Methods of Study of Power Converters

Transcription

1 N N Mehod of udy of Power onerer for a yemac analy by arlo. Marn N - / wh he uppor of - ouloue, rance -8 May 4 N cceleraor chool - Warrngon, UK N opc of he preenaon Par Par he phae plane repreenaon ere-parallel reonan conerer N crcu M me doman waeform - ON HOY U - HO O PH PN ONUON -8 May 4 N cceleraor chool - Warrngon, UK

2 N opc of he preenaon Par Par yemac analy of power conerer - Ue of he phae plane repreenaon Pg rcu and frng gnal Pg g D P - YM PPOH - PH PN NY ld ld ld D P ld me doman waeform??? Workng prncple?? ably ue?? Dmenonng?? g p a p DP ld??????? N -8 May 4 N cceleraor chool - Warrngon, UK 3 N opc of he preenaon Par Par Modellng of power conerer UK conerer N <Vn > V n OO conerer?? ND MODNG UK conerer agan D V n D-lnk fler nable aboe a ceran power.6kw D-lnk bu olage, V D Oupu D curren 5kW D-lnk bu olage, V D Oupu D curren How?? Why?? oluon?? -8 May 4 N cceleraor chool - Warrngon, UK 4

3 N onen Par N. orced ae and free ae n and nd order crcu - ecall..-ae arable;..-epone of a lnear yem...-ree ae;...-orced ae;. epone of a ype crcu o olage and curren ep:- he phae plane mehod..-heorecal analy: -ae equaon;..-graphcal repreenaon;.3.-epone of a crcu wh dampng effec.4.-praccal eample.4..-hargng a capacor from a D olage ource.4..-hyror recfer wh W OW -8 May 4 N cceleraor chool - Warrngon, UK 5 N onen Par 3. lafcaon of Mehod of udy 3..-nalycal mehod; 3..-Graphcal repreenaon; 3.3.-Graphcal/analycal mehod:-he phae plane; 3.4.-mulaon mehod; unconal baed mehod; equenal analycal mehod; Whou a pror knowledge; Wh a pror knowledge; N 4. equenal analycal mehod 4..-he prncple; 4..-lowchar for a yemac analy - remark; 4.3.-hoce of he fr equence; 4.4.-ample:- udy of a hyror chopper -8 May 4 N cceleraor chool - Warrngon, UK 6

4 N onen Par N 5. Modellng of Power onerer 5..- Purpoe: - conrol orened modellng 5..-ae pace model; 5.3.-qualen aerage crcu model -8 May 4 N cceleraor chool - Warrngon, UK 7 N opc of he preenaon Par Par he phae plane repreenaon N crcu M - ON HOY U - HO O PH PN ONUON -8 May 4 N cceleraor chool - Warrngon, UK 8

5 N. orced ae and free ae: ecall-.. ae arable ae arable defnon N - ny lnear yem behaour can be decrbed by a e of man arable, whoe alue defne drecly ae. ny oher quane of he yem can be epreed a a funcon of hee ae arable and yem npu. ae arable propere - ae arable canno change alue nananeouly. hey hae o be connuou funcon n me ae arable n elecrcal crcu - urren flowng hrough each ndependen nducor; - Volage acro each ndependen capacor; -8 May 4 N cceleraor chool - Warrngon, UK 9 N. orced ae and free ae: ecall- N.. epone of a lnear yem - ree ae and forced ae near yem can be modelled by a e of dfferenal equaon d d d d d d crcu oluon of he dfferenal equaon yem me doman ull repone ree ae repone orced ae repone Φ umpon: orced ae repone fne ree ae repone Φ : repone of he crcu whou ecaon ource: - olage ource hor crcued; - curren ource n open crcu orced ae repone : repone of he crcu n eady ae - capacor behae lke open crcu; - nducor behae lke hor crcu -8 May 4 N cceleraor chool - Warrngon, UK

6 N. orced ae and free ae: ecall-3.. epone of a lnear yem nal condon nal condon N he nal condon hall be compued once he equaon for he free ae and forced ae repone are added co ω Φ on K ompuaon of conan, from nal condon: Φ co ω K Φ K K Order of he yem he order of he yem equal o: he number of ae arable Σ ndependen capacor ndependen nducor -8 May 4 N cceleraor chool - Warrngon, UK N. orced ae and free ae: ecall-4.. epone of a lnear yem ample rcu ree ae orced ae N Ocllaed crcu Φ Ocllaed crcu Φ -8 May 4 N cceleraor chool - Warrngon, UK Non-ocllaed crcu Non-ocllaed crcu

7 N. he phae plane mehod -.. heorecal analy: -ae equaon Purpoe udy he repone of he followng ype crcu wh: - wo D ecaon ource, olage and curren ource; - nal condon, nducor curren and capacor olage ; - no power loe*; N crcu ree ae eady ae ull crcu repone, ree repone Φ, Φ orced repone, * n praccal cae, he loe e pecally n he nernal reance of he nducor. Howeer, he me conan ofen much larger han he wchng perod. f o, he dampng effec can be negleced a he wchng perod cale. Dampng effec due o loe wll be uded laer. -8 May 4 N cceleraor chool - Warrngon, UK 3 N. he phae plane mehod -.. heorecal analy: -ae equaon orced repone,, ree repone, Φ, Φ N ompuaon of he full repone,, co ω n ω ω co ω ω n ω nal condon eady ae ω ω -8 May 4 N cceleraor chool - Warrngon, UK 4 φ ree ae φ φ φ d d d d d φ φ φ d φ co ω n ω ω co ω ω n ω ω

8 -8 May 4 N cceleraor chool - Warrngon, UK 5 N N. he phae plane mehod heorecal analy: -ae equaon n n co co n n co co ω ω ω ω ω ω ω ω from he full repone equaon y y y y ; y ; y ; y quaon of a crcle: - cenred n pon, y ; - pang n pon, y ; wh n co n co ω ω ω ω ull repone equaon, earchng for he equaon of a crcle y y r y -8 May 4 N cceleraor chool - Warrngon, UK 6 N N. he phae plane mehod Graphcal repreenaon Phae plane conrucon ule: ery ype crcu whoe free ae correpond o a ere crcu, wll hae an ocllan repone whch may be repreened on he phae plane, / by a crcle: - enred on he forced ae operang pon, / ; - Pang hrough pon, /, repreenng he nal condon; crcu M

9 N. he phae plane mehod Graphcal repreenaon Obanng he waeform n he me doman N M he pon M moe clockwe around he crcle: - he nducor curren correpond o he pon n he ordnae; - he olage acro he capacor he abca Drec compuaon of waeform quane Ocllaon frequency f oc π Ocllaon magnude radu r Mamum nducor curren Mnmum nducor curren. ma r -8 May 4 N cceleraor chool - Warrngon, UK 7. mn r N. he phae plane mehod epone of a crcu wh dampng effec N Dfferenal equaon: free ae wh dampng, φ d φ d d φ d ull repone wh GH dampng effec, e co ω n ω e co ω n ω 3 4 pral: -arng n he nal condon pon; -olng clockwe, nally along he un-damped crcle; -onergng oward he eady ae operang pon -8 May 4 N cceleraor chool - Warrngon, UK 8

10 N. he phae plane mehod Praccal eample hargng a capacor from a D olage ource N h apacor charger crcu ree ae eady ae Half-crcle: -hyror wched on wh zero curren/zero olage; -hyror wche off when he curren reache zero; -he capacor charged a wce he D olage ource, hyror «on» Phae plane hyror «off» me doman waeform -8 May 4 N cceleraor chool - Warrngon, UK 9 N.4. Praccal eample ecfer brdge. he phae plane mehod hyror recfer wh ree-wheel hyror W OW / magne -OD: - reak-oer Dode -W urn on f V W > V OD ; -W urn off f W ; N ae / ae permenal oberaon a P man upple, followng man hudown -n cae : W wche on only once and aure full magne dcharge; Howeer, mporan peak-curren on dcharge of capacor ; -n cae : W wche on/off connuouly NG-NG mode n ome cae planaon??? -8 May 4 N cceleraor chool - Warrngon, UK

11 N. he phae plane mehod Praccal eample hyror recfer wh ree-wheel hyror W OW ehaoural udy followng man hudown N magne ecfer brdge afer hudown W / OD NG!!! NG!!! ae / / V / ree ae eady ae OD W «on» W «off» Phae plane rdge «off» OD -8 May 4 N cceleraor chool - Warrngon, UK N. he phae plane mehod -.4. Praccal eample hyror recfer wh ree-wheel hyror W OW. MX OD r ondon. MX ondon > - ecfer brdge urn off ; - W operae n NG-NG mode. MX OD OD / π aan OD ondon <. MX OD N f O - ecfer brdge keep wched on ; - W neer wche on magne dcharge made rough he recfer brdge ondon -8 May 4 N cceleraor chool - Warrngon, UK

12 N opc of he preenaon Par Par yemac analy of power conerer - Ue of he phae plane repreenaon rcu and frng gnal D Workng prncple?? P ably ue?? Dmenonng?? ld ld ld D P ld N Pg g - YM PPOH - PH PN NY - lafcaon of mehod of udy - lowchar for a yemac analy -8 May 4 N cceleraor chool - Warrngon, UK 3 N 3. lafcaon of Mehod of udy -8 May 4 N cceleraor chool - Warrngon, UK 4 N 3. lafcaon of Mehod of udy 3..-nalycal mehod: - aed on equaon deraon and me-doman waeform; 3..-Graphcal repreenaon: - ook-up-able; Graph n P.U. un; 3.3.-Graphcal/analycal mehod:- nalycal mehod Phae plane; 3.4.-mulaon mehod:- aed on dedcaed compuer ofware and D ool unconal baed mehod: - Power conerer condered a a black bo. Power conerer a an npu/oupu block dagram. No nernal deal are condered. No ald for dconnuou operaon equenal analycal mehod:- he conerer operaon decompoed n eeral equence. n each equence here no wchng Whou a pror knowledge: - all he equence hae o be analyed; Wh a pror knowledge: - ome neen equence are elmnaed a he begnnng of he udy

13 N 4. equenal analycal mehod he prncple. N - Decrpon of he power conerer operaon on a equenceby-equence ba; - nalye: a- ondon for equence ranon; b- ae eoluon durng each equence -8 May 4 N cceleraor chool - Warrngon, UK 5 N 4. equenal analycal mehod he prncple. N a- equence ranon wchng of one or eeral emconducor e. condon for wchng on: - dode: V > - hyror: V > & gae gnal on - ranor: gae gnal on e. condon for wchng off: - dode & hyror: - ranor: gae gnal off -8 May 4 N cceleraor chool - Warrngon, UK 6

14 N 4. equenal analycal mehod he prncple. b- ae eoluon durng each equence or a gen equence, compue he ae arable: - Volage acro he capacor - urren hrough he nducor N ompue he epreon of he curren and olage acro he wche: Go back o pon a - heck for condon for a new equence ranon -8 May 4 N cceleraor chool - Warrngon, UK 7 N 4. equenal analycal mehod lowchar for a yemac analy. or a gen equence. earch for he order of he yem. ompue epreon forremark - Volage acro open emconducor, - urren acro cloed emconducor N eru ource alue, ae arable 3. e of compably: - heck for he eence of a gen equence - or all wche ecep he la one changng ae: all olage acro open dode mu be <, all curren hrough cloed wche mu be > -8 May 4 N cceleraor chool - Warrngon, UK 8

15 N 4. equenal analycal mehod - 6 N 4.. lowchar for a yemac analy or a gen equence 4. ompue he epreon for ae arable - oluon of dfferenal equaon yem n forced and free ae, nal condon fnal ae of he former equence - phae plane repreenaon 5. heck for he een ha may generae a wchng remark5 6. elecon of he een leadng o a equence ranon -8 May 4 N cceleraor chool - Warrngon, UK 9 N 4. equenal analycal mehod May 4 N cceleraor chool - Warrngon, UK 3 N 4.3. hoce of he fr equence - n ome cae, a bad choce of he fr equence may lead o a dergen reul n he crcu analy urn-around; - h namely he cae of crcu where nal condon for a eady ae cycle are no obou o deermne hey depend on he way ranen operaon behae, pre-chargng procedure, ec.; - Praccal rule for choong he fr equence yeldng analy conency and conergence : a - choe a equence where he load conneced o he ource ace phae; b - choe a equence correpondng o a free-wheelng ae; c - choe a equence correpondng o a dconnuou conducon;

16 N 4. equenal analycal mehod - 8 N 4.4.-ample:- udy of a hyror chopper rcu and frng gnal me doman waeform Pg D P g Pg g Phae plane? ld ld ld D P ld p a p????? DP? ld? -8 May 4 N cceleraor chool - Warrngon, UK 3 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n ace phae gue D P ld DP 3- e of compably D < ; DP < ; P > ; > no gae gnal uppoon: < eq. OK 4- oluon of ae arable No eoluon 5- en ha may generae a wchng < > wche on f gae gnal 6- he een leadng o a equence ranon wche on when gae gnal nal cond: ; -8 May 4 N cceleraor chool - Warrngon, UK 3 N - earch for he order of he yem crcu open No eoluon of he ae arable - Volage & urren on emconducor D DP P ld

17 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n ha wched on D ree orced ld P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 33 N - earch for he order of he yem ree ae crcu of nd order rcle n he phae plane - Volage & urren on emconducor D 3- e of compably DP 4- oluon of ae arable rcle:,, ; ;, 5- en ha may generae a wchng may wch off f > ; D and DP keep off; P may wch off f P > ld 6- he een leadng o a equence ranon P wche off before nal cond: ; P ld < ; < ; eq. OK D DP P > ld N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 3 P ha wched off D ree ld P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 34 N - earch for he order of he yem ree ae crcu n open loop ragh lne n phae plane - Volage & urren on emconducor D 3- e of compably ld DP D < DP ld P ; < ; > eq. OK 4- oluon of ae arable ragh lne: ld ; ld /* 5- en ha may generae a wchng keep on; D keep off; DP wche on f > P wche on f > and gang gnal appled 6- he een leadng o a equence ranon P mu no wch on lo of conrol;dp wche on when > nal cond: ; ld

18 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 4 DP ha wched on D ld ree orced ld P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 35 N - earch for he order of he yem ree ae crcu of nd order rcle n he phae plane - Volage & urren on emconducor D 3- e of compably 4- oluon of ae arable rcle:,, ; ;, ld 5- en ha may generae a wchng wche off f ; D keep off; DP wche off f ld P wche on f gang gnal appled 6- he een leadng o a equence ranon P mu no wch on lo of conrol; wche off before D nal cond: / ; DP ld P < ; > ; > no gae gnal D P ld eq. OK N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 4-b ha wched off D ld P ld DP N - earch for he order of he yem crcu open No eoluon of he ae arable - Volage & urren on emconducor D 3- e of compably DP ld P D P DP > ; > no gae gnal ; > Volage acro dode D poe D wche on mmedaely eq. no OK h equence ha no phycal eence D wche on a he ame me wche off -8 May 4 N cceleraor chool - Warrngon, UK 36

19 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 5 D ha wched on D ld ree orced ld P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 37 N - earch for he order of he yem ree ae crcu of nd order rcle n he phae plane - Volage & urren on emconducor D 3- e of compably 4- oluon of ae arable rcle:,, ; ; ld /, 5- en ha may generae a wchng keep off; D wche off f ; DP wche off f ld P wche on f gang gnal appled 6- he een leadng o a equence ranon P mu no wch on lo of conrol;d wche off before DP nal cond: / ; DP ld P < ; > ; > no gae gnal eq. OK DP P ld N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 6 D ha wched off D P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 38 N - earch for he order of he yem crcu open No eoluon of he ae arable - Volage & urren on emconducor D 3- e of compably DP ld P > no gae gnal;dp > ;P > no gae gnal eq. OK 4- oluon of ae arable No eoluon 5- en ha may generae a wchng wche on f gae gnal; D keep off; DP keep on; P wche on f gang gnal appled 6- he een leadng o a equence ranon mu no wch on lo of conrol; P wche on wh gae gnal nal cond: / ; ld

20 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 6 - b P ha wched on D P ld DP N - earch for he order of he yem crcu open No eoluon of he ae arable - Volage & urren on emconducor D 3- e of compably DP D > DP ld P ; < ; < hor crcu curren of eq. no OK ld Volage acro dode D poe D wche on mmedaely urren on dode DP negae DP wche off mmedaely h equence ha no phycal eence Once P wche on; DP wche off and D wche on -8 May 4 N cceleraor chool - Warrngon, UK 39 N 4. equenal analycal mehod ample:- udy of a hyror chopper equence n 7 DP ha wched off, D ha wched on D ree orced ld P ld DP -8 May 4 N cceleraor chool - Warrngon, UK 4 N - earch for he order of he yem ree ae crcu of nd order rcle n he phae plane - Volage & urren on emconducor DP D 3- e of compably < ; eq. OK DP < 4- oluon of ae arable rcle:,, ; ; - ld /, 5- en ha may generae a wchng keep off; D wche off f ; DP keep off P wche off f ld 6- he een leadng o a equence ranon D wche off before P nal cond: / ; P ld ld

21 N 4. equenal analycal mehod ample:- udy of a hyror chopper Pg omplee phae plane and g waeform N ld ld 5 4 ld P P DP ld May 4 N cceleraor chool - Warrngon, UK 4 N opc of he preenaon Par Par Modellng of power conerer N OO conerer?? ND MODNG wo mehod: ae pace aerage model; qualen aerage crcu model -8 May 4 N cceleraor chool - Warrngon, UK 4

22 N 5. Modellng of power conerer Purpoe:- onrol orened modellng. Open loop yem u power conerer p y N u-npu: duy-cycle, frng angle, y-oupu: delered olage, p-perurbaon: man durbance, loed loop yem r conroller u power conerer y r-reference: command leel ym-meaure: olage enor, D ym enor p - Power conerer model: - mahemacal repreenaon of he yem dynamc behaour e of dfferenal equaon; - Model are ued whn conrol heory n order o mproe dynamc performance and perurbaon mmuny -8 May 4 N cceleraor chool - Warrngon, UK 43 N 5. Modellng of power conerer ae pace model. & u u reference ecor,,,d conan marce y Du ae ecor uppor eample he OO D/D conerer connuou mode, > D c equence equence N D c c on on/ duy-cycle Goal: ompue he ranfer funcon beween and : func equence cloed, duraon open, duraon - equence d d ; d d & / & & u D u & y -8 May 4 N cceleraor chool - Warrngon, UK 44 y u [ ]; D D equence d d ; d d & / / & / & & y u u D u

23 -8 May 4 N cceleraor chool - Warrngon, UK 45 N N 5. Modellng of power conerer ae pace model. negraon of he ae dfferenal equaon e e d e e u conan u.. τ τ & e e e e G G pplcaon o he preen eample wh e G e e G e ; ; -8 May 4 N cceleraor chool - Warrngon, UK 46 N N 5. Modellng of power conerer ae pace model. ompuaon of a unque equaon, G G G wh G G G G G ppromaon of he eponenal o a order...!...! e e G.... mplfcaon of he marce and G

24 N 5. Modellng of power conerer ae pace model. Dcree-me ae equaon G onnuou-me ae equaon lnear nerpolaon & &. [ ] [ ] wh ae pace model generc power conerer, equence eragng N Marce and are he um of, and,, repecely, pondered by her «eence duraon» y D. wh D D D ame apple for marce and D n a generc cae -8 May 4 N cceleraor chool - Warrngon, UK 47 N 5. Modellng of power conerer ae pace model. omng back o he former OO D/D conerer / / - / - / / / 3 / N ae pace model for he OO D/D conerer / & back Mar dependen on -> non lnear model common for mo of he power conerer rucure -8 May 4 N cceleraor chool - Warrngon, UK 48

25 -8 May 4 N cceleraor chool - Warrngon, UK 49 N N 5. Modellng of power conerer ae pace model. mall gnal lnear model ; conan Purpoe: - ablh a mall gnal ae model around a predefned operang pon umpon.. & & ompuaon of he D operang pon nearaon con, f, &,, f f &..,, D D D wh D y wh f 443 & from he former ae pace model [ ] [ ] & D D D y -8 May 4 N cceleraor chool - Warrngon, UK 5 N N 5. Modellng of power conerer ae pace model. mall gnal ae pace model D D D wh D y ; ; & aplace ranformaon [ ]. D y

26 -8 May 4 N cceleraor chool - Warrngon, UK 5 N N 5. Modellng of power conerer ae pace model. rom he mall gnal ae pace model omng back o he former OO D/D conerer ; wh & D operang pon. / May 4 N cceleraor chool - Warrngon, UK 5 N N 5. Modellng of power conerer ae pace model. omng back o he former OO D/D conerer aplace ranformaon of he ae equaon [ ]. ranfer funcon / and / ^ ^ ^ ^

27 N 5. Modellng of power conerer qualen aerage crcu model. Valdy hypohe: - me conan >> amplng perod -8 May 4 N cceleraor chool - Warrngon, UK 53 N Prncple: - replacng he wche by equalen olage or curren ource n order o oban a lnear/me-connuou equalen crcu; - he equalen crcu ald for aerage alue a he wchng frequency cale ecpe o oban he equalen crcu. elec any equence whoe duraon known; for ha equence:. ompue:.. - he curren hrough all cloed wche a a funcon of ae arable and/or ource alue;.. - he olage acro all open wche a a funcon of ae arable and/or ource alue; 3. Draw an equalen elecrcal crcu, by replacng: 3.. he cloed wche by he relaed curren pondered by her eence duraon; 3.. he open wche by he relaed olage ource pondered by her eence duraon; N 5. Modellng of power conerer qualen aerage crcu model. emplfcaon on he OO conerer N equence : - duraon - qual o he ae pace model on lde Mod Power on-6 equence : - duraon - - equence : - duraon equence : - duraon d d d d & / { & u { { 3 & d d d d -8 May 4 N cceleraor chool - Warrngon, UK 54

28 -8 May 4 N cceleraor chool - Warrngon, UK 55 N N 5. Modellng of power conerer qualen aerage crcu model. mall gnal lnearaon.. D operang pon con u f, f, &,, f f & nearaon u & & & [ ]. aplace ranformaon -8 May 4 N cceleraor chool - Warrngon, UK 56 N N he ND H ND

29 N emark on pon 4. N MK ON N 4. OWH O YM NY -8 May 4 N cceleraor chool - Warrngon, UK 57 N emark. earch for he order of he yem 4.. lowchar for a yemac analy.. earch for he order of he yem back N nalye he equalen crcu correpondng o he free ae: - he order of he yem correpond o he number of ndependen ae arable,.e. Σ ndependen nducor ndependen capacor -8 May 4 N cceleraor chool - Warrngon, UK 58

30 N emark. preon for olage and curren on he wche 4.. lowchar for a yemac analy. N. ompue epreon for olage and curren on emconducor back - he curren hrough each emconducor aken a poe when flow n he ene of he conducon; - he olage acro each emconducor aken n he oppoe ene of he curren flow recepon conenon; - ach emconducor a cloed ae condered a a olage ource, V D pn juncon drecly polared D D D -8 May 4 N cceleraor chool - Warrngon, UK 59 N emark3. e of compably 4.. lowchar for a yemac analy. 3. e of compably back N - ae change of a emconducor may nduce an nananeou change on anoher emconducor, leadng o eeral wchng een a he ame nan; - h new wchng een produce anoher equence; - new e of compably ha o be performed n order o fnd he able equence D ld on > D off ; nananeouly off > D on ; nananeouly on and D on: neen equence -8 May 4 N cceleraor chool - Warrngon, UK 6

31 N emark4. preon for ae arable 4.. lowchar for a yemac analy. 4. ompue he epreon for ae arable back N - y knowng he free ae and forced ae crcu repone, he eoluon of he ae arable ha o be drawn: - olng he dfferenal equaon yem n me doman; - Ue of he phae plane mehod uable for mo of he praccal cae -8 May 4 N cceleraor chool - Warrngon, UK 6 N emark5. en leadng o a wchng 4.. lowchar for a yemac analy. 5. heck for he een ha may generae a wchng back N ype of een leadng o a poble equence ranon wche wh naural wchng - naural urnng off: curren on he wch a cloed ae ; - naural urnng on: olage acro he wch a open ae > ; wche wh forced wchng - forced urnng off: curren on he wch a cloed ae > & gae gnal off; - forced urnng on: olage acro he wch a open ae > & gae gnal on; -8 May 4 N cceleraor chool - Warrngon, UK 6

32 N emark6. he een ha lead o a equence ranon 4.. lowchar for a yemac analy. 6. elecon of he een leadng o a equence ranon back N - nd he een, among hoe couned a pon 5, occurrng earler n me; - h ak demand ofen deep reflecon and knowledge of he yem operang condon -8 May 4 N cceleraor chool - Warrngon, UK 63