gets students pactising calculations of the foce
More informationNETWORK TRAFFIC PRIORITIZATION USING MAP OF ARRIVALS
Seion 1. Statitic Method and Thei Alication Poceeding of the 11 th Intenational Confeence eliability and Statitic in Tanotation and Communication (elstat 11), 19 22 Octobe 2011, iga, Latvia,. 8287. ISBN
More informationDatabase Management Systems
Contents Database Management Systems (COP 5725) D. Makus Schneide Depatment of Compute & Infomation Science & Engineeing (CISE) Database Systems Reseach & Development Cente Couse Syllabus 1 Sping 2012
More informationThe LCOE is defined as the energy price ($ per unit of energy output) for which the Net Present Value of the investment is zero.
Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the
More informationDoppler Effect. wavelength
Dopple Eet The Dopple Eet i the hange in the obeed equeny o a oue due to the elatie motion between the oue and the eeie. The elatie motion that aet the obeed equeny i only the motion in the LineOSight
More informationTrigonometry in the Cartesian Plane
Tigonomet in the Catesian Plane CHAT Algeba sec. 0. to 0.5 *Tigonomet comes fom the Geek wod meaning measuement of tiangles. It pimail dealt with angles and tiangles as it petained to navigation astonom
More informationProblems on Force Exerted by a Magnetic Fields from Ch 26 T&M
Poblems on oce Exeted by a Magnetic ields fom Ch 6 TM Poblem 6.7 A cuentcaying wie is bent into a semicicula loop of adius that lies in the xy plane. Thee is a unifom magnetic field B Bk pependicula to
More informationSTABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL DATA 1. INTRODUCTION
Jounal of Machine Engineeing, Vol. 11, No. 4, 211 Batosz POWALKA 1 Macin CHODZKO 1 Kzysztof JEMIELNIAK 2 milling, chatte, opeational modal analysis STABILITY ANALYSIS IN MILLING BASED ON OPERATIONAL MODAL
More informationMechanics 1: Motion in a Central Force Field
Mechanics : Motion in a Cental Foce Field We now stud the popeties of a paticle of (constant) ass oving in a paticula tpe of foce field, a cental foce field. Cental foces ae ve ipotant in phsics and engineeing.
More informationAvoided emissions kgco 2eq /m 2 Reflecting surfaces 130
ANALYSIS OF GLOBAL WARMING MITIGATION BY WHITE REFLECTING SURFACES Fedeico Rossi, Andea Nicolini Univesity of Peugia, CIRIAF Via G.Duanti 67 0615 Peugia, Italy T: +9075585846; F: +90755848470; E: fossi@unipg.it
More informationMATHEMATICAL SIMULATION OF MASS SPECTRUM
MATHEMATICA SIMUATION OF MASS SPECTUM.Beánek, J.Knížek, Z. Pulpán 3, M. Hubálek 4, V. Novák Univesity of South Bohemia, Ceske Budejovice, Chales Univesity, Hadec Kalove, 3 Univesity of Hadec Kalove, Hadec
More informationSemipartial (Part) and Partial Correlation
Semipatial (Pat) and Patial Coelation his discussion boows heavily fom Applied Multiple egession/coelation Analysis fo the Behavioal Sciences, by Jacob and Paticia Cohen (975 edition; thee is also an updated
More informationGross Trade Accounting, Cross Country Production Sharing and Global ValueChain
Go Tade ccounting, Co Count Poduction Shaing and Gloal ValueChain Zhi Wang United State Intenational Tade Commiion aed on Tacing alueadded and doule counting in go expot Koopmam, Wang and Wei, meican
More informationGravitation and Kepler s Laws Newton s Law of Universal Gravitation in vectorial. Gm 1 m 2. r 2
F Gm Gavitation and Keple s Laws Newton s Law of Univesal Gavitation in vectoial fom: F 12 21 Gm 1 m 2 12 2 ˆ 12 whee the hat (ˆ) denotes a unit vecto as usual. Gavity obeys the supeposition pinciple,
More informationSolution Derivations for Capa #8
Solution Deivations fo Capa #8 1) A ass spectoete applies a voltage of 2.00 kv to acceleate a singly chaged ion (+e). A 0.400 T field then bends the ion into a cicula path of adius 0.305. What is the ass
More informationFXA 2008. Candidates should be able to : Describe how a mass creates a gravitational field in the space around it.
Candidates should be able to : Descibe how a mass ceates a gavitational field in the space aound it. Define gavitational field stength as foce pe unit mass. Define and use the peiod of an object descibing
More informationComplex Envelope Vectorization for the solution of midhigh frequency acoustic problems. A. Sestieri
Complex Envelope Vectoization fo the solution of midhigh fequency acoustic poblems A. Sestiei Depatment of Mechanical and Aeospace Engineeing Univesity of Rome la Sapienza Pesentation layout  Low fequency
More informationDYNAMICS AND STRUCTURAL LOADING IN WIND TURBINES
DYNAMIS AND STRUTURAL LOADING IN WIND TURBINES M. Ragheb 12/30/2008 INTRODUTION The loading egimes to which wind tubines ae subject to ae extemely complex equiing special attention in thei design, opeation
More informationThe impact of migration on the provision. of UK public services (SRG.10.039.4) Final Report. December 2011
The impact of migation on the povision of UK public sevices (SRG.10.039.4) Final Repot Decembe 2011 The obustness The obustness of the analysis of the is analysis the esponsibility is the esponsibility
More informationIlona V. Tregub, ScD., Professor
Investment Potfolio Fomation fo the Pension Fund of Russia Ilona V. egub, ScD., Pofesso Mathematical Modeling of Economic Pocesses Depatment he Financial Univesity unde the Govenment of the Russian Fedeation
More informationChannel selection in ecommerce age: A strategic analysis of coop advertising models
Jounal of Industial Engineeing and Management JIEM, 013 6(1):89103 Online ISSN: 0130953 Pint ISSN: 013843 http://dx.doi.og/10.396/jiem.664 Channel selection in ecommece age: A stategic analysis of
More informationVISCOSITY OF BIODIESEL FUELS
VISCOSITY OF BIODIESEL FUELS One of the key assumptions fo ideal gases is that the motion of a given paticle is independent of any othe paticles in the system. With this assumption in place, one can use
More informationGauss Law. Physics 231 Lecture 21
Gauss Law Physics 31 Lectue 1 lectic Field Lines The numbe of field lines, also known as lines of foce, ae elated to stength of the electic field Moe appopiately it is the numbe of field lines cossing
More information