CODEN:LUTEDX/TEIE-514/1-141/6 Indusral Elecrcal Engneerng and Auomaon Auxlary Module for Unbalanced Three Phase Loads wh a Neural Connecon Nls Lundsröm Rkard Sröman Dep. of Indusral Elecrcal Engneerng and Auomaon Lund Unversy
Absrac The company Land Sysems Hägglunds AB s a leadng manufacurer of comba vehcles and all erran vehcles. One of Land sysems Hägglunds projecs for he fuure s he mul purpose comba vehcle, SEP, usng a hybrd desel-elecrcal drve ran. Because of he desel-elecrcal drve ran, all he mechancal power produced by he desel engnes s ransformed no elecrcy. The elecrcal sysem of he vehcle s by ha dmensoned for hgh elecrcal power. Ths power could be used, besdes for racon of he vehcle, for numerous purposes. For example exernal elecrcal ools, moors, PC:s, rados, radar equpmen ec. To make he elecrcal power useful for an arbrary load, needs o be ransformed no a four wre hree-phase 3/4V 5Hz AC sysem, usng he dc-lnk volage of he SEP as raw maeral. Ideally, he hree phase sysem should ac smlar o an ordnary connecon o he man elecrc grd. The purpose of he hess s o examne he possbly o acheve hs by usng a 5 kva DC/AC power elecronc converer wh four half brdges, provdng hree phase ermnals and one neural ermnal. The converer s called ACM Auxlary Converer Module The hess deals n a srucured way wh he problems and ssues concernng desgn of he converer and especally s conrol. Effecs of unbalanced hree phase loads, volages and currens, n a four wre sysem, are hghlghed. I covers heory of hree-phase sysems and her represenaon n phasors, sequences and vecors. The vecors are presened n saonary α -β -γ and roang d-q- coordnae sysems. I also covers he heory of pulse-wdh modulaon as well as crcu models and desgn mehods for vecor conrol n roang d-q--coordnaes. Dmensonng aspecs of man physcal componens and loss calculaons of he semconducors are covered bu no hghlghed. Fnally some ssues concernng he mplemenaon of a dgal conrol are deal wh. A model of he desgned converer, ncludng conrol sysems, s bul n Malab/Smulnk. The model conans he mporan aspecs of a physcal converer. Specfed load scenaros are smulaed and he resuls are presened. 1
Acknowledgemens Frs we would lke o hank our supervsor Per Karlsson for hs advce, experse and suppor. We also wan o hank our examner Mas Alaküla for, durng he years, srongly conrbung o our neress n power elecroncs. Anders Robersson deparmen of Auomac Conrol, LTH has also been very helpful o us n our work. The people we were conneced wh a Land Sysems Hägglunds deserve a specal apprecaon for provdng a nce and frendly workng envronmen. Especally Örjan Sjösröm, Urban Lundgren, Svane Bylund and Lars-Gunnar Larsson. Fnally we wan o hank our famles for her suppor durng our years of sudes a Lund Insue of Technology, LTH. Nls Lundsröm Rkard Sröman
Conens Absrac... 1 Acknowledgemens... Conens... 3 1. Inroducon... 5 1.1 Background... 5 1. Problem... 6 1.3 Purpose... 6 1.4 Delmaon... 7 1.5 Oulne... 8. Theory... 9.1 Three-phase sysems... 9.1.1 Three-phase sysems n phasor represenaon... 9.1. Three-phase sysems n sequense represenaon...1.1.3 Y- and -connecons...1.1.4 Three-phase sysems n vecor represenaon n fxed coordnaes...13.1.5 Vecor represenaon n synchronous coordnaes...15.1.6 Unbalanced sysem...17. Loads o evaluae...1.3 Three leg converers...4.3.1 The hree leg brdge...4.3. Pulse-wdh modulaon...6.3.3 Symmerzed modulaon...9.3.4 Overmodulaon...3.3.5 Unbalanced condons...31.3.6 The creaon of a neural connecon...3.4 The four legged converer...34.4.1 The four leg brdge...35.4. Over modulaon...37.4.3 Unbalanced condons...37.5 Crcu model of he sysem...38.5.1 The sysem n abc-coordnaes...39 3
.5. The sysem n d-q--coordnaes...4.6 Dmensonng...43.6.1 Dc-lnk volage...43.6. Power elecronc swches...44.6.3 Swchng frequency and converer losses...45.6.5 Dc lnk capacor...5.7 Conrol of he sysem...54.7.1 Model of he sysem o conrol...55.7. Delays...56.7.3 Volage conrol...56.7.4 Conrol mehods...57.7.5 Model of he sysem, ncludng conrollers and delays...64.7.6 Parameers of he conrollers...65 3. Mehod...67 3.1 The smulnk model of he converer...67 3. Smulaons and ess...76 3..1 Smulaed load scenaros...76 3.. Sengs of smulaed converer model...77 4. Resuls...79 5. Implemenaon...9 5.1 Dgal conrol...9 5. Proposed man componens...96 6. Conclusons...97 6.1 Summary...97 6. Dscusson for he fuure...99 References...11 Appendx A Dmensonng he dc lnk capacance...13 Appendx B The Smulnk model...16 Appendx C n.m...113 Appendx D losscalc.m...114 Appendx E - Dealed represenaon conrol sgnals...117 Appendx F - Losses semconducors...133 Appendx G - Nomenclaure...137 4
1. Inroducon 1.1 Background The company Land Sysems Hägglunds AB s a leadng manufacurer of comba vehcles and all erran vehcles. Hägglunds has delvered mlary vehcles o more han 4 counres worldwde. The company s suaed n Örnsköldsvk, a own 55 km norh of Sockholm. Land Sysems Hägglunds employs around 11 personnel and had n 4 a urnover of 3 bllon Swedsh kronor. One of Land sysems Hägglunds projecs for he fuure s he mul purpose comba vehcle SEP Swedsh abbrevaon for Splerskyddad Enhes Plaform, Modular Armoured Taccal Sysem. The neresng par of SEP from hs hess pon of vew, s he fac ha SEP ulzes a hybrd desel-elecrcal drve ran see fg. 1.1-1. From a vehcle pon of vew hs gves advanages lke: volume effcency, fuel effcency, reduced lfe cycle coss, reduced envronmenal mpac and ncreased sealh characerscs. Snce he desel engnes are decoupled from he fnal drves, an ncreased flexbly n placng of he sysems n he vehcle s acheved, as well as an easly nsallaon of wo smaller desel engnes nsead of one larger. Wh baeres negraed no he elecrc drve sysem, he vehcle s also allowed o be drven slenly, wh he desel engnes shu down. There s however a furher advanage wh he hybrd desel-elecrcal drve ran. All he mechancal power produced by he desel engnes s ransformed no elecrcal power by generaors and recfed before s ransformed back o mechancal power by elecrcal machnes. The cenral par of hs elecrc ransmsson s he dc-lnk and s here he basc possbly for he purpose of hs hess s provded. Snce he generaors and he dc-lnk are dmensoned for he full racon power of he vehcle, hey creae a possbly of supplyng exernal loads wh hgh power, o he cos of less racon power, a for example sand sll of he vehcle. The srucure of he drve ran of he SEP may be smplfed as a deselelecrc UPS Unnerrupble Power Supply ha feeds he elecrcal racon moors. If only he frs pars of he drve ran are consdered, he SEP s an UPS. 5
Desel engne Generaor Recfer DC-lnk converer converer converer ACM Tracon moor Tracon moor Tracon moor Auxlary load Fgure 1.1-1. Prncple dagram of he drve ran of SEP. 1. Problem Snce he possbly of usng he vehcle as an UPS s gven, he exenson of he usefulness of he SEP would provde s an advanage ha no should be foreseen. Possble loads for he SEP, parly workng as an UPS, could be dfferen knds of nernal or exernal elecrcal sysems and machnes, for example elecrcal ools, moors, PC:s, rados, radar equpmen ec. To make he elecrcal power useful for an arbrary load, needs o be ransformed from DC level of he vehcle o a hree-phase four-wre 3/4V 5 Hz AC sysem. To ge he mos ou of he hree phase sysem should be flexble and sable enough o regulae he oupu volage correcly durng any load sngle-phase load, wo-phase load, hree-phase load or combnaons less han, or equal o nomnal load. The deal case would be f he hree-phase connecon could be seen as an ordnary connecon o he man grd. Ths forms he need of hree lne oupu ermnals and one neural oupu ermnal, as well as a gh conrol sysem for he equpmen performng he ransformaon. 1.3 Purpose The purpose of hs hess s o examne he possbles of ransformng he dc-lnk volage n he vehcle o a four-wre hree-phase 3/4V 5 Hz AC sysem by ulzaon of a power elecronc converer. The converer s from now on referred o as he ACM Auxlary Converer Module. Ths s done by sudyng exsng heory, examne dfferen alernave soluons, buldng a model, performng 6
smulaons on he model and examne he resuls. The dmensonng process of he man physcal componens of he converer s also explaned. For hs purpose, one need o nvesgae he effecs of unbalanced hree phase loads, how he unbalance affecs he volage regulaon, and wha counermeasures may be used o reduce her mpacs. Undersandng of he desgn process of power elecronc converers and her conrol mehods, as well as he behavor and represenaons of unbalanced hree phase sysems, are herefore needed. The man objecve of he hess s o provde hs undersandng. 1.4 Delmaon Due o he always presen lack of me and resources, one has o pu lmaons o he scope of a work. The heory needed for he undersandng of he effecs, desgn, model buldng ec., menoned n he secon above, s covered. Some lmng smplfcaons are however made n he model and he smulaons: In he model of he converer he dc lnk volage s assumed o be deal. The volage s no affeced by he load conneced o he converer or oher loads or sources conneced o he dc lnk. Probably here wll be a need for some knd of sep-up converer wh volage regulaon beween he dc lnk of he vehcle and he dc-lnk used by he converer descrbed n hs hess. There are only smulaons performed wh balanced and unbalanced, ressve and nducve loads conneced o he converer. The conrol sysems of he converer are smulaed n Malab and Smulnk. Lle s covered abou he mplemenaon of he conrol sysem n sofware for a real converer for example C-code for a DSP. The projec s purely heorecal. The consrucon of a physcal converer s no he arge of he projec. The mos obvous lmaon s he lack of a prooype of a physcal converer for praccal ess and verfcaons of he resuls obaned from smulaons. 7
1.5 Oulne The ambon of he hess s o rea, n a srucured way, he problems and ssues concernng he desgn of a power elecronc converer, workng as a provder of a hree phase volage source. The srucured oulne nvolves passng hrough some heory n he frs secons of he hess ha he laer secons are dependng on. The am s o presen he conens of he hess n a pedagogcal and logcal order. The conen s now presened n shor: Chaper 1 s he nroducon. Chaper handles he heory and s he major par of he hess. Secon.1 concerns he basc heory of hree-phase sysems, unbalanced volages and currens, and how o represen hem. In secon. dfferen load scenaros and her mpacs on he converer are presened. Secon.3 deals wh he basc heory of ordnary hree phase converers wh hree half-brdges and her lmaons. Secon.4 expands he hree half-brdge converer wh a fourh half-brdge o acheve a four legged converer wh a neural connecon. In secon.5 crcu models of he whole converer, ncludng flers and loads, are presened. Secon.6 deals wh dmensonng ssues, for example dc-lnk volage, swches, swchng frequences and flers. Secon.7 fnally presens a srucured mehod for he desgn of he conrol sysems for he converer. Chaper 3 presens a smulaon model of he converer. In secon 3.1 he consrucon of he model, bul n Malab and Smulnk s horoughly explaned. In secon 3. he smulaon scenaros, based on he load scenaros from secon., are presened. Chaper 4 gves a presenaon of he resuls from he smulaons n chaper 3. Chaper 5 concerns mplemenaon of a physcal converer. Secon 5.1 covers some ssues concernng a dgal conrol. Secon 5. gves a suggeson of wha hardware o use. Chaper 6 s an evaluaon of he projec, as well as a dscusson for he fuure. 8
. Theory.1 Three-phase sysems The projec concerns he ransformaon of he avalable DC-lnk volage o a hreephase 4V AC volage, ncludng a neural connecon. Commonly used subjecs n he hess are for example: phase represenaon, sequence represenaon, vecor represenaon, defnon of power, Y- and -connecons and unbalanced volages and currens. To clarfy he mehods and conceps, he hess s opened wh a secon provdng he heory of he above menoned subjecs n shor..1.1 Three-phase sysems n phasor represenaon In a hree phase sysem, he hree phases are denoed a, b, and c. The frequency f s he same n all hree phases. Durng deal condons, he phase componens are dsrbued by phase b lags 1 and her ampludes are equal. If phase a s aken as reference, 1 behnd phase a. The phasors roae counerclockwse. In an deal suaon lke above, he hree phase sysem has equal ampludes n all hree phases and exacly symmerc or balanced. 1 phase dsrbuon. The sysem s hen called v v v a b c = = = V b V c V a cosπf cosπf cosπf π 4π 3 3 Equaon.1.1 v c 1 v a v b Fgure.1-1. Phasor dagram of hree-phase sysem. 9
.1. Three-phase sysems n sequense represenaon When phase b lags 1 behnd phase a, as n eq..1.1, he sysem s sad o have a posve sequence. If he rule of orderng he phases n secon.1.1 s no followed and phase b s aken as he phase laggng 4 behnd phase a: v v v a b c = = = V b V c V a cosπf cosπf cosπf 4π π 3 3 Equaon.1. he sysem s sad o have a negave sequence. Posve and negave sequence can be vsualzed as roang counerclockwse and clockwse, respecvely. An mporan propery of a hree phase sysem wh only posve sequence, negave sequence, or a sum of boh, s ha he nsananeous sum of he phase componens s zero. va + vb + vc = Equaon.1.3 If eq..1.3 no holds, he mean value: v va + vb + vc = Equaon.1.4 3 s called he zero sequence componen. The zero sequence componen v represens a un-symmery componen whch s he same n all hree phases. As long as here s no neural conducor n a hree phase sysem a hree wre sysem, no zero sequence curren s possble. However, n a four wre sysem he possbly of zero sequence currens exss. Fnally: An un-symmerc, or unbalanced, hree phase sysem can be decomposed no a posve sequence componen, a negave sequence componen and a zero sequence componen: 1
11 + + = + + + = 3 cos 3 4 cos cos 3 4 cos 3 cos cos cos cos cos v v v f V f V f V f V f V f V f V f V f V v v v n n n p p p c c b b a a c b a π π π π π π π π π π ρ π ρ π ρ π Equaon.1.5 Where: 3 cos v v v f V v c b a + + = + = ρ π Equaon.1.6 The decomposon n eq..1.5 s vsualzed n fg..1-. Fgure.1-. Vsualzaon of decomposon n sequences. Posve sequence lef, negave sequence cener, zero sequence rgh. The ransformaon beween a-b-c componens and sequence componens s expressed n eq..1.7 and eq..1.8. [] = c b a n p X X X a a a a X X X 1 1 1 1 1 3 1 Equaon.1.7 = 1 1 1 1 1 X X X a a a a X X X n p c b a Equaon.1.8 Where X may be volages or currens and 3 / j π e a = s a dsplacemen wh 1. v ap v b v cp v c v a v bp v an v cn v bn
.1.3 Y- and -connecons A ree phase load conssng of hree mpedances Z 1, Z, Z 3 can be conneced n a Y or n a, as shown n fg..1-3. Assumng balanced load Z 1 =Z =Z 3, he volages can be llusraed as he phasor dagram n fg..1-3 rgh. v bc v a v b v c a b c Z Z Z v ca v ab v bc a b c Z Z Z v c v b 3 v a v ca v ab Fgure.1-3. Three phase loads. Y connecon lef, connecon, cener, Phasor dagram Y and rgh. From he geomery of fg..1-3 rgh s seen ha, compared wh he lne o neural volages or currens, he lne o lne volages or currens have her peak values a facor 3 hgher and her argumens dsplaced by3. Because of hs he oal power developed n a hree phase load s decreased by a facor 3 when changng he connecon from o Y. In he followng equaonsu s he volage over one of he mpedances Z. load Conclusons Y-connecon U load = U lne neural = U lne lne 1 3 I load = I lne Equaon.1.9 P Y = 3 U load I load U lne lne cos ρ = cos ρ Z Conclusons -connecon U = load U lne lne I I 1 3 Equaon.1.1 load = lne P = 3 U load I load U lne lne cos ρ = 3 cos ρ Z 1
Equvalen Y Durng balanced loads, s of no concern, from he sandpons of dynamcs and conrol, f he load s conneced n Y or. A conneced load can be reaed as f were conneced n a Y, bu wh all he mpedances reduced o1/3 of he acual values. Ths s called an equvalen Y. [1].1.4 Three-phase sysems n vecor represenaon n fxed coordnaes The sysem expressed as a vecor n wo dmensons Assumng a balanced hree phase hree-wre sysem, followng equaon holds []: X a + X b + X c =. Equaon.1.11 Where X may be volages or currens. Ths means ha he sysem s over-deermned and ha one of he componens always can be expressed n he oher wo. Therefore s possble o descrbe he sysem as equvalen wo phase sysem, wh wo perpendcular axes, denoed as α and β. These axes are consdered o be he real and magnary axes n a complex plane. The wo componens, α and β forms a vecor X αβ. The hree phase/wo phase ransformaon s gven by eq..1.1: j π / 3 j 4π / 3 [ X + e X e X ] X αβ = X α + jx β = a b 3 + Equaon.1.1 c Fg..1-4 shows he consrucon of he vecor n α - β -coordnaes graphcally. j π / 3 e β v e c j 4π / 3 s v va 3 v s α v e j π / 3 b j 4π / 3 e Fgure.1-4. Consrucon of he vecor n alpha-bea-coordnaes. 13
14 The ransformaon beween a-b-c coordnaes and α - β coordnaes s expressed n eq..1.13 and.1.14. = 3 1/ 3 1/ 3 1/ 3 1/ 3 / 1 X X X X X c b a T 444 4 3 444 14 β α Equaon.1.13 = 3 / 1/ 3 / 1/ 1 1 1 X X X X X T c b a β α 44 4 3 4 14 Equaon.1.14 The sysem expressed as a vecor n hree dmensons. When he hree wre sysem above s exended wh a forh neural wre, he possbly of a zero sequence load curren s gven. Because of hs eq. 1.1.11 does no necessarly hold []. + + X X X c b a Equaon.1.15 Ths means ha he sysems componens are ruly ndependen varables and could no be mapped no a wo dmensonal vecor. Insead a hree dmensonal vecor, n a hree dmensonal space wh he orhogonal α - β -γ -coordnaes s used. kx jx X X γ β α αβγ + + = Equaon.1.16 Fg..1-5 demonsraes how he hree phasors n a-b-c may relae o he α - β -γ - coordnae sysem.
15 Fgure.1-5. Relaonshp beween he phasors n a-b-c and he alpha- bea-gamma-coordnae sysem. The ransformaons beween a-b-c coordnaes and α - β -γ -coordnaes are expressed n eq..1.17 and.1.18. = 1/ 1/ 1/ 3 / 3 / 1/ 1/ 1 3 X X X X X X c b a T 444 4 3 444 14 γ β α Equaon.1.17 = 1 3 / 1/ 1 3 / 1/ 1 1 1 X X X X X X T c b a γ β α 44 4 3 44 14 Equaon.1.18.1.5 Vecor represenaon n synchronous coordnaes In a sysem, durng seady sae, he vecor represenaons above would boh be roang n her α - β or α - β -γ -coordnae sysems. The conrollers for such a sysem would have consanly oscllang reference sgnals even a seady sae, whch would lead o saonary errors n he oupu sgnals []. To avod hs problem and acheve a saonary DC operang pon a seady sae a leas n a balanced sysem, whch wll be dscussed laer, he sysem s ransformed no he roang d-q- or d-q--coordnae sysem. The d-q- or d-q-- ransformaon can be regarded as an observaon of he roang vecor from a coordnaes sysem ha roaes wh he same frequency as he fundamenal frequency of he vecor n heα - β -plane. Snce he α - β o d-q ransformaon α β a b c γ
jus s a smplfcaon of he α - β -γ o d-q-o ransformaon, only he laer wll be deal wh here. Fg..1-6 demonsraes how he fxed coordnae sysem n α - β -γ relaes o he roang coordnae sysem n d-q-. As can be seen, he d and q axes roae on he α - β plane, whle he o axs essenally s he preserved γ axs. γ q β α d Seady sae Fgure.1-6. Relaonshp beween he alpha-bea-gamma- and d-q-o-coordnaes. The ransformaon from α - β -γ -coordnaes o d-q--coordnaes s expressed n eq..1.19. X X X d cos ω sn ω X = sn ω cos ω X 1 X 144444444 3 T3 q β γ α Equaon.1.19 Physcally, for a vecor n he d-q--coordnaes, he d-componen s he reacve componen and he q-componen s he acve componen volage or curren. Drec ransformaon a-b-c o d-q-o Laer, n models and smulaons, ransformaons wll be made drecly from phasor represenaon n a-b-c o vecor represenaon n d-q-. Ths s done by combnng T and T 3, expressed n eq..1. and eq..1.1. 16
17 + + = 1/ 1/ 1/ 3 sn 3 sn sn 3 cos 3 cos cos 3 4 X X X X X X c b a T q d 4444444 4 3 4444444 14 π ω π ω ω π ω π ω ω Equaon.1. + + = 1 3 sn 3 cos 1 3 sn 3 cos 1 sn cos 1 4 X X X X X X q d T c b a 44444 4 3 44444 14 π ω π ω π ω π ω ω ω Equaon.1.1.1.6 Unbalanced sysem In mos cases a converer s desgned under he assumpon ha he load s balanced and an unbalanced load s reaed as an abnormal condon. However, n he real world, as well as n he proposed use for he converer n hs projec, unbalanced loads are expeced. Unbalanced loads wll resul n unbalanced load currens, whch n urn, wh nsuffcen conrol, may cause unbalanced oupu volages []. Snce he load condons have mpacs on he performance and desgn of he converer, wll now be shown how unbalance appears and behave n dfferen represenaons, as well as how unbalance can be defned. Unbalance n a-b-c phase represenaon Compared o wha was sad n secon.1.1, unbalance or asymmery n phase represenaon s characerzed by phasors wh dfferen peak values and/or phase dsrbuons dfferen from 1. An example of unbalanced phase volages and phasors s shown n fg..1-7. Compare wh fg.1-1.
Phase volages 3 1-1 va vc v c va - -3 vb v b.6.65.7.75.8 Fgure.1-7. Phase volages lef and phasor dagram rgh of a hree-phase unsymmercal sysem. Unbalance n sequence represenaon Accordng o secon.1., unbalance or asymmery wll n sequence represenaon lead o he appearance of negave and/or zero sequences. As an example he phase volages n fg..1-7 can be spl up n a posve, a negave and a zero sequence accordng o fg..1-8. Posve sequence Negave sequence Zero sequence 3 v a p v b p v c p 3 3 1 1 v cn v b n v a n 1 v a z =v b z =v c z -1-1 -1 - - - -3-3 -3.6.7.8.6.7.8.6.7.8 Fgure.1-8. Vsualzaon of decomposon n sequences. Unbalance n α - β -γ -coordnae vecor represenaon Durng balanced condons, he vecor descrbed n secon.1.4, wll roae crcularly on he α - β plane. No movemen wll appear n he γ -drecon. Fg..1-9a shows he vecor rajecory durng balanced condons. Compare wh he sequence represenaon, where only he posve sequence exss. Durng unbalanced condons however, f here s a negave sequence, he backwards roang negave sequence componen wll be added o he vecor as well. The vecor wll hen conss of wo componens: One par roang wh he fundamenal frequency n he posve drecon and one supermposed par roang 18
wh he fundamenal frequency n he negave drecon. Ths wll resul n an ellpsodal vecor rajecory on he α - β plane. If here s a zero sequence componen, hs wll appear as a movemen wh he fundamenal frequency n he γ -drecon. Fg.1-9b shows he vecor rajecory durng unbalanced condons, assumng ha posve, negave, and zero sequences exs. Compare wh he sequence represenaon durng unbalance. Fgure.1-9a. Vecor rajecory n he saonary coordnae sysem durng balanced condons. Fgure.1-9b. Vecor rajecory n he saonary coordnae sysem durng unbalanced condon Unbalance n d-q-o-coordnae vecor represenaon As menoned n secon.1.5, he d-q--ransformaon can be regarded as an observaon of he roang vecor from a coordnae sysem ha roaes wh he same frequency as he fundamenal frequency of he vecor n he α - β plane. The d and q axs roae on he α - β plane, whle he o axs essenally s he preserved γ axs. Thus, unbalance leads o he followng behavor of he d-,q- and -componens of a vecor n he d-q--coordnae sysem see fg.1-1b. 19
Balanced condons Unbalanced condons d 4-4 - -4.6.65.7.75.8-4.6.65.7.75.8 4 4 q - - -4.6.65.7.75.8-4.6.65.7.75.8 4-4 - -4.6.65.7.75.8-4.6.65.7.75.8 Fgure.1-1a. Behavor of he d- q- and - componens of a vecor n he d-q-- coordnae sysem durng balanced condons. Fgure.1-1b. Behavor of he d- q- and - componens of a vecor n he d-q-- coordnae sysem durng unbalanced condons. Snce he added negave sequence causes an ellpsodal vecor rajecory on he α - β plane, boh d and q wll have a snusodal componen, a wce he fundamenal frequency, added o her saonary DC componens. The zero sequence componen wll n he -drecon, as n heγ -drecon, appear as a snusodal componen a he fundamenal frequency. Defnon of unbalance There are dfferen ways o defne unbalanced loads. One way s based on he dfferences beween he maxmum per phase load and he mnmum per phase load [9]: Max per _ phase _ load Mn per _ phase _ load % UnBal = 1 Toal _ hree _ phase _ load Equaon.1. The drawback of hs defnon s ha no concern s aken of he load power facors. If dfferen phases are conneced o loads wh dfferen power facors, condons ha very well may have mpacs of he converers performance, wll no be dsngushed [].
Anoher way s o base he defnon on he sequence represenaon. Accordng o [], IEC gves he defnon of unbalance n a hree phase sysem as he rao beween he rms values of he negave sequence, or he zero sequence, and he posve sequence. negave _ sequence _ componen % UnBal _ N = 1 Equaon.1.3 posve _ sequence _ componen and zero _ sequence _ componen % UnBal _ = 1 Equaon.1.4 posve _ sequence _ componen In he nex chaper, where dfferen load condons are dscussed, boh defnons wll be used.. Loads o evaluae The ulmae goal s o creae a balanced hree-phase volage source ha, ndependen of he load condon, always provdes he correc volage. Now, hs s more of a arge o ake am a, han an n pracce achevable goal. The presened smulaons of he converer wll be lmed by a number of dfferen load condons. To pu a lm o he number of expermens, fve dfferen load scenaros consdered o be reasonable are chosen. Only ressve and nducve loads, wh power facor beween. and 1, are evaluaed. Capacve loads, ha are assumed o be rarer, are pu on hold for he me beng. Unbalanced loads are assumed o be a common load for he converer and wll herefore be carefully examned. The unbalance may be caused by unevenly dsrbued sngle-phase loads, or by a combnaon of sngle-phase loads and hreephase loads. The converers possbly o regulae volage durng ransens s of neres. Ths wll be smulaed by sudden seps n he load. 1
The followng scenaros of load condons wll be examned and smulaed: Scenaro 1 Balanced load wh power facor 1 and a sep n he load. Sarng a low power approxmaely no load and by a sep, reach nomnal power 5 kva. The scenaro smulaes ha he converer sars wh no load conneced and hen s subjec o a purely ressve load, correspondng o raed power of he converer. I a curren / powerfacor I b curren / powerfacor I c curren / powerfacor %unbalance %neg.seq. unbalance %zero.seq. unbalance I n curren Before sep: A/ 1 A/ 1 A/ 1 % % % A Afer sep: 7. A/ 1 7. A/ 1 7. A/ 1 % % % A Table.-1. Load scenaro 1. Scenaro Balanced load wh power facor. and a sep n he load. Sarng a low power approxmaely no load and by a sep, reach nomnal power 5kVA. The scenaro smulaes ha he converer sars wh no load conneced and hen s subjec o a heavly nducve load, correspondng o raed power of he converer. The neresng par here s o see how well he nverer copes under nducve load condons. I a curren / powerfacor I b curren / powerfacor I c curren / powerfacor %unbalance %neg.seq. unbalance %zero.seq. unbalance I n curren Before sep: A/. A/. A/. % % % A Afer sep: 7. A/. 7. A/. 7. A/. % % % A Table.-. Load scenaro. Scenaro 3 Unbalanced load wh power facor.8. The phase currens I b and I c are se equal o. The phase curren I a s se equal o nomnal curren I n.
The scenaro smulaes ha a parly nducve sngle-phase load s conneced o phase a. Phase b and c are no conneced. The neresng par here s o see how well he converer copes under unbalanced load condons. I a curren A/ powerfacor I b curren A/ powerfacor I c curren A/ powerfacor % unbalance % neg.seq. unbalance % zero.seq. unbalance I n curren A No sep 7. A/.8 A A 1 % 1 % 1 % 7. A Table.-3. Load scenaro 3. Scenaro 4 A combnaon of one balanced hree-phase load and one sngle-phase load wh a sep n he hree-phase load. Boh loads have a power facor of.8. Inally he phase currens I b and I c are se o.5 I and he phase curren I a s se o no mn al I nomnal. Then, here s a sudden change n he load so ha I b and I c are se o and I a s se o.5 I. no mn al The scenaro smulaes ha one parly nducve hree-phase load as well as one parly nducve sngle-phase load a phase a are conneced o he converer. Then he hree-phase load s dsconneced. The neresng par here s o see how he removal of a que heavy hree-phase load affecs he volage over a smulaneously conneced sngle-phase load. I a curren A/ powerfacor I b curren A/ powerfacor I c curren A/ powerfacor % unbalance % neg.seq. unbalance % zero.seq. unbalance I n curren A Before sep: 7. A/.8 36.1 A/.8 36.1 A/.8 5 % 5 % 5 % 36.1 A Afer sep: 36.1 A/.8 A A 1 % 1 % 1 % 36.1 A Table.-4. Load scenaro 4. Scenaro 5 A combnaon of one heavly nducve sngle-phase load and one ressve sngle-phase load. The nducve phase c has a power facor of.. I a and I c are boh se equal o nomnal curren I nomnal. The scenaro smulaes ha one heavly nducve sngle-phase load, as well as one purely ressve sngle-phase load are conneced o he converer. The neresng 3
par here s o see how he converer behaves under hs heavly unbalanced load where he neural curren exceeds he lne currens. I a curren A/ powerfacor I b curren A/ powerfacor I c curren A/ powerfacor % unbalance % neg.seq. unbalance % zero.seq. unbalance I n curren A No sep: 7. A/ 1 A 7. A/. 5 % % 1 % 134 A Table.-5. Load scenaro 5..3 Three leg converers Ths secon deals wh he basc heory of hree leg power elecronc converers. For hs projec, as wll be shown laer, he choce has fallen on he use of a four leg converer. Though, for a sar, he hree leg converer s examned o demonsrae heory, funcon and properes of hree phase converers..3.1 The hree leg brdge The prncples for he physcal layou of hree phase converers, also known as volage-source converers VSC:s are shown n fg..3-1. The brdge s conneced o he DC-lnk, whose volage s raw maeral n he creaon of he hree-phase oupu volage. The lnk volage s from now on called dc-lnk. The md poenal of he dc-lnk s defned as neural. V DC va vb v c LOAD V DC Fgure.3-1.Three-phase converer nework. Beween he wo poles of he dc lnk, he hree half-brdges are conneced. Each half-brdge has wo power elecronc swches. By swchng hem, beween fully conducng and fully blockng, he poenals of each half-brdge v a, v b, v c, wh respec o he md poenal of he dc lnk, can aan ± /. V DC The swch saes are denoed a, b, c. Wh, for example he sae a, b, c = +,-,- lke n fg..3- a v a = V / and v b = v c = - V /. DC DC 4
If he poenals v a, v b, v c = V /, -V /, -V /, lke n he example DC DC above, are ransformed o a vecor n α - β -coordnaes accordng o eq..1.13, DC wll aan he value: VDC vα =, v β = as n fg..3- b 3 The swch sae a, b, c can aan he saes +,-,-, +,+,-, -,+,-, -,+,+, -,-,+ and +,-,+, who are creang he sx possble acve values of he volage vecor, and +,+,+ and -,-,-, who are creang he zero-vecors, n he α - β -coordnaes accordng o fg..3-b. Accordng o eq..1.13, he oupu volage vecor v n he α - β -plane can herefore only aan he followng values: v v α β V =, ± 3 DC V = ± DC, 3 V, ± 3 DC Equaon.3.1 The maxmum modulus of he volage vecor s: v VDC = Equaon.3. 3 The resulng vecor dagram s shown n fg..3-b. β V DC -,+,- +,+,- V DC v a v b v c LOAD -,+,+ V DC +,-,- 3 -,-,- +,+,+ α Fgure.3-a. The hree phase converer swchng nework. -,-,+ +,-,+ Fgure.3-b. The aanable volage vecors. 5
By combnng he egh possble swchng saes, ncludng he zero vecors, usng pulse wdh modulaon descrbed below, any volage vecor whn he hexagon n fg..3-b can be generaed n average. However, here s an even gher lmaon for he volage vecor o acheve a lnear modulaon, namely he crcle ha ouches he nner sdes of he hexagon. The crcle has a radus of 3 mes he maxmum modulus of he volage vecor. Crcle radus = V base = v 3 = V 3 Equaon.3.3 max DC The radus of he crcle s denoed V base whch s furher referred o n he secon below. v ref s he desred value of he mean volage vecor..3. Pulse-wdh modulaon Pulse-wdh modulaon s a way of choosng he sequence of he swch-saes above so ha he mean value v mean, becomes he desred v ref. Referrng o fg..3-3 he average value can be expressed as: v mean 1 T [ V + V ] = + base base Equaon.3.4 Where T s he swch-perod and + and - are he perods when he swches, n he curren half brdge, are connecng he phase o V base or -V base respecvely. For example: If + = T, hen v mean = V base ; f + = - = T/, hen v mean = and f + =, v mean = -V base. The resulng volage waveform s pulse-wdh modulaed and hs operaon of he nverer s called pulse-wdh modulaon PWM. See fg..3-3. v V base V base + Fgure.3-3. Pulse-wdh modulaed waveform and mean value. The classcal mehod o generae approprae swchng sgnals from he reference sgnal v ref, s he rangle wave comparson mehod. The dea s o compare v ref o a 6
rangular carrer sgnal of amplude V base. When v ref s larger han he carrer, he poenal of he curren half-brdge s se o V base, and oherwse o -V base. Ths s llusraed n fg..3-4. The only dfference compared o fg..3-3 s ha he swchngs are made whn he perod < < T and no a he begnnng and end of he perod. v V base V base V ref T/ T V base v + V base Fgure.3-4.Trangle comparson mehod. As menoned above, V base was orgnally se o V base = V DC 3 o acheve a lnear modulaon. I s proven o be an unreachable volage wh a snusodal reference volage, snce only he poenals ± / are avalable for he poenals delvered V DC from each half-brdge, wh respec o he dc-lnk defned neural. Bu, f V base nsead s seleced o V DC /, s no possble o ulze all of he avalable dc lnk volage, as shown below. Snce he lne o lne volage s equal o he lne o neural volage mes 3, U U 3, he maxmum lne o lne volage from he converer wll be see ab = an fg. 6a, b, c: U V = 3 = V 3. 87 V DC max_ phase phase DC DC Equaon.3.5 Snce he converer, as laer wll be seen, wll need o delver as much volage as possble, hs s a drawback. 7
Phase reference poenal Phase reference poenal 5 V D C / -V D C / -5 5-5.1..3.4 Lne o lne reference volage V D C 5 5.1..3.4 Lne o lne reference volage -5-5 V D C.1..3.4.1..3.4 Fgure.3-5a. Phase reference poenal and lne o lne reference volage, compared o avalable dc lnk volage when V base =V DC sq. /sq.roo3 Fgure.3-5b. Phase reference poenal and lne o lne reference volage, compared o avalable dc lnk volage when V base =V DC /. V β V α V DC V DC 3 Fgure.3-5c. V base =V DC / and V base =V DC / sq.roo3 A way o acheve full ulzaon of he dc lnk volage, and sll have a lnear modulaon, s o allow some movemens of he neural pon. Ths mehod s called he Symmerzed rangle wave comparson mehod. 8
.3.3 Symmerzed modulaon If he same devaon s added or subraced from all reference sgnals v a, v b, v c, a zero-sequence s added. The volage vecor v n he α - β -plane s by ha no alered. By sudyng he hree snusodal phase poenal waves as a group, one can see ha hey are movng n an unsymmercal way compared o he cener of he rangular wave. For example, when v a reaches s maxmum value, v b and v c are a half of her mnmum values See fg..3-6a. The key o exend he modulaon range s o selec so ha: max v a ', v b ', v ' = mn v ', v ', v '. Equaon.3.6 c a b c Ths mples selecng: max v a, vb, vc + mn va, vb, vc = Equaon.3.7 and a b c a b c v ', v ', v ' = v, v, v Equaon.3.8 where v ', v ', v ' are he symmerzed phase volage references see fg..3-6b a b c 9
Snusodal modulaon Symmerzed modulaon V D C / 5 5 -V D C / -5-5.5.1.15. Fgure.3-6a.Snusodal modulaon. Phase and neural reference poenals..5.1.15. Fgure.3-6b. Symmerzed modulaon. Phase reference poenals and zero sequence devaon dela. By dong hs, one can see ha he amplude of he symmerzed phase poenal references fg..3-6b, compared o he cener of he rangular wave, s less han n he snusodal case.3-6a. Ths makes possble o ncrease he amplude of he lne o neural reference volage by a facor 3 and o selec V = 3, sll usng he maxmum phase poenals ±. base V DC V DC Snce he lne o lne volage s U ab = 3 U, he maxmum lne o lne volage an wll by hs mehod reach be ulzed: 3 V 3 = V, and all of he dc lnk volage may DC DC U = V max_ phase phase DC Equaon.3.9 The lne o lne volages wll no be affeced by he movemens n he neural pon. Only he phase poenals and he poenal of he neural, wh respec o he dc lnk defned neural pon, s alered..3.4 Overmodulaon Usng he symmerzed modulaon mehod s possble, under lnear modulaon, o reach V DC as he maxmum lne o lne volage amplude and VDC 3 as he maxmum lne o neural volage amplude. The lm for reachable oupu volages 3
s hereby se by he dc lnk. If he reference volage vecor v ref reaches ousde he lm se by he crcle radus = VDC 3 nsde he hexagon n fg..3-7a, he PWM goes no overmodulaon. Then he oupu volage vecor wll follow he reference vecor when he reference vecor s nsde he hexagon and he hexagon when he reference vecor s ousde he hexagon fg. 8b. In he followng smulaons, hs wll be avoded by lmng he reference sgnal o he lnear modulaon area: VDC v ref Vbase = Equaon.3.1 3 Vβ Vβ V α V α V base Fgure.3-7a. Lm for overmodulaon. Fgure.3-7b Oupu volage durng overmodulaon..3.5 Unbalanced condons Accordng o he assumpon ha he load conneced o he converer s balanced, he reference volage vecor wll follow a crcular rajecory n he α - β -plane. The defnon n eq..3.1 for he dc lnk volage may hen be suffcen for conrol see fg..3-8a. Durng balanced load condons, he reference volage vecor wll only conss of he posve sequence componen menoned earler n secon.1.6. Durng unbalanced load however, a negave sequence componen wll be added o he reference volage vecor as well. Ths combnaon of posve and negave sequence volages wll gve he rajecory of he reference volage vecor he shape of an ellpse see fg..3-8b. To be able o conrol he negave sequence reference 31
volage as well as he posve, he major radus of he ellpse mus be confned whn he nscrbed crcle of he hexagon, wh he radus V base. VDC v ref _ pos. seq + vref _ neg. seq Vbase = Equaon.3.11 3 The mnmum dc lnk volage n he unbalanced case depends on he degree of unbalance of he load. However, a hgher dc lnk volage wll lead o a hgher ably of he converer o conrol he oupu volage. Ths may be even more mporan f he load s unbalanced. β β V DC 3 α V DC 3 α Fgure.3-8a.Volage reference vecor rajecory under balanced condons. Fgure.3-8b.Volage reference vecor rajecory under unbalanced condons..3.6 The creaon of a neural connecon For a hree-phase hree-wre sysem, due o he opology, he sum of he hree phase currens are zero and he volage n he neural pon s floang. Durng balanced load condon hs s no a problem. Snce he poenal n he neural pon durng balance always wll be zero, he load volages can be correcly conrolled. Durng unbalanced load condons however, he lne o neural oupu volages wll unavodable become unbalanced as well snce he volage n he neural pon canno be conrolled separaely. The conrol arge of balanced hree-phase volages conradcs wh he fac ha he zero-sequence curren canno exs []. Only he posve and negave sequence curren exss n he sysem. In order o make he conrol arge possble, a neural conducor mus be provded so ha he zero sequence curren can flow hrough. For a hree-phase four-wre sysem here s a neural connecon ha provdes curren o flow from he neural pon of he load. Here he sum of he hree phase currens and he neural curren 3
are zero and he volage n he neural pon may be defned. In hs sysem boh posve, negave and zero sequence exss. Passve mehods There are passve mehods o provde he neural connecon for unbalanced loads []: Transformer The Υ ransformer s a zero sequence rap. Connecng he wndngs o he nverer and he Y wndngs o he load, he zero sequence curren caused by he load s rapped no he wndngs. Crculang whn he ransformer wndng, s prevened from ravelng back o he nverer and he dc lnk. Anoher passve way o provde he neural connecon s o use a zg-zag ransformer, whch also balances he load o some exen. The zero sequence currens from each phase are shfed a dfferen phase angles, and hus can be canceled wh each oher. The problem wh he approaches menoned above, s ha hey add he ransformer o he converer. Transformers for hgh power are very bulky componens. Spl dc lnk capacor Anoher passve approach o provde a neural connecon s o use wo capacors o spl he dc lnk and connec he neural pon o he md-pon of he wo capacors see fg..3-9. V DC va vb v c V DC Z 1 Z Z3 Fgure.3-9. Spl dc lnk capacor o provde he neural pon. There are wo problems wh hs approach. Frsly, he neural pon wll be fxed o he mddle of he dc lnk, whch wll cause poor ulzaon of he dc lnk volage. The movaon for hs s n secon.3., eq..3.5. Secondly, a huge ncrease of he capacance s needed o manan he dc lnk volage rpple a a reasonable level []. 33
The rpple wll conss of wo frequences, ω andω. The ω rpple s caused by he negave sequence load curren and he ω rpple s caused by he zero sequence load curren. The rpple caused by he negave sequence curren wll occur under unbalanced condons n any case. The rpple caused by he zero sequence curren on he oher hand, s drecly caused by he connecon of he neural conducor o he spl dc lnk capacor. See Appendx A for calculaons of capacor sze. A fourh leg By replacng he hree leg swchng nework n fg..3-1 wh a four leg swchng nework, as shown n fg. X1, a four half-brdge power elecronc converer s obaned. By yng he neural connecon of he load o he md pon of he fourh half-brdge, he four-legged PWM converer can handle he neural curren caused by an unbalanced load. A balanced oupu volage can be acheved wh a ghly regulaed neural pon. The mehod should, compared o he above menoned approaches, have he advanages of: 1. Possbly for hgh ulzaon of he dc lnk volage.. No bulky ransformers / much smaller dc lnk capacors. Dsadvanages are ha one more swch par and one more oupu fler nducor are added o he desgn. Ths approach seems o be he mos preferable and s he one chosen for he projec. From now on, when a converer s menoned, refers o a four leg converer f nohng else s menoned..4 The four legged converer The choce s made o use a converer wh a fourh half-brdge o oban he neural connecon. Ths converer has much n common wh he regular hree-phase converer. Wh he fourh half-brdge, he possbly o connec he neural s acheved as well. By hs a hrd degree of freedom s added. Insead of usng he α - β coordnaes, one have o add ye anoher dmenson and work n he α - β - γ -coordnae sysem. 34
.4.1 The four leg brdge The layou of a four legged hree phase converer s shown n fg..4-1. V DC vo va vb v c V DC Z Z 1 Z3 Fgure.4-1. Four-legged converer nework. Each half-brdge has wo power elecronc swches. By swchng hem beween fully conducng and fully blockng, he poenals of each half-brdge v a, v b, v c, v n can all aan ± /, wh respec o he neural pon defned as he md V DC poenal of he dc lnk. Ths means ha he volages v an, v bn, v cn, can aan ±. VDC The swch saes are now denoed a, b, c, n, see fg..4-. Compared o he 8 swch saes n he hree half-brdge case, he converer wh four half-brdges can aan 16 swch saes. Snce a hrd degree of freedom s added wh he neural half-brdge and s possbly of a neural curren, he α - β -coordnae sysem needs an exenson o he α - β -γ -coordnae sysem. If he oupu volage componens v an, v bn, v cn, accordng o he 16 possble swch saes of a, b, c, n, are ransformed usng eq..1.17 no a oupu volage vecor v n he α - β -γ -coordnaes, can aan he followng values: v v v α β γ V =, ± 3 DC V, ± 3 V = ± DC, 3 VDC V =, ±, ± 3 3 DC DC Equaon.4.1 35
The resulng vecor dagram conanng all aanable vecors s shown n fg..4-3. V DC v a v o v b v c V DC Z Z 1 Z3 Fgure.4-.The four legged converer swchng nework. Fgure.4-3. The oupu volage vecors n alfa-bea-gamma coordnaes. By combnng he 16 possble swchng saes, usng pulse wdh modulaon, any volage vecor whn he polygon n fg..4-4 can be generaed n average. Compare hs wh he hexagon n he hree half-brdge converer case. 36
Fgure.4-4. The polygon lmng he oupu volage vecor reference volage vecor n he four leg converer case..4. Over modulaon The phenomenon s smlar o he case wh a hree leg converer. If he reference volage vecor v ref reaches ousde he lm se by he polygon n fg..4-4, he PWM goes no overmodulaon. The oupu volage vecor wll hen follow he reference vecor when he reference vecor s nsde he polygon and he surface of he polygon when he reference vecor s ousde he sphere..4.3 Unbalanced condons Durng balanced load condons, he reference volage wll only conss of he posve sequence componen menoned earler n.1.6. I wll herefore follow a crcular rajecory n he α - β -plane see fg..4-5a. Durng unbalanced load however, he reference volage wll no only conss of he posve sequence componen, bu boh negave and zero sequence componens may be added as well. The combnaon of posve, negave and zero sequence volages wll gve he rajecory of he reference volage vecor he shape of a skewed ellpse see fg..4-5b. 37
Fgure.4-5a. The reference volage vecor rajecory durng balance and he polygon lmng he reference volage vecor n he four leg converer case. Fgure.4-5b.The reference volage vecor rajecory durng unbalance and he polygon lmng he reference volage vecor n he four leg converer case. To be able o creae boh he posve, negave and zero sequences of he reference volage vecor, he major radus of he ellpse mus be confned whn he polygon, accordng o fg..4-5b. Obvous, a hgher dc lnk volage wll lead o a hgher ably of he converer o conrol he oupu volage. Ths may be especally mporan durng unbalanced load condons..5 Crcu model of he sysem The followng secon deals wh he sysem n overall. The sysem consss of he fler nducors, he fler capacors, he load, and he conrol volage sources, whch are he volages from he converer. The model assumes ha he swchng frequency s very hgh compared o he fundamenal frequency, so ha volage and curren rpple are neglgble. In hs way he swchng model can be approxmaed as an average crcu model. The sysem s frs modeled as he real sysem n a-b-c coordnaes. Then he model s ransformed, for conrol-purposes, o he correspondng sysem n d-q--coordnaes. 38
.5.1 The sysem n abc-coordnaes The average crcu model of he sysem s modeled accordng o fg..5-1. v an a L a _ load V DC v bn v cn b c L L v b _ load v c _ load b _ load c _ load v n C C C n L n Fgure.5-1. The average crcu model n a-b-c-coordnaes. Assumng he dc lnk volage o be an deal volage source V DC, he conrol volage sources v, v, v can be expressed as: an bn cn v v v an bn cn v = v v a b c v v v n n n = V DC d d d an bn cn Equaon.5.1 an bn cn d, d, d are he phase o neural duy raos of he converer. The dfferenal equaons descrbng he sysem are expressed as: d d a b c = L n L d d n n n V + L DC d d d an bn cn v 1 v L v a _ load b _ load c _ load Equaon.5. + + = Equaon.5.3 a + b c n d d v v v a _ load b _ load c _ load 1 = C a b c a _ load b _ load c _ load Equaon.5.4 39
Where,, are he nducor currens he converer currens, a b c a _ load b _ load c _ load v, v, v are he oupu capacor volages he load volages and,, are he load currens. a _ load b _ load c _ load I can be seen ha he sysem s a second order sysem wh V T DC d an, d bn, d cn as he npu sgnals, he nducor currens a, b, c, as saes and he capacor volages v, v, v as saes as well as oupu sgnals. a _ load b _ load c _ load The phase load currens wll n urn depend on he oupu capacor volages and he load mpedances as: a _ load b _ load c _ load v = v v a _ load b _ load c _ load [ Z Z Z ] a b c Equaon.5.5 There are problems conrollng such a sysem. The seady sae soluons for all he varables are snusodal. Due o he me varyng naure of he model n a-bc-coordnaes, here s no DC operaon pon for he sysem. The conrollers for a sysem lke hs would have snusodal reference sgnals even a seady sae, whch would lead o consanly saonary errors n he oupu sgnals. The conrol mehods for a sysem lke hs would also suffer from poor performance due o conflcs among he hree phase conrollers []. To avod he problems above and acheve a DC operang pon a seady sae, he sysem s ransformed no he roang d-q--coordnae sysem.5. The sysem n d-q--coordnaes In secon.1.5 s shown how varables, represened n he a-b-c-coordnaes, are ransformed no represenaon n d-q--coordnaes. Ths s wha wll be done nex o he whole sysem descrbed n secon.5.1. [] 4
41 The sysems average crcu model n d-q--coordnaes can be obaned by applyng he coordnae ransformaon marx T 4 from secon.1.5 o boh sdes of eq..5. and eq..5.4. To make he ransformaons easer, he followng expressons may be used: = o n n n T 3 4 Equaon.5.6 d dx X d dt T d dx T dq dq abc 1 4 4 4 + = Equaon.5.7 and = 1 4 4 ω ω d dt T Equaon.5.8 By usng hem on equaon.5., and.5.4, he resulng crcu model n d-q--coordnaes s expressed accordng o: + + + = 3 1 1 1 3 1 1 1 d q q d n q d n DC q d v v v L L L L d d d L L L L V d d ω Equaon.5.9 and + = 1 _ d q load load q load d q d q d v v C v v v d d ω Equaon.5.1 Where,, q d s he nducor curren he converer curren,,, d d d q d s he duy raos of he converer,,, v v v q d s he oupu capacor volage
he load volage and,, s he load curren, now d _ load q _ load _ load expressed as vecors n he d-q--coordnaes. In d-q--coordnaes, he second order sysem has V d, d, d DC d q T as he npu sgnals, he nducor currens d d, d q, d, as saes and he capacor volages vd, vq, v as saes as well as oupu sgnals. The equvalen crcu model, expressed by eq..5.9 and eq..5.1 s shown n fg..5-. Noe he cross couplng erms beween d and q caused by he las erms n eq..5.9 and eq..5.1. d L ωl q d d d V dc ωcv q C vd load _ d q L ωl d V DC q d q V dc ωcv d C vq load _ q L + 3L n o d V dc C v load _ Fgure.5-.The average crcu model n d-q--coordnaes. If concern s aken o he equvalen seres ressances ESR:s n he nducors and capacors, hey should be modeled lke n fg..5-3 [7]. 4
d R L _ esr L ωl q d d d V dc ωcv q v q R C _ esr C load _ d q R L _ esr L ωl d V DC q d q V dc ωcv d v d R C _ esr C load _ q R L _ esr L + 3L n o d V dc R C _ esr v load _ C Fgure.5-3.The average crcu model n d-q--coordnaes, wh ESR:s. Ths s he model laer used n he conrol of he converer..6 Dmensonng Ths secon deals wh he choces concernng: Dc lnk volage, swchng frequences and parameers of he componens n he sysem. For example how dfferen choces of componens affec he properes of he converer, wha rade offs have o be made beween dfferen characerscs, and some defne specfcaons and lmaons..6.1 Dc-lnk volage The selecon of dc lnk volage s a rade-off beween power swch volage sress and conrol margn for ransens and unbalanced load condons. I s of course also lmed, unless he use of some sep-up converer, by he avalable dc volage. Assumng balanced load condons and ha he waned lne o neural oupu volage s 3VAC, he volage reference vecor s needed o be a leas 3 35V. The dc lnk volage would hen, accordng o eq..3.1, need o be a leas 3 3 564V. There wll however be volage drops durng heavy load n he ESR:s parasc ressances n he 43
oupu flers. There s also a need for some conrol margn. A reasonable dc lnk volage would herefore be somehng lke 7-75 V. Under unbalanced condons however, accordng o eq..3.11 and fg..6-1, he demand on he dc lnk volage s hgher han n he balanced case. If he volage reference vecor reference exends ousde he crcle wh V base as radus, he converer has no possbly o correc all of he conrol error. β V 3 DC α Fgure.6-1.Example of volage reference vecor rajecory under unbalanced condons..6. Power elecronc swches The power elecronc swches of he converer need o, under a specfed maxmum operang emperaure, whsand he volages and curren appled o hem. They mus also, for conrol ssues, be able o swch a a ceran rae a reasonable losses. The choce has fallen on usng IGBT:s Isolaed Gae Bpolar Transsors. The IGBT:s compromses he ables of whsandng hgh volage and hgh curren densy, wh he possbly of shor swch nervals and low on-sae volage drop [5]. The volage he IGBT:s needs o whsand s he maxmal dc lnk volage. For commercal IGBT:s here are dfferen sandardzed volage levels. In hs case he volage levels 6V, 1V and 17V may be of neres. On he phase half brdges, he curren he IGBT:s has o whsand s he maxmal lne curren durng full load. Assumng a nomnal 3-phase load for he converer of S n, he nomnal lne curren I lne wll be: I lne S = 3 U n lne neural = S 3 U n lne lne Equaon.6.1 44
On he neural half brdge, he curren he IGBT has o whsand depends on boh he maxmal load and he assumed wors case of unbalanced load. Assumng balanced condon, no curren passes rough he neural half brdge. Assumng 33% zero sequence unbalance see secon.1.6, he curren rough he neural half brdge wll be equal o he raed per phase curren..6.3 Swchng frequency and converer losses The swchng frequency s a rade-off beween hermal losses and conrol bandwdh. From a conrol pon of vew, he swchng frequency should be seleced as hgh as possble. The hgher he frequency s, he more ofen he conrol sgnals can be updaed. The swchng frequency hereby has a drec connecon o he possble conrol bandwdh of he converer. The emperaure normally ses he lmaon for he swchng frequency when he hea, caused by he losses, no longer can be suffcenly removed by coolng devses. Anoher lmaon may be when he effcency of he converer s assumed o be oo low. In converers for hgh power, lke n hs case, mos probably coolng ssues wll be he lmng facor for he swchng frequency. Loss calculaons The calculaons of he losses are made for one half brdge of he converer see fg..6- IGBT1 dode1 IGBT dode Z Fgure.6- One half brdge of he converer. Fg..6-3 shows he fundamenal componens of he oupu volage and oupu curren for he half brdge. 45
û î Tn Fgure.6-3. Converer oupu volage blue and curren red. The curren s dsplaced by an angle ph, relave he volage. The losses are of wo ypes: Frs, he losses durng he urn-on and urn-off saes of he semconducors, when here for a shor momen boh s a hgh volage across he semconducor and a hgh curren hrough. And second, he losses durng he conducng sae of he semconducors, due o he curren gong hrough and he forward volage drop of he semconducor. Turn-on, urn-off losses A mehod presened n [1] may be used o calculae he urn-on and urn-off losses. For he IGBT:s of one half-brdge,.e. one leg of he converer, he urnon and urn-off losses are esmaed as: P sw, IGBT E = on, n V 1 = T + E dc, n I E = π n Tn off, n n on, n V P dc, n on Vdc f T + E I off, n n + P n off sw V d = Tn dc I f f T sw sw n Tn E on + E off d = ˆ sn ω ϕ d = Equaon.6. Where T n s he perod me of he fundamenal frequency, P on and urn-on and urn-off power, P off are E on and E off urn-on and urn-off energy, E on, n and E off, n urn-on and urn-off energy a V dc, n and I n, gven by he daa shee for he IGBT. f sw s he swchng frequency, V dc he dc lnk volage, and I he curren hrough he IGBT. 46
In daa shees, E on and E off are gven a specfc values V dc, n and I n. The V erm V dc dc, n I I n compensaes for ha so he losses are gven a Vdc and I. The urn-on and urn-off losses for he freewheelng dodes of one half brdge, are calculaed n a smlar way. However, he losses for he freewheelng dodes may be approxmaed as he urn-off losses only. The urn-on losses for he dodes are small compared o he urn-off losses caused by he reverse recovery curren durng urn off. P sw, dode E V off, n dc, n I 1 = T n E = π V n Tn Vdc f T off, n dc, n I P n n sw on V + P Tn dc I off f sw d = f T sw n Tn E = π V E Drr, n dc, n on ˆ sn ω ϕ d = Equaon.6.3 I n + E V dc off I d = f sw Where E Drr, n s he reverse recovery energy a dc n V, and I n, gven by he daa shee for he dode. Conducon losses A mehod presened n [1] and [11] may be used o calculae he conducon losses for he half brdge. The calculaons are made for one IGBT and one freewheelng dode. To ge he losses for he whole half brdge, he resul s mulpled by wo. Frs he conducon losses of he IGBT are calculaed. To do ha he forward volage drop, V IGBT on, of he IGBT s needed. V IGBT on VIGBT, + RIGBT on = Equaon.6.4 V s he hreshold volage and R IGBT on s he on-sae ressance. Where IGBT, The duy cycle for IGBT 1 s gven by: 47
d IGBT1 1 uˆ sn ω + ϕ = + Equaon.6.5 V dc The conducon loss for IGBT1 becomes: P = V d Equaon.6.6 cond, IGBT1 IGBT on IGBT1 To calculae he average losses P cond, IGBT, P cond, IGBT n eq..6.6 s negraed over a half perod and dvded by he whole perod me. Ths s because IGBT1 s only conducng half of he perod,.e when he curren s posve. Tn 1 Pcond, IGBT = VIGBT on d T n IGBT1 d Equaon.6.7 Usng eq..6.4 and eq..6.5 resuls n: Tn u + V + R ˆ ˆ 1 ˆ sn ω sn ω sn ω + d 1 ϕ Pcond IGBT = IGBT IGBT on T n V,, dc Equaon.6.8 By solvng eq..6.8, he resul s: P cond, IGBT1 Equaon.6.9 ˆ ˆ ˆ VIGBT, RIGBT on uˆ ˆ = + + cos ϕ VIGBT, R + π 8 V dc 4 3π IGBT on The conducon losses for he freewheelng dode are calculaed n a smlar way: The forward volage for he dode s gven by: V dode on = Vdode, + Rdode on The duy cycle for dode dffers from IGBT1 and s gven by: 48
d dode = 1 d IGBT1 1 uˆ sn ω + ϕ = Vdc Equaon.6.1 The conducon loss for dode becomes: P = V d Equaon.6.11 cond, dode dode on dode and he average losses: 1 Pcond, dode = Vdode on d T n Tn dode d Equaon.6.1 Wh he same calculaons as for he IGBT hs resuls n: P cond, dode Equaon.6.13 ˆ ˆ ˆ Vdode, Rdode on uˆ ˆ = + cos ϕ Vdode, R + π 8 V dc 4 3π dode on As menoned before, he calculaons of he conducon losses above only concerns one of he IGBTs and one of he dodes n he half brdge. To ge he oal conducon losses for he half brdge, he resuls mus be mulpled by wo. Smulaed connues converer losses The mehods descrbed above for calculaons of he losses are only usable durng seady sae and wh snusodal oupu volages and currens. Therefore, anoher mehod s used n he smulaons of he converer. The mehods above were however used o verfy he resuls from he mehod below. The losses are calculaed n real me from volages and currens acheved n he smulaons. To clarfy he calculaons n eq..5.14 -.6.5, fg..6-4 shows a shor sequence of he oupu volage and he currens n IGBT1 and dode durng operaon. 49
Oupu volage Oupu curren T s Curren IGBT1 Curren dode n+1 n+ Fgure.6-4. Oupu volage and currens n IGBT1 and dode durng operaon. Durng a swchng nerval T sw, followng calculaons are made: A n, urn-on loss energy of IGBT1 and urn-off loss energy of dode: E on _ IGBT1 V dc = Eon, n _ IGBT1 Equaon.6.14 Vdc, n I n E off _ dode V dc = Eoff, n _ dode Equaon.6.15 Vdc, n I n A n+1, urn-off loss energy of IGBT1 and urn-on loss energy of dode: E off _ IGBT1 V dc = Eoff, n _ IGBT1 Equaon.6.16 Vdc, n I n E on _ dode V dc = Eon, n _ dode Equaon.6.17 Vdc, n I n A n+1, conducon loss energy of IGBT1: 5
V IGBT on VIGBT, + RIGBT on = Equaon.6.18 n + n+ 1 = Equaon.6.19 E cond, IGBT1 n 1 n = V IGBT on + Equaon.6. A n+, conducon loss energy of dode: V dode on Vdode, + Rdode on = Equaon.6.1 n+ 1 + n+ = Equaon.6. E V dode on 1 Equaon.6.3 cond, dode = n+ n+ A n+, oal loss durng swchng perod: The connuous power loss. P loss = E Equaon.6.4 on, IGBT1 + Eon, dode + Eoff, IGBT1 + Eoff, dode + Econd, IGBT1 + T sw E cond, dode And he average power loss, durng a specfed me perod T. T 1 P loss = Ploss d T Equaon.6.5 Appendx D conans he m-fle performng he loss calculaons for he smulaed converer. 51
.6.4 Fler componens The swchng causes harmoncs. The harmonc conen n he nducor currens and he oupu volages are of wo ypes: Dfferenal mode DM harmoncs, n a b c,, and u, u, u, and common mode harmoncs CM, n u,,, n a b c ab bc ca and n. The DM harmoncs n he lne nducor currens,, are aenuaed by L. a b c The CM harmoncs n he lne- and neural nducor currens,, and n are aenuaed by L + 3Ln. a b c L and C forms a nd order low pass fler ha aenuaes he DM harmoncs n he oupu volages u ab, ubc, uca. L + 3Ln and C forms a nd order low pass fler ha aenuaes he CM harmoncs n u n. The oal harmonc conens n he nducor currens,, and n, and he a b c lne o neural oupu volages u, u, u are calculaed by addng he DM an bn cn and CM harmonc specra. Ths s no rval and for he followng smulaed model of he converer he fler componens are dmensoned based of resuls acheved n smulaons..6.5 Dc lnk capacor The desgn mehod s reaed n Appendx A. The negave sequence load curren s he lmng desgn consran of he dc lnk capacor. Eq. A.5 n Appendx A may hereby be used n dmensonng he dc lnk capacor..6.6 Dmensonng man componens of he converer n he projec Specfcaons Oupu volage: 3*3/4V Oupu frequency: 5Hz Nomnal power: 5kVA 5
Oupu maxmum per phase power: 5 3 kva Load power facor:. - 1 Max emperaure coolng waer IGBT-modules: 7 C Swchng frequency: 5kHz Max dc-lnk volage: 75V. Power elecronc swches, phase half brdges The swch modules needs o whsand he volages and currens appled o hem. Wh waer coolng of he modules and a maxmal waer emperaure of 7 C, he juncon emperaure of he modules s assumed o always be below 1 C. Snce he DC-lnk volage s 75V, 1V IGBT-modules are needed. The maxmal lne curren s gven by eq..6.1 Or he load scenaros n secon.. Wh S n = 5kVA and U = V 7.A 1A peak value. lne neural 3, he maxmal curren s IGBT-module, Semkron SKM GB13D, fulflls he requremens and s proposed for he projec. Power elecronc swches, neural half brdge Excep from he curren level, he condons for he swches of he neural half brdge are he same as for he swches of he phase half brdges. The maxmal curren however, s dfferen. Load scenaro 5, n secon., covers he wors scenaro for he neural half brdge whn he specfcaon above. The curren hrough he neural s hen 134A 19A peak value. IGBT-module, Semkron SKM 3GB14D, fulflls he requremens and s proposed for he projec. LC-fler componens The dmensonng of he fler componens are based on resuls acheved n smulaons. Followng fler componens provded a lne-o-neural load volage rpple of.6%, a lne-nducor curren rpple of 6 power, and a neural-nducor curren rpple of 9 A. p p Ap p 3% a nomnal 53
C=33.8µF L=3mH Ln=1.5mH The capacors needs o whsand he volage appled o hem. In hs case, 3V a 5 Hz. Accordng o Hägglunds, long lfe me s mporan. Polypropylene flm ype capacors are herefore o prefer before elecrolyc capacors. Capacor, Epcos B33-C1356 35µF, fulflls he requremens and s proposed for he projec. The nducors need o whsand he curren hrough hem. The maxmal curren hrough he lne nducors, L, are 7.A a 5Hz. The maxmal curren hrough he neural nducor, Ln, s 134A a 5Hz. Inducors, cusom made by Tramo ETV AB, are proposed for he projec. DC-lnk capacor When desgnng he DC-lnk capacor, concern has o be aken o he global demands of he dc-lnk volage of he vehcle as well as he dc-lnk capacance n he whole sysem. Hägglunds do no see hs area as whn he scope of hs hess. However, he mehod descrbed n Appendx A may be used for he desgn. The capacor needs o whsand he appled volage, n hs case 75V DC. Accordng o Hägglunds, long lfe me s mporan. The lfe me s largely dependng of he currens fundamenal and harmoncs ha wll flow hrough he capacor bank. Ths aspec s however no evaluaed..7 Conrol of he sysem Ths secon deals wh ssues concernng he conrol of he converer. The ulmae goal s o acheve a sable, balanced hree-phase volage, ndependen of he load condons specfed n secon.. Brough up subjecs are for 54
example: PI-conrollers, delays, feedback conrol n cascade, decouplng and feed-forward conrol..7.1 Model of he sysem o conrol The sysem whch s he arge of he conrol, s he one descrbed n secon.5. and fg..5-3. The sysem s represened n he roang d-q--coordnae sysem. From secon.6, he values of he componens are known as well. Fg..7-1 shows he sysem, now represened as a block schemac and expressed n Laplace. d _ load d d V DC R 1 L _ esr + sl d R 1 C _ esr + sc v d ωl ωc ωl ωc d q V DC R 1 L _ esr + sl q R 1 C _ esr + sc v q q _ load d V DC 1 R + 3L + s L+ 3L L n n o R 1 C _ esr + vo sc o _ load Fgure.7-1.The sysem o conrol represened as a block schemac. 55
.7. Delays The conrol of he sysem wll n a real converer be made dgal. Due o he dgal mplemenaon here wll be delays nroduced n he conrol-loops. The ransducer sgnals are low pass flered and sampled and he dgal sgnal processor wll need me o calculae he new conrol sgnals. Accordng o secon 5., he flerng, samplng, and calculaon me wll lead o a delay n he conrol sgnals of 1,4 sample perods. The delay s modeled as a dead me n he block schemac of he crcu model n fg..7-..7.3 Volage conrol As menoned before, he ulmae goal s o acheve a sable, balanced hreephase load volage, ndependen of he load condon. The load curren wll however affec he sysem, as can be seen n fg. 15, and s consdered as a dsurbance n he conrol consrans. The goal s o acheve he volage n each channel d, q and o follows s respecvely reference value, where d represens he reacve componen, q represens he acve componen and represens he zero componen of he oal volage vecor. Consderng he behavor of he conrol volage vecor durng unbalance descrbed n secon.1.6, dfferen properes consderng conrol bandwdh are preferred n he dfferen channels. Durng balanced condons only posve sequence exss. In d-q--coordnaes a posve sequence wll appear as a pure DC componen n he d-, q- and -channels. Durng unbalance however, negave- and zero sequence exs as well. See secon.1.5 and.1.6. The zero sequence causes, n he d-q--sysem, an addon of a snusodal componen, wh he fundamenal frequency, o he -channel. The negave sequence causes, n he d-q--sysem, an addon of a snusodal componen, wh wce he fundamenal frequency, o he d- and q-channels. Snce hese snusodal componens are caused by errors, who he conrol volage vecor s supposed o suppress, he conrollers mus be able o respond 56
o hem. Because of hs, s apprecaed o have a conrol bandwdh way above 5 Hz n he o-channel and 1 Hz n he d- and q-channels..7.4 Conrol mehods To smplfy he explanaons of he conrol mehods, frs only one of he channels channel d, s examned. Wh he cross couplng erms and load dsurbances foreseen a he momen doed lnes, fg..7- shows how a sngle loop volage conrol could be mplemened n he sysem. v d * G s d d V DC std e 1 R sl L _ esr + d R sc 1 C _ esr + v d Fgure.7-.Channel d of he sysem black, ncludng he conroller red. Sngle loop conrol [4],[6] The sysem s, as descrbed n secon.5, a second order sysem, wh he nducor curren and he capacor volage as saes. The converer oupu volage, d V whch s he conrol sgnal for he oal channel d sysem, d DC affecs he nducor curren d, whch n urn affecs he capacor volage v d, whch s he oupu sgnal. If, as n fg..7-, only he capacor volage sae s measured and used for conrol, he closed loop ransfer funcon for he sysem wh he delay block foreseen and he conroller Gs as a proporonal conroller wh gan K wll be: H CL v s = v d * d s = s s C R L _ esr K1 + s C R C _ esr + s L + K1 + s C R C _ esr Equaon.7.1 57
Snce R C _ esr and L esr R _ are small, he poles of hs sysem are boh close o he magnary axs and by ha he sysem s close o unsable. If R _ and C esr R _ approaches zero, s approaches: L esr H CL H CL vd s K s = = Equaon.7. * v s s C L + K d Where he poles of he sysem boh are on he magnary axs. Wh a purely proporonal P or a proporonal and negral conroller PI hs sysem s hard o sablze he bandwdh wll be low. To acheve sably, he conroller needs a dervave par D. A dervave conroller however, s sensve o dsurbances and nose. Snce he capacor volage mos ceranly conans nose and rpple, he dervaon of hs s rcky. There s a way around hs problem. To dervae he capacor volage s acually he same hng as measurng he curren hrough he capacor. If he load curren, whch s seen as a dsurbance and s deal wh by feed forward conrol explaned below s foreseen, he curren rough he capacor s he same as he curren rough he nducor. Therefore, as an alernave o he dervave conroller, he nducor curren, whch s he oher sae n he sysem, may be measured and conrolled as well as he capacor volage above. By ha a sae feedback conrol from he wo saes nducor curren and capacor volage s acheved, and P or PI conrollers wll be adequae [4]. Cascade conrol [6] A generalzaon of he mehod menoned above, ofen used when here are dfferen mescales n a sysem, s he cascade conrol. Cascade conrol means ha wo conrol loops, wh dfferen bandwdh, are used o conrol he sysem. The nner loop needs o be much faser han he slower ouer loop. The nner loop should, from an ouer loop pon of vew, reac nsanly See fg..7-3. 58
vd * s d * G v G C s d V d DC std e 1 R L _ esr + sl d 1 R C _ esr + sc v d Fgure.7-3. Channel d of he sysem black, ncludng he feedback conrollers red conneced n cascade. The nducor curren conroller, whch provdes he converer volage reference d d V DC drecly as conrol sgnal, can reac quckly. Because of hs, he nducor curren conrol loop should be he nner loop. The capacor volage conrol, whch uses he nducor curren as conrol sgnal and by ha only ndrecly s conrolled by d V, should be he ouer loop and mus, d DC compared o he curren loop, reac slower. In hs way, when he ouer volage conrol loop senses an error n he oupu volage, he volage loop changes he reference value for he nner curren loop, whch wh d V quckly ses he nducor curren o a value ha d DC correcs he oupu volage. By usng dfferen bandwdh n he wo conrol loops, hey can be reaed as wo ndependen loops durng desgn and by ha smplfy he conrol desgn sgnfcanly. Ideally, he curren loop sees he volage loop as saonary very slow reacon and he volage loop sees he curren loop as perfec curren source very fas reacon. The dfference n bandwdh beween he loops should preferably be a leas one decade. Curren loop When desgnng he nducor curren conroller, followng smplfcaon of he sysem, seen by he conroller, can be made See fg..7-4. d * d d V DC G C s s std e H C d Fgure.7-4.Smplfed curren loop of channel d. The sysem as he curren conroller sees black and he conroller red. 59
6 The sysem may hen be descrbed as [6]: esr L esr L T s esr L T s c T s o c R L s R e L s R e s H e s H d d d 1 1 1 + = + = = Equaon.7.3 Where he delay T d s caused by he lowpass fler, he dgal conrol and he PWM. By usng a PI conroller: P c Tc s Tc s Kc s G + = 1 Equaon.7.4 Where Kc P s he proporonal par and Tc s he negral me of he PI conroller, he open loop ransfer funcon of he sysem ncludng conroller, wll be: esr L esr L T s P o c c R L s R e Tc s Tc s Kc s H s G d _ 1 1 1 + + =. Equaon.7.5 And he closed loop ransfer funcon for he sysem wll be: 1 _ s H s G s H s G s H o C C o C C CL C + = Equaon.7.6 By unng he values of Kc P and Tc unl he phase margn for he open loop ransfer funcon s abou 5 degrees and he sep response for he closed loop ransfer funcon looks nce, he curren conroller can be consdered uned. Ths s preferably done by smulang he sysem above wh Malab Conrol Toolbox, unl he resul s sasfyng.
Volage loop When desgnng he capacor volage conroller, he followng smplfcaon of he sysem, seen by he conroller, s made See fg..7-5. The curren loop s here modeled as he dynamc of he closed loop ransfer funcon of he curren loop above. v d * * G v s d H d C _ CL H v s v d Fgure.7-5 Smplfed volage loop of channel d. The sysem as he volage conroller sees black and he conroller red. The sysem may hen be descrbed as: H v _ o s = H C _ CL s H s = H v C _ CL s R C _ esr 1 + = H s C C _ CL 1+ s RC _ s s C esr C Equaon.7.7 By usng a PI conroller: G s Kv 1+ s Tv v = P Equaon.7.8 s Tv Where Kv P s he proporonal par and Tv s he negral me of he PI conroller, he open loop ransfer funcon of he sysem ncludng conroller, wll be: G s H v v _ o s = Kv P 1+ s Tv s Tv H C _ CL 1 + s RC _ s s C esr C Equaon.7.9 61
And he closed loop ransfer funcon for he sysem wll be: H v _ CL Gv s H v _ o s s = Equaon.7.1 1 + G s H s v v _ o By unng he values of Kv P and Tv unl he phase margn for he open loop ransfer funcon s abou 5 degrees and he sep response for he closed loop ransfer funcon looks nce, he volage conroller can be consdered uned. As wh he curren conroller, hs s preferably done by smulang he sysem above wh Malab Conrol Toolbox, unl he resul s sasfyng. Compensaon of he dsurbance sgnals. Unl now, no concern has been aken o he dsurbance sgnals n he model caused by he capacor volages load volages, he load currens and he cross couplng erms see fg..7-6. Durng he desgn of he feedback conrollers, he dsurbance sgnals were assumed o be neuralzed by oher mehods. These mehods are now deal wh. d _ load vd * d * G v s d d V DC std G s e C s H C s H v V d ωlq ωcvq Fgure.7-6.Channel d of he sysem black, ncludng he dsurbance sgnals hghlghed and he feedback conrollers conneced n cascade red. Decouplng The mehod of reducng he nerconnecon beween he channels d and q s called decouplng. For smplcy, sll only channel d s suded. The conrol sysem n fg..7-6, s n fg..7-7 exended wh he decouplng conrol sgnal pahs. 6
v d * s std G v G C s H C s s e H v Vd ωc ωl ωlq ωcvq Fgure.7-7.Channel d of he sysem black, ncludng he feedback conrollers conneced n cascade red and he decouplng conrol sgnal pahs green. Referrng o fg..7-7, he nfluence of he cross couplng sgnals ω C v q _ load and ω L q, may be reduced by measurng and use he capacor volage v q and he nducor curren q from channel q. By mulply hem wh he known ω C and ω L and add he produc wh oppose sgn compared o he cross couplng erms o he conrol sgnals from he volage conroller and he curren conroller respecvely, he decouplng sgnals reduce he cross couplng erms. Feed forward conrol The mehod of reducng he mpacs from he load currens and he load volages capacor volages s called feed forward conrol. For smplcy, sll only channel d s suded. The conrol sysem n fg..7-7, s n fg..7-8 exended wh he feed forward conrol sgnal pahs. d _ load v * s d 1 1 G v G C s std H C s s e H v Vd ωc ωl ωlq ωcvq Fgure.7-8.Channel d of he sysem black, ncludng he feedback conrollers conneced n cascade red, he decouplng conrol sgnal pahs green and he feed forward conrol sgnal pahs purple. Referrng o fg..7-8, he nfluence of he load dsurbances n v q and q_load may be reduced by measurng and addng hem wh oppose sgn compared o he load dsurbance sgnals o he conrol sgnals from he volage 63
conroller and he curren conroller respecvely. The feed forward sgnals wll hen reduce he nfluence from he load dsurbances. Sensors To be able o use he conrol mehods menoned above, some measuremens of volages and currens n he converer are needed. How many sensors o use s a rade-off beween conrol possbles and coss. The mehods used above wll requre followng sgnals o be measured: The curren conrol loops: The nducor currens The volage conrol loops: The capacor volages The decouplngs: The nducor currens and he capacor volages. The feed forward conrols: The capacor volages and he load currens. For calculaons of he duy-cycles, he dc-lnk volage mus be measured as well. Snce he sysem s a four wre sysem, he measuremens needs o be done on all hree phases. So, o be able o use all mehods menoned above, hree nducor currens, hree capacor volages, hree load currens and he dc lnk volage need o be measured. In oal en sensors..7.5 Model of he sysem, ncludng conrollers and delays Now, when more s known of he oal sysem, ncludng all conrol mehods and delays, he earler schemac of he sysem n fg..7-1 can be exended o he schemac n fg..7-9. 64
1 ωc 1 ωl * v d v _ s G C _ d s H C _ d s H v_ d s G d e std V d ωl ωc ωl ωc * v q G v_ q s G C _ q s e std H C _ q s H v _ q s V q 1 ωc 1 ωl q _ load * v G v_ s _ s G C std e H C _ s H v _ s V 1 1 _load Fgure.7-9.The oal sysem o be conrolled black, ncludng he feedback conrollers conneced n cascade red, he decouplng conrol sgnal pahs green and he feed forward conrol sgnal pahs purple..7.6 Parameers of he conrollers By usng he mehods descrbed above and smulang he conrol loops one by one, followng suable parameers for he PI-conrollers are obaned: Channel d Channel q Channel Kc P 1 1 4 Tc...89 Kv P.75.75.11 Tv.47.47.47 Table.7-1. Parameers PI_conrollers. From smulaons, he bes resuls n response and sably are acheved wh followng feed forward- and decouplng erms: A facor 1 of he load volages n d, q and for he feed forward conrol. 65
A facor 1 of he converer currens n d and q for he calculaons of he decouplng erms. A facor.8 of he load currens n d, q and for he feed forward conrol. A facor.8 of he load volages n d and q for he calculaons of he decouplng erms. 66
3. Mehod The man objec for he projec s of cause o fnd ou how he converer mgh be expeced o work. Unl now, only basc heorecal ssues have been deal wh. Secon.1 covered he bascs for hree phase sysems and dfferen ways o represen hem. Secon. covered expeced load scenaros. Secon.3 and.4 covered he prncpals for hree and four legged converers. Secon.5 descrbed he hree-phase crcu model of he converer, ncludng fler and load, as well as he ransformaon of he whole sysem from a-b-c- o d-q-- coordnaes for conrol ssues. Secon.6 deal wh he dmensonng of dclnk volage, swches, swchng frequences and flers. Secon.7 covered he heory of suable conrol mehods for he converer. Fnally, s me o see wha hs heory mgh be used for n a smulaon model of he converer. Ths chaper deals wh he srucure of he model, wha he dfferen blocks does and he heory ha has been used buldng hem. 3.1 The smulnk model of he converer The model of he sysem see fg 3.1-1 s bul n Malab and Smulnk. These ools are user frendly, gve a nce graphcal presenaon of calculaons and sgnal roungs and are very useful for he purpose. Ths secon only covers he basc funcon of each block and he sgnals enerng and leavng he block. There are also references o where n he hess he heory of he block s covered. The blue colored blocks are smulang sofware mplemenaons, whle he orange colored blocks are smulang physcal hardware mplemenaons. Dealed layous of he model are presened n appendx B. 67
Fgure 3.1-1. Layou of he smulnk model. 68
Block 1. The phase-neural reference volages n channel d, q and are creaed here. See secon.1.5 and.1.6 for nformaon abou d-q--represenaon. Block. Ths block conans he volage conrollers for channel d, q and respecvely. Secon.7, and especally secon.7.4, gves nformaon abou he used conrol mehods. The volage conrollers are he ouer loop conrollers n he cascade conrol. The feedback conrollers are of PI-ype eq..7.8. They use he dfferences beween he reference volage sgnals from block 1 and he measured oupu volages from he converer, as npu sgnals error sgnals. The sgnals hey reurn works as he reference curren sgnals for he nner loop curren conrollers n he followng block 4. The block also conans he decouplng and load curren feed-forward funcons, whose sgnals are added o he sgnals from he volage PIconrollers. A funcon called an-wndup s negraed n he block as well. Wndup occurs when he conrol error remans for a longer me and he negral par of he PIconroller becomes very large. An-wndup pus a lm o he maxmal value of he sgnal conrbuon from he negral par of he PI-conroller. Block 3. Durng unng of he regulaor parameers of he curren conrollers he nner loop conrollers, s useful o dsconnec he ouer volage loop. Then he reference values for he currens n channel d, q and are provded here. Block 4. Ths block conans he curren conrollers for channel d, q and respecvely. Secon.7, and especally secon.7.4, gves nformaon abou he used conrol mehods. The curren conrollers are he nner loop conrollers n he cascade conrol. The feedback conrollers are of PI-ype eq..7.8. They use he dfferences 69
beween he reference curren sgnals from he volage conrollers n block and he measured converer currens, as npu sgnals error sgnals. The sgnals hey reurn works, afer some modfcaons, as he reference volage n he pulse wdh modulaon laer n block 8. The block also conans he decouplng and oupu volage feed-forward funcons, whose sgnals are added o he sgnals from he curren PIconrollers. The an-wndup funcon s negraed n hs block as well. See Block above. The fnal funcon of he block s a lmaon of he oupu sgnals. Snce he dc-lnk volage lms he aanable oupu volages here s no use n provdng he pulse wdh modulaor wh hgher reference volages. Block 5. Ths block ransforms he reference volage sgnals n channel d, q and o conrol volage sgnals for phase a, b and c secon.1.5, eq..1.1. The roang reference angle s aaned from block 17. Block 6. Ths block exracs he zero sequence componen from he reference volage sgnals of phase a, b and c See fg. 3.1-. The zero sequence componen s also recalculaed for symmerzed modulaon descrbed n secon.3.3, eq..3.3 -.3.6. 7
4 sgnals n - -4.6.6.64.66.68.7.7.74.76.78.8 4 sgnals ou - -4.6.6.64.66.68.7.7.74.76.78.8 Fgure 3.1-. Reference sgnals no above and ou of below block 6, symmerzaon. Block 7. Ths block smulaes he effecs of a dgal conrol see secon 5.1. The reference sgnals, whch unl here have been connuous, are sampled and delayed one sample perod See fg. 3.1-3. The delay s added because s assumed he dgal sgnal processor needs one sample perod o calculae he new reference sgnals. 4 sgnals afer samplng and delay - -4.7.71.7.73.74.75.76.77.78.79.8 Fgure 3.1-3. Reference sgnals ou of block 7, samplng and delay. 71
Block 8. The pulse-wdh modulaon PWM s performed here. The carrer wave he rangular wave s creaed and compared o he reference volages of phase a, b and c. The oupu sgnals are he swch sgnals duy cycles for he power elecronc swches. The sgnals are represened as pulse rans See fg. 3.1-4. Secon.3. covers he heory of he PWM. 4 PWM - -4.7.71.7.73.74.75.76.77.78.79.8 oupu sgnal 1-1 -.7.71.7.73.74.75.76.77.78.79.8 Fgure 3.1-4. Pulse wdh modulaon of phase a. Reference sgnal and carrer wave above, oupu sgnal o he power elecronc swches below. Block 9. Ths block smulaes he power elecronc swches. The npu sgnals are he pulse rans provded by block 8. The oupus v a, v b, v c, v n are volage pulses of ± V DC wh he duy-cycles provded from he npu sgnals see secon.3. and fg..5.1. Block 1. Ths block smulaes he :nd order LC-flers of he converer. The volage pulses provded from block 9 are flraed o acheve oupu volages and currens a he fundamenal frequency as well as wh low rpple. Secon.5.1 covers he crcu schemes fg..5-1 and equaons for he flers. The fler model s based on equaons.5.1-.5.4. 7
Fg. 3.1-5 and 3.1-6 shows examples of volages and currens n phase a of he fler durng a smulaon. Compare hem wh he crcu schemac n fg..5-1. v a 5-5.6.6.64.66.68.7.7.74.76.78.8 v n v -v a n u L u L n 5-5.6.6.64.66.68.7.7.74.76.78.8 5-5.6.6.64.66.68.7.7.74.76.78.8 5-5.6.6.64.66.68.7.7.74.76.78.8 5-5.6.6.64.66.68.7.7.74.76.78.8 5 v a - l o a d -5.6.6.64.66.68.7.7.74.76.78.8 Fgure 3.1-5. Volages n he LC-fler of he converer. From op o boom: v a, v n, v an, u L, u Ln,v a_load. 73
1 a -1.6.6.64.66.68.7.7.74.76.78.8 1 n -1.6.6.64.66.68.7.7.74.76.78.8 1 a - c a p -1.6.6.64.66.68.7.7.74.76.78.8 1 a - l o a d -1.6.6.64.66.68.7.7.74.76.78.8 Fgure 3.1-6. Currens n he LC-fler of he converer. From op o boom: a, n, a_cap, a_load. Block 11 and 1 Block 11 and 1 smulaes loads conneced o he converer. Block 11 s a - conneced load model and block 1 s a Y-conneced load model. They calculae he load currens correspondng o he volage appled o he load models. See secon.5.1 and eq..5.5 The loads may be made ressve, nducve, balanced or unbalanced, consan or varable n me as seps. 74
Block 13. These blocks low pass fler he sgnals measured for conrol purposes. The reason for he flers n a real converer s o avod alasng see secon 5.1. The reason for addng he flers o he model as well s ha hey, n a real converer, add some delay o he measured sgnals, whch may affec he conrol. The flers are modeled as :nd order Bessel flers wh cu-off frequences a half he swchng frequency. Block 14. Ths block ransforms he measured and flered converer currens a, b, c n fg.5-1 for phase a, b and c o d-q--coordnaes see secon.1.5, eq..1.. The converer currens are used for he feedback conrol of he nner curren loop see secon.7.4. Block 15. Ths block ransforms he measured and flered load volages v a_load, v b_load, v c_load n fg.5-1 for phase a, b and c o d-q--coordnaes see secon.1.5, eq..1.. The load volages are used for he feedback conrol of he ouer volage loop and he feed forward o he oupu of he curren conrollers see secon.7.4. Block 16. Ths block ransforms he measured and flered load curren a_load, b_load, c_load n fg.5-1 for phase a, b and c o d-q--coordnaes see secon.1.5, eq..1.. The load volages are used for he feed forward o he oupu of he volage conrollers see secon.7.4. Block 17. Ths block provdes he roang reference angle used n he coordnae ransformaons beween a-b-c- and d-q--coordnaes See fg. 3.1-7. p -p 4 - reference angle -4.1..3.4.5.6.7.8 Fgure 3.1-7. Reference angle for he creaon of he roang d-q--coordnae sysem. 75
3. Smulaons and ess The smulaons of he Smulnk model wll be based on he fve load scenaros specfed n secon. and he dmensonng of he componens made n secon.6.6. 3..1 Smulaed load scenaros The loads are all conneced lne o neural balanced or unbalanced Y- connecon. The load currens,, are shown n he crcu scheme of a _ load b _ load c _ load he converer n fg..5-1. The load mpedances Z, Z, Z are calculaed a b c from eq..5.5, where v, v, v are he deal lne o neural load volages. a _ load b _ load c _ load I a_load curren A/ I b_load curren A/ I c_load curren A/ Z a medance Z b medance Z c medance powerfacor powerfacor powerfacor Ω/ pf Ω/ pf Ω/ pf Scenaro 1 Before sep: A/ 1 A/ 1 A/ 1 Ω Ω Ω Afer sep: 7. A/ 1 7. A/ 1 7. A/ 1 3.17 Ω / 1 3.17 Ω / 1 3.17 Ω / 1 Scenaro Before sep: A/. A/. A/. Ω Ω Ω Afer sep: 7. A/. 7. A/. 7. A/. 3.17 Ω/. 3.17 Ω/. 3.17 Ω/. Scenaro 3 Consan load: 7. A/.8 A A 3.17 Ω/.8 Ω Ω Scenaro 4 Before sep: 7. A/.8 36.1 A/.8 36.1 A/.8 3.17 Ω/.8 6.34 Ω/.8 6.34 Ω/.8 Afer sep: 36.1 A/.8 A A 6.34 Ω/.8 Ω Ω Scenaro 5 Consan load: 7. A/ 1 A 7. A/. 3.17 Ω / 1 Ω 3.17 Ω /. Table 3.-1. Smulaon scenaros based on he load scenaros specfed n secon.. 76
3.. Sengs of smulaed converer model To be able o repea he smulaons, one need o know he sengs for he model when he smulaons are performed. They are presened below: Msc. daa: Dc-lnk volage Reference phase-neural load volage Swchng frequency Samplng frequency 75 V 3 V 5 khz 1 khz LC-fler: Inducance lne nducors Parasc ressance lne nducors Inducance neural nducor Parasc ressance lne nducors Capacance lne o lne capacors Parasc ressance ESR capacors 3 mh.1 Ω 1.5 mh.1 Ω 33.8 μf.1 Ω Curren conroller nner loop conroller: Kp feedback conroller d and q 1 T feedback conroller d and q. Kp feedback conroller 4 T feedback conroller.89 Max conrol sgnal 375 V Mn conrol sgnal -375 V A facor 1 of he load volages n d, q and s used for he feed forward conrol. A facor 1 of he converer currens n d and q s used n he calculaons of he decouplng erms. Volage conroller ouer loop conroller: Kp feedback conroller d and q.75 T feedback conroller d and q.47 Kp feedback conroller.11 T feedback conroller.47 77
A facor.8 of he load currens n d, q and s used for he feed forward conrol. A facor.8 of he load volages n d and q s used n he calculaons of he decouplng erms. Sofware The smulnk model s ncluded n appendx B and he naon fle n appendx C. The used naon fle s n_ver576.m and he used smulaon model s converer_ver576.mdl. Appendx D conans he fle losscalc.m, performng he loss calculaons for he converer. 78
4. Resuls Ths chaper presens he resuls from he smulaons descrbed n chaper 3. From each of he fve smulaed scenaros followng daa are provded: o Lne o neural load volages oupu volage of each phase. o Lne currens n each phase. o Curren n he neural conducor. o Conrol volage n d, q and. o Conrol volage and load volage oupu volage n heα - β -γ - coordnae sysem. The daa provdng he plos are measured when seady sae s acheved durng =.1-.1s. More dealed presenaons of he conrol sgnals durng he smulaons are provded n appendx E. Losses n he semconducors are presened n appendx F. 79
Scenaro 1 Fgure 5.1-1. The hree plos on op from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below lef from op: Conrol volage n d, conrol volage n q, and conrol volage n. The plo below rgh: Conrol volage red ogeher wh load volage oupu volage blue n heα - β -γ - coordnae sysem. 8
o Due o oscllaons n he LC-fler, some ransens occur n he oupu volage durng sar a =.1s peakng a 56 V, bu he oupu volage s sablzed when =.s. o The load s conneced a =.6s. A =.7s he oupu volage s agan sablzed a 3V 35V peak value. o The load currens are 7A 1A peak value. o There s no curren flowng hrough he neural. The converer model copes well wh hs load scenaro. 81
Scenaro Fgure 5.1-. The hree plos on op from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below lef from op: Conrol volage n d, conrol volage n q, and conrol volage n. The plo below rgh: Conrol volage red ogeher wh load volage oupu volage blue n heα - β -γ - coordnae sysem. 8
o Due o oscllaons n he LC-fler, some ransens occur n he oupu volage durng sar a =.1s peakng a 56 V, bu he oupu volage s sablzed when =.s. o The load s conneced a =.6 s. There are once agan ransens peakng a 86 V. A =.8 s he oupu volage s sablzed, bu no a he raed volage of 3V. The oupu volage only reaches 8V 94V peak value. The conrol volage of channel q sauraes because he avalable dc-lnk volage s o low. o The load currens are 66A 93A peak value. o There s no curren flowng hrough he neural. The converer model has some problems keepng he oupu volage a raed level. 83
Scenaro 3 Fgure 5.1-3. The hree plos on op from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below lef from op: Conrol volage n d, conrol volage n q, and conrol volage n. The plo below rgh: Conrol volage red ogeher wh load volage oupu volage blue n heα - β -γ - coordnae sysem. 84
o Due o oscllaons n he LC-fler, some ransens occur n he oupu volage durng sar a =.1s peakng a 56 V, bu he oupu volage s sablzed when =.s. o Due o he unbalance here are volage oscllaons n channel d, q and of he conrol volage 1 Hz n d and q and 5 Hz n and he conrol of he converer s pu on es. I can bee seen ha he converer copes que well n conrollng he oupu volages. However, here are devaons. The oupu volages vary beween 3 51V 315-355V peak value. o The load curren of phase a s 7A 99A peak value. o Snce only phase a s conneced o a load, he curren n phase a 7 A flows back hrough he neural connecon. The converer model conrols he oupu volages que well. There are however devaons beween he volages of he dfferen phases. Due o he unbalanced load, curren s flowng hrough he neural connecon. 85
Scenaro 4 Fgure 5.1-4. The hree plos on op from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below lef from op: Conrol volage n d, conrol volage n q, and conrol volage n. The plo below rgh: Conrol volage red ogeher wh load volage oupu volage blue n heα - β -γ - coordnae sysem. 86
o Due o oscllaons n he LC-fler, some ransens occur n he oupu volage durng sar a =.1s peakng a 47 V, bu he oupu volage s sablzed when =.s. In hs scenaro a load s conneced from sar. o Due o he unbalance here are volage oscllaons n channel d, q and of he conrol volage 1 Hz n d and q and 5 Hz n. I can be seen ha he converer copes que well n conrollng he oupu volages. However, here are errors. The oupu volages vary beween 5 4V 318-34V peak value. o The load currens are 36A, 38A and 71A 51A, 54A and 1A peak value. o The curren rough he neural connecon s 35A 49A peak value. o A =.6 s he change n he load occur. There are once agan ransens peakng a 68 V. A =.7s he oupu volage s sablzed, bu here are sll errors n he oupu volages. They vary beween 6 4V 3-34V peak value. o The load curren n phase a s now 36A 51A peak value. o Snce now only phase a s conneced o a load, he curren n phase a 36 A flows back hough he neural connecon. Also n hs case he oupu volages look nce. There are however devaons beween he volages of he dfferen phases durng boh of he load scenaros. Due o he unbalanced loads, curren s flowng hrough he neural connecon. 87
Scenaro 5 Fgure 5.1-5. The hree plos on op from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below lef from op: Conrol volage n d, conrol volage n q, and conrol volage n. The plo below rgh: Conrol volage red ogeher wh load volage oupu volage blue n heα - β -γ - coordnae sysem. 88
o Due o oscllaons n he LC-fler, some ransens occur n he oupu volage durng sar a =.1s peakng a 55 V, bu he oupu volage s sablzed when =.s. o Due o he unbalance here are volage oscllaons n channel d, q and of he conrol volage 1 Hz n d and q and 5 Hz n. I can be seen ha he converer copes que well n conrollng he oupu volages. However, here are errors. The oupu volages vary beween 19 4V 31-34V peak value. o The load currens are 69A and 75A 97A and 16A peak value. o The curren rough he neural connecon s 19A 18A peak value. The converer model conrols he oupu volages que well. There are however devaons beween he volages of he dfferen phases. Due o he heavy unbalanced load, a large curren s flowng hrough he neural connecon. Effecs of low dc lnk volage To see he effecs of a oo low dc lnk volage wo more smulaons are performed. The frs scenaro s he same as he laer par of scenaro 1, bu wh he dfference ha he dc lnk volage sars o decrease a =,4 see fg. 5.1-6. A =.7 he converer sars o lose he conrol of he oupu volage and he conrol volage of channel q sauraes. A hs pon he dc lnk volage s 571V. Snce he mnmal dc lnk volage s calculaed o 564V secon.6. and some volage s los n he flers, hs seems reasonable. The same smulaon was performed on scenaro 5, wh smlar resul see fg. 5.1-7. 89
5..4.6.8.1.1 4 - -4..4.6.8.1.1 -..4.6.8.1.1 -..4.6.8.1.1 4 - -4..4.6.8.1.1 4 - -4..4.6.8.1.1 4 - -4..4.6.8.1.1 Fgure 5.1-6. The plo on op: Dc lnk volage. The hree followng plos from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below from op: Conrol volage n d, conrol volage n q, and conrol volage n. 9
5..4.6.8.1.1 4 - -4..4.6.8.1.1 -..4.6.8.1.1 -..4.6.8.1.1 4 - -4..4.6.8.1.1 4 - -4..4.6.8.1.1 4 - -4..4.6.8.1.1 Fgure 5.1-7. The plo on op: Dc lnk volage. The hree followng plos from op: Lne o neural load volages oupu volage of each phase, lne currens n each phase, and curren n he neural conducor. The hree plos below from op: Conrol volage n d, conrol volage n q, and conrol volage n. 91
5. Implemenaon Ths chaper concerns he mplemenaon of a physcal converer n shor. For example, some ssues concernng an mplemenaon of a dgal conroller are covered. The chaper also ncludes suggeson of wha hardware o use for he man componens n he desgn. 5.1 Dgal conrol All conrol mehods n secon.7 are made wh connuous conrollers. The conrol algorhms for a real converer wll however mos probably be made dgal and calculaed by a dgal sgnal processor DSP. Because of hs some phenomenon concernng he dgalzaon of he conrol needs o be consdered. Ths secon wll n shor menon subjecs lke: samplng, analas, delays, dgal PI-conrollers, dgal algorhms and dummy sofware code. Samplng The measured sgnals for example he nducor currens or he oupu volages wll be sampled See fg. 5.1-1. 33 3 31 3 Ts 9 4.5 5 5.5 6 6.5 x 1-3 Fgure 5.1-1.Samplng of he measured sgnals. The samplng wll be a a rae wce he swchng frequency of he converer. The reason for hs rae s ha he reference value n he PWM hen can be updaed every me he rangular wave reaches s maxmum and mnmum value See fg. 5.1-. In hs way s assured ha only wo swchngs per rangular wave perod s possble. 9
5-5.6.8.1.1.14.16.18...4 Fgure 5.1-.By samplng a a rae wce he swchng frequency, he reference for he PWM can be updaed every me he rangle wave reaches s maxmum and mnmum. Slow compuer I s assumed ha he dgal sgnal processor DSP s able o perform he calculaons of he new oupu sgnals n less han one sample perod and updae hem a he end of he sample perod. By hs, he DSP always provdes a conrol sgnal ha s based on he measuremens made a he begnnng of he prevous samplng nerval. See fg. 5.1-3 Ths causes a delay of one sample perod. Applyng conrolsgnal n Applyng conrolsgnal n+1 Calculaon of conrolsgnal n Calculaon of conrolsgnal n+1 n n+1 n+ n+ 3 n+ 4 Samplng of process oupu sgnal n Samplng of process oupu sgnal n+1 Fgure 5.1-3.Conrol sgnal updaes relaed o samplng me nsans. An-alas When samplng an analogue sgnal, here s always he rsk of alasng caused by hgh frequency dsurbances. Frequences hgher han half he samplng frequency he Nyqvs frequency may n he sampled sgnal cause new frequences ha ddn exs n he orgnal analogue sgnal. To avod hs, he analogue sgnal s low-pass flered before s sampled. The cu-off frequency 93
of he fler should be half he samplng frequency. Ths fler also adds some delay o he conrol loop. Delays A drawback of he dgal mplemenaon of he conrollers s he delay causes n he conrol loop. As menoned above, he calculaon and updae of he conrol sgnal akes 1 sample perod. If usng a second order Bessel fler as he low pass fler, a delay of.4 more sample perods s added as well [1]. The oal delay caused by he dgal mplemenaon wll hen be 1.4 sample perods. Dgal PI conroller The connuous PI conroller has he equaon: 1 K u = K e + e s ds = K e + e s ds = P + I T T Equaon 5.1.1 Where e s he npu sgnal o he conroller, u s he conrol sgnal, K s he proporonal gan and T s he negral me. The dgal PI conroller s smlarly gven by [1]: u kh = P kh + I kh Equaon 5.1. Where k s he sample, h s he sample perod and: P kh = K e kh Equaon 5.1.3 and K h I kh + h = I kh + e kh Equaon 5.1.4 T The dscree npu sgnal ekh a sample k, when he sample perod s h, s calculaed as: 94
e kh = ref kh y kh Equaon 5.1.5 Where refkh s he value of he reference sgnal and ykh s he acual measured value a me nsan kh. Compuer algorhms A smple code ha calculaes he algorhms above for dgal PI conroller may look lke hs: y = yin.ge; //read he sysems oupu sgnal e = yref - y; //calculae he error eq. 5.1.5 u = K*e+ I; //calculae he conrol sgnal eq. 5.1. I = I + K*h/T*e; //updae he negral erm eq. 5.1.4 waunl uou.puu; //wa for rgh momen //updae he conrol sgnal To preven negraor wndup, whch occur when he acuaors ges sauraed and he negral erm of he conroller ncreases o much, an an wndup funcon may be mplemened as well. f I>I_max { I= I_max; } f I< I_mn { I= I_mn } Ths funcon lms he maxmal value of he negral erm and may be mplemened beween calculae he conrol sgnal and updae he negral erm n he code above. When calculang I_max and I_mn, respec should be aken o he presen proporonal par of he conrol sgnal and he presen maxmum avalable conrol volage level. 95
5. Proposed man componens In secon.6.6, he man componens of he converer are dmensoned, usng he mehods covered n secon.6.1-.6.5. Table 5.-1 presens hese componens. Componen ype Componen Manufacurer Sze mm/weghkg IGBT, phases GB13D Semkron 16x61x3/.35 IGBT, neural 3GB14D Semkron 16x61x3/.35 Oupu fler capacors B33 35µF, 5V Epcos Dameer=35, hegh=71 * Oupu fler nducors, phases 3.mH, 9A one phase TRAMO-ETV AB x16x31/ 7 * Oupu fler nducor, phases 3.mH, 9A hree phase TRAMO-ETV AB 4x18x4/ 7 Oupu fler nducor, neural 1.5mH, 14A TRAMO-ETV AB 4x16x36/ 35 Table 5.-1. Suggesons of man componens for he converer. * Three one phase nducors, or one hree phase nducor may be used. Wh hs choce of componens, s obvous ha he fler componens, especally he nducors, wll domnae he oal sze and wegh of he converer. Even whou covers and coolng devces, he oal mass of he nducors are above 1kg and her oal volume abou.4m 3. Excep from he componens above, here are of cause a need for: DSP, DSPcard, drvers, curren sensors, volage sensors, ransen proecon devces, an-alas flers, coolng devces and more. Snce he physcal desgn of he converer no s he arge of he projec, hese are no deal wh. 96
6. Conclusons The hess presens he bases for a fuure desgn of a DC/AC power elecronc converer wh four half brdges, provdng a hree-phase four-wre 3/4V 5Hz AC volage source. The goal s a hgh power converer ha s able o delver a balanced load volage durng specfed load scenaros. Unbalanced hree-phase loads and sngle-phase loads are hghlghed. The heory of he power elecronc converer and he conrol of he converer are he man objecves of he hess. The desgn of he man componens are covered, bu no hghlghed. Effors are no made o reach a specfed specfcaon. The focus s on undersandng and evaluaon of possbles. A model of he converer and he conrol sysems s bul and smulaons based on he specfed load scenaros are performed on he model. Frs, a summary of he work and obaned resuls s gven. Second, some suggesons of fuure work and research are provded. 6.1 Summary In hs secon, he resuls from he projec are summarzed. The conrol sysem The conrol of he converer s performed n he roang d-q- coordnae sysem. A cascade conrol wh an nner nducor curren conrol loop and an ouer load volage conrol loop for each channel d, q and s proposed. To ncrease he bandwdh, feed forward conrol of he load currens and load volages are used. The cross couplngs beween channel d and q, due o he fler componens, are reduced by decouplng. Ths conrol gves he converer a fas response n all channels. Ths s mporan because of he consan 1 Hz dsurbance sgnals n channel d and q, and he 5 Hz dsurbance sgnals n channel, durng conrol of unbalanced loads. I also gves a fas load volage regulaon durng load changes. A dsadvanage of hs conrol mehod s he large amoun of sensors needed. In hs converer, where hgh power and hgh qualy of he load volage are requred, lmaons of he conrol bandwdh are due he swchng frequency and he oupu fler. 97
The smulaon model By usng he heory and equaons provded n he hess, he model made n Malab/Smulnk smulaes he mporan aspecs of he converer. The man aspecs are: conrol sysems, coordnae ransformaons, effecs of he DSP, pulse wdh modulaon, power elecronc swches, oupu flers and loads. The model gves a verfcaon and undersandng of he converer heory. I also provdes smulaed resuls of wha possbles, lmaons and behavor o expec from a physcal converer. Resuls The smulaed converer s esed wh specfed load scenaros. The scenaros are chosen o smulae possble loads for a converer workng as a mul purpose volage source. The converer copes well wh he smulaed scenaros. Devaons beween he load volages of he phases are small, even under heavly unbalanced load. Ths s due o a hgh conrol bandwdh. A slower conrol leads unavodable o a lower qualy of he load volages, especally durng unbalanced condons. By avodng he mos exreme scenaros of unbalance a hgh qualy of he load volage s achevable. The need of a hgh dc lnk volage s apparen. Smulaon shows he lm of he dc lnk volage o manan a conrolled load volage. Especally heavly nducve loads, and LC-fler, requre a hgh dc lnk volage. Durng sar of he converer, or sudden load changes, oscllaons n he fler cause hgh ransen volage peaks n he load volages. These oscllaons are o fas o be conrollable by he converer, bu may be lmed by devces for over volage proecon varsors. Componens and physcal sze A dmensonng s performed of he man componens of he smulaed converer. Snce he physcal sze and wegh of he converer s of mporance much s focused on he physcal sze and wegh of he componens. The domnang componens n sze and wegh are he fler nducors. The semconducors and fler capacors wegh wll be reduced o a few klos. 98
To reduce he curren rpple hrough he semconducors and fler nducors o a reasonable level of a few percen, he phase fler nducances are se o 3mH and he neural nducance o 1.5mH. Wh a nomnal power of 5kVA of he converer hs leads o physcally large nducor componens 15 kg n oal. By reducng he fler nducances by 1/3 and ncreasng he fler capacances by 3, and keep he oupu volage rpple unchanged he oal wegh of he nducors was reduced o 57 kg. Allowng a larger curren rpple may however lead o ncreased losses n he nducors, whch leads o he need of nducors wh hgher rae and more wegh. Due o he wors case scenaro of unbalance, he neural nducor s dmensoned for almos wce he curren n a phase nducor. However, by lmng he maxmal allowed case of unbalance, he physcal sze of hs nducor may be largely reduced. 6. Dscusson for he fuure The smulaon model may be exended wh a model of he dc lnk. Smulaons of he dc lnk volage, durng dfferen load scenaros of he converer, would gve a deeper undersandng of he converers effecs on he oal elecrc sysem and he desgn of dc lnk capacors. Smulaons of nonlnear load scenaros are no performed on he model. An exenson of he load model o smulae nonlnear loads would be neresng snce nonlnear loads are common and plausble loads for hs converer. The effecs of he delay n he conrol, due o he calculaon me of he DSP, may be reduced by mplemenng a smh predcor n he conrol [4]. Ths soluon demands a ceran level of dc-lnk volage. The defnve lm s 4 he peak value of he lne-lne volage, bu a more reasonable level s 7-75V. If hs volage s no avalable oher soluons mus be consdered. One soluon may be a sep-up converer beween he dc-lnk of he SEP and he ACM. Anoher soluon may be a hree half-brdge nverer and conneced ransformer o acheve he neural connecon. Υ - 99
The man mprovemen of he undersandng of he converer would of cause be obaned by specfy, desgn and buld a prooype of he converer. Then he resuls acheved from he smulaons could be verfed. Ths hess, and he model of he converer, would provde a base for he desgn process. 1
References [1] L. Harnefors, Conrol of Varable-Speed Drves, Appled sgnal processng and conrol, deparmen of elecroncs, Mälardalen unversy, Väserås, Sweden, 3 [] R. Zhang, Hgh performance power converer sysems for nonlnear and unbalanced load/source, Ph.D dsseraon, Faculy of he Vrgna Polyechnc Insue, 1998 [3] G. Olsson, M. Alakula, Elmasknsysem, Deparmen of elecrcal engneerng and auomaon, Lund nsue of echnology, Sweden, [4] M. Alakula, Power Elecronc Conrol Deparmen of elecrcal engneerng and auomaon, Lund nsue of echnology, Sweden, [5] P. Karlsson, Krafelekronk, Deparmen of elecrcal engneerng and auomaon, Lund nsue of echnology, Sweden, 1998 [6] B. Lennarson, Reglereknkens grunder, ISBN 91-44-416-9, [7] R. A. Ganne, Conrol sraeges for hgh power four-leg volage source nverers, MSc dsseraon, Faculy of he Vrgna Polyechnc Insue, 1 [8] J. Duncan Glover, Mulukula S. Sarma, Power Sysems analyses and desgn, ISBN -534-95367-, 1 [9] MIL-STD-74E, Arcraf elecrc power characerscs, Deparmen of defence nerface sandards, 1991 11
[1] P. Karlsson, DC Dsrbued Power Sysems Analyss, Desgn and Conrol for a Renewable Energy Sysem Ph.D dsseraon, Deparmen of elecrcal engneerng and auomaon, Lund nsue of echnology, Sweden, [11] R. Schnell, U. Schlapbach, Realsc benchmarkng of IGBTmodules wh he help of a fas and easy o use smulaon-ool PCIM'4 Power Elecroncs Conference, Nuremberg [1] K. J. Åsröm, B Wenmark, Compuer conrolled sysems, ISBN -13-314899-8, 1997 [13] M. Bojrup. Advanced Conrol of Acve flers n a Baery Charger Applcaon Deparmen of elecrcal engneerng and auomaon, Lund nsue of echnology, Sweden, 1999. ISBN 91-88934-13-6 1
Appendx A Dmensonng he dc lnk capacance Followng ex concerns he dmensonng of he dc lnk capacor, wh and whou he use of a spl dc lnk capacor as he neural connecon o hghlgh he dfferences. The mehod s receved from []. Whou spl dc-lnk capacance as neural connecon The rpple power delvered o he load s caused by he negave sequence power due o he unbalanced load and can be expressed as: P n [ v, v, v ] [, ] T = Equaon A.1 an bn cn a _ n b _ n, c _ n Where [ ], are he negave sequence load currens. The a _ n b_ n, c _ n negave sequence power can from hs be expressed as: P n 3 = vˆ ˆ n cosω + ϕ n Equaon A. where vˆ s he peak AC oupu volage and î n s he peak negave sequence load curren. The ω frequency s vsble here. From eq. A., he peak o peak energy rpple requred by he load s: 3 vˆ ˆ n E pp = Equaon A.3 ω The peak o peak energy rpple across he dc lnk capacor can also be expressed as: 1 1 Cdc VDC + VDC Cdc VDC VDC E pp = = C Equaon A.4 dc V DC V DC 13
By usng eq. A.3 and eq. A.4, followng expresson for he mnmum dc lnk capacance CDC mn_ n for a volage rpple VDC s gven by: C = 3 vˆ ˆ n dc mn_ n Equaon A.5 4 ω VDC VDC By hs, eq. A.5 expresses he mnmum sze of he dc lnk capacance, wh respec o only negave sequence rpple. CDC mn_ n can also be expressed as [13]: C I V 3 I q q f q dc mn_ n = = Equaon A.6 ω VDC VDC ω VDC VDC V where V q s he value of he rms scaled oupu volage vecor, Iq s he value of he rms scaled negave sequence lne curren vecor and I f s he rms scaled negave sequence phase curren vecor. Wh a spl dc-lnk capacance as neural connecon If a spl dc lnk capacance s used, he capacors, ha are hen conneced n seres, are each expressed as Cdc. Snce he neural curren, expressed n eq. A.6, flows hrough he mddle pon of he wo dc lnk capacors, equvalenly hese wo dc lnk capacors appear o be n parallel 4 from he neural curren pon of vew. Cdc ˆ cos 3 ˆ neural = neural ω + ρ = cos ω + ρ Equaon A.7 where î neural s he peak of he neural curren and î s he peak of he zero sequence curren. Therefore he peak volage rpple across each of he dc lnk capacors, caused by he neural curren, s expressed as: VC dc = ˆ 3 ω C dc = 1 V DC Equaon A.8 14
From eq. A.7, fnally he mnmum dc lnk capacance wh respec o he zero sequence load curren s expressed as: C dc 3 ˆ = _ mn_ Equaon A.9 ω V DC 15
Appendx B The Smulnk model 16
Block. Volage conroller 17
Block 4. Curren conroller 18
Block 6. Symmerzaon Block 8. Modulaon 19
Block 9. Power elecronc swches 11
Block 1. LC-fler model Block 1.1. LC-fler model phase a 111
Block 1. Load model Y-conneced load Block 1.1. Load model Y-conneced load phase a 11
Appendx C n.m %---------------------------------------------------------------------- %Msc daa: Udc=75; Uref=3*sqr; Fsw=5e3; Tsw=1/Fsw; Ts=Tsw/; %dc lnk volage %reference volage %swchng frequency %swchng nerval %samplng nerval %---------------------------------------------------------------------- %Fler: L=.3; R_esr_L=.1; Ln=L/; R_esr_Ln=.1; C=33.8e-6; R_esr_C=.1; %fler nducor phase %fler nducor neural %fler capacor phase %----------------------------------------------------------------------- %Curren conroller: Umax=Udc/; Umn=-Udc/; %Lmed conrol sgnal %Lmed conrol sgnal Kp=1; %P-par conroller d och q T=.; %I-par conroller d och q Kpo=4; To=.89; %P-par conrollero %I-par conrollero %------------------------------------------------------------------------ %Volage conroller: Imax=; Imn=-; %Lmed conrol sgnal %Lmed conrol sgnal Kpv=.75; %P-par conroller d och q Tv=.47; %I-par conroller d och q Kpvo=.11; Tvo=.47; %P-par conroller o %I-par conroller o 113
Appendx D losscalc.m %m-fle calculang oal losses n semoconducors of ACM code ncludes phase a only: %daa used n calculaons of losses phase half brdges: Eon_n=4e-3; %urn on energy for IGBTphase a Vdc=6V and I=15 Eoff_n=17e-3; %urn off energy for IGBTphase IGBT wh dode ncluded a Vdc=6V and I=15 Vdcn=6; %Vdc nomnal Inom=15; %I nomnal Vdc=75; V_IGBT=1.8; R_IGBTon=1.66e-3; V_dode=1.; R_dodeon=7e-3; %reshold volage drop of IGBTphase %on sae ressance of IGBTphase %reshold volage drop of dodephase %on sae ressance of dodephase %daa from smulnk model: %d=me of smulnk sample %Va, Vb, Vc, Vn=oupu volage swches %Ia_conv,Ib_conv,Ic_conv,In_conv = curren hrough swches %Tsw=swch perod me pos=1; k=1; I_urnon=; I_urnoff=; _urnon=; _urnoff=; %oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo %Phase a for n=1:lenghva %-------------------------------------------------------------------------- %posve curren Ia> f Van>.9*Vdc/ && pos== && Ia_convn> %swch has swched from -Vdc/ o Vdc/, curren posve E_urnon=Eon_n*Vdc*I_urnon/Vdcn*Inom; %urn on energy loss, IGBT1+dode E_urnoff=Eoff_n*Vdc*I_urnoff/Vdcn*Inom; %urn off energy loss, IGBT1+dode I_avr=I_urnon+I_urnoff/; %avrage curren durng on sae, IGBT1 V_IGBTon=V_IGBT+R_IGBTon*I_avr; %forward volage drop of IGBT1 E_cond_IGBT=I_avr*V_IGBTon*_urnoff-_urnon; %conducon energy loss, IGBT1 I_avr=I_urnoff+Ia_convn/; %avrage curren durng on sae, dode V_dodeon=V_dode+R_dodeon*I_avr; %forward volage drop of dode E_cond_dode=I_avr*V_dodeon*dn-_urnoff; %conducon energy loss, dode 114
P_loss_ak=E_urnon+E_urnoff+E_cond_IGBT+E_cond_dode/Tsw; % avrage dssapaed power durng one swch perod. Losses from _urnon=dn; I_urnon=Ia_convn; %me a urn on for IGBT1 urn off for dode %curren a urn on for IGBT1 urn off for dode _loss_ak=dn; pos=1; k=k+1; %swch value hgh end f Van<.9*-Vdc/ && pos==1 && Ia_convn> %swch has swched from Vdc/ o - Vdc/, curren posve _urnoff=dn; I_urnoff=Ia_convn; %me a urn off for IGBT1 urn on for dode %curren a urn off for IGBT1 urn on for dode end pos=; %-------------------------------------------------------------------------- %negave curren Ia_conv< f Van>.9*Vdc/ && pos== && Ia_convn< %swch has swched from -Vdc/ o Vdc/, curren posve E_urnon=Eon_n*Vdc*I_urnon/Vdcn*Inom; %urn on energy loss, IGBT+dode1 E_urnoff=Eoff_n*Vdc*I_urnoff/Vdcn*Inom; %urn off energy loss, IGBT+dode1 I_avr=I_urnon+I_urnoff/; %avrage curren durng on sae, dode V_dodeon=V_dode+R_dodeon*I_avr; %forward volage drop of dode1 E_cond_dode1=I_avr*V_dodeon*_urnoff-_urnon; %conducon energy loss, dode1 I_avr=I_urnoff-Ia_convn/; %avrage curren durng on sae, IGBT V_IGBTon=V_IGBT+R_IGBTon*I_avr; %forward volage drop of IGBT E_cond_IGBT=I_avr*V_IGBTon*dn-_urnoff; %conducon energy loss, IGBT P_loss_ak=E_urnon+E_urnoff+E_cond_IGBT+E_cond_dode1/Tsw; % avrage dssapaed power durng one swch perod. Losses from _urnon=dn; I_urnon=-Ia_convn; %me a urn off for IGBT urn on for dode1 %curren a urn off for IGBT urn on for dode1 _loss_ak=dn; pos=1; k=k+1; %swch value hgh end f Van<.9*-Vdc/ && pos==1 && Ia_convn< %swch has swched from Vdc/ o - Vdc/, curren posve _urnoff=dn; I_urnoff=-Ia_convn; %me a urn off for IGBT urn on for dode1 %curren a urn off for IGBT urn on for dode1 pos=; 115
end end %oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo %Average losses phase a: %---1:s: P_loss_a_o=; =; for n=1:lengh_loss_a f _loss_an>.4 && _loss_an<.6 P_loss_a_o=P_loss_a_o + P_loss_an; =+1; end end P_loss_a_average=P_loss_a_o/; %---:nd: P_loss_a_o=; =; for n=1:lengh_loss_a f _loss_an>.1 && _loss_an<.1 P_loss_a_o=P_loss_a_o + P_loss_an; =+1; end end P_loss_a_average=P_loss_a_o/; %oooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo subplo5,1,1,plo_loss_a, P_loss_a hold on subplo5,1,1,plo_loss_a:3, P_loss_a_average,'red' AXIS[.1 1] subplo5,1,1,plo_loss_a5:59, P_loss_a_average,'red' YLABEL'a' Grd mnor 116
Appendx E - Dealed represenaon conrol sgnals In chaper four, he resuls from he smulaon of he load scenaros were presened. To provde a smpler presenaon, focus was pu on he oupu volages and load currens n phase represenaon. For deeper sudes of he sgnals n he conrol sysem, followng plos are provded. The resuls are from he same scenaros as n chaper four. However, o gve a more dealed presenaon, neresng momens of he smulaons are hghlghed and he me scales of hese momens are narrowed. All conrol sgnals are represened n d-q-. The sgnals n he followng plos are shown n fg. E-1. v d * d 1 d d 3 v _ s G C _ d s e H C _ d s H v _ d s d std G d 1 d 5 ωc d 8 1 d 11 d d 4 7 d 9 1 ω L d 13 V d d 6 d 1 ω L ω C q 6 q 1 ω L ω C v q * q 1 q 3 G v _ q s q 4 q 5 q 7 q 9 G C _ q s q 1 q 11 q 13 e std H C _ q s H v _ q s V q q 1 ωc q 8 1 ωl q _ load v o * o 1 o G s 4 o v_ o 3 o 5 o o 7 o 8 o G C _ o 9 s o 1 1 1 o 11 o 13 std e H o s C _ H v _ o s V o o _ load Fgure E-1.Layou of he conrol sysem and sgnal pahs. 117
Scenaro 1: -.5.1.15..5 1 A B -.55.6.65.7.75 1-1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-. Sgnals scenaro 1, channel d. A: Reference oupu volage d1 green, oupu volage d blue, error sgnal d3 red. B: conrol sgnal PI conroller d4 green, load curren feed forward sgnal d5 red, decouplng sgnal d6 blue. C: Reference curren d7 blue. D: Reference curren d7 green, converer curren d8 blue, error sgnal d9 red. E: Conrol sgnal PI conroller d1 green, oupu volage feed forward sgnal d11 red, decouplng sgnal d1 blue. F: Reference volage converer d13 blue. 118
6 4.5.1.15..5 1 6 A 4.55.6.65.7.75 B 1.5.1.15..5.55.6.65.7.75 1 C 1.5.1.15..5.55.6.65.7.75 1 D 1.5.1.15..5 6 4.5.1.15..5.55.6.65.7.75 6 4 E.55.6.65.7.75 6 4 F.5.1.15..5 6 4.55.6.65.7.75 Fgure E-3. Sgnals scenaro 1, channel q. A: Reference oupu volage q1 green, oupu volage q blue, error sgnal q3 red. B: conrol sgnal PI conroller q4 green, load curren feed forward sgnal q5 red, decouplng sgnal q6 blue. C: Reference curren q7 blue. D: Reference curren q7 green, converer curren q8 blue, error sgnal q9 red. E: Conrol sgnal PI conroller q1 green, oupu volage feed forward sgnal q11 red, decouplng sgnal q1 blue. F: Reference volage converer q13 blue. 119
-.5.1.15..5 1 A - B.55.6.65.7.75 1-1.5.1.15..5-1.55.6.65.7.75 1 C 1-1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 E -.5.1.15..5 -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-4. Sgnals scenaro 1, channel. A: Reference oupu volage -1 green, oupu volage - blue, error sgnal -3 red. B: conrol sgnal PI conroller -4 green, load curren feed forward sgnal -5 red. C: Reference curren -7 blue. D: Reference curren -7 green, converer curren -8 blue, error sgnal -9 red. E: Conrol sgnal PI conroller -1 green, oupu volage feed forward sgnal -11 red. F: Reference volage converer -13 blue. 1
Scenaro : -.5.1.15..5 1 A B -.55.6.65.7.75 1-1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-5. Sgnals scenaro, channel d. A: Reference oupu volage d1 green, oupu volage d blue, error sgnal d3 red. B: conrol sgnal PI conroller d4 green, load curren feed forward sgnal d5 red, decouplng sgnal d6 blue. C: Reference curren d7 blue. D: Reference curren d7 green, converer curren d8 blue, error sgnal d9 red. E: Conrol sgnal PI conroller d1 green, oupu volage feed forward sgnal d11 red, decouplng sgnal d1 blue. F: Reference volage converer d13 blue. 11
6 4.5.1.15..5 1 6 4 A.55.6.65.7.75 B 1.5.1.15..5.55.6.65.7.75 1 C 1.5.1.15..5.55.6.65.7.75 1 D 1.5.1.15..5 6 4.5.1.15..5.55.6.65.7.75 6 4 E.55.6.65.7.75 6 4 F.5.1.15..5 6 4.55.6.65.7.75 Fgure E-6. Sgnals scenaro, channel q. A: Reference oupu volage q1 green, oupu volage q blue, error sgnal q3 red. B: conrol sgnal PI conroller q4 green, load curren feed forward sgnal q5 red, decouplng sgnal q6 blue. C: Reference curren q7 blue. D: Reference curren q7 green, converer curren q8 blue, error sgnal q9 red. E: Conrol sgnal PI conroller q1 green, oupu volage feed forward sgnal q11 red, decouplng sgnal q1 blue. F: Reference volage converer q13 blue. 1
-.5.1.15..5 1 A -.55.6.65.7.75 1 B -1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-7. Sgnals scenaro, channel. A: Reference oupu volage -1 green, oupu volage - blue, error sgnal -3 red. B: conrol sgnal PI conroller -4 green, load curren feed forward sgnal -5 red. C: Reference curren -7 blue. D: Reference curren -7 green, converer curren -8 blue, error sgnal -9 red. E: Conrol sgnal PI conroller -1 green, oupu volage feed forward sgnal -11 red. F: Reference volage converer -13 blue. 13
Scenaro 3: -.5.1.15..5 1 A B -.55.6.65.7.75 1-1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-8. Sgnals scenaro 3, channel d. A: Reference oupu volage d1 green, oupu volage d blue, error sgnal d3 red. B: conrol sgnal PI conroller d4 green, load curren feed forward sgnal d5 red, decouplng sgnal d6 blue. C: Reference curren d7 blue. D: Reference curren d7 green, converer curren d8 blue, error sgnal d9 red. E: Conrol sgnal PI conroller d1 green, oupu volage feed forward sgnal d11 red, decouplng sgnal d1 blue. F: Reference volage converer d13 blue. 14
6 4.5.1.15..5 1 6 4 A.55.6.65.7.75 B 1.5.1.15..5.55.6.65.7.75 1 C 1.5.1.15..5.55.6.65.7.75 1 D 1.5.1.15..5 6 4.5.1.15..5.55.6.65.7.75 6 4 E.55.6.65.7.75 6 4 F.5.1.15..5 6 4.55.6.65.7.75 Fgure E-9. Sgnals scenaro 3, channel q. A: Reference oupu volage q1 green, oupu volage q blue, error sgnal q3 red. B: conrol sgnal PI conroller q4 green, load curren feed forward sgnal q5 red, decouplng sgnal q6 blue. C: Reference curren q7 blue. D: Reference curren q7 green, converer curren q8 blue, error sgnal q9 red. E: Conrol sgnal PI conroller q1 green, oupu volage feed forward sgnal q11 red, decouplng sgnal q1 blue. F: Reference volage converer q13 blue. 15
-.5.1.15..5 1 A -.55.6.65.7.75 1 B -1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 E -.5.1.15..5 -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-1. Sgnals scenaro 3, channel. A: Reference oupu volage -1 green, oupu volage - blue, error sgnal -3 red. B: conrol sgnal PI conroller -4 green, load curren feed forward sgnal -5 red. C: Reference curren -7 blue. D: Reference curren -7 green, converer curren -8 blue, error sgnal -9 red. E: Conrol sgnal PI conroller -1 green, oupu volage feed forward sgnal -11 red. F: Reference volage converer -13 blue. 16
Scenaro 4: -.5.1.15..5 1 A B -.55.6.65.7.75 1-1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-11. Sgnals scenaro 4, channel d. A: Reference oupu volage d1 green, oupu volage d blue, error sgnal d3 red. B: conrol sgnal PI conroller d4 green, load curren feed forward sgnal d5 red, decouplng sgnal d6 blue. C: Reference curren d7 blue. D: Reference curren d7 green, converer curren d8 blue, error sgnal d9 red. E: Conrol sgnal PI conroller d1 green, oupu volage feed forward sgnal d11 red, decouplng sgnal d1 blue. F: Reference volage converer d13 blue. 17
6 4.5.1.15..5 1 6 4 A.55.6.65.7.75 B 1.5.1.15..5.55.6.65.7.75 1 C 1.5.1.15..5.55.6.65.7.75 1 D 1.5.1.15..5 6 4.5.1.15..5.55.6.65.7.75 6 4 E.55.6.65.7.75 6 4 F.5.1.15..5 6 4.55.6.65.7.75 Fgure E-1. Sgnals scenaro 4, channel q. A: Reference oupu volage q1 green, oupu volage q blue, error sgnal q3 red. B: conrol sgnal PI conroller q4 green, load curren feed forward sgnal q5 red, decouplng sgnal q6 blue. C: Reference curren q7 blue. D: Reference curren q7 green, converer curren q8 blue, error sgnal q9 red. E: Conrol sgnal PI conroller q1 green, oupu volage feed forward sgnal q11 red, decouplng sgnal q1 blue. F: Reference volage converer q13 blue. 18
-.5.1.15..5 1 A -.55.6.65.7.75 1 B -1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-13. Sgnals scenaro 4, channel. A: Reference oupu volage -1 green, oupu volage - blue, error sgnal -3 red. B: conrol sgnal PI conroller -4 green, load curren feed forward sgnal -5 red. C: Reference curren -7 blue. D: Reference curren -7 green, converer curren -8 blue, error sgnal -9 red. E: Conrol sgnal PI conroller -1 green, oupu volage feed forward sgnal -11 red. F: Reference volage converer -13 blue. 19
Scenaro 5: - A -.5.1.15..5 1.55.6.65.7.75 1 B -1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 - E -.5.1.15..5.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-14. Sgnals scenaro 5, channel d. A: Reference oupu volage d1 green, oupu volage d blue, error sgnal d3 red. B: conrol sgnal PI conroller d4 green, load curren feed forward sgnal d5 red, decouplng sgnal d6 blue. C: Reference curren d7 blue. D: Reference curren d7 green, converer curren d8 blue, error sgnal d9 red. E: Conrol sgnal PI conroller d1 green, oupu volage feed forward sgnal d11 red, decouplng sgnal d1 blue. F: Reference volage converer d13 blue. 13
6 4.5.1.15..5 1 6 4 A.55.6.65.7.75 B 1.5.1.15..5.55.6.65.7.75 1 C 1.5.1.15..5.55.6.65.7.75 1 D 1.5.1.15..5 6 4.5.1.15..5.55.6.65.7.75 6 4 E.55.6.65.7.75 6 4 F.5.1.15..5 6 4.55.6.65.7.75 Fgure E-15. Sgnals scenaro 5, channel q. A: Reference oupu volage q1 green, oupu volage q blue, error sgnal q3 red. B: conrol sgnal PI conroller q4 green, load curren feed forward sgnal q5 red, decouplng sgnal q6 blue. C: Reference curren q7 blue. D: Reference curren q7 green, converer curren q8 blue, error sgnal q9 red. E: Conrol sgnal PI conroller q1 green, oupu volage feed forward sgnal q11 red, decouplng sgnal q1 blue. F: Reference volage converer q13 blue. 131
-.5.1.15..5 1 A -.55.6.65.7.75 1 B -1.5.1.15..5 1-1.55.6.65.7.75 1 C -1.5.1.15..5-1.55.6.65.7.75 1 1 D -1.5.1.15..5-1.55.6.65.7.75 -.5.1.15..5 E -.55.6.65.7.75 - F -.5.1.15..5.55.6.65.7.75 Fgure E-16. Sgnals scenaro 5, channel. A: Reference oupu volage -1 green, oupu volage - blue, error sgnal -3 red. B: conrol sgnal PI conroller -4 green, load curren feed forward sgnal -5 red. C: Reference curren -7 blue. D: Reference curren -7 green, converer curren -8 blue, error sgnal -9 red. E: Conrol sgnal PI conroller -1 green, oupu volage feed forward sgnal -11 red. F: Reference volage converer -13 blue. 13
Appendx F - Losses semconducors The losses for each half brdge, as well as oal loss for he converer, durng he smulaed scenaros are calculaed here. Boh connues losses and average losses are presened. The daa provdng he average loss calculaons are measured when seady sae s acheved durng =.4-.6s and durng =.1-.1s. Daa are aken from daa shees of IGBT-modules; Semkron GB13D on phase a, b and c half brdges and Semkron 3GB14D on neural half brdge. Scenaro 1 a b c n 5..4.6.8.1.1 5..4.6.8.1.1 5..4.6.8.1.1 5 1 o 5..4.6.8.1.1..4.6.8.1.1 Fgure F-1.Losses for each half brdge and oal loss of he converer. Connuous losses blue and average losses durng seady sae red. The larges average loss of a half brdge s equal n all of he phase half brdges and abou 3 W. The larges oal average loss of he converer s abou 9 W. 133
Scenaro a b 5 5..4.6.8.1.1 c n..4.6.8.1.1 5..4.6.8.1.1 5 1 o 5..4.6.8.1.1..4.6.8.1.1 Fgure F-.Losses for each half brdge and oal loss of he converer. Connuous losses blue and average losses durng seady sae red. The larges average loss of a half brdge s equal n all of he phase half brdges and abou 5 W. The larges oal average loss of he converer s abou 75 W. Scenaro 3 a b c n o 5 5 5 5 1 5..4.6.8.1.1..4.6.8.1.1..4.6.8.1.1..4.6.8.1.1..4.6.8.1.1 Fgure F-3.Losses for each half brdge and oal loss of he converer. Connuous losses blue and average losses durng seady sae red. 134
The larges average loss of a half brdge s equal n he half brdge of phase a and he neural half brdge and are abou 75 W. The larges oal average loss of he converer s abou 55 W. Scenaro 4 a b c 5..4.6.8.1.1 5..4.6.8.1.1 5 n..4.6.8.1.1 5.. 4 1 o 5.6. 8.1.1..4.6.8.1.1 Fgure F-4.Losses for each half brdge and oal loss of he converer. Connuous losses blue and average losses durng seady sae red. The larges average loss of a half brdge s n he half brdge of phase a and s abou 75 W. The larges oal average loss of he converer s abou 65 W. Scenaro 5 a b c n o 1 5 1 5 1 5 1 5..4.6.8.1.1..4.6.8.1.1..4.6.8.1.1 1..4. 6.8.1.1..4.6.8.1.1 Fgure F-5.Losses for each half brdge and oal loss of he converer. Connuous losses blue and average losses durng seady sae red. 135
The larges average loss of a half brdge s n he neural half brdge and s abou 55 W. The larges oal average loss of he converer s abou 11 W. 136
Appendx G - Nomenclaure Abbrevaons ACM DSP ESR IGBT PWM SEP UPS Auxlary Converer Module Dgal Sgnal Processor Equvalen Seres Ressance Isolaed Gae Bpolar Transsors Pulse-Wdh Modulaon Splerskyddad Enhes Plaform Unnerupable Power Supply Symbols C oupu fler capacance d an d bn d cn d d d dode d IGBT1 d q d phase a o neural duy rao phase b o neural duy rao phase c o neural duy rao duy rao n d-drecon n d-q- coordnaes duy cycle for dode duy cycle for IGBT 1 duy rao n q-drecon n d-q- coordnaes duy rao n -drecon n d-q- coordnaes E Drr, n reverse recovery energy of free wheelng dode E off E off _ dode E off _ IGBT1 E on E on_ dode E on_ IGBT1 e urn off energy of IGBT gven n daa shee urn off energy of dode urn off energy of IGBT1 urn on energy of IGBT gven n daa shee urn on energy of dode urn on energy of IGBT1 npu sgnal o conroller f f rpple f sw frequency rpple frequency swch frequency 137
I I lne I load I n rms curren hrough half brdge rms lne curren rms load curren curren hrough IGBT a whch E E on and off are gven I pp _ lne peak-o-peak of he raed oupu curren I pp _ rpple peak-o-peak curren rpple a converer curren phase a a _ load load curren, phase a b converer curren phase b b _ load load curren, phase b c converer curren phase c c _ load load curren, phase c d converer curren n d-drecon n d-q- coordnaes d _ load load curren n d-drecon n d-q- coordnaes î n q nsananeous curren hrough half brdge peak curren hrough half brdge average curren hrough half brdge converer curren n neural lne converer curren n q-drecon n d-q- coordnaes q _ load load curren n q-drecon n d-q- coordnaes converer curren n -drecon n d-q- coordnaes _ load load curren n -drecon n d-q- coordnaes K Kc P Kv P L L n M proporonal gan of PI-conroller proporonal gan of curren PI-conroller proporonal gan of volage PI-conroller phase lne nducance neural lne nducance Modulaon ndex P cond,dode P cond,igbt1 conducon loss power for dode conducon loss power for IGBT1 138
P loss connuous power loss of one half brdge P loss average power loss of one half brdge P off P on urn-off power of IGBT urn-on power of IGBT P sw, dode average urn-off losses of dode P sw, IGBT average urn-on and urn-off losses for one IGBT P Y P load power, Y-conneced load load power, -conneced load R C _ esr Equvalen Seres Ressance of C R dodeon R IGBT on on-sae ressance of dode on-sae ressance of IGBT R L _ esr Equvalen Seres Ressance of L S n Tc T d T n T T sw Tv load power of he converer negral me of curren PI conroller me delay perod me negral me of PI conroller swch perod me negral me of volage PI conroller me U ab U an U bc U bn U ca U cn U load lne o lne volage, phase a and phase b lne o neural volage, phase a and neural lne o lne volage, phase b and phase c lne o neural volage, phase b and neural lne o lne volage, phase c and phase a lne o neural volage, phase c and neural load volage over one mpedance Z Ulne lne lne o lne volage Ulne neural lne o neural volage V a peak volage, phase a 139
V b V c V DC peak volage, phase b peak volage, phase c DC-lnk volage V dc, n volage over IGBT a whch E E on and off are gven V dodeon V dodeon V dode, V IGBT on V IGBT on V IGBT, v a v ab forward volage drop of dode average forward volage drop of dode hreshold volage of dode forward volage drop of IGBT average forward volage drop of IGBT hreshold volage of IGBT phase volage, phase a lne o lne volage, phase a and phase b v a _ load load volage of phase a v an v ap v a V base v bc negave sequence volage componen, phase a posve sequence volage componen, phase a zero sequence volage componen, phase a maxmum lengh of volage vecor n lnear modulaon lne o lne volage, phase b and phase c v b _ load load volage of phase b v bn v bp v b v ca negave sequence volage componen, phase b posve sequence volage componen, phase b zero sequence volage componen, phase b lne o lne volage, phase c and phase a v c _ load load volage of phase c v cn v cp v c v d v q v ref v negave sequence volage componen, phase c posve sequence volage componen, phase c zero sequence volage componen, phase c volage n d-drecon n d-q- coordnaes volage n q-drecon n d-q- coordnaes volage reference volage n -drecon n d-q- coordnaes X αβ vecor n α - β -coordnaes X αβγ vecor n α - β - γ -coordnaes 14
Z a Z b Z c ϕ ω load mpedance, phase a load mpedance, phase b load mpedance, phase c phase dsplacemen angular frequency 141