Diode Circuits or Uncontrolled Rectifier

Transcription

1 EE 45- Elecric Drives Chaper Dr. Ali M. Elaaly Dide Circuis r Ucrlled ecifier. rduci Because f heir abiliy cduc curre i e direci, dides are used i recifier circuis. The defiii f recificai prcess is he prcess f cverig he aleraig vlages ad curres direc curres ad he device is kw as recifier is exesively used i chargig baeries; supply DC rs, elecrcheical prcesses ad pwer supply secis f idusrial cpes. The s faus dide recifiers have bee aalyzed i he fllwig secis. Circuis ad wavefrs draw wih he help f PM siulai prgra. There are w differe ypes f ucrlled recifiers r dide recifiers, half wave ad full wave recifiers. Full-wave recifiers has beer perfrace ha half wave recifiers. Bu he ai advaage f half wave recifier is is eed less uber f dides ha full wave recifiers. The ai disadvaages f half wave recifier are: - High ripple facr, - Lw recificai efficiecy, - Lw rasfrer uilizai facr, ad, 4- DC saurai f rasfrer secdary widig.. Perfrace Paraeers s recifier applicais, he pwer ipu is sie-wave vlage prvided by he elecric uiliy ha is cvered a DC vlage ad AC cpes. The AC cpes are udesirable ad us be kep away fr he lad. Filer circuis r ay her haric reduci echique shuld be isalled bewee he elecric uiliy ad he recifier ad bewee he recifier upu ad he lad ha filers u he udesired cpe ad allws useful cpes g hrugh., careful aalysis has be de befre buildig he recifier. The aalysis requires defie he fllwig ers: The average value f he upu vlage,, The average value f he upu curre,, The rs value f he upu vlage, rs, The rs value f he upu curre, rs The upu DC pwer, P * (.) The upu AC pwer, P ac rs * rs (.) The effeciecy r recificai rai is defied as η P / Pac (.) The upu vlage ca be csidered as beig cpsed f w cpes () he DC cpe ad () he AC cpe r ripple. The effecive (rs) value f he AC cpe f upu vlage is defied as:- ac rs The fr facr, which is he easure f he shape f upu vlage, is defied as shw i equai (.5). Fr facr shuld be greaer ha r equal e. The shape f upu vlage wavefr is eare be DC as he fr facr eds uiy. FF rs / (.5) The ripple facr which is a easure f he ripple ce, is defied as shw i (.6). ipple facr shuld be greaer ha r equal zer. The shape f upu vlage wavefr is eare be DC as he ripple facr eds zer. (.4)

2 Dide Circuis r Ucrlled ecifier 9 ac rs rs F FF (.6) Where ad are he rs vlage ad rs curre f he rasfrer secdery respecively. Tal Haric Disri (THD) easures he shape f supply curre r vlage. THD shuld be grearer ha r equal zer. The shape f supply curre r vlage wavefr is ear be siewave as THD eds be zer. THD f ipu curre ad vlage are defied as shw i (.8.a) ad (.8.b) respecively. THD i, ad THD v (.8) where ad are he fudaeal cpe f he ipu curre ad vlage, ad respecively. geeral, pwer facr i -siusidal circuis ca be baied as fllwig: eal Pwer P PF csφ (.) Appare laperes Where, φ is he agle bewee he curre ad vlage. Defiii is rue irrespecive fr ay siusidal wavefr. Bu, i case f siusidal vlage (a supply) bu -siusidal curre, he pwer facr ca be calculaed as he fllwig: Average pwer is baied by cbiig i-phase vlage ad curre cpes f he sae frequecy. P cs φ PF cs φ Disri Facr* Displacee Faacr (.) Where φ is he agle bewee he fudaeal cpe f curre ad supply vlage. Disri Facr fr siusidal perai ad displacee facr is a easure f i. displacee bewee v( ) ad ( ) igle-phase Half Wave Dide ecifier Wih esisive Lad Fig.. shws a sigle-phase half-wave dide recifier wih pure resisive lad. Assuig siusidal vlage surce, he dide beigs cduc whe is ade vlage is greaer ha is cahde vlage as a resul, he lad curre flws., he dide will be i ON sae i psiive vlage half cycle ad i OFF sae i egaive vlage half cycle. Fig.. shws varius curre ad vlage wavefrs f half wave dide recifier wih resisive lad. These wavefrs shw ha bh he lad vlage ad curre have high ripples. Fr his reas, siglephase half-wave dide recifier has lile pracical sigificace. Fig.. igle-phase half-wave dide recifier wih resisive lad.

3 Chaper Tw Fig.. arius wavefrs fr half wave dide recifier wih resisive lad. The average r DC upu vlage ca be baied by csiderig he wavefrs shw i Fig.. as fllwig: si d (.) Where, is he axiu value f supply vlage. Because he lad is resisr, he average r DC cpe f lad curre is: The r ea square (rs) value f a lad vlage is defied as: rs si d (.4) rs iilarly, he r ea square (rs) value f a lad curre is defied as: rs is clear ha he rs value f he rasfrer secdary curre, is he sae as ha f he lad ad dide curres The D (.5) Where, D is he rs value f dide curre. Exaple : The recifier shw i Fig.. has a pure resisive lad f Deerie (a) The efficiecy, (b) Fr facr (c) ipple facr (d) Peak iverse vlage (P) f dide D. lui: Fr Fig.., he average upu vlage is defied as: d si( ) ( cs cs()) The,

4 Dide Circuis r Ucrlled ecifier rs ( si ), rs ad, The rs value f he rasfrer secdery curre is he sae as ha f he lad: The, he efficiecy r recificai rai is: * P * η 4.5% Pac rs * rs * rs (b) FF. 57 ac (c) F FF.57. (d) is clear fr Fig. ha he P is.... Half Wave Dide ecifier Wih -L Lad case f L lad as shw i Fig.., The vlage surce, if vs si( ), v s is psiive whe < <, ad v s is egaive whe < <. Whe v s sars becig psiive, he dide sars cducig ad he surce keeps he dide i cduci ill reaches radias. A ha isa defied by radias, he curre hrugh he circui is zer ad here is se eergy sred i he iducr. The vlage acrss a iducr is psiive whe he curre hrugh i is icreasig ad i beces egaive whe he curre hrugh i eds fall. Whe he vlage acrss he iducr is egaive, i is i such a direci as frward-bias he dide. The plariy f vlage acrss he iducr is as shw i he wavefrs shw i Fig..4. Whe v s chages fr a psiive a egaive value, he vlage acrss he dide chages is direci ad here is curre hrugh he lad a he isa radias ad he dide ciues cduc ill he eergy sred i he iducr beces zer. Afer ha, he curre eds flw i he reverse direci ad he dide blcks cduci. The eire applied vlage w appears acrss he dide as reverse bias vlage. A expressi fr he curre hrugh he dide ca be baied by slvig he defereial equai represeig he circui. Fig.. Half Wave Dide ecifier Wih -L Lad

5 Chaper Tw Fig..4 arius wavefrs fr Half wave dide recifier wih -L lad. Assue Z φ j wl The Z w L, L Z csφ, L Z siφ ad a φ Z wl a φ Φ i ( ) si( φ) si( φ) e Z (.4) arig fr, as icreases, he curre wuld keep decreasig. Fr se value f, say β, he curre wuld be zer. f > β, he curre wuld evaluae a egaive value. ice he dide blcks curre i he reverse direci, he dide sps cducig whe reaches β. The value f β ca be baied by subsiuig ha i( ) w i (.4) we ge: β β a ( ) φ i β si( ) si( ) β φ φ e (.5) Z The value f β ca be baied fr he abve equai by usig he ehds f uerical aalysis. This average value ca be baied as shw i (.6). The rs upu vlage i his case is shw i equai (.7). β * si *( cs β ) d (.6) β rs * ( si ) * β.5( si( β ) dw (.7).4 igle-phase Full-Wave Dide ecifier The full wave dide recifier ca be desiged wih a ceer-aped rasfrer as shw i Fig..8, where each half f he rasfrer wih is assciaed dide acs as half wave recifier r as a bridge dide recifier as shw i Fig... The advaage ad disadvaage f ceer-ap dide recifier is shw belw:

6 Dide Circuis r Ucrlled ecifier Advaages The eed fr ceer-apped rasfrer is eliiaed, The upu is wice ha f he ceer apped circui fr he sae secdary vlage, ad, The peak iverse vlage is e half f he ceer-ap circui. Disadvaages requires fur dides isead f w, i full wave circui, ad, There are always w dides i series are cducig. Therefre, al vlage drp i he ieral resisace f he dides ad lsses are icreased. The fllwig secis explai ad aalyze hese recifiers..4. Ceer-Tap Dide ecifier Wih esisive Lad he ceer ap full wave recifier, curre flws hrugh he lad i he sae direci fr bh half cycles f ipu AC vlage. The circui shw i Fig..8 has w dides D ad D ad a ceer apped rasfrer. The dide D is frward bias ON ad dide D is reverse bias OFF i he psiive half cycle f ipu vlage ad curre flws fr pi a pi b. Whereas i he egaive half cycle he dide D is reverse bias OFF ad dide D is frward bias ON ad agai curre flws fr pi a pi b. Hece DC upu is baied acrss he lad. Fig..8 Ceer-ap dide recifier [ Fig..9 arius curre ad vlage wavefrs fr ceer-ap dide recifier wih resisive lad. case f pure resisive lad, Fig..9 shws varius curre ad vlage wavefr fr cverer i Fig..8. The average ad rs upu vlage ad curre ca be baied fr he wavefrs shw i Fig..9 as shw i he fllwig: si d ad (.6)

7 Chaper Tw 4 ( si ) rs d ad rs (.8) P f each dide (.4) (.4) The rs value f he rasfrer secdery curre is he sae as ha f he dide: D (.4) Exaple. The recifier i Fig..8 has a purely resisive lad f Deerie (a) The efficiecy, (b) Fr facr (c) ipple facr (d) Peak iverse vlage (P) f dide D. lui:- The efficiecy r recificai rai is * P * η 8.5% Pac rs * rs * rs (b) FF. ac (c) F FF.. 48 (d) The P is.4. igle-phase Full Bridge Dide ecifier Wih esisive Lad Aher aleraive i sigle-phase full wave recifier is by usig fur dides as shw i Fig.. which kw as a sigle-phase full bridge dide recifier. is easy see he perai f hese fur dides. The curre flws hrugh dides D ad D durig he psiive half cycle f ipu vlage (D ad D4 are OFF ). Durig Fig.. igle-phase full bridge dide recifier. he egaive e, dides D ad D4 cduc (D ad D are OFF ). psiive half cycle he supply vlage frces dides D ad D be "ON". sae ie i frces dides D ad D4 be "OFF"., he curre ves fr psiive pi f he supply vlage acrss D he pi a f he lad he fr pi b he egaive arked pi f he supply vlage hrugh dide D. he egaive vlage half cycle, he supply vlage frces he dides D ad D be "OFF". sae ie i frces dides D ad D4 be "ON"., he curre ves fr egaive arked pi f he supply vlage acrss D he pi a f he lad he fr pi b he psiive arked pi f he supply vlage hrugh dide D4., i

8 Dide Circuis r Ucrlled ecifier 5 is clear ha he lad curres ves fr pi a pi b i bh psiive ad egaive half cycles f supply vlage., a DC upu curre ca be baied a he lad i bh psiive ad egaive halves cycles f he supply vlage. The cplee wavefrs fr his recifier is shw i Fig... Fig.. arius curre ad vlage wavefrs f Full bridge sigle-phase dide recifier. Exaple 4 The recifier shw i Fig.. has a purely resisive lad f 5 Ω ad, si 4 ad uiy rasfrer rai. Deerie (a) The efficiecy, (b) Fr facr, (c) ipple facr, (d) The peak iverse vlage, (P) f each dide,, ad, (e) pu pwer facr. lui: si d ,. 74 A / rs ( si) d. P (a) η 8.6 % Pac rs rs rs (b) FF., rs 4. 4A ac rs rs (c) F FF. 48 (d) The P e al Pwer csφ (e) pu pwer facr Appera Pwer.4.4 Full Bridge igle-phase Dide ecifier wih DC Lad Curre The full bridge sigle-phase dide recifier wih DC lad curre is shw i Fig..4. his circui he lad curre is pure DC ad i is assued here ha he surce iducaces is egligible. his case, he circui wrks as explaied befre i resisive lad bu he curre wavefr i he supply will be as shw i Fig..5. Ad he rs value f he ipu curre is

9 Chaper Tw 6 Fig..4 Full bridge sigle-phase dide recifier wih DC lad curre. Fig..5 arius curre & vlage wavefrs fr sigle-phase dide bridge recifier fr pure DC lad. The supply curre i case f pure DC lad curre is shw i Fig..5, as we see i is dd fuci, he a cefficies f Furier series equal zer, a, ad [ ] [ ] ,,, 4 cs cs cs *si fr d b (.5) The fr Furier series cceps we ca say:...) 9 si 9 7 si 7 5 si 5 si *(si 4 ) ( i (.5) 46% )) ( ( THD s r we ca bai )) ( ( THD s as he fllwig: Fr (.5) we ca bai he value f is % 4 4 )) ( ( s THD

10 Dide Circuis r Ucrlled ecifier 7 Exaple 5 slve Exaple 4 if he lad is A pure DC lui: Fr exaple , rs. P rs (a) η 9 % (b) FF. P ac rs rs (c) F ac rs rs FF. 48 (d) The P 4 4 * (e) 7. A e al Pwer pu Pwer facr Appera Pwer * csφ A ad rs A *csφ 7. * Effec Of L O Curre Cuai Of igle-phase Dide Bridge ecifier. Fig..5 hws he sigle-phase dide bridge recifier wih surce iducace. Due he value f L he rasiis f he AC side curre i fr a value f (r vice versa) will be isaaeus. The fiie ie ierval required fr such a rasii is called cuai ie. Ad his prcess is called curre cuai prcess. arius vlage ad curre wavefrs f sigle-phase dide bridge recifier wih surce iducace are shw i Fig..6. Lag Fig..5 igle-phase dide bridge recifier wih surce iducace. Fig..6 arius curre & vlage wavefrs fr sigle-phase dide bridge recifier wih surce iducace.

11 Chaper Tw 8 Le us sudy he cuai ie sars a s as idicaed i Fig..6. A his ie he supply vlage sars be egaive, s dides D ad D have swich OFF ad dides D ad D4 have swich ON as explaied i he previus case wihu surce iducace. Bu due he surce iducace i will preve ha happe isaaeusly., i will ake ie cpleely ur OFF D ad D ad ake D ad D4 carry he eire lad curre ( ). Als i he ie he supply curre will chage fr which is very clear i Fig..6. Fig..7 shws he equivale circui f he dide bridge a ie. Fig..7 The equivale circui f he dide bridge a cuai ie L s u cs (.56) 4 L rd 4 f L (.6) The DC vlage wih surce iducace ackig i accu ca be calculaed as fllwig: acual wihu surceiduc ce rd 4 fls a (.6) s u. (.64) 8 u *si (.68) u si( u) pf (.69) u u Exaple 6 igle phase dide bridge recifier ceced k, 5 Hz, surce iducace X s 5H supply feed A pure DC lad, fid: (i) Average DC upu vlage, (ii) Pwer facr. Ad (iii) Deerie he THD f he uiliy lie curre. lui: (i) Fr (.6), * 5556 acual wihu surceiduc ce rd 4 fls a

12 Dide Circuis r Ucrlled ecifier 9 *5556 acual 4*5*.5* 97 (ii) Fr (.56) he cuai agle u ca be baied as fllwig: Ls * * * 5 *.5 * u cs cs.85rad The ipu pwer facr ca be baied fr (.69) as fllwig ( ) ( ) u *si u *si.85 pf * cs u u.85 u * A 8 u 8*.85 *si *si A u *.85 THD i %.5 Three Phase Dide ecifiers.5. Three-Phase Half Wave ecifier Fig.. shws a half wave hree-phase dide recifier circui wih dela sar hree-phase rasfrer. his circui, he dide wih highes peial wih respec he eural f he rasfrer cducs. As he peial f aher dide beces he highes, lad curre is rasferred ha dide, ad he previusly cduc dide is reverse biased OFF case. Fr he recifier shw i Fig.. he lad vlage, priary dide curres ad is FFT cpes are shw i Fig.., Fig.. ad Fig..4 respecively Fig.. ecdary ad lad vlages f half wave hree-phase dide recifier.

13 Chaper Tw Fig.. Priary ad dide curres. Priary curre Dide curre Fig..4 FFT cpes f priary ad dide curres. 5 By csiderig he ierval fr i he upu vlage we ca calculae he average 6 6 ad rs upu vlage ad curre as fllwig: 5 / 6 si d. 87 / 6 5 / 6 ad * rs / 6 ( si ) d..87 * * * (.7) (.7).847 (.7) The he dide rs curre is equal secdery curre ad ca be baied as fllwig: 847 r (.74) rs

14 Dide Circuis r Ucrlled ecifier Ne :he rs value f dide curre has bee baied fr he rs value f lad curre divided by because he dide curre has e hird pulse f siilar hree pulses i lad curre. TheP f he dides is (.75) LL Exaple 7 The recifier i Fig.. is peraed fr 46 5 Hz supply a secdary side ad he lad resisace is Ω. f he surce iducace is egligible, deerie (a) ecificai efficiecy, (b) Fr facr (c) ipple facr (d) Trasfrer uilizai facr, (e) Peak iverse vlage (P) f each dide. lui: 46 (a) 65.58, 65.58* , 87 rs. 847,.847 P rs The, η Pac rs rs % rs (b) FF.657 % (c) F ac rs rs FF 8.8 % (e) The P Three-Phase Half Wave ecifier Wih DC Lad Curre ad zer surce iducace case f pure DC lad curre as shw i Fig..5, he dide curre ad priary curre are shw i Fig..6. T calculae Furier rasfr f he dide curre f Fig..6, i is beer ve y axis ake he fuci as dd r eve cacel e cefficie a r b respecively. f we pu Y-axis a pi he we ca deal wih he secdary curre as eve fucis. The, b f secdary curre. alues f a ca be calculaed as fllwig: / a a d / / / *cs dw [ si ] / / * fr,,7,8,,4,... * fr 4,5,,,6,7 fr all replea harics (.77)

15 Chaper Tw... si8 8 si 7 7 si 5 5 si 4 4 si si ) ( O O s (.78) 9.4%.94 9 * / )) ( ( O s THD Fig..6 Priary ad secdary curre wavefrs ad FFT cpes f hree-phase half wave recifier wih lad curre New axis

16 Dide Circuis r Ucrlled ecifier Exaple 8 lve exaple 7 if he lad curre is A pure DC 46 lui: (a) 65.58, 65.58* , A , rs A rs 759 P.6* η 98.7 % Pac rs rs 5.759* rs (b) FF.657 % ac rs rs (c) F FF 8.8 % (d) The P Three-Phase Full Wave Dide ecifier.5. Three-Phase Full Wave ecifier Wih esisive Lad he circui f Fig.., he AC side iducace L is egleced ad he lad curre is pure resisace. Fig.. shws cplee wavefrs fr phase ad lie lie ipu vlages ad upu DC lad vlages. Fig.. shws dide curres ad Fig.. shws he secdary ad priary curres ad P f D. Fig..4 shws Furier Trasfr cpes f upu DC vlage, dide curre secdary curre ad Priary curre respecively. L p s 5 L a b 4 6 c Fig.. Three-phase full wave dide bridge recifier. Fr he recifier shw i Fig.. he wavefrs is as shw i Fig... The average upu vlage is :- / si d / LL /.654 LL.55 9 * ( si ) d LL rs 56 4 rs / LL LL (.9) (.9) (.9).6554 (.94)

17 Chaper Tw 4 The he dide rs curre is.6554 r (.95).9667 (.96) Fig.. shws cplee wavefrs fr phase ad lie lie ipu vlages ad upu DC lad vlages. Fig.. Dide curres.

18 Dide Circuis r Ucrlled ecifier 5 Fig.. ecdary ad priary curres ad P f D. Fig..4 Furier Trasfr cpes f upu DC vlage, dide curre secdary curre ad Priary curre respecively f hree-phase full wave dide bridge recifier. Exaple The recifier shw i Fig.. is peraed fr 46 5 Hz supply ad he lad resisace is Ω. f he surce iducace is egligible, deerie (a) The efficiecy, (b) Fr facr (c) ipple facr (d) Peak iverse vlage (P) f each dide. 46 lui: (a) 65.58, 65.58* , A 9* rs , rs. 876 A

19 Chaper Tw 6 P rs η 99.8 % ad (b) FF.8 % P ac rs rs (c) F ac rs rs FF 4 % ad (d) The P Three-Phase Full Wave ecifier Wih DC Lad Curre The supply curre i case f pure DC lad curre is shw i Fig..5. Fas Furier Trasfr f ecdary ad priary curres respecively is shw i Fig.6. As we see i is dd fuci, he a, ad b b b 5 / 6 / 6 *si d [ cs ], b5 ( ), b7 ( 5 7, fr,,4,6,8,9,,,4,5,... 5 / 6 / 6 ), b ( s ( ) si si 5v si 7 si si (.98) 5 7 THD( s ( )) Als THD( s ( )) ca be baied as fllwig: 9 ), 5 b ( % ),... (.97) *, he, / ( ( )) THD s */.% Pwer Facr * cs( ) Fig..5 The D ad D curres, secdary ad priary curres.

20 Dide Circuis r Ucrlled ecifier 7 Fig.6 Fas Furier Trasfr f ecdary ad priary curres respecively..5.4 Three-Phase Full Wave Dide ecifier Wih urce ducace The surce iducace i hree-phase dide bridge recifier Fig..7 will chage he shape f he upu vlage ha he ideal case (wihu surce iducace) as shw i Fig... The DC cpe f he upu vlage is reduced. Fig..8 shws The upu DC vlage f hreephase full wave recifier wih surce iducace. Fig..7 Three-phase full wave recifier wih surce iducace Fig..8 The upu DC vlage f hree-phase full wave recifier wih surce iducace

21 Chaper Tw 8 Cuai agle is, L u cs LL (.9) 6 L The DC vlage reduci due surce iducace is : rd 6 fl (.4) The DC vlage wihu surce iducace ackig i accu ca be calculaed as fllwig:.5 6 fl (.5) acual wihu surceiduc a ce u 6 u 6 ad si u The pwer facr ca be calculaed fr he fllwig equai: 6 u si u u u *si( u) pf cs cs u u u 6 6 rd Exaple Three phase dide bridge recifier ceced ree phase k, 5 Hz supply has 8 H surce iducace feed A pure DC lad curre Fid; (i) Cuai ie ad cuai agle. (ii) DC upu vlage. (iii) Pwer facr. (iv) Tal haric disri f lie curre. lui: (i) By subsiuig fr * * 5, d A, L. 8H, LL i (.9), he u.549 rad (ii) The he acual DC vlage ca be baied fr (.5) as fllwig:.5 6 fl acual wihu surceiduc a ce acual.5* 6 *5*.8* 48 (iii) he pwer facr ca be baied fr (.) he *si( u) si(.549) pf.9644 Laggig u.549 u.549* 6 6 (iv) The rs value f supply curre ca be baied as fllwig: rd LL d u *.549 s * 9. 99A 6 6 The rs value f fudaeal cpe f supply curre ca be baied fr (.) as 4 u 4 *.549 fllwig: si * *si. 8A u *.549* u pf * cs * cs.9644 Laggig THD i s LL 4.5% d d