Lab no. THEE-PHASE MIDPOINT ECTIFIES WITH CUENT FILTES. Inroducon Mdpon recfers (M are usually suppled hrough a cenre-apped ransformer. In he case of he hree-phase mdpon recfer (M, he ransformer may be mssng, f here s an access o he neural pon of he power grd. Many mes, he presence of he ransformer s jusfed by he necessy o opmze he magnude of he recfer oupu volage o he level demanded by he load. However, he presence of he ransformer s expensve, because each secondary wndng supples he recfer durng only a sngle half-cycle of he npu AC volage. Consequenly, for a gven load power, he ransformer mus be overszed. The advanages of he mdpon recfers conss n he small number of semconducor devces used by he power srucure and also n he smplcy of he conrol crcu (gae rgger crcu. On he oher hand, compared wh he hree-phase brdge recfer (B6 he pulses frequency of he oupu volage s half of he pulse frequency of he oupu volage provded by a hree-phase brdge recfer. Therefore, he curren and volage flers used by he hree-phase mdpon recfers mus be hgher. In addon, he maxmum value of he DC volage provded by a M recfer s half of he maxmum value provded by he B6 recfer and o he M recfer he dsconnuous conducon mode may be appear a a lower delay (frng angle. If one aes no accoun all hese dsadvanages and he endency n he modern power elecroncs o elmnae and reduce, as much as possble, he nducances and he capaces of he power elecronc sysems by adopng slcon alernaves, s easly explaned why he mdpon recfers are rarely used. Ther analyss s jusfed by ddacc reasons because hey are smpler and he brdge srucure s acheved hrough a combnaon of wo mdpon srucures. In applcaons whose power exceedng W, hree-phase recfers are recommended. Compared wh a sngle-phase recfer, a hree-phase recfer has he followng advanages: loadng symmercal he hree-phase power grd (uly grd; he pulse frequency from he oupu volage waveform s hgher, whch allows he flers sze reducon; Auhors: M. Albu,. Bojo, M.P. Daconescu
Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory for he same npu AC volage, he maxmum oupu DC volage s hgher n case of hree-phase recfers; dsconnuous conducon mode may occur over a delay angle of o he M phase-conrolled recfer and over a delay angle of 6 o he B6 phase-conrolled recfer (a he sngle-phase recfers dsconnuous conducon mode can occur as soon as he delay angle leavng o value.. Three-phase mdpon recfers (M A hree-phase mdpon opology (M s shown n Fg... Ths ncludes a hree-phase lne-frequency ransformer (T whose secondary wndngs, n sar connecon, supply a power srucure wh hree dodes (unconrolled recfer or wh hree hyrsors (phase-conrolled recfers. The DC load of he recfer s conneced beween he posve bus (cahode ermnals conneced ogeher and he common pon (mdpon of he secondary wndngs, as shown n he fgure. For smplcy we wll analyze he recfer wh a ressve-nducve -L load (recfer wh curren fler. The ransformer T s suppled wh he hree-phase volages of he power grd: v, v S, v T. v T v s T T v S v ss T T v T v st T T d I d v d d I d (- L f - ( load - Fg.. Three-phase mdpon recfer (M wh curren flers. The fler nducance L f ncluded n he load crcu s consdered suffcenly large o fler well he oupu DC curren and o manan he recfer n a normal operaon mode connuous conducon mode. Consequenly, one can approxmae: d ( I d consan. Based on he naural commuaon process, hs curren s cyclcally commuaed beween hree pahs correspondng o he T, T, T hyrsors. a Naural commuaon process n he case of a hree-phase mdpon recfer (M In power elecroncs he exended noon of he commuaon (swchng means he passng of he elecrc curren from one crcu pah (branch o anoher crcu pah (branch.
Lab no.: Three-phase mdpon recfers wh curren flers Naural commuaon mples he naural ransfer of he curren from one branch crcu o anoher branch under he pressure of a commuaon volage ha appears afer he semconducor devce found on he nex branch s urned on. Ths curren commuaon s used n power srucures made exclusvely wh power semconducor devces whou urn-off conrol (dodes, hyrsor and racs. These devces canno sop, a order he curren flow hrough a crcu branch. Thus, a curren devaon echnque s used wh he help of a volage ha decreases he curren hrough he frs pah and ncreases he curren hrough he new, second, pah. A cyclcal commuaon of he curren beween wo or more crcu branches can occur f he commuaon volages are alernave. For hs reason, he naural commuaon echnque can be used only n power srucures suppled by he AC power sources. The M hree-phase mdpon recfer s a suggesve power srucure wh he help of whch can be explaned n deal he naural commuaon process. Thus, n Fg.. he oupu DC curren I d, consdered consan, s perodcally commuaed beween he hree T, T, T branches wh he me perod T p T/f, where f s he frequency of he npu AC volage. In order o descrbe mahemacally he successve seps whch occur durng he naural commuaon we consder he nal suaon n whch he T hyrsor s on. Thus, he equvalen crcu whch may descrbe he naural commuaon of he I d curren from he ( pah ha ncludes he T hyrsor o he ( pah ha ncludes he T hyrsor s shown n Fg... v s L T T T T d I d v d I d I d u p vss T L T T T v d ( L f load T urn-on (a (b Fg.. (a Equvalen crcu ha llusraes he naural commuaon process; (b Currens evoluon hrough crcu branches durng he commuaon me. In he overall case, each branch nvolved n he curren commuaon process can be equvalen wh a seres crcu ha ncludes an AC source, an ressance, an L nducance and a hyrsor whose urn-on momen sars he naural commuaon Auhors: M. Albu,. Bojo, M.P. Daconescu
4 Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory process. For he mdpon hree-phase srucure shown n Fg.., he npu AC source consss of he hree volages nduced n he T secondary wndngs, v s, v ss and v st. Due o hese volages he commuaon volage v appears whose polary maes possble he curren commuaon. In Fg.. was represened he polary of v volage ha favours he I d commuaon from he ( branch o ( branch. The L nducances from he branches are hose who have he las mpac on he naural commuaon process. Due o her presence, he curren canno suddenly commuae from one branch o anoher branch. Thus, a commuaon me nerval appears n whch I d flows hrough he boh branches (I d T T see Fg... A suggesve explanaon can be made f one aes no consderaon he commuaon curren mposed by he v commuaon volage. As shown n he fgure, hs volage decreases he curren from he ( pah and ncreases he curren from he ( pah. T ( d T I ( ; ( ( (. To oban he curren waveform and he value of he commuaon me nerval wll be wren he volage equaon (Krchhoff n he loop formed by he wo branches: d d( Id v L ( Id L (. d d where he v commuaon volage s gven by dfference of he wo sne wave volages from he branches: v vss vs ( Vs sn( ω 5 (. Wh V s s labelled he rms value of phase volage from he ransformer secondary wndngs. Vs s he rms lne-o-lne volage from he hree-phase ransformer secondary wndngs. For smplcy, he commuaon volage v s consdered as a reference volage: v V snω (.4 (max Tang no consderaon ha he dervave of he I d curren (consan s zero, he equaon (. becomes: d ( ( L L V (max snω Id (.5 d I was obaned a frs-order dfferenal equaon whose soluon consss of hree erms as follows: Frs erm (he ransory soluon of he homogeneous dfferenal equaon: τ ( K e (.6
Lab no.: Three-phase mdpon recfers wh curren flers Auhors: M. Albu,. Bojo, M.P. Daconescu 5 where K s he negraon consan and L L τ s he me consan of he loop formed by he wo branches. The second erm (he seady-sae soluon gven by V ω sn (max : ( Z V ϕ ω sn ( (max (.7 where ( ( L L Z ω s he whole mpedance of he loop and ( arcg L L ω ϕ s he phase dsplacemen beween and v. The hrd erm (he seady-sae soluon gven by d I : d I ( (.8 Therefore, he whole soluon of he dfferenal equaon (.5 can be wren as: ( d I Z V e K (max sn ( ( ( ( ϕ ω τ (.9 Assumng ha α/ω s he momen when he naural commuaon process sar, when he T hyrsor s urned on (see Fg...b, he K negraon consan can be calculaed nowng ha he commuaon curren s zero n hs momen: ( d I Z V e K (max sn ( ϕ ω τ (. Afer arbung he value for he consan K n he expresson (.9 we can calculae he commuaon me nerval consdered complee when he hyrsor T branch aes he whole I d curren ( me, descrbed mahemacally by he equaly: ( d d I Z V e K I (max sn ( ϕ ω τ (. Equaon (. can be solved by numercal mehods o oban he me value. Based of hs, can be calculaed he value of he commuaon me nerval: ( I d f, α (.
6 Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory One can observe ha he duraon of he commuaon process s nfluenced by he value of he conrol angle (α ω and by he value of he load curren I d. Correspondng o he commuaon me nerval, one can defne an elecrc angle, parameer used n pracce. Ths angle s called commuaon angle or overlappng anodc angle. The laer denomnaon s jusfed by he fac ha durng he curren commuaon process, he boh hyrsors or he boh dodes are n on-sae (conducon whch s equvalen wh a superposon of he anode ermnals (shor crcu. In he leraure we fnd varous noaons for he commuaon angle u, µ, γ ec. Whaever he noaon, s value s gven by he equaon: γ ω [ o el.degree] (. Nex, he commuaon angle wll be noed wh γ (gamma. Because depends on he load curren and on he delay angle hrough he K consan, s evden ha he commuaon angle value depends, also, on hese varables γ f (α, I d. Ths aspec s very mporan, because he commuaon angle modfes he average (DC value of he volage from he oupu of he lne-commuaed recfers. If we analyze he equvalen crcu shown n Fg...(a durng commuaon me nerval and we apply he second Krchhoff law, we can wre he followng equaons: d For he frs pah: vd ( vs L (.4 d d For he second pah: vd ( vss L (.5 d Consderng ha he recfer branches are symmercally, we can wre: and L L. Under hese condons, f we sum he equaon (.4 wh (.5 we ge: vs( vss ( vd ( vs( vss ( vd (, (.6 The equaon (.6 emphaszes ha durng he commuaon me nerval he volage a he recfer oupu s he mean of he AC volages from he wo branches whch are n he naural commuaon process. b Analyss of hree-phase mdpon recfers M The waveforms whch hghlgh he operaon of hree-phase mdpon recfers ang no consderaon he naural commuaon process are presened n Fg... The naural commuaon pon for he T hyrsor s placed n he poson n whch he commuaon volage u u ss u s passes hrough zero and becomes posve. I can be noced ha, he naural commuaon pons for hree-phase recfers are placed a he nersecon of he phase volages waveforms. For he
Lab no.: Three-phase mdpon recfers wh curren flers 7 hyrsors whch operae durng he posve half-waves, as n he case of M srucure from Fg.., hese pons are labeled P, P and P (see Fg... Wh a delay from hem, wh he same frng angle, are rggered he hyrsors T, T, and T (n he fgure are shown he waveforms for α 6 o. The Fg.. shows he commuaon curren, when he T curren decreases and he T curren ncreases durng he γ commuaon angle. Afer T/ me nerval (T/f s he me perod of he npu AC volage he nex naural commuaon of he I d curren occurs, from he T hyrsor branch o he T hyrsor branch, followed by he commuaon o he T hyrsor branch, bac agan. Thus, each hyrsor say n conducon a T p T/ me nerval or a π/ radans angle durng he whole T me perod. v s, v ss, v st V s(max α v s α 6 o v ss α Trgger pulses P T P π T P T π ω v d v st Area Aγ Area A v d ω Area B v, V l(max T p T/ v v ss - v s ω ω I d ω α γ T, T, T I d T T T T T T I d T T ω Fg.. eal waveforms whch ae no consderaon he naural commuang process a he hree-phase mdpon phase-conrolled recfer M. Auhors: M. Albu,. Bojo, M.P. Daconescu
8 Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory Analyzng he waveform of he oupu volage we can observe ha, durng he γ commuaon angle, he volage v d ( s equal wh he mean value of he phase volages from he commung branches, accordng o he relaon (.6. In deal curren commuaon condons (γ L L L and when he ressances of he commuaon branches are negleced ( he v d ( oupu volage waveform consss of successve pulses gven by dencal porons of he phase volages v s, v ss, v st, whou Aγ areas, as shown n Fg..4. Thus, he oupu DC volage can be calculaed applyng he average formula durng a pulse me perod T p : T p no Vd α average value of vd ( vd ( d [ Area A Area B] T (.7 π / p -π/ α 6 o P T v s π/ α P T v ss α P v st. T Trgger pulses ω v d Area A v d -π/α Area B π/α ω [rad, o el] d T p T/π/ d T T T T I d ω Fg..4 Waveforms n he case of an deal curren commuaon for he mdpon hree-phase conrolled recfer. A fas mehod o calculae he V dα expresson s o place he me orgn n fron of an oupu volage pulse for whch s appled he average value formula, a mdway locaon beween wo naural commuaon pons, as shown n Fg..4.
Lab no.: Three-phase mdpon recfers wh curren flers 9 Consequenly, n expresson (.7, v d ( can be descrbed wh he cosne funcon durng a pulse me perod T p (π/ rad. I follows: V d α π / π α π α V s V cos( ω d( ω π V π π 6 sn α sn α π V s π s s π α [ sn( ω ] π α cosα (.8 If we consder he conrol angle α o he operaon of he hyrsor recfer becomes smlar wh ha of a dode recfer and he average oupu volage s: V 6 Vs 6 Vs d cos, 7 π π V s (.9 Thus, n case of deal curren commuaon (nsananeous, he average value of oupu volage of he same conrolled recfer wh a ceran delay angle α can be wren as: V d α V d cosα (. whch s a nown and vald equaon, as was presened before n Lab no.8, f he recfer operaes n connuous conducon mode and n deal curren commuaon condons. In case of real curren commuaon condons should be aen no consderaon Area Aγ whch s mssng from Area A >. Correspondng o he mssng area he average value of he oupu volage decreases wh: Vdα Area Aγ Area Aγ (. T π / p The Area Aγ from Fg.. can be calculaed ang no consderaon he oupu volage decreases due o he naural commuaon process: Area Aγ v ( d α γ α L L d d( ω d d d d (. In he equaon (. he ressances and nducances were consdered equals on he wo commuaon branches: and L L L. Wh hs equaon s que dffcul o calculae Area Aγ. For hs reason s neglecng he Auhors: M. Albu,. Bojo, M.P. Daconescu
Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory ressances ( whch are much lower han he nducve reacance ( <<ωl.. In hs smplfed condons he equaon (. negral can be easly calculaed: α γ Id d L d( ω ω L d α Area A γ d ω L I (. Usng he equaon (. resuls he expresson of he average oupu volage f s aen no consderaon he real commuaon process, bu neglecng he volage drops on he branches ressances: ' ωl Id Vdα Vd cosα Vdα Vd cosα (.4 π / The equaon (.4 reveals ha he DC volage provded by a conrolled recfer do no depends only on he delay angle, even he converer operaes n connuous conducon mode. The oupu DC volage has small decreases once he load curren I d ncreases, as shown n Fg..5 where are presened he load characerscs whose slope s nduced by he naural commuaon process and by he nernal mpedances of he AC source. d V dα V d,7,5,4 I d V dα α α 45 α 6 α 7 I d Fg..5 Load characerscs of he phase-conrolled recfers. The volage drop U d α gven by equaon (.4 s greaer f we ae no consderaon he ressances from he commuaon branches ( and he nernal mpedances of he AC source (Z s. U f ωl,, Z, I (.5 dα ( s d The load characerscs shown n Fg..5 are presened wh dashed lnes a small I d currens, because no maer how large s he fler nducance, n he small currens range he recfer operaes n dsconnuous conducon mode and he DC oupu volage ncreases. These ncreases are no presened n he fgure.
Lab no.: Three-phase mdpon recfers wh curren flers The V dα dependence on he load curren can be reduced f he recfers are suppled by ransformers whose leaage nducances and wndng ressances have low values. A furher mprovemen can be obaned f he recfer s suppled drecly from he power grd, whou ransformer. In hs varan, n he naural curren commuaon process are nvolved only he low values of he grd nducance and ressance.. Laboraory applcaon In order o acheve he laboraory seup wh he hree-phase mdpon conrolled recfer wll be used a flexble laboraory nsallaon especally desgned for he hreephase recfers sudy see Fg..6. (a Fron vew (b ear vew Fg..6 Laboraory nsallaon for hree-phase recfers sudy. The laboraory equpmen conans wo pars: he power par and he conrol par. The crcu elemens ncluded n he power par (hyrsors, power dodes, hea sns, -C snubbers, fuses ec. are mouned on he bac of a panel, as shown n he Fg..5(b. On he fron of hs panel s ploed he crcu dagram wh he avalable power semconducor devces (hyrsors, dodes and are mouned sandard connecors (banana soces for he devces ermnals. Thus, wh he help of especally bars and banana plug cables, we can modfy he connecons beween ermnals n order o oban dfferen opologes of he hree-phase recfers: mdpon recfer, full-conrolled brdge recfer, half-conrolled brdge recfer. The connecors on he fron panel also mae possble an easy access o varous pons n he power srucure for measurng or for dsplayng he waveforms of ceran varables (volages, currens ncludng he rgger pulses from he hyrsors gae ermnals. Auhors: M. Albu,. Bojo, M.P. Daconescu
Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory The conrol par has a modular srucure wh boards crcus (cards mouned n a specal drawer hrough gudes and couples. I can be lsed he followng modules (from he lef o he rgh n he fron vew of Fg..5.(a: he conrol module ha ncludes a poenomeer for he α delay angle adjusmen and he STAT/STOP buons for he man conacor ha supples he power par; he DC source module ha ncludes a regulaed double DC source (±5V dc for he conrol par supply; modules wh he gae rgger crcus for he hyrsors of he hree-phase brdge legs; he module ha dsrbues he gae rgger pulses o he 6 hyrsors; he module wh synchronzaon ransformers for he gae rgger crcus. The gae rgger crcus are acheved wh he UAA45 negraed crcus n a mproved scheme: wh a consan curren crcu n order o oban a lnear slop of he saw-ooh sgnal, wh poenomeers mouned on he module fron panels o adjus he wdh of he zero-crossng sync pulses and of he gae rgger pulses, ec. On he fronal panel of he modules are placed also connecors o measure and dsplay he followng sgnals: zero-crossng sync pulses, saw-ooh sgnals, gae rgger pulses and synchronzaon volages. The las ones are obaned wh he help of he synchronzaon ransformers suppled wh he lne-o-lne volages because her zero-crossng mars he naural commuaon pons for he hyrsors ncluded n a hree-phase recfer. Each rgger crcu (module provdes gae rgger pulses, wh he same delay angle value, for boh, he upper and boom hyrsors of he brdge legs. v v S v T K T 4/8V ac v s v ss v st T T T d v d L f (AT v - (heosa Fg..7 The laboraory seup for he hree-phase mdpon recfer sudy. Because wh he help of he laboraory seup we wan o oban also he hreephase full-brdge opology, he conrol par conans a module ha dsrbues he gae rgger pulses o he 6 hyrsors, module acheved wh a logc crcu havng he role of ransmng wo rgger pulses, 6 o shfed, for each hyrsor gae. The second pulse s
Lab no.: Three-phase mdpon recfers wh curren flers useful o sar he hree-phase brdge recfer and o manan he operaon of hs recfer n dsconnuous conducon mode (see Lab no.. The pulse ransformers are placed n close proxmy of each hyrsor o avod he possbly of nducng a false conrol sgnals. In he same purpose he connecng wres hrough whch are ransmng he gae rgger pulses are wsed. In order o oban he expermenal mdpon hree-phase srucure (Fg..7, wll be used from he laboraory nsallaon, above descrbed, only he hyrsors whch operae on he posve half-wave T, T and T. Thus, her anode ermnals wll be conneced, by means of he bananas plugs cables, o he secondary wndngs of he hree-phase ransformer T. The ressve-nducve (-L load of he M phaseconrolled recfer wll be conneced beween he posve DC bus (bar ha connecs he hyrsors cahode ermnals and he mdpon of he T secondary wndngs n sar connecon. As fler nducance wll be used an auoransformer (AT and as a load ressance a rheosa (. In Fg..8 s shown he mage of he laboraory seup. T M AT heosa Shun Fg..8 Image of he laboraory seup. To smulaneously dsplay he waveforms of he oupu volage v d and curren d (v mus be used a wo spo osclloscope and for measurng he average value of he oupu volage V dα wll be used a volmeer. I can be dsplayed he waveforms correspondng o he M phase-conrolled recfer n case of a purely ressve load by movng he cursor of he auoransformer n he zero poson. 4. Objecves and procedures. I wll be analyzed he naural curren commuaon process a he hree-phase mdpon recfers and how s affeced he oupu volage waveform durng he commuaon angle. Auhors: M. Albu,. Bojo, M.P. Daconescu
4 Gheorghe Asach Techncal Unversy of Ias, Power Elecroncs Laboraory. I wll be suded he heorecal aspecs regardng he operaon of he hreephase mdpon recfers wh curren flers: waveforms, average volage equaon n case of deal curren commuaon and n case of real curren commuaon, load characerscs, ec.. I wll be performed he laboraory seup wh he crcu dagram from Fg..7 and wll be sared he operaon of he converer n connuous conducon mode (hgh L f n order o vew he waveforms v d and d for varous delay angles n recfer mode (α<9 o ; 4. I wll be measured he oupu DC (average volage V dα for varous delay angles wh he help of he volmeer n case of connuous conducon mode; 5. I wll be fxed a delay angle hgher han o and wll be progressvely decreased he nducance from he load crcu by acng on he auoransformer's cursor unl he dsconnuous conducon mode appear and wll be noced he ncreasng of he average volage as hs mode emphaszes; 6. I wll be dsplayed he waveforms v d and d a he lm, when he nducance L f s zero (he load s purely ressve and wll be noced ha he dsconnuous conducon mode appear afer he delay angle ncreases beyond o (α> o. eferences: [] Mohan N., Undeland T., obbns W., Power Elecroncs: Converers, Applcaons and Desgn, Thrd Edon, Publshed by John Wlley &Sons Inc., USA,. [] Ercson., Masmovc D, Fundamenals of Power Elecroncs, Unversy of Colorado, Boulder, Colorado, Publshed by Kluwer Academc Publshers, USA,. [] Albu M., Elecroncă de puere - vol I: Noţun nroducve, dspozve, conversa sacă alernav-connuu a energe elecrce, Casa de Edură Venus Iaş, 7. [4] Albu M., Daconescu M., Bojo., Comanda semconducoarelor de puere, converoare sace cu comuaţe naurală, Casa de Edură Venus, Iaş, 8. [5] Daconescu M.P., Graur I.,: Converoare sace baze eorece, elemene de proecare, aplcaţ, Ed. Gh. Asach, Iaş, 996. [6] Ionescu Fl., Florcău D., Nţu S., Sx J.P, Delarue Ph., Boguş C.: Elecroncă de puere - converoare sace, Ed. Tehncă, Bucureş, 998. [7] Kelemen A., Imecs M., Elecroncă de puere, Ed. Ddaccă ş Pedagogcă, Bucureş, 98.