CH.4 Full-wave and Three- phase rectifiers (Converting AC to DC)

1. 4-1Introduction TheaveragecurrentinACsourceiszerointhefull-waverectifier, thusavoidingproblemsassociatedwithnonzeroaveragesourcecurrents, particularlyintransformers. Theoutputofthefull-waverectifierhasinherentlylessripplethanthehalf-waverectifier. Uncontrolledandcontrolledsingle-phaseandthree-phasefull-waveconvertersusedasrectifiersareanalyzed. CH.4Full-waveandThree- phaserectifiers(ConvertingACtoDC)

2. 4-2Single-phasefull-waverectifiers Fig.4-1 Bridgerectifier： Thelowerpeakdiodevoltagemakeitmoresuitableforhigh-voltageapplications.

4. Fig.4-2 center-tappedtransformerrectifier Withelectricalisolation,onlyonediodevoltagedropbetweenthesourceandload, suitableforlow-voltage, high-currentapplications

5. Resistiveload： powerabsorbedbytheloadresistor： powerfactor ：Pf=1

6. R-Lload：　Fig.4-3

7. IfLisrelatively large, theloadcurrentisessentiallydc. ( ) Sourceharmonics arerichintheodd-numberedharmonics. Filters：reducingtheharmonics.

8. R-L source load：　Fig.4-5

9. Forcontinuouscurrentoperation, theonlymodificationtotheanalysisthatwasdoneforR-LloadisinthedctermoftheFourierseries .Thedccomponentof currentinthiscircuitis. ThesinusoidaltermsintheFourieranalysisareunchangedbythedcsource, providedthatthecurrentis continuous. Discontinuouscurrentisanalyzedlikesection3-5.

10. Capacitanceoutputfilter: Fig. 4-6

11. Assumingidealdiodes ：theanglewherethediodesbecomereversebiased, which isthesameasforthehalf-waverectifierandis =？　　solvednumericallyfor Peak-to-peakvariation(ripple)：

12. InpracticalcircuitswhereωRC , minimaloutputvoltageoccursat ishalfthatofthehalf-waverectifier.

13. Fig. 4-7(a) Voltagedoubler Fig. 4-7(b) Dualvoltagerectifier =full-waverectifier(sw.open)+ voltagedoubler(sw.closed)

14. L-Cfilteredoutput： Fig.4-8 C holdstheoutputvoltageataconstantlevel, andtheLsmoothesthecurrentfromrectifierandreducesthepeakcurrentindiodes.

15. =0 , full-waverectified ContinuousCurrent： Thevariationincanbeestimatefromthefirst Acterm(n=2) intheFourierseries. Theamplitudeoftheinductorcurrentforn=2is where ForContinuouscurrent, 

16. Discontinuouscurrent： Whenispositive ( at ) ,

17. ProcedurefordeterminingVo： • EstimateaValueforVoslightlybelowVm, andsolve (2) Solvenumerically, (3) Solve (4) SloveVo= (5) Repeatstep(1)~(4) untilthecomputedVoinstep(4) equalstheestimatedVoinstep(1) OutputVoltagefordiscontinuouscurrentislargerthan forcontinuouscurrent.(seeFig4-8(d))

18. 4-3controlledfull-waverectifiers Resistiveload： 　Fig.4-10

19. Thepowerdeliveredtotheload Thermscurrentinsourceisthesameasthermscurrentin theload.

20. R-Lload : Fig.4-11

21. discontinuouscurrent : for Fordiscontinuouscurrent Analysisofthecontrolledfull-waverectifieroperatinginthediscontinuouscurrentmodeisidenticaltothatofthecontrolledhalf-waverectifier, exceptthattheperiodfortheoutputcurrentis.

22. continuouscurrent

23. Fig4-12

25. R-LSourceload　：　Fig.4-14 TheSCRSmaybeturnedonatanytimethattheyareforwardbiased, whichisatanangle

26. Forcontinuouscurrentcase, theaveragebridgeoutputvoltageis averageloadcurrentis TheacvoltagetermsareunchangedfromthecontrolledrectifierwithanR-Lload. Theaccurrenttermsaredeterminedfromcircuit. Powerabsorbedbythedcvoltageis Powerabsorbedbyresistorintheloadis

27. ControlledSingle-phaseconverteroperatingasaninverter： seeing Fig4-14. 4-15 .

28. Forinverteroperation, powerissuppliedbythedcsource, andpowerisabsorbedbythebridgeandistransferredtotheacsystem. VdcandVomustbenegative rectifieroperation   inverteroperation

29. 4-4Three-phaserectifiers Resistiveload : Fig4-16

31. 上、下半部Diode，每次僅一個ON；同相上、下Diode不可同時ON；DiodeON由瞬間最大線電壓決定。上、下半部Diode，每次僅一個ON；同相上、下Diode不可同時ON；DiodeON由瞬間最大線電壓決定。 Atransitionofthehighestline-to-linevoltagemusttakeplaceevery . Becauseofthesixtransitionsthatoccurforeachperiodofthesourcevoltage, thecircuitiscalledasix-pulserectifier. vo(t)之基頻為3 電源頻率之6倍 Diode turnoninthesequence1,2,3,4,5,6,1,..

32. Eachdiodeconductsone-thirdofthetime, resultingin Apparentpowerfromthethree-phasesourceis

33. Sincetheoutputvoltageisperiodicwithperiod1/6oftheac supplyvoltage, theharmonicsintheoutputareoforder6kω, k=1,2,3,… Adevantage：outputisinherentlylikeadcvoltage, andthehigh-frequencylow-amplitudeharmonicsenablefilterstobeeffective.

34. Foradcloadcurrent (constant I0) ---Fig4.17

35. whichconsistsoftermsatfundamentalfrequencyoftheacsystemandharmonicsoforder6kwhichconsistsoftermsatfundamentalfrequencyoftheacsystemandharmonicsoforder6k 1, k=1,2,3,… Filters(Fig.4-18) arefrequentlynecessarytopreventharmoniccurrentsto entertheacsystem. Resonantfiltersfor5thand7thharmonics. High-passfiltersforhigherorderharmonics.

36. 4-5Controlledthree-phaserectifiers

37. Harmonicsforoutputvoltageremainoforder6k, butamplitudearefunctionsof .seeingFig. 4-20

39. Twelve-pulserectifiers：usingtwosix-pulsebridges

40. Thepurposeofthetransformerconnectionistointroduce phaseshiftbetweenthesourceandbridge. Thisresultsininputstotwobridgeswhichare apart. Thetwobridgeoutputsaresimilar, butalsoshiftedby . Thedelayanglesforthebridgearetypicallythesame. Thepeakoutputofthetwelve-pulseconverteroccursmidwaybetweenalternatepeaksofthesix-pulseconverters.Addingthevoltagesatthatpointfor gives

41. SinceatransitionbetweenconductingSCRsevery , thereareatotalof12suchtransitionsforeachperiodoftheacsource. Theoutputhasharmonicfrequencieswhicharemultipleof12timesthesourcefre. (12kk=1,2,…) Cancellation of harmonics 6(2n-1) 1 , n=1, 2, … has resulted from this transformer and converter configuration.

42. Thisprinciplecanbeexpandedtoarrangementsofhigherpulsenumberbyincorporatingincreasednumberofsix-pulseconverterswithtransformerswhichhavetheappropriatephaseshifts.Thisprinciplecanbeexpandedtoarrangementsofhigherpulsenumberbyincorporatingincreasednumberofsix-pulseconverterswithtransformerswhichhavetheappropriatephaseshifts. Thecharacteristicacharmonicsofap-pulseconverterwillbe pk 1, k=1,2,3… Moreexpenseforproducinghigh-voltage transformerswiththeappropriatephaseshifts.

43. Three-phaseconverteroperatingasainverter： seeing4-22.

44. ThebridgeoutputvoltageVomustbenegative.

45. 4-6DCpowertransmission ․ Byusingcontrolledtwelve-pulseconverter (generally). ․ Usedforverylongdistancesoftransmissionlines. Advantages：(1) , voltagedrop↓inlines (2) , lineloss ) ( (3) Twoconductorsrequiredratherthanthree (4) Transmissiontowersaresmaller. (5 ) Powerflowinadctransmission lineiscontrollablebyadjustmentofdelayanglesattheterminals. (6) Powerflowcanbemodulatedduringdisturbanceson oneoftheacsystem. Systemstabilityincreased. (7) Thetwoacsystemsthatareconnectedbythedclinedonotneedtobeinsynchronization. Disadvantages：costlyac-dcconverter, filter, andcontrolsystemrequiredateachendofthelinetointerfacewiththeacsystem.

46. Fig.4-23usingsix-pulseconverter

47. Forcurrentbeingripplefree Powersuppliedbytheconverteratterminal1is Powersuppliedbytheconverteratterminal2is

48. Fig.4-24usingtwelve-pulseconverter (abipolarscheme)

49. Oneofthelinesisenergizedatandtheotherisenergizedat - . Inemergencysituations, onepoleofthelinecanoperatewithouttheotherpole, withcurrentreturningthroughthegroundpath.

50. 4-7 commutation ：effectofsourceinductance ( ) Single-phasebridgerectifier: Fig.4-25