Energy Converters CAD and System Dynamics
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- Jemima Moody
- 6 years ago
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1 Engy Convt CAD n Syt Dync. Bc gn l fo lctcl cn. Dgn of Incton Mcn 3. Ht tnf n coolng of lctcl cn 4. Dync of lctcl cn 5. Dync of DC cn 6. Spc vcto toy 7. Dync of ncton cn 8. Dync of yncono cn Soc: SPEED pog Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
2 Engy Convt - CAD n Syt Dync 7. Dync of ncton cn Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
3 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
4 7. Dync of ncton cn P nt clclton p.. Epl: O lw: - U V, R Ω : How bg cnt I? - Rt voltg n cnt: U 5 V, I 5 A Clclt wt pycl nb: - Cck of pycl nt: V/Ω V/V/A A Clclt wt p nt nb: U / U /5, Z U / I 5/5 Ω. R / Z / / / p. I I I I I U / R V / Ω 5 A. ot:. ql to / 5 A 5 A Dwbck: p.. v t pycl nt, o cckng of lt of nlytcl clclton by pycl nt cck no long pobl. Bnft: T clclton lt gv ctly n pon of t g of long of t lctc vc. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
5 7. Dync of ncton cn Bc l fo p nt clclton - Vl fo p nt clclton tkn fo cn t plt -In t p yt t t pnc Z to b clclt wt p vl to of t pvoltg v tp cnt. - Dt plt voltg & cnt vl ALWAYS ln vl! -Elctc cn ol b on p vl n o to b npnnt fo t kn of wnng conncton Y o D.Fo p nt voltg, cnt n pnc clclton: t p vl tkn. - Sybol fo p nt vl ll lttt, t,... - Fo t vyng voltg, cnt tc. n pycl nt cptl ltt Ut, It,... Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
6 7. Dync of ncton cn Typcl t plt of lctc cn Epl: S-pol cg AC ncton cn: Typ MKG- M6 F3B-9... Moto Copny/3 AC-Moto V Y 84 A 45 kw 49/3 /n S 75 Hz coϕ.88 T.Cl. F IP 44 W clclt fo t t plt t t & p vl n t t pnc: U, p U / 3 4/ 3 3 V 3 V, I, p I Z U, p / I, p 3 / 84.74Ω Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6
7 7. Dync of ncton cn - P nt t: t Sy of p nt vl - P nt lctc ngl fqncy: Ω / Ω / - P nt cncl ngl fqncy: Ω p / - P nt lctc tnc: R / Z R / Z Z U, p / I, p.g. : f 5Hz, t : t π g.: f 5Hz, f 5Hz : Ω πf π 5/ 94.5/ π / Ω / 94.5/ g.: f Ω Ω 5Hz, πn π /6 4.7/ yn π f Ω p / 34.6/, n / n, p 8: / p π 5/ / 4.74/ Ω / Ω yn 4.7/ Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7
8 7. Dync of ncton cn Sy of p nt vl - P nt nctnc: L / Z L / Z L / Z - P nt lctc voltg: U / U, p U / U, p - P nt lctc cnt: I / I, p I / I, p - P nt gntc fl lnkg: Ψ / Ψ.g. : L X H, Z L.g. : Ψ 3V, U, Ω, f 5Hz : Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8 Ψ L / Z π Ω X / Z U p 3V, f 5Hz : Ψ Ψ / Ψ U, p 3/ π 5./.57, p 3.4/.57 3 π 5.4V Rlt: Hg fl lnkg g on tton t b pct!
9 7. Dync of ncton cn P nt lctc p voltg n cnt - In ync clclton ntntno vl Ut, It v lt. -Tfo n AC cny t p nt clclton on wtt onty pk vl plt of t ttony nol t optonl vl. U t/ U p I t/ I,, p - Epl: Snol t opton: I U t I, p nπf t U I U t/ I, p n On RATED p-nt po ALWAYS π, npnnt fo Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9 t fqncy f f.g. : t : t π π f f
10 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn P nt toq: - Rfnc: Rt ppnt toq M B t APPARET pow S v. yncono p! - T M B ncl pow fcto coϕ n cn ffcncy η! p S M M M B B / / ot: Incton oto opton: Rt ppnt toq M B bgg tn t toq M : B M P P p S M η ϕ η ϕ Ω Ω η ϕ co co /co / B M M ϕ η co b P nt ont of nt: - Roto nt J clclt fo T J p nt ttng t contnt J. B J J J M p J T T / Sy of p nt vl 3
11 Epl: Z M M M B U p S 7. Dync of ncton cn P nt clclton fo t plt vl, p / I, 3/ Ω Ω yn, V Y 34.5 A 8.5 kw 465 /n S 5 Hz coϕ.84 J.54 kg T.Cl. F IP π 5/.33 M 3 U, p P Ω, p I π 465/ 6.6 ˆ 3 coϕ Ψ.36 V 34 η TJ J TJ B S η S P coϕ kva Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
12 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Dync p.. qton t t t I R t U Ψ Ψ t U t I I U t I R U t U t p p p p p,,,,, - Voltg qton p p n pycl nt: b n p nt yt: t M t M t t J Ω / Ω J B B M t M t M t p t M p J - Mcncl qton n pycl nt: b n p nt yt:
13 Engy Convt CAD n Syt Dync Sy: P nt clclton - -plt t fo p-nt clclton - Ully p qntt fo p.. -ot t t l toq M, bt t t ppnt toq M B fo p.. -Ft tt of pcntg of long of vc pobl by p.. vl Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
14 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
15 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5 7. Dync of ncton cn T p ync voltg qton W W W V V V U U U ,,,,,,,,, 3,,, W V U 3,,,, W V U Fo 3 p voltg OE pc vcto qton OE zo qnc qton Voltg pc vcto: Zo qnc voltg:
16 7. Dync of ncton cn Rfnc f Co-ont yt - tto fnc f S: - R -, β- I - - oto fnc f R: - R - -, β- I - q- - bty fnc f K: - R K -, β- I K - q- B- β-, - V t V t Spc vcto V t t, A-, - Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6
17 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7 7. Dync of ncton cn n tto fnc f n oto fnc f n fnc f K V V γ V V δ K V V γ V V δ K V V Spc vcto tnfoton: - fo tto fnc f to fnc f K: ltplcton by δ - fo oto fnc f to f K : by ltplcton wt γ δ. Spc vcto V n ffnt fnc f / γ γ γ Ω γ Ω γ t p t t t p t t t γ t Roto fnc f ft by otton ngl, n "lctc g : γ δ δ γ γ δ K V V V V
18 7. Dync of ncton cn T p oto ync voltg qton Spc vcto oto voltg qton: n oto fnc f Sbcpt n: n oto fnc f ot: Cg ncton cn: Q p: My b tt 3-p cn, tnfo nto pc vcto folton! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8
19 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9 7. Dync of ncton cn K K K K δ δ δ δ K K K K γ δ γ δ γ δ γ δ Tnfoton of voltg qton btwn fnc f δ δ δ δ δ δ - Rl fo ffntton of poct of two fncton: - Tnfoton of voltg qton nto bty co-ont yt K: K K K K K K K K γ δ δ
20 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Tnfo n oty ncton K K K K K K K K γ δ δ Tnfo ncton Roty ncton
21 7. Dync of ncton cn Mnly fnc f Rfnc f tto fnc f, β oto fnc f, q yncono fnc f, b Angl otton of fnc f δ δ : K γ δ γ : K Ωyn Ω K / p Stto n oto qton n tto fnc f -β-yt: Incton cn: Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
22 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Mnly fnc f : δ δ K K γ γ δ : Stto fnc f, β Roto fnc f, q Syncono fnc f A, B yn yn yn yn yn yn yn yn yn K p Ω Ω /
23 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3 7. Dync of ncton cn β β β β β β / / / / - In tto fnc f: -β-yt: coponnt: Epl: Voltg qton n tto fnc f β β β β Tnfo pt Roty pt of voltg ncton β, R β, I β
24 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4 Engy Convt CAD n Syt Dync ß ot t t U U t U p Ψ Ω Ψ / :,,,,, l B v t B l t U ß c c /, ß ß c ß c ß c ß c B l l B l B v Ψ Ω Φ Ω Ω Ω Φ B l β Φ β B l β β Φ Ψ c Φ Ψ c Epl:Rottng oto col c tn n tto B-fl Tnfo n oty pt of ncton Tnfo Roty ß R / Fl lnkg R t I t U t U R t I t U t U Ψ t Ψ β t v Ω. v Ω. Ω l c B t B β t l c B v t t U / Ψ
25 Engy Convt CAD n Syt Dync Sy: Dync voltg qton n fnc f of ncton cn - Spc vcto folton llow on voltg qton nt of t U, V, W - On tto n on oto voltg qton - Dffnt fnc f y b : tto, oto, bty - Voltg ncton pt nto tnfo n oty pt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
26 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6
27 7. Dync of ncton cn Mgntzng pc cnt vcto Mn fl lnkg Mn fl lnkg fnntl wv, ct by nol tbt cnt ly of tto n oto gntzng cnt ly: Snol tbt cnt ly Rltng n gntc fl ln Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7
28 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8 7. Dync of ncton cn - Stto n oto pc cnt vcto ct ALSO lkg fl lnkg: Dync tto n oto fl lnkg Z L Z L, - P nt ty nctnc: - Rltng fl lnkg n tto n oto: - Totl lkg fl pc vcto cb by Blonl totl lkg coffcnt:
29 7. Dync of ncton cn Clclton of p nt tto n oto fl lnkg Epl : Incton cn opt t t-p ytcl n voltg yt wt t fqncy. - Stto tnc nglct, clclton n tto fnc f: - Inctnc t:.5,.6,. 58: o-lo cnt: voltg pc vcto: fl lnkg.38.6 I R Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
30 7. Dync of ncton cn Roto fl lnkg t vy g oto lp ZERO - Incton cn: Roto wnng ot-cct: - At vy g oto lpt oto fl lnkg cng vy ft: << - Roto voltg qton n oto f. f, vy g oto lp: / / / cont. Rlt: - Roto fl lnkg t vy g lp zo! o DC oto fl: cont. - Stto & oto n fl n oto ty fl cncl, o totl oto fl zo!... Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
31 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3 / 7. Dync of ncton cn / / Stto fl lnkg t g oto lp totl lkg / Stto fl lnkg: o: / Wt : Stto fl lnkg t g lpnly ql to t totl lkg fl! Roto fl lnkg zo! Vy glp >> :
32 . Dgn of Incton Mcn At g lp ly! t oto nn pt nly f of fl oto lng ffct At no-lo, oto cnt zo At tn tll lock oto clly clclt two-nonl gntc fl nty B of t-p, 4-pol g voltg cg ncton cn wt wg oto lot Q / Q 6/44 t t voltg Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
33 7. Dync of ncton cn Clclton of p nt tto n oto fl lnkg Epl: Incton cn opt t t-p ytcl n voltg yt wt t fqncy t g lp: - Clclton n tto fnc f: - Inctnc t:.5,.6,. 58: - Cnt t t bg lp: >> : / /.5/ Lkg nctnc:.6.5., Totl lkg coffcnt: Stto fl lnkg t : wt totl lkg fl lnkg Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/33
34 7. Dync of ncton cn Epl: Roto fl lnkg t vy g oto lp ZERO Vy glp >> :.5,., /.8:. 969 Alo t oto lkg fl lnkg to t oto lng ffct lnk wt t tto wnng! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/34
35 Engy Convt CAD n Syt Dync Sy: Dync fl lnkg qton - Stto n oto cnt pc vcto ct ltng gp fl lnkg vcto - Spton of n n ty fl pobl - Pycl pton of tto n oto ty fl by nt not pobl - Roto totl fl lnkg c wt ncng lp to oto ot-cct - Stton y b ntoc by cnt-pnng nctnc Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/35
36 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/36
37 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/37 7. Dync of ncton cn δ ϕ δ π co ˆ B A l p M p δ π Ψ B l k p w ˆ p w p I A A k A ˆ Ψ coϕ δ ˆ ˆ 3 I p M co co ˆ ˆ 3 3 /,, ϕ ϕ Ψ δ δ p p B t t t I p I U p M t M co ϕ δ B M t M Toq qton - Intocton of fl lnkg n cnt: Aplt of fl lnkg Aplt of cnt long: - P nt toq qton: Toq poct of n fl lnkg vcto n otogonl coponnt of cnt pc vcto! 3
38 7. Dync of ncton cn P nt toq qton Epl: Stto cnt long n ltng tto & oto fl Potv toq on tto F I Bδ l M coϕ MB δ δ Potv toq on oto ACTIO EST REACTIO coϕ δ Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/38
39 7. Dync of ncton cn Roto toq cton - Potv contng of oto toq n cont-clockw n! Mttcl potv contng n! - Fl lnkg pc vcto tn nto cton of cnt pc vcto Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/39
40 7. Dync of ncton cn Otogonl vcto coponnt fn toq - Intocton of vcto poct: β β I { *} If ttocnt pc vcto coponnt 9 lngto fl lnkgpc vcto toq on oto potv. Potv cton of toq on ROTOR I I { *} I { *} I { } { β β β β} β β ß ß ß ß Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
41 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4 7. Dync of ncton cn { } * I β β { } { } * * I I - Stto ty fl o not gnt toq! Dffnt folton fo t toq { } { } { } { } { } * * * * * * * * I I I I I Poof: { } { } * * I I - Stto fl o not gnt toq wt tto cnt! { } { } { } * * * * I I I - ot: { } { } * I I * z b z b z b z
42 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4 7. Dync of ncton cn { } * I β β Dffnt folton fo t toq { } { } * * I I { } { } { } * * * * * * I I I - Ot folton fo toq wt oto fl lnkg! β β { } * I β β
43 Engy Convt CAD n Syt Dync Sy: Toq qton - Otogonl coponnt of fl n cnt pc vcto yl toq - Dffnt folton of toq wt tto o oto qntt - Sty fl o not gnt toq Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/43
44 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/44
45 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/45 7. Dync of ncton cn J / / / / β β β β β β β β β β β β β β - St of ync qton - Coponnt - In tto fnc f - -β-yt Dync qton n tto fnc f VOLTAGE: 4 qton FLUX LIKAGE: 4 qton TORQUE: qton 9 qton In TOTAL!
46 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/46 7. Dync of ncton cn A ffnt fl lnkg folton In t wy:
47 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/47 7. Dync of ncton cn β β β β β β β β β β Pvo ffnt folton fo fl lnkg, fl fo MATLAB/Slnk ol, n coponnt n t tto fnc f: Fl lnkg folton fo MATLAB/Slnk ol
48 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/48 7. Dync of ncton cn Dync qton n tto fnc f fo MATLAB/Slnk ol WITHOUT cncl qton β β β β β β β β β β β β β β / / / /
49 7. Dync of ncton cn P nt folton of qton n tto fnc f Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/49
50 7. Dync of ncton cn Eqton n tto fnc f n pycl nt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
51 Engy Convt CAD n Syt Dync Sy: Dync qton of ncton cn n tto fnc f -In t -β-f: 4 voltg qton, fo fl lnkg qton, on cncl qton - Mcncl qton y b plc by o tl cpton:.g. toon ocllton onnc fqnc - T-tp olton v RUGE-KUTTA Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
52 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
53 7. Dync of ncton cn Opton of ncton cn t contnt p -At contnt p OLYvoltg n fl lnkg qton n to b olv, O toqqton! - Eqton ln, o Lplc tnfoton to gt tnf fncton cnt fo voltg. Epl: Swtcng voltg to n ly nnng oto:.g. Y-D-tt-p: Moto nnng ft Y-tt p wt no-lo p cont.: tn tto wnng wtc n D to t-p g voltg yt. G voltg: Spc vcto: U co, V co π / 3, W co 4π / 3 U V W 3 Lplctnfo: Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/53
54 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/54 7. Dync of ncton cn Lplc-tnfo of voltg & fl lnkg qton n tto fnc f Intl conton: Epl: Fl, cnt, voltg zo!, Unknown: Stto n oto cnt pc vcto,
55 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/55 7. Dync of ncton cn Solton of n o ln lgbc qton yt b b Solton fo tto cnt vcto:
56 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/56 7. Dync of ncton cn Scon o ccttc polynol P P,, W fn: - Stto n oto ot-cct t contnt: - Stto n oto opn-cct t contnt: T polynol cb t tnnt lctcl bvo of t ncton cn! b P
57 7. Dync of ncton cn Stto opn-cct & ot-cct t contnt - Stto opn-cct t contnt - Stto ot-cct t contnt - Roto cct ntpt - Roto cct no tnc Slp: zo o oto cnt OPE cct ± Slp: nfnt ±, cnt l to: Slp: Unty Cng of totl fl, nclng n fl / Slp /... 5 SHORT cct STAD STILL Cng of ty fl Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/57
58 7. Dync of ncton cn Typcl vl fo opn-cct & ot-cct t contnt., 3,.6 - Stto n oto ot-cct t contnt SHORT t contnt.3.6 5, , Stto n oto opn-cct t contnt LOG t contnt 3.6 5, ot: 5 n 5/π 8 po t t fqncy! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/58
59 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/59 7. Dync of ncton cn Copl ln tnf fncton of lctcl pfonc -Two pol oot, b n Lplc -pln, pnng on SPEED! A SPEED ZERO SLIP : : o ntl ocllton fqncy, b l nb! B SUFFICIET HIGH SPEED:.g.: yncono p: SLIP, Two ot t contnt n two ntl ocllton fqnc!, b : copl nb plf: Only copl nb! W c two pcl c: q p p q p p q p b, ±, 4 p q p b
60 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6 7. Dync of ncton cn Two l oot, b of t ccttc polynol t Zo p opton tn tll: b, : > : > Wot c: o n fl lnkg T two oot, b n ny ct l nb! Epl: Sttng t ncton cn t zo p n block oto wtcng t-p g voltg yt to tto wnng t
61 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6 7. Dync of ncton cn Two l oot, b of t ccttc polynol t ± ±, 4 b A ~. ll:, / << b / / b ot t contnt cng of ty fl long t contnt cng of n fl
62 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6 7. Dync of ncton cn Two copl oot, b of t ccttc polynol t At bgg p:, > If ~., ~. ll tn :, / << Two ot t contnt only ty fl cng ± ± b 4 4, ±, b b,.g.: yncono p,,, Two ntl fqnc
63 7. Dync of ncton cn Splf lctc t contnt fo, A At zo p n low p: o ntl ocllton fqncy l nb! Sot t contnt: / Long t contnt: B Hg p opton: Two ot t contnt: tl ocllton fqnc:,, 5 O / 5 O O, 5... Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/63
64 7. Dync of ncton cn IM lctc t contnt, pn on p l l / / / /.6673/ / l l Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/64
65 7. Dync of ncton cn Igny pt, of oot of lctc tnf fncton l l Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/65
66 7. Dync of ncton cn Dync pfonc of ncton cn t contnt p cont. - Incton cn ct wt cnt to n cng n voltg wt TWO t contnt,, bc w v TWO copl lctc cct tto n oto cct. - T t contnt, pn on p! - T p wnng U, V, W copl v t n fl n ct OE wnng yt OE t contnt p wnng yt! - At not too low p, nly ql, bng t ot tto n otoot-cct t contnt,. Dng otton t ncton cn n fl Φ n lo t n cng nlycontnt; only t ty fl Φ cng. - At low p & tn tll ot n long t of tto n oto opn-cct t contnt Cop: DC cn: - Only on ot lctc t contnt to on t cct: T L /R - T contnt T npnnt of p n! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/66
67 7. Dync of ncton cn T-contnt fo cng of n n ty fl - Long tto n oto opn-cct t contnt: Cng of n fl -Sot tto n oto ot-cct t contnt: Cng of tto n oto ty fl Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/67
68 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/68 7. Dync of ncton cn b C B A b C B A Lplctnfo cnt pc vcto : Epl: Swtcng tto wnng to g t cont. Inv tnfo cnt pc vcto : b Solton fo tto cnt vcto: G voltg: Spc vcto: 3 / 4 co 3, / co, co π π W V U W V U 3 Lplctnfo:
69 7. Dync of ncton cn Inv Lplc tnfoton Inv tnfo cnt pc vcto : Hoogno pt of olton: b Ptcl olton: Stto n oto cnt cng wt two t contnt, b R R vng two ntl ocllton fqnc, I,,, b I b, b,,,,, pn on tnc,, nctnc, AD on oto p, p, A, A B C b B C b B, C / /,, Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/69
70 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7 7. Dync of ncton cn Hoogno olton tnnt pt,, / /, C B,,,, p A, Ptcl olton ty-tt pt Rottng tto cnt pc vcto wt contnt plt ccong to p voltg pc vcto C B / /, Tnnt AC pt tnnt DC pt C by oto DC fl tto DC fl
71 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7 7. Dync of ncton cn Dtnton of contnt A, B, C by Hv l : : b A : : b B : : 3 3 b b b b C b t n k n k k n Z Z L b C B A Hv l: So w gt: Conton: O of nto polynol l tn of nonto polynol!
72 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7 7. Dync of ncton cn on-p olton: b ± ± 4, b b
73 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/73 7. Dync of ncton cn { } { } n n co R R R U T fncton of U p cnt: on-p tnnt olton npnnt of p Splfcton: Dpng nglct:, : Dtnton of oot b, :, /, B C A b Inv tnfoton: tnnt ttony olton R
74 β, I 7. Dync of ncton cn on-p tto cnt: Intl conton:, R U { } co R U U R π π π Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/74
75 7. Dync of ncton cn Two pcl ntl conton fo t voltg pc vcto β, I Intl conton bt c : ± Intl conton wot c :, R Intl conton bt c : Intl conton wot c : Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/75
76 7. Dync of ncton cn on-p tto cnt: Intl conton: β, I I, R R U { } n R U U R U co π π π π Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/76
77 7. Dync of ncton cn Dync tn-on cnt - pn on wtcng-on ntnt U non-p DC coponnt co π / n U Swtcng on t zo voltg Cnt: DC coponnt AD AC coponnt Swtcng on t voltg Cnt: no DC coponnt Pk cnt % Pk cnt % Pk occ t lf po ft wtcng on Pk occ t qt po ft wtcng on / / / / , pk wot c U U co, pk bt c Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/77
78 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/78 7. Dync of ncton cn Coplt ttony olton p Slp Slp Slp, p A, Sty tt olton ptcl olton of ffntl qton: b A - Sttony olton gv fo tto cnt pc vcto t wll-known ccl g - Loc of ll olton fo vyng p b Slp Slp Slp Slp
79 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/79 Roto n tto cnt: Solton of t two ln qton of T-qvlnt cct: Unknown I I, I X I X I R U I X I X I R X R X I I 7. Dync of ncton cn Sttony olton qvlnt cct R X X R X X R R X R U I p Slp Slp Slp, Cop: Slp
80 7. Dync of ncton cn Epl: Coplt tnnt olton wt png / /.6673/ , / /.6673/.4 5. :.97, b Root fo tnnt olton Solton fo "n" cnt of ncton cn, bng wtc to g, wn ly nnng t yncono p: t t p:, Slp.96, Slp , , b b Sty tt cnt no-lo cnt.33 ty tt cnt t cnt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8
81 7. Dync of ncton cn Stto cnt pc vcto olton wt png Slp - Solton fo "n" cnt pc vcto of ncton cn -Swtc to nol g, wn nnng t ynconop. -Wot-c fo p U, w wtcng occ t zo voltg, ylng cnt pk Soc: H. Klnt, Spng-Vlg Sty tt olton no-lo cnt.33 p.. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8
82 7. Dync of ncton cn Stto n cnt U t, Slp Incton cn wtc to nol g, wn nnng t yncono p.667, 3, 3,.3,.4 Bt-c fo p U: Swtcng occ t voltg Wot-c fo p U: Swtcng occ t zo voltg 4-t t pk cnt t π/ 6.3-t t pk cnt t π Sty tt olton no-lo cnt.33 p.. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8
83 7. Dync of ncton cn Stto cnt pc vcto olton wt png Rt lp.4 Soc: H. Klnt, Spng-Vlg - Solton fo "n" cnt pc vcto of ncton cn Sty tt olton t cnt,. p.. -Swtc to nol g wn nnng t t p. -Wot-c fo p U, w wtcng occ t zo voltg, ylng cnt pk Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/83
84 7. Dync of ncton cn Stto n cnt U t.96, Slp.4 Incton cn wtc to nol g, wn nnng t yncono p , 3, 3,.3,.4 Bt-c fo p U: Swtcng occ t voltg Wot-c fo p U: Swtcng occ t zo voltg 4-t t pk cnt t π/ 6.3-t t pk cnt t π Sty tt olton no-lo cnt. p.. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/84
85 7. Dync of ncton cn Tnnt pon of ncton cn t lvt p bov.3 Voltg wtcng c wtcng on oto n- cnt, b n ot-cct,... l to DC cnt coponnt, wc lgt, wn wtcng occ t zo voltg. DC cnt coponntlt by ty nctnc n tnc DC cnt coponnt vn wt two ot t contnt, tn by t tto n oto ty nctnc n tnc Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/85
86 7. Dync of ncton cn Sn ot-cct of 4-pol no-lo ncton oto - M ot cct cnt, wn ot cct occ t voltg zo cong - Stto cnt pc vcto t nly contnt p contn tnnt DC n AC coponnt: / / / o-lo cnt 5/n o-lo.33 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/86 cl olton fo p n toq 45/n Zo cnt - M ot cct p cnt plt: ˆ, U 6.87 t π, np - Sot cct toq: kw, 38 V, A, 7, { } * 4 pol oto, 5 Hz,.97 I n 3,
87 Engy Convt CAD n Syt Dync Sy: Solton of ync qton fo contnt p - Ln voltg & fl lnkg qton t contnt p - LAPLACE on olton wt tnf fncton - T-contnt n ntl fqnc pn on p - Hoogno olton tnnt pt DC coponnt n nctv cct - Ptcl olton fo ty-tt olton -Epl: Swtcng of voltg on tto wnng of nnng cn Sn ot cct t tto tnl Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/87
88 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/88
89 7. Dync of ncton cn Solton of ync qton fo vyng p - Solton of ll 9 qton ltnoly - Eqton non-ln, o ncl olton ncy Epl: VOLTAGE: 4 qton FLUX LIKAGE: 4 qton TORQUE: qton 9 qton n TOTAL! o-lo tt-p of ncton oto n b ftw long wt t toq nvtgt. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/89
90 7. Dync of ncton cn Incton cn bg Rt pow.8 kw.8 kw Rt voltg 38 V 38 V Rt cnt A.6 A Effcncy 93.4 % 85.5 % Pow fcto.85.8 Rt lp % 8 % Rt p 47/n 38/n Rt toq 7 8. Incton cn ll R 5 Ω.4 p Ω.3 p.. R Ω.9 p.. 6. Ω.73 p.. L 9.7 H.95 p H.49 p.. L 9.55 H.9 p.. 66 H.46 p.. L 9.7 H.78 p H.36 p J.8 kg J kg J 5.8 T J wt M 6 67 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
91 7. Dync of ncton cn Sclng: Bg v. ll ncton oto U / U P / P I / I M / M R / R / 4 L / L J / J 8 T J / TJ /7 Bg cn v ll tnc n nctnc, cop to ll cn of t voltg tng Bg cn v vy bg nt, cop to ll cn Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
92 7. Dync of ncton cn Sclng of oto t ll / bg cn Roto nt: oto pow: clng to: J 4 l ~ ~ l 3 l ~ 5 4 P ~ l, 5 / 4 / J P / P J Epl: 5 / 4 Bg v ll cn: J / J /. 36. Rl to: J J.8 / / T t tong oto n to t bot fcto bgg nt bot t long to tt p. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
93 7. Dync of ncton cn Clclt lctogntc toq of bg ncton cn o-lo ttng t 5 Hz g voltg; oto lo t.8 wt t toq Low fqnt toq plton M Hz toq plton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/93
94 7. Dync of ncton cn Clclt ottonl p of ncton cn o-lo ttng wt.5j, J, J Vyng nt Ln fqnt p ppl Sttng t t J long T J, bc Mt M Dcy t of p ppl nc wt cng p, bc t contnt T nc Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/94
95 7. Dync of ncton cn Clclt ync toq-p ccttc of ncton cn o-lo ttng t 5 Hz g voltg; oto lo t.8 wt t toq D ln: Sttc toq-p ccttc fo qvlnt cct g Dync bk-own toq M b,yn, low tn ttony bk-own toq M b,tt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/95
96 7. Dync of ncton cn Clclt lctogntc toq of ncton cn o-lo ttng t 5 Hz g voltg wt tn t nc nt T t-contnt 3T fo DC cnt coponnt to cy:.3 Ln-fqnt toq plton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/96
97 7. Dync of ncton cn Inflnc of cncl p n on t contnt fo cy of oclltng ttng toq T of cy of 5 Hz oclltng toq J J b J J.5.3 Cb: Bgnt J low cclton Dcyof tnnt DC cnt coponnt occ t tll low p n, o zo p fol fo t contnt T n ppl. Aft 3T nbotdc cnt & toq ocllton v vn! T L / R L / R T C: Sll nt J ft cclton Dcyof tnnt DC cnt coponnt occ t ly lvt p, o t contnt T n> < T n ot! Tn TOWARDS Sot cct t contnt! : T n> T. T n/. T n>.5. T n Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/97
98 7. Dync of ncton cn Ln-fqnt ttng toq ocllton -Tnnt olton: At p n : DC cnt pc vcto,dc o not ott - Sttony olton: AC cnt pc vcto ott wt ln fqncy n t fl nc t oto cg - Rottng AC oto cnt pc vcto - Splf: Unp:,DC cont.:, AC, DC I, AC { *} { * } I, AC, DC I, DC, AC I, DC, AC co n ˆ, co Fct: Contnt ttng toq,, bt toq, plt wt ln fqncy, AC { } { } * * I cont., I, AC, AC, AC, AC β, I, AC, AC { * } { * }, ϕ,dc,ac, R Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/98
99 7. Dync of ncton cn Pnon of ync ttng pfonc Oclltng ttng toq: Swtcng on of tto voltg: DC cnt coponnt DC occ n tto noto wnng. T 5 Hz AC tto cnt,ac ct wt t DC fl of oto DC cnt,dc, ylng ft pltng 5 Hz-toq coponnt T 5 Hz AC oto cnt,ac ct wt t DC fl of tto DC cnt,dc, ylng con pltng 5 Hz-toq coponnt conttt t oclltng ttng toq! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/99
100 7. Dync of ncton cn Pnon of ync ttng pfonc b Dync bk-own toq: Mn fl cngng wt bg lctc t contnt / / Tfo t bk-own lp b tll fll fl ng, cng t ync bk-own toq M b,yn < M b,tt Epl: Rcton by 5% wt pct to ttc bk-own toq c Egn-fqncy of ncton cn t yncono n t p "yncono cn ffct n yncono cn": Low fqncy ocllton fqncy t c lo tp. Eplnton: Roto n fl cng wt bg oto t contnt /, y b g "fozn" fo ot t It ct lk t contnt oto fl n yncono cn. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
101 7. Dync of ncton cn Clclt ottonl p of ncton cn o-lo ttng t g voltg wt.5j, J, J Vyng nt Ln fqncy tl oto fqncy f, ~ J Dcy t nc wt cng p c by ncng nt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
102 7. Dync of ncton cn - Sp ocllton Ω t ppo.g. t yncono p: Ω t Ω Ω t tl ocllton of ncton cn yn - Mgntc bkng foc of "fozn" oto fl on tto cnt: M ϑ -c ϑ ϑ. ϑ : ngl ffnc btwn oto fl n tto pc cnt vcto ϑ t p Ω - Mcncl qton: Ω J M ϑ c ϑ ϑ t Ω t Ω t ϑ J pc ϑ ϑ ϑ t ~ n, t, co, t t tl fqncy of ocllton: f,, π π pc J ϑ Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
103 7. Dync of ncton cn Clclt ottonl p of ncton cn o-lo ttng wt t nt wtot tonl oto tnc, b wt R v -t oto tnc b Vyng oto tnc Ln fqncy Dcy t c wt ncng tnc tl oto fqncy nflnc by oto tnc * << Rc oto t contnt llow ft cng of oto fl no fozn oto fl pnonon v Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
104 7. Dync of ncton cn Dync ttng of lp ng ncton cn Atonl oto tnc: Bk-own toq ft fo lp b.8 to.88: R b R * b R * b b.8.88 Moto now tt nly wt bk-own toq, nc cng tt-p t Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
105 7. Dync of ncton cn Clclt lctogntc toq of ll ncton cn o-lo ttng t 5 Hz g voltg; oto lo t.35 wtt toq Vy qck tt-p, o no cl tncton btwn ln fqncy ocllton n ntl ocllton o-lo tt-p.35 : Long wt M Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
106 7. Dync of ncton cn Sttng pfonc of ll ncton oto o-lo ttng, lo t.35 wt t toq ln: Sttc toq-p ccttc fo qvlnt cct g Sll oto cclt c ft tn oto. On cnnot pt clly t ffnt tg of 5 Hz oclltng toq n of bkown toq, o ync bkown toq not ctly vbl. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6
107 7. Dync of ncton cn Rto of ync v. ttc bkown toq Pfff & Jon n pnnc of pt P Apton: DC cnt coponnt of tt-p ly cy, bfo oto p fo to n yn! b.7 Soc: G. Pfff, H. Jon, ETZ-A P.7 P J b P Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7
108 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8 7. Dync of ncton cn Epl: Dt of ncton cn : Bk own lp b 8%. Ln tt t 5 Hz, t voltg: / 5 3 π π π π p f R J L L U f P b Cv wt P: 7. /,, tt b yn b M M Cop: cl olton yl.74! ffcnt concnc! Dync bk own toq: Pfff-Jon pt P 3 p f R J L L U f P b b J π π
109 7. Dync of ncton cn Eplnton of Pfff-Jon pt P Hg pt P l ync ttng P ~ J Hg nt low oto cclton l ync ttng P ~ Hg tto lkg fl low oto toq l oto cclton l ync ttng P ~ Hg tto fl lnkg g oto toq ft oto cclton o ync ttng Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
110 Engy Convt CAD n Syt Dync Sy: Solton of ync qton fo ncton cn wt vyng p - on-ln cncl qton: cl olton ncy - T ync pnon: - Rc bkown toq M b,yn < M b,tt, - Ln-fqnt ttng toq ocllton - Low-fqnt ntl ocllton lk n yncono cn - cl pl fo bg n ll oto -Inflnc of nt J - PFAFF-JORDA pt P fo tton of ync bkown toq Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
111 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
112 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Dcopoton of tnf fncton of lctcl yt nto -β-coponnt n cont. { } { } I R / G G G b β G G G b b b * * * * * * c bc b c c c c b c c c b c b z * * ~, b b G G β I R * * I R Root: * *,,, b b
113 7. Dync of ncton cn Tnf fncton of lctcl yt t n cont. Coplpc vcto... Copltnf fnctonof pc vcto Two-coponnt... Rltnf fnctonof coponnt Two ootof copl tnf fncton, b two pof congt copl oot of l tnf fncton, 4 &, 5, b, b, b, 4,,, b b, 5, b -OTE: Wt vbl pync qton non-ln, o noln tnf fncton t. - BUT: Sll gnl lnz qton llow tnf fncton folton. b Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
114 7. Dync of ncton cn Root of lnz lctocncl tnf fncton n -pln Tnf fncton of lnz pfonc ll gnl toy of ncton cn fo lctocncl pfonc vbl p: 3 δ δ δ 3,, 4 5 δ δ,, T fv oot of ncton cn lcto-cncl tnf fncton cop two p of congt copl pol n on l pol cncl nflnc! Cop: DC cn: Two pol fo lctocncl pfonc. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
115 7. Dync of ncton cn Stto fnc f Roto fnc f Syncono fnc f Do not ott Rott wt γ / U n ncton cn Rott wt δ yn / U n yncono cn U n ncton cn fo ll gnl toy β q yn b W U V 3 γ yn δ T p n voltg yt K yn Stto fnc f Spc vcto ott Syncono fnc f Spc vcto o not ov t ln opton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
116 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6 7. Dync of ncton cn Voltg qton n yncono fnc f yn yn yn yn yn yn yn yn γ δ δ γ δ δ Elntng, v t fl lnkg: Sbcpt yn kpp!
117 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7 7. Dync of ncton cn Toq qton wt fl lnkg { } { } { } * * * I I / I Elntng, v t fl lnkg: { } * I
118 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8 7. Dync of ncton cn Sll gnl toy n qlb pont In yncono fnc f: Cnt & voltg pc vcto n qlb pont contnt ty tt opton to qvlnt cct Elctocncl yt of qton n yncono fnc f, b: { } I * J Lnzton of 3 nknown: & fl lnkg, p cn pfonc b of 3 npt: tto voltg, tto fqncy, lo toq Unknown: Inpt:,,,,
119 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9 7. Dync of ncton cn Lnzton of nknown: Lnzton of known npt: Lnzton of tto voltg qton wt /,, tc.: qlb pont: vton: Lplc tnfoton: Lnzton of yt qton
120 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Lnzton of oto voltg qton Roto pc vcto voltg qton n qlb pont: Lnz oto pc vcto voltg qton of ll vton fo qlb: Lnz oto pc vcto voltg qton n LAPLACE on: /
121 7. Dync of ncton cn Lnzton of toq qton Dcopoton of copl pc vcto n -b-coponnt: b b J b b b b b b b b Cncllng of qlb conton n lnzton,.g.: J b b b b Lplc-tnfoton : b b b b J Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/
122 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/ 7. Dync of ncton cn Lnz voltg qton n -b-coponnt b b b b b b b b b b
123 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3 7. Dync of ncton cn J b b b b b J J b J J b b U Ψ Lplc t qton yt of ncton cn Lnz, n yncono fnc f Ψ U
124 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4 7. Dync of ncton cn J J J b J J b b b b Z U Ψ Incton cn "yt pon" fo p:,,, 5 P f Dt Z Dt b CRAMER l fo clclton of
125 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5 7. Dync of ncton cn Tnf fncton t no-lo fo ll tnc & not too ll fqnc >.5. f - Sll tnc:, << << - ot too ll tto fqnc: 6 >.5... b : - Con qlb pont no-lo opton: Stto voltg pc vcto con l: /, :,, b, b :
126 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/6 7. Dync of ncton cn : ot-cct t contnt: 3 not too ll tto fqnc << 4 lly ll tnc << <<, Ccttc polynol of lnz tnf fncton, 5 P Dt -Ccttc polynol: P OTE: 4
127 7. Dync of ncton cn Root of lnz lctocncl tnf fncton n -pln - Fv oot fv pol n -pln: 3 δ δ δ 3,, 4 5 δ δ,, Mcncl yt ntl fqncy:, J δ δ3 δ,,, -Pol, 3, 4 :DC coponnt n cnt n fl, toq n p ocllton wt tto fqncy. -Pol, 5 : fozn" oto fl "yncono" cn pnonon! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/7
128 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/8 7. Dync of ncton cn, J Fozn" oto fl "yncono" cn pnonon! Mcncl yt ntl fqncy P nt vl:, 3 Ω Ω T U L J p b L U p M Ω ± Pycl nt: Bkown toq R : of KLOSS-fncton, Ω T J pm b 3 Vl fo ll gnl t no-lo opton! o-lo, <<
129 7. Dync of ncton cn Mcncl yt ntl fqncy fo ll gnl Fozn" oto fl "yncono" cn pnonon! Incton cn: << o-lo,, COMPARE: Syncono cn wtot png: At no-lo qlb: c M / M p ϑ ϑ ϑ Syncono cn wt png: o-lo << Ω, Ω pm J p pm b J T, T pm p Ω, Ω J p J c ϑ /T Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/9
130 7. Dync of ncton cn Clclton of ntl fqncy of ncton cn Epl: kw 4-pol cg ncton cn:.4,.9,.95,.9,.78,.94, J 55.5.,.93, T / 3.3/π f,,, f , Hz, 3.3 T.35. / kw, 4-pol oto t t 4 T 4 T t 5 T Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
131 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3 7. Dync of ncton cn Eqlb pont:./ Rt opton: Slp Slp Slp Rt oto fl lnkg: Slct qlb pont t:,,, Epl: o-lo qlb pont wt t oto fl lnkg:, ~ <<
132 7. Dync of ncton cn Clclton of ntl fqncy of ncton cn Epl: 3 kw 4-pol cg ncton cn:.3, 3.,.667, J T T / 6.67 /π 5.3. Opton pont qlb pont: f δ,, f , Hz, , : T.38 /.9 84 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/3
133 7. Dync of ncton cn Sll gnl tnf fncton fo vyng tto fqncy.3,.4, 3.,.667, J 75 nlytcl ~.75 ~.38 Wk png U-f-p of nvt Soc: H. Klnt, Acv f. Elktotcnk - Vton of png δ n ntl ngl fqncy, wt vyng fng tto fqncy n contnt t oto fl lnkg no-lo cn opton,, Slp. WEAK DAMPIG AT LOW FREQUECY, f cn not contoll! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/33
134 7. Dync of ncton cn Sll gnl tnf fncton fo ncng tto tnc Untbl opton ncng plt Soc: H. Klnt, Acv f. Elktotcnk - Vton of png δ n ntl ngl fqncy, wt vyng tto tnc t t tto fqncy n contnt t oto fl lnkg no-lo cn opton,, Slp. USTABLE OPERATIO AT BIG STATOR RESISTACE! Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/34
135 7. Dync of ncton cn Sttng cn t no lo, contnt tto voltg & fqncy ctly.3,.667,.4, J 75 3.,.56.6 gtv png! b wt 3-fol nc tto tnc n by /3 c oto nt: 75 / 3 5. Rc bkown toq:.39 J.6.56 Sp ocllton plt nc USTABLE opton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/35
136 7. Dync of ncton cn Mnt of ntblty t bg tto tnc 3 6 kv, 5 Hz Swtc S t Vbl tnc R V Incton oto t no-lo Cg ncton oto wt p b oto 6 kv Y, 35 kw, 45 A, 5 Hz Z 8.35 Ω, p 4 R.46 Ω C,.46/8.35.5% o-lo cnt: I 74. A Ft pot nt n toy of ncton cn ntblty BBC, Mnn, Gny, 969: - Dct no-lo tt p of t ncton oto t t kv-g wt kv/6 kvtnfo t clo wtc S. Tnfo pnc X T X lp to tblz! - Opnng of t wtc S ft coplt tt-p t no-lo p - Mnt of t 5 Hz-no-lo cnt t Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/36
137 7. Dync of ncton cn M tto cnt wt bg tto tnc Envlop of 5 Hz cnt Envlop of 5 Hz cnt pl wtcng tnnt f 3.6 Hz Stbl opton RV 3.3 Ω RV /R 75.8 V.39 wtc S opn f.9 Hz RV 3.97 Ω Zo png Lt of tblty: RV /R 93. V.48 Soc: BBC, Mnn, Gny Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/37
138 wtc S opn 7. Dync of ncton cn M ntbl no-lo tto cnt wt bg tto tnc Epnt tnt to bg no of t oto, c by cncl vbton f.76 Hz R V 4.44 Ω R V /R 4. V.54 Soc: BBC, Mnn, Gny Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/38
139 7. Dync of ncton cn A l nctnc l cbl tblz t cn Moto no-lo opton / c c , ,.4 J 75 / c c Fo long cbl nvtgt wt pt, nvtgt wt pt c c { } c - Stto tnc & nctnc vy :. 3. c c - Popotonl to cbl lngt: c ~ c ~ l,.7,.34,. 68 ntbl tbl opton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/39
140 Engy Convt CAD n Syt Dync Sy: Lnz tnf fncton of ncton cn n yncono fnc f - Sll gnl toy fo Tnf fncton n LAPLACE on -Sot-cct oto cg n lt fl t contnt pln yncono cn ffct - Wkly p ocllton t U/f-contol n low p - Untbl opton t tongly nc tto tnc -Sp contol tblz t ntbl o wkly p ocllton of t ncton cn Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
141 Engy Convt CAD n Syt Dync 7. Dync of ncton cn 7. P nt clclton 7. Dync voltg qton n fnc f of ncton cn 7.3 Dync fl lnkg qton 7.4 Toq qton 7.5 Dync qton of ncton cn n tto fnc f 7.6 Solton of ync qton fo contnt p 7.7 Solton of ync qton fo ncton cn wt vyng p 7.8 Lnztnf fncton of ncton cn n yncono fnc f 7.9 Invt-f ncton cn wt fl-ont contol Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
142 7. Dync of ncton cn Invt-f cg ncton cn wt - cool Invt Soc: Sn AG Incton oto Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/4
143 7. Dync of ncton cn Vbl p opton of ncton cn voltg oc nvt b cnt oc nvt DC lnk cpcto C U : DC lnk voltg DC lnk ncto cok L I : DC lnk cnt contoll AC voltg, vbl fqncy contoll AC cnt, vbl fqncy oto- nvt opt npnntly oto wnng pt of oto- nvt plll opton of oto pobl oto bk own lp: bu,..... Moto cn opt wtot contol wtn lp ng... b contoll c oto n pt nvt oto bk own lp: b, I Moto optng n ntbl lp ng > b. Contol n fo tbl pfonc. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/43
144 7. Dync of ncton cn Voltg-f ncton cn t R HEYLAD ccl I U X / R X R I U φ R opt Stbl Moto b,u I M - Gnto - b,u R Hylnccl M Ω yn U X R Bk-own lp: R X bu, R X M coϕt: R opt X n t tbl of ng toq wt lp X Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/44
145 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/45 7. Dync of ncton cn Toq-p-cv of cnt-f ncton cn Ip cnt I, o cng of voltg op of no potncon cnt loc! I X R { } * R yn I U M P Ω δ X R X R X I X R X X R X I U U X R X R X I I U * { } * R X R R X I I U yn I X R R X M Ω U b I b X R M,, ,, U b I b cont. I I b, M b M n
146 7. Dync of ncton cn Cnt-f ncton cn R > b,i R opt I X I Stbl Moto Gnto M U X I φ - I U b, I R X R << X b,i c ll tn t voltg-f cn R X I X R - b,i M coϕt: R opt X n t ntbl of fllng toq wt lp Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/46
147 7. Dync of ncton cn Vbl p opton of ncton cn voltg oc nvt b cnt oc nvt contoll Ip voltg b.... coϕ g low Opton pont M b I b M n cont. b Ip cnt Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/47
148 7. Dync of ncton cn Voltg oc nvt Stto voltg pl wt olt voltg pttn Stto cnt nly nol wt ppl to voltg wtcng G : o ctf - no pow flow to g! Fo lctc bkng copp DC lnk bk to n Cotly ltntv: g PWM convt IGBT-pow wtc: pow ng. kw... MW, voltg < 6 V. Bgg pow tng wt IGCT- o GTO-pow wtc p to MW wt voltg.g. 63 V. Cnt oc nvt Stto voltg: nol to ncton by cn fl ct by p cnt Stto cnt cont of block tp cnt o. G : contoll tyto bg fo vbl ctf voltg U fo tng potv I >. At U <, > 9 gntv bk pow flow U < to g pobl. I Tyto pow wtc: bg ncton n yncono oto... MW Wol-w bggt oto: MW n ASA cnt /Lngly/USA, p wn cnnl Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/48
149 7. Dync of ncton cn Vbl p opton of yncono oto Cnt oc nvt opton ASA Lngly Rc Cnt, Hpton, Vgn, USA Syncono -pol oto wn tnnl v MW, two tyto cnt oc nvt n plll:.5 kv 36 X 6 Hz 36 X 6/n Soc: ABB, Swtzln Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/49
150 7. Dync of ncton cn Vbl p opton of yncono oto Cnt oc nvt opton -pol yncono lnt pol oto nyn, f,/p 6/6 / 6/n Soc: ABB, Swtzln Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
151 7. Dync of ncton cn Pncpl of fl-ont contol Dcopoton of tto pc cnt vcto n toq- n fl-gntng coponnt F. BLASCHKE, Elngn & K. HASSE, Dtt, 969 Mn fl cttonby tto n oto cnt pc vcto Toq gntonn ncton cn by n fl n p- gntzng cnt pnclcnt coponnt - Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
152 7. Dync of ncton cn Pncpl of fl-ont contol Mn fl ctton by gntzng Toq gnton by ppncl cnt v n nctnc cnt coponnt v totl lkg nctnc.. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/5
153 7. Dync of ncton cn Pncpl of fl-ont contol 3 Toq gnton { *} { * } { *} * I I I Long t contnt fo cngng : Sot t contnt fo cngng : / / / By copoton of t tto cnt n fl ctng n toq gntng coponnt, t contol v n ppopt tto voltg cn kp t fl ctng coponnt contnt contnt n fl b cn vy t toq gntng coponnt vbl toq. A b cng vy ft wt ot cct t contnt, w gt ync toq vton! Fl-ont contol pncpl of Blck n HGny, 969 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/53
154 7. Dync of ncton cn Copon of p contol of DC n AC ncton cn Typ of cn DC cn Cg ncton cn Contol At voltg contol Fl ont contol Gng vbl At voltg Stto voltg F n fl Sptly ct n fl Φ Mn fl lnkg Mgntzton Fl cnt f Mgntzng cnt Long fl t contnt Fl t contnt L f /R f Opn-cct t contnt / Toq cng by At cnt Fl-ppncl cnt pc vcto coponnt Sot t contnt fo toq cng At t contnt L /R Sot-cct t contnt / Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/54
155 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/55 7. Dync of ncton cn Roto fl lnkg pc-vcto fo tto qntt VW UW W V W U W W W W V U V U W V U Fo tto voltg n fl lnkg qton n tto fnc f w gt: / W V U
156 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/56 7. Dync of ncton cn Roto fl lnkg pc-vcto fo tto & oto qntt / R - Roto fl lnkg v by ntgtng tto cnt pc vcto v oto opn cct t contnt. - D to PT -pfonc no ntgton o wll occ, o oto fl lnkg y b tn t ny bty p,.g. lo n. M tto cnt pc vcto tnfo nto oto fnc f: oto p no n!
157 Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/57 7. Dync of ncton cn Roto fl lnkg pc-vcto pn on! W tto cnt pc vcto to b ttony ottng wt tto fqncy / Dffntl qton: Solton n oto fnc f: / Sttony olton : Sttony olton poblwtot ny ntgton o lo t low p << Fl lnkg plt n p ngl pn on. Only t no-lo no nflncof.
158 7. Dync of ncton cn Dtnton of oto fl lnkg fo fl ont contol fo tto cnt n voltg: -At g pvoltg bg n cn b wt g cccy. -At vy low pvoltg vy low. Mnt o c.g. offt wll b ntgt to bg vl, o t low p t to OT fl. b fo tto cnt n oto p: -Fl lnkg y b tn t ny bty p,.g. lo n. -In cg ncton cn t ffclt to tn on-ln oto tnc, wc y cng btwn C n.g. 5 C by 5%: Tl ol of t cn n. Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/58
159 Engy Convt CAD n Syt Dync Sy: Invt-f ncton cn wt fl-ont contol - Voltg oc nvt c w tn cnt oc nvt -Fl-ont contol tlz pton of cnt pc vcto nto fl-plll n fl-otogonl coponnt - Fl-plll coponnt gntz n fl long t contnt - Fl-otogonl coponnt gntz ty fl ot t contnt - Ft cng of toq v ft cng of fl-otogonl cnt - Dync cng of toq v fl-ont cnt pc vcto pton Pof. D. A. Bn, Engy Convt - CAD n Syt Dync 7/59
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Chapter 2--Asset and Liability Valuation and Income Measurement
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High-performance sensorless vector control of induction motor drives using a Luenberger Observer
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Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1872 Colby College Catalogue 1872-1873 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
Pricing Arithmetic Average Reset Options With Control Variates
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J. Org. Chem., 1997, 62(12), , DOI: /jo961896m
J. Org. Chem., 1997, 62(12), 392-399, DO:1.121/jo961896m Terms & Conditions Electronic Supporting nformation files are available without a subscription to ACS Web Editions. The American Chemical Society
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Colby College Catalogue
Colby College Digital Commons @ Colby Colby Catalogues College Archives: Colbiana Collection 1871 Colby College Catalogue 1871-1872 Colby College Follow this and additional works at: http://digitalcommonscolbyedu/catalogs
TABLES AND INFORMATION RETRIEVAL
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