AC VOLTAGE CONTROLLER CIRCUITS (RMS VOLTAGE CONTROLLERS)

Transcription

1 TU NTE QUETN PAPER NEW REUT AC TAGE CNTRER CRCUT (RM TAGE CNTRER) AC volage conrollers (ac line volage conrollers) are eployed o vary he RM value of he alernaing volage applied o a load circui by inroducing Thyrisors beween he load and a consan volage ac source. The RM value of alernaing volage applied o a load circui is conrolled by conrolling he riggering angle of he Thyrisors in he ac volage conroller circuis. n brief, an ac volage conroller is a ype of hyrisor power converer which is used o conver a fixed volage, fixed frequency ac inpu supply o obain a variable volage ac oupu. The RM value of he ac oupu volage and he ac power flow o he load is conrolled by varying (adjusing) he rigger angle (RM) AC npu olage f s s f s AC olage Conroller ariable AC RM /P olage f There are wo differen ypes of hyrisor conrol used in pracice o conrol he ac power flow n-ff conrol Phase conrol These are he wo ac oupu volage conrol echniques. n n-ff conrol echnique Thyrisors are used as swiches o connec he load circui o he ac supply (source) for a few cycles of he inpu ac supply and hen o disconnec i for few inpu cycles. The Thyrisors hus ac as a high speed conacor (or high speed ac swich). PHAE CNTR n phase conrol he Thyrisors are used as swiches o connec he load circui o he inpu ac supply, for a par of every inpu cycle. Tha is he ac supply volage is chopped using Thyrisors during a par of each inpu cycle. The hyrisor swich is urned on for a par of every half cycle, so ha inpu supply volage appears across he load and hen urned off during he reaining par of inpu half cycle o disconnec he ac supply fro he load. By conrolling he phase angle or he rigger angle (delay angle), he oupu RM volage across he load can be conrolled. The rigger delay angle is defined as he phase angle (he value of ω) a which he hyrisor urns on and he load curren begins o flow. Thyrisor ac volage conrollers use ac line couaion or ac phase couaion. Thyrisors in ac volage conrollers are line couaed (phase couaed) since he inpu supply is ac. When he inpu ac volage reverses and becoes negaive during he negaive half cycle he curren flowing hrough he conducing hyrisor decreases and TU NTE

2 TU NTE QUETN PAPER NEW REUT falls o zero. Thus he N hyrisor naurally urns off, when he device curren falls o zero. Phase conrol Thyrisors which are relaively inexpensive, converer grade Thyrisors which are slower han fas swiching inverer grade Thyrisors are norally used. For applicaions upo 4Hz, if Triacs are available o ee he volage and curren raings of a paricular applicaion, Triacs are ore coonly used. Due o ac line couaion or naural couaion, here is no need of exra couaion circuiry or coponens and he circuis for ac volage conrollers are very siple. Due o he naure of he oupu wavefors, he analysis, derivaions of expressions for perforance paraeers are no siple, especially for he phase conrolled ac volage conrollers wih R load. Bu however os of he pracical loads are of he R ype and hence R load should be considered in he analysis and design of ac volage conroller circuis. TYPE F AC TAGE CNTRER The ac volage conrollers are classified ino wo ypes based on he ype of inpu ac supply applied o he circui. ingle Phase AC Conrollers. Three Phase AC Conrollers. ingle phase ac conrollers operae wih single phase ac supply volage of 3 RM a 5Hz in our counry. Three phase ac conrollers operae wih 3 phase ac supply of 4 RM a 5Hz supply frequency. Each ype of conroller ay be sub divided ino Uni-direcional or half wave ac conroller. Bi-direcional or full wave ac conroller. n brief differen ypes of ac volage conrollers are ingle phase half wave ac volage conroller (uni-direcional conroller). ingle phase full wave ac volage conroller (bi-direcional conroller). Three phase half wave ac volage conroller (uni-direcional conroller). Three phase full wave ac volage conroller (bi-direcional conroller). APPCATN F AC TAGE CNTRER ighing / lluinaion conrol in ac power circuis. nducion heaing. ndusrial heaing & Doesic heaing. Transforer ap changing (on load ransforer ap changing). peed conrol of inducion oors (single phase and poly phase ac inducion oor conrol). AC agne conrols. PRNCPE F N-FF CNTR TECHNQUE (NTEGRA CYCE CNTR) The basic principle of on-off conrol echnique is explained wih reference o a single phase full wave ac volage conroller circui shown below. The hyrisor swiches T and T are urned on by applying appropriae gae rigger pulses o connec he inpu ac supply o he load for n nuber of inpu cycles during he ie inerval N. The TU NTE

3 TU NTE QUETN PAPER NEW REUT hyrisor swiches T and T are urned off by blocking he gae rigger pulses for nuber of inpu cycles during he ie inerval FF usually consiss of an inegral nuber of inpu cycles.. The ac conroller N ie N R R oad Resisance Fig.: ingle phase full wave AC volage conroller circui s n w o i o w i g Gae pulse of T w i g Gae pulse of T w Fig.: Wavefors Exaple Referring o he wavefors of N-FF conrol echnique in he above diagra, n Two inpu cycles. Thyrisors are urned N during N for wo inpu cycles. TU NTE 3

4 TU NTE QUETN PAPER NEW REUT ne inpu cycle. Thyrisors are urned FF during FF for one inpu cycle Fig.: Power Facor Thyrisors are urned N precisely a he zero volage crossings of he inpu supply. The hyrisor T is urned on a he beginning of each posiive half cycle by applying he gae rigger pulses o T as shown, during he N ie N. The load curren flows in he posiive direcion, which is he downward direcion as shown in he circui diagra when T conducs. The hyrisor T is urned on a he beginning of each negaive half cycle, by applying gaing signal o he gae of T, during N. The load curren flows in he reverse direcion, which is he upward direcion when T conducs. Thus we obain a bi-direcional load curren flow (alernaing load curren flow) in a ac volage conroller circui, by riggering he hyrisors alernaely. This ype of conrol is used in applicaions which have high echanical ineria and high heral ie consan (ndusrial heaing and speed conrol of ac oors). Due o zero volage and zero curren swiching of Thyrisors, he haronics generaed by swiching acions are reduced. For a sine wave inpu supply volage, v sinω sinω s RM value of inpu ac supply RM phase supply volage. f he inpu ac supply is conneced o load for n nuber of inpu cycles and disconneced for nuber of inpu cycles, hen n T, T N FF Where T inpu cycle ie (ie period) and f f inpu supply frequency. conroller on ie n T. N conroller off ie T. FF T upu ie period ( ) ( nt T ) N + +. FF TU NTE 4

5 TU NTE QUETN PAPER NEW REUT We can show ha, N upu RM volage ( RM ) i ( RM ) T T N Where i( RM ) is he RM inpu supply volage. T DERE AN EXPREN FR THE RM AUE F UTPUT TAGE, FR N-FF CNTR METHD. upu RM volage in ω. d ( ω) RM ω N ω T ω N in d RM ωt ω. ( ω ) ω ubsiuing for Cosθ in θ ω N Cos ω d RM ωt ( ω ) ωn ωn. RM d ω Cos ωd( ω) ωt ωt ωn inω ( ω) RM ω N sin ωn sin ωt ( ωn ) RM Now N An inegral nuber of inpu cycles; Hence T, T,3 T, 4 T,5 T,... & ω,4,6,8,,... N N Where T is he inpu supply ie period (T inpu cycle ie period). Thus we noe ha sin ω N RM ω ω T T N N TU NTE 5

6 TU NTE QUETN PAPER NEW REUT N RM i( RM ) T T N Where i ( RM ) RM value of inpu supply volage; N nt n T + nt + T n + N N FF n k ( + n) RM k duy cycle (d). PERFRMANCE PARAMETER F AC TAGE CNTRER RM upu (oad) olage n sin. RM ωd( ω) ( n+ ) n RM i( RM ) k k ( + n) k k i( RM ) RM Where i ( RM ) RM value of inpu supply volage. Duy Cycle N N nt k T + + nt N FF Where, k n ( + n) duy cycle (d). RM oad Curren RM upu AC (oad) Power ( RM ) ( RM ) Z R ; for a resisive load Z R. P R RM TU NTE 6

7 TU NTE QUETN PAPER NEW REUT npu Power Facor P oupu load power P PF A inpu supply vol aperes R RM PF i( RM ) in( RM ) ; in( RM ) RM inpu supply curren. The inpu supply curren is sae as he load curren in Hence, RM supply curren RM load curren; in RM ( RM ). R RM ( RM ) i ( RM ) k PF i RM in RM i RM i RM k PF k n + n The Average Curren of Thyrisor T ( Avg ) i T Wavefor of Thyrisor Curren n 3 ω n sin ωd. T Avg + ( n) n sin ωd. T Avg + ( n) ( ω ) ( ω ) n cosω + ( n) T Avg n + n [ cos + cos ] T Avg TU NTE 7

8 TU NTE QUETN PAPER NEW REUT n ( ) + ( + n) T Avg n + n [ ] T Avg n k. ( + n) T Avg N k duy cycle ( + ) ( n+ ) N FF n n k. ( + n) T Avg, Where R axiu or peak hyrisor curren. RM Curren of Thyrisor T ( RM ) n sin ω. ( ω ) d T RM ( n+ ) n sin. T RM ωd( ω) ( n+ ) ( cos ω ) n T RM d( ω) ( n+ ) n T ( RM ) d d 4 ( n+ ) 4 ( n ) T RM ( ω ) cos ω. ( ω ) n sin ω ( ω) + ( n ) T RM n sin sin ( ) TU NTE 8

9 TU NTE QUETN PAPER NEW REUT n { } T RM 4 n+ n 4 ( n+ ) 4( n+ ) T RM n n ( + n) T RM k T RM k PRBEM. A single phase full wave ac volage conroller working on N-FF conrol echnique has supply volage of 3, RM 5Hz, load 5Ω. The conroller is N for 3 cycles and off for 4 cycles. Calculae N & FF ie inervals. RM oupu volage. npu P.F. Average and RM hyrisor currens. 3, in RM, 35.69, T.sec f 5Hz, T s. n nuber of inpu cycles during which conroller is N; n 3. nuber of inpu cycles during which conroller is FF; 4. n T 3 s 6s.6sec N N n T.6sec conroller N ie. T 4 s 8s.8sec FF FF T.8sec conroller FF ie. Duy cycle n 3 k.485 ( + n) ( 4 + 3) RM oupu volage i( RM ) ( + n) RM n TU NTE 9

10 TU NTE QUETN PAPER NEW REUT ( + ) RM RM 5.57 RM RM RM ( RM ) A Z R 5Ω RM P R W npu Power Facor PF. k n 3 PF 7 ( + n).485 PF Average Thyrisor Curren Raing n k T ( Avg ) + n where R A Peak (axiu) hyrisor curren. T Avg A T Avg RM Curren Raing of Thyrisor n k T RM + n A T RM TU NTE

11 TU NTE QUETN PAPER NEW REUT PRNCPE F AC PHAE CNTR The basic principle of ac phase conrol echnique is explained wih reference o a single phase half wave ac volage conroller (unidirecional conroller) circui shown in he below figure. The half wave ac conroller uses one hyrisor and one diode conneced in parallel across each oher in opposie direcion ha is anode of hyrisor T is conneced o he cahode of diode D and he cahode of T is conneced o he anode of D. The oupu volage across he load resisor R and hence he ac power flow o he load is conrolled by varying he rigger angle. The rigger angle or he delay angle refers o he value of ω or he insan a T is riggered o urn i N, by applying a suiable gae rigger pulse which he hyrisor beween he gae and cahode lead. The hyrisor T is forward biased during he posiive half cycle of inpu ac supply. can be riggered and ade o conduc by applying a suiable gae rigger pulse only during he posiive half cycle of inpu supply. When T is riggered i conducs and he load curren flows hrough he hyrisor T, he load and hrough he ransforer secondary winding. By assuing T as an ideal hyrisor swich i can be considered as a closed swich when i is N during he period ω o radians. The oupu volage across he load follows he inpu supply volage when he hyrisor T is urned-on and when i conducs fro ω o radians. When he inpu supply volage decreases o zero a ω, for a resisive load he load curren also falls o zero a ω and hence he hyrisor T urns off a ω. Beween he ie period ω o, when he supply volage reverses and becoes negaive he diode D becoes forward biased and hence urns N and conducs. The load curren flows in he opposie direcion during ω o radians when D is N and he oupu volage follows he negaive half cycle of inpu supply. Fig.: Halfwave AC phase conroller (Unidirecional Conroller) TU NTE

12 TU NTE QUETN PAPER NEW REUT Equaions npu AC upply olage across he Transforer econdary Winding. vs sinω in ( RM ) RM value of secondary supply volage. upu oad olage v o v ; for ω o v v sinω ; for ω o. o upu oad Curren i i o o vo sinω i ; for ω o. R R i ; for ω o. T DERE AN EXPREN FR RM UTPUT TAGE ( RM ) sin d. RM ω ( ω) cos ω. d RM ( ω) TU NTE

13 TU NTE QUETN PAPER NEW REUT ( cos ). d RM ω ( ω) 4 d( ω) cos ωd. ω RM sin ω ( ω) RM sin ω ( ) RM sin 4 sin ;sin 4 RM sin + ( ) RM sin + ( ) RM sin + ( ) RM sin + ( i RM ) RM sin + ( ) RM Where, i ( RM ) RM value of inpu supply volage (across he ransforer secondary winding). Noe: upu RM volage across he load is conrolled by changing ' ' as indicaed by he expression for ( RM ) TU NTE 3

14 TU NTE QUETN PAPER NEW REUT PT F ( RM ) ERU TRGGER ANGE FR A NGE PHAE HAF- WAE AC TAGE CNTRER (UNDRECTNA CNTRER) sin + ( ) RM sin + ( ) RM By using he expression for ( RM ) we can obain he conrol characerisics, which is he plo of RM oupu volage ( RM ) versus he rigger angle. A ypical conrol characerisic of single phase half-wave phase conrolled ac volage conroller is as shown below Trigger angle in degrees Trigger angle in radians 3 ; 6 ( 6) 6 ; 3 ( 6) 9 ; ( 3 6) ; 3 ( 4 6) 5 5 ; 6 ( 5 6) 8 ;( 6 ) ( RM ) (RM) % 7.7% 6% % 6 8 Trigger angle in degrees TU NTE 4

15 TU NTE QUETN PAPER NEW REUT Fig.: Conrol characerisics of single phase half-wave phase conrolled ac volage conroller Noe: We can observe fro he conrol characerisics and he able given above ha he range of RM oupu volage conrol is fro % of o 7.7% of when we vary he rigger angle fro zero o 8 degrees. Thus he half wave ac conroller has he draw back of liied range RM oupu volage conrol. T CACUATE THE AERAGE AUE (DC AUE) F UTPUT TAGE sin ωd. ( ω) d sin ω. ( ω ) cosω [ cos + cos ] ; cos [ cos ] ; Hence ( cos ) When ' ' is varied fro o. varies fro o DADANTAGE F NGE PHAE HAF WAE AC TAGE CNTRER. The oupu load volage has a DC coponen because he wo halves of he oupu volage wavefor are no syerical wih respec o level. The inpu supply curren wavefor also has a DC coponen (average value) which can resul in he proble of core sauraion of he inpu supply ransforer. The half wave ac volage conroller using a single hyrisor and a single diode provides conrol on he hyrisor only in one half cycle of he inpu supply. Hence ac power flow o he load can be conrolled only in one half cycle. Half wave ac volage conroller gives liied range of RM oupu volage conrol. Because he RM value of ac oupu volage can be varied fro a axiu of % of a a rigger angle o a low of 7.7% of a Radians. These drawbacks of single phase half wave ac volage conroller can be over coe by using a single phase full wave ac volage conroller. TU NTE 5

16 TU NTE QUETN PAPER NEW REUT APPCATN F RM TAGE CNTRER peed conrol of inducion oor (polyphase ac inducion oor). Heaer conrol circuis (indusrial heaing). Welding power conrol. nducion heaing. n load ransforer ap changing. ighing conrol in ac circuis. Ac agne conrols. Proble. A single phase half-wave ac volage conroller has a load resisance R 5Ω, inpu ac supply volage is 3 RM a 5Hz. The inpu supply ransforer has a urns raio of :. f he hyrisor T is riggered a 6. Calculae RM oupu volage. upu power. RM load curren and average load curren. npu power facor. Average and RM hyrisor curren. Given, p 3, RM priary supply volage. f npu supply frequency 5Hz. R 5Ω 6 radians. 3 RM secondary volage. p Np N Therefore 3 Where, p N p Nuber of urns in he priary winding. N Nuber of urns in he secondary winding. TU NTE 6

17 TU NTE QUETN PAPER NEW REUT RM alue of upu (oad) olage ( RM ) d RM sin ω. ( ω ) We have obained he expression for ( RM ) as sin + ( ) RM RM sin RM [ ] RM RM oad Curren ( RM ) RM upu oad Power P ( RM ) Aps R 5 P R Was RM P KW npu Power Facor P PF RM secondary supply volage 3. RM secondary supply curren RM load curren Aps RM W PF W ( ) TU NTE 7

18 TU NTE QUETN PAPER NEW REUT Average upu (oad) olage sin d. ω ( ω) We have obained he expression for he average / DC oupu volage as, [ cos ] cos( 6 ) [.5 ] ols [ ] Average DC oad Curren ( ) Aps R 5 Average & RM Thyrisor Currens i T ( + ) 3 ω Fig.: Thyrisor Curren Wavefor Referring o he hyrisor curren wavefor of a single phase half-wave ac volage conroller circui, we can calculae he average hyrisor curren T ( Avg ) as sin d. T Avg ω ( ω) sin d. T Avg ω ( ω) TU NTE 8

19 TU NTE QUETN PAPER NEW REUT ( cosω) T Avg cos( ) cos T Avg + [ + cos ] T Avg Where, R Peak hyrisor curren Peak load curren Aps R [ + cos ] T Avg + T Avg T Avg 3 cos [ ].553 Aps T Avg RM hyrisor curren T ( RM ) can be calculaed by using he expression sin d. T RM ω ( ω) ( ω) cos. d T RM ( ω) d( ) cos d. T RM ω ω ( ω) 4 sin ω T ( RM ) ( ω) 4 TU NTE 9

20 TU NTE QUETN PAPER NEW REUT sin sin 4 ( ) T RM sin 4 + ( ) T RM sin + ( ) T RM T RM sin ( ) T RM A T RM.9746 Aps T RM NGE PHAE FU WAE AC TAGE CNTRER (AC REGUATR) R RM TAGE CNTRER WTH RETE AD ingle phase full wave ac volage conroller circui using wo CRs or a single riac is generally used in os of he ac conrol applicaions. The ac power flow o he load can be conrolled in boh he half cycles by varying he rigger angle ' '. The RM value of load volage can be varied by varying he rigger angle ' '. The inpu supply curren is alernaing in he case of a full wave ac volage conroller and due o he syerical naure of he inpu supply curren wavefor here is no coponen of inpu supply curren i.e., he average value of he inpu supply curren is zero. A single phase full wave ac volage conroller wih a resisive load is shown in he figure below. is possible o conrol he ac power flow o he load in boh he half cycles by adjusing he rigger angle ' '. Hence he full wave ac volage conroller is also referred o as o a bi-direcional conroller. TU NTE

21 TU NTE QUETN PAPER NEW REUT Fig.: ingle phase full wave ac volage conroller (Bi-direcional Conroller) using CRs The hyrisor T is forward biased during he posiive half cycle of he inpu supply volage. The hyrisor T is riggered a a delay angle of ' ' ( radians). Considering he N hyrisor T as an ideal closed swich he inpu supply volage appears across he load resisor R and he oupu volage v v during ω o radians. The load curren flows hrough he N hyrisor T and hrough he load resisor R in he downward direcion during he conducion ie of T fro ω o radians. A ω, when he inpu volage falls o zero he hyrisor curren (which is flowing hrough he load resisor R ) falls o zero and hence T naurally urns off. No curren flows in he circui during ω +. o The hyrisor T is forward biased during he negaive cycle of inpu supply and when hyrisor T is riggered a a delay angle ( + ), he oupu volage follows he negaive halfcycle of inpu fro ω ( ) + o. When T is N, he load curren flows in he reverse direcion (upward direcion) hrough ω + o radians. The ie inerval (spacing) beween he gae rigger pulses of T and T is kep a radians or 8. A ω he inpu supply volage falls o zero and hence he load curren also falls o zero and hyrisor T urn off naurally. T during nsead of using wo CR s in parallel, a Triac can be used for full wave ac volage conrol. Fig.: ingle phase full wave ac volage conroller (Bi-direcional Conroller) using TRAC TU NTE

22 TU NTE QUETN PAPER NEW REUT Fig: Wavefors of single phase full wave ac volage conroller EQUATN npu supply volage v sinω sinω; upu volage across he load resisor R ; v v sinω ; for ω o and ω ( + ) o upu load curren v sinω i sinω ; R R for ω o and ω ( + ) o T DERE AN EXPREN FR THE RM AUE F UTPUT (AD) TAGE The RM value of oupu volage (load volage) can be found using he expression RM v d ; ( ω RM ) TU NTE

23 TU NTE QUETN PAPER NEW REUT For a full wave ac volage conroller, we can see ha he wo half cycles of oupu volage wavefors are syerical and he oupu pulse ie period (or oupu pulse repeiion ie) is radians. Hence we can also calculae he RM oupu volage by using he expression given below. RM sin ωd. ω RM v d ;. ( ω ) v v sinω; For ω o and ( + ) o ω Hence, ( sin ) d( ) ( sin RM ω ω ω ) d( ω) + + sin ωd. ( ω) sin ωd. ( ω) + + cos ω cos ω d( ω) d( ω) + + d( ω) cos ωd. ( ω) + d( ω) cos ωd. ( ω) + + sin ω sin ω + 4 ( ω) ( ω) ( ) ( ) ( sin sin ) sin 4 sin ( ) sin sin 4 + ( ) ( ) ( ) sin sin ( + ) ( ) ( + ) sin sin ( ) TU NTE 3

24 TU NTE QUETN PAPER NEW REUT sin sin.cos cos.sin sin & cos Therefore, ( ) ( ) ( ) 4 sin sin + + RM sin 4 + ( ) sin RM 4 + Taking he square roo, we ge ( ) sin RM + ( ) sin RM + ( ) sin RM + sin + ( ) RM sin + ( ) RM sin + i ( RM ) ( ) RM sin + ( ) RM Maxiu RM volage will be applied o he load when, in ha case he full sine wave appears across he load. RM load volage will be he sae as he RM supply volage. When is increased he RM load volage decreases. TU NTE 4

25 TU NTE QUETN PAPER NEW REUT ( ) RM sin + ( ) RM + i( RM ) RM The oupu conrol characerisic for a single phase full wave ac volage conroller wih resisive load can be obained by ploing he equaion for ( RM ) CNTR CHARACTERTC F NGE PHAE FU-WAE AC TAGE CNTRER WTH RETE AD The conrol characerisic is he plo of RM oupu volage ( RM ) versus he rigger angle ; which can be obained by using he expression for he RM oupu volage of a full-wave ac conroller wih resisive load. sin + ( ) RM ; Where RM value of inpu supply volage Trigger angle Trigger angle in degrees in radians 3 ; 6 ( ) 6 ; 3 ( ) 9 ; ( ) ; 3 ( ) 5 5 ; 6 ( ) 8 ;( 6 6) ( RM ) % % 98.54% 89.69% 7.7% 44.% 6.98% TU NTE 5

26 TU NTE QUETN PAPER NEW REUT (RM) Trigger angle in degrees We can noice fro he figure, ha we obain a uch beer oupu conrol characerisic by using a single phase full wave ac volage conroller. The RM oupu volage can be varied fro a axiu of % a o a iniu of a 8. Thus we ge a full range oupu volage conrol by using a single phase full wave ac volage conroller. Need For solaion n he single phase full wave ac volage conroller circui using wo CRs or Thyrisors T and T in parallel, he gaing circuis (gae rigger pulse generaing circuis) of Thyrisors T and T us be isolaed. Figure shows a pulse ransforer wih wo separae windings o provide isolaion beween he gaing signals of T and T. Gae Trigger Pulse Generaor G K G K Fig.: Pulse Transforer NGE PHAE FU-WAE AC TAGE CNTRER WTH CMMN CATHDE is possible o design a single phase full wave ac conroller wih a coon cahode configuraion by having a coon cahode poin for T and T & by adding wo diodes in a full wave ac conroller circui as shown in he figure below TU NTE 6

27 TU NTE QUETN PAPER NEW REUT Fig.: ingle phase full wave ac conroller wih coon cahode (Bidirecional conroller in coon cahode configuraion) Thyrisor T and diode D are forward biased during he posiive half cycle of inpu supply. When hyrisor T is riggered a a delay angle, Thyrisor T and diode D conduc ogeher fro ω o during he posiive half cycle. The hyrisor T and diode D are forward biased during he negaive half cycle of inpu supply, when rigged a a delay angle, hyrisor T and diode D conduc ogeher during he negaive half cycle fro ω ( ) + o. n his circui as here is one single coon cahode poin, rouing of he gae rigger pulses o he hyrisor gaes of T and T is sipler and only one isolaion circui is required. Bu due o he need of wo power diodes he coss of he devices increase. As here are wo power devices conducing a he sae ie he volage drop across he N devices increases and he N sae conducing losses of devices increase and hence he efficiency decreases. NGE PHAE FU WAE AC TAGE CNTRER UNG A NGE THYRTR D D 3 + T AC upply D 4 D R - TU NTE 7

28 TU NTE QUETN PAPER NEW REUT A single phase full wave ac conroller can also be ipleened wih one hyrisor and four diodes conneced in a full wave bridge configuraion as shown in he above figure. The four diodes ac as a bridge full wave recifier. The volage across he hyrisor T and curren hrough hyrisor T are always unidirecional. When T is riggered a ω, during he posiive half cycle ( ), he load curren flows hrough D, T, diode D and hrough he load. Wih a resisive load, he hyrisor curren (flowing hrough he N hyrisor T ), he load curren falls o zero a supply volage decreases o zero a ω ω, when he inpu, he hyrisor naurally urns FF. n he negaive half cycle, diodes D3& D 4 are forward biased during ω o radians. When T is riggered a ω ( + ), he load curren flows in he opposie direcion (upward direcion) hrough he load, hrough D 3, T and D 4. Thus D 3, D4 and T conduc ogeher during he negaive half cycle o supply he load power. When he inpu supply volage becoes zero a ω, he hyrisor curren (load curren) falls o zero a ω and he hyrisor T naurally urns FF. The wavefors and he expression for he RM oupu volage are he sae as discussed earlier for he single phase full wave ac conroller. Bu however if here is a large inducance in he load circui, hyrisor T ay no be urned FF a he zero crossing poins, in every half cycle of inpu volage and his ay resul in a loss of oupu conrol. This would require deecion of he zero crossing of he load curren wavefor in order o ensure guaraneed urn off of he conducing hyrisor before riggering he hyrisor in he nex half cycle, so ha we gain conrol on he oupu volage. n his full wave ac conroller circui using a single hyrisor, as here are hree power devices conducing ogeher a he sae ie here is ore conducion volage drop and an increase in he N sae conducion losses and hence efficiency is also reduced. The diode bridge recifier and hyrisor (or a power ransisor) ac ogeher as a bidirecional swich which is coercially available as a single device odule and i has relaively low N sae conducion loss. can be used for bidirecional load curren conrol and for conrolling he RM oupu volage. NGE PHAE FU WAE AC TAGE CNTRER (BDRECTNA CNTRER) WTH R AD n his secion we will discuss he operaion and perforance of a single phase full wave ac volage conroller wih R load. n pracice os of he loads are of R ype. For exaple if we consider a single phase full wave ac volage conroller conrolling he speed of a single phase ac inducion oor, he load which is he inducion oor winding is an R ype of load, where R represens he oor winding resisance and represens he oor winding inducance. TU NTE 8

29 TU NTE QUETN PAPER NEW REUT A single phase full wave ac volage conroller circui (bidirecional conroller) wih an R load using wo hyrisors T and T ( T and T are wo CRs) conneced in parallel is shown in he figure below. n place of wo hyrisors a single Triac can be used o ipleen a full wave ac conroller, if a suiable Traic is available for he desired RM load curren and he RM oupu volage raings. Fig: ingle phase full wave ac volage conroller wih R load The hyrisor T is forward biased during he posiive half cycle of inpu supply. e us assue ha T is riggered a ω, by applying a suiable gae rigger pulse o T during he posiive half cycle of inpu supply. The oupu volage across he load follows he inpu supply volage when T is N. The load curren i flows hrough he hyrisor T and hrough he load in he downward direcion. This load curren pulse flowing hrough T can be considered as he posiive curren pulse. Due o he inducance in he load, he load curren i flowing hrough T would no fall o zero a he inpu supply volage sars o becoe negaive. ω, when The hyrisor T will coninue o conduc he load curren unil all he inducive energy sored in he load inducor is copleely uilized and he load curren hrough T falls o zero a ω β, where β is referred o as he Exincion angle, (he value of ω ) a which he load curren falls o zero. The exincion angle β is easured fro he poin of he beginning of he posiive half cycle of inpu supply o he poin where he load curren falls o zero. TU NTE 9

30 TU NTE QUETN PAPER NEW REUT The hyrisor T conducs fro ω o β. The conducion angle of T is δ ( β ), which depends on he delay angle and he load ipedance angle φ. The wavefors of he inpu supply volage, he gae rigger pulses of T and T, he hyrisor curren, he load curren and he load volage wavefors appear as shown in he figure below. Fig.: npu supply volage & Thyrisor curren wavefors β is he exincion angle which depends upon he load inducance value. Fig.: Gaing ignals TU NTE 3

31 TU NTE QUETN PAPER NEW REUT Wavefors of single phase full wave ac volage conroller wih R load for > φ. Disconinuous load curren operaion occurs for > φ and β < ( + ) ; i.e., ( β ) <, conducion angle <. Fig.: Wavefors of npu supply volage, oad Curren, oad olage and Thyrisor olage across T Noe The RM value of he oupu volage and he load curren ay be varied by varying he rigger angle. This circui, AC RM volage conroller can be used o regulae he RM volage across he erinals of an ac oor (inducion oor). can be used o conrol he eperaure of a furnace by varying he RM oupu volage. TU NTE 3

32 TU NTE QUETN PAPER NEW REUT For very large load inducance he CR ay fail o couae, afer i is riggered and he load volage will be a full sine wave (siilar o he applied inpu supply volage and he oupu conrol will be los) as long as he gaing signals are applied o he hyrisors T and T. The load curren wavefor will appear as a full coninuous sine wave and he load curren wavefor lags behind he oupu sine wave by he load power facor angle φ. T DERE AN EXPREN FR THE UTPUT (NDUCTE AD) CURRENT, DURNG ω o β WHEN THYRTR T CNDUCT Considering sinusoidal inpu supply volage we can wrie he expression for he supply volage as v sinω insananeous value of he inpu supply volage. e us assue ha he hyrisor T is riggered by applying he gaing signal o T a ω be found fro he equaion. The load curren which flows hrough he hyrisor T during ω o β can di + Ri sinω d ; The soluion of he above differenial equaion gives he general expression for he oupu load curren which is of he for + ; Z τ i sin ( ω φ) Ae Where axiu or peak value of inpu supply volage. ( ω ) Z R + oad ipedance. φ ω R an oad ipedance angle (power facor angle of load). τ oad circui ie consan. R Therefore he general expression for he oupu load curren is given by he equaion R i sin ( ω φ) + Ae ; Z TU NTE 3

33 TU NTE QUETN PAPER NEW REUT The value of he consan A can be deerined fro he iniial condiion. i.e. iniial value of load curren i, a ω. Hence fro he equaion for i equaing i o zero and subsiuing ω, we ge i sin ( φ) + Ae Z R R sin Z Therefore Ae ( φ) By subsiuing A sin R Z e + R Z ( φ) e sin ( φ) A R ( ω) ω e sin ( φ) A Z ω, we ge he value of consan A as R ( ) ω e sin ( φ) A Z ubsiuing he value of consan A fro he above equaion ino he expression for i, we obain R R( ) ω i sin ( ω φ) + e e sin ( φ) Z Z ; ( ω ) ( ) R R i e e + Z Z ω ω sin ( ω φ) sin ( φ) + Z Z R i e ω ω sin ( ω φ) sin ( φ) Therefore we obain he final expression for he inducive load curren of a single phase full wave ac volage conroller wih R load as i sin ( ω φ) sin ( φ) e Z R ( ω ) ω ; Where ω β. TU NTE 33

34 TU NTE QUETN PAPER NEW REUT The above expression also represens he hyrisor curren i T, during he conducion ie inerval of hyrisor T fro ω o β. To Calculae Exincion Angle β The exincion angle β, which is he value of ω a which he load curren i falls o zero and T is urned off can be esiaed by using he condiion ha i, a ω β By using he above expression for he oupu load curren, we can wrie As i sin sin Z ( β φ) ( φ) e R ( β ) ω Z we can wrie ( β φ) ( φ) Therefore we obain he expression R ( β ) ω sin sin e sin ( β φ) sin ( φ) e R ( β ) ω The exincion angle β can be deerined fro his ranscendenal equaion by using he ieraive ehod of soluion (rial and error ehod). Afer β is calculaed, we can deerine he hyrisor conducion angle δ ( β ). β is he exincion angle which depends upon he load inducance value. Conducion angle δ increases as is decreased for a known value of β. For δ < radians, i.e., for ( β ) < radians, for ( + ) > β he load curren wavefor appears as a disconinuous curren wavefor as shown in he figure. The oupu load curren reains a zero during ω β +. This is referred o as o disconinuous load curren operaion which occurs for β < ( + ). When he rigger angle is decreased and ade equal o he load ipedance angle φ i.e., when φ sin β φ, we obain fro he expression for ( β φ) ; Therefore sin β φ radians. Exincion angle β ( + φ) ( + ) ; for he case when φ δ β radians 8 ; for he case when φ Conducion angle Each hyrisor conducs for 8 ( radians ). T conducs fro + φ and provides a posiive load curren. T conducs fro ( φ) ω + o ( φ) φ o + and provides a negaive load curren. Hence we obain a coninuous load curren and he TU NTE 34

35 TU NTE QUETN PAPER NEW REUT oupu volage wavefor appears as a coninuous sine wave idenical o he inpu supply volage wavefor for rigger angle φ and he conrol on he oupu is los. v v v φ 3 ω φ φ φ i φ ω Fig.: upu volage and oupu curren wavefors for a single phase full wave ac volage conroller wih R load for φ Thus we observe ha for rigger angle φ, he load curren ends o flow coninuously and we have coninuous load curren operaion, wihou any break in he load curren wavefor and we obain oupu volage wavefor which is a coninuous sinusoidal wavefor idenical o he inpu supply volage wavefor. We loose he conrol on he oupu volage for φ as he oupu volage becoes equal o he inpu supply volage and hus we obain ( RM ) ; for φ Hence, RM oupu volage RM inpu supply volage for φ T DERE AN EXPREN FR RM UTPUT TAGE RM F A NGE PHAE FU-WAE AC TAGE CNTRER WTH R AD. TU NTE 35

36 TU NTE QUETN PAPER NEW REUT When >, he load curren and load volage wavefors becoe disconinuous as shown in he figure above. β sin d. RM ω ( ω) upu vo sinω, for ω o β, when T is N. ( ω) β cos ( RM ) d( ω) β β d d RM ( ω ) cos ω. ( ω ) ( ω) RM β β sin ω sin β sin β + RM sin sin β + ( β ) RM sin sin β + ( β ) RM The RM oupu volage across he load can be varied by changing he rigger angle. For a purely resisive load, herefore load power facor angle φ. ω φ an ; R Exincion angle β radians 8 TU NTE 36

37 TU NTE QUETN PAPER NEW REUT PERFRMANCE PARAMETER F A NGE PHAE FU WAE AC TAGE CNTRER WTH RETE AD sin + RM upu olage ( ) inpu supply volage. RM ; RM ( RM ) ( RM ) RM value of load curren. R RM value of inpu supply curren. ( RM ) upu load power npu Power Facor P R RM R R P ( RM ) ( RM ) PF RM Average Thyrisor Curren, ( RM ) sin PF ( ) + i T ( + ) 3 ω Fig.: Thyrisor Curren Wavefor i d d T Avg T ( ω ) sin ω. ( ω ) sin ωd. ( ω) cosω T Avg T Avg [ cos + cos ] [ + cos ] TU NTE 37

38 TU NTE QUETN PAPER NEW REUT Maxiu Average Thyrisor Curren, for, T ( Avg ) RM Thyrisor Curren sin d. T RM ω ( ω) sin + ( ) T RM Maxiu RM Thyrisor Curren, for, T ( RM ) n he case of a single phase full wave ac volage conroller circui using a Triac wih resisive load, he average hyrisor curren. Because he Triac conducs in T Avg boh he half cycles and he hyrisor curren is alernaing and we obain a syerical hyrisor curren wavefor which gives an average value of zero on inegraion. PERFRMANCE PARAMETER F A NGE PHAE FU WAE AC TAGE CNTRER WTH R- AD The Expression for he upu (oad) Curren The expression for he oupu (load) curren which flows hrough he hyrisor, during ω o β is given by R ( ω ) ω i it sin ( ω φ) sin ( φ) e Z ; for ω β Where, Maxiu or peak value of inpu ac supply volage. ( ω ) Z R + oad ipedance. ω φ an R oad ipedance angle (load power facor angle). Thyrisor rigger angle Delay angle. β Exincion angle of hyrisor, (value of curren falls o zero. β is calculaed by solving he equaion sin ( β φ) sin ( φ) e R ( β ) ω ω ) a which he hyrisor (load) TU NTE 38

39 TU NTE QUETN PAPER NEW REUT Thyrisor Conducion Angle δ ( β ) Maxiu hyrisor conducion angle δ ( β ) radians 8 for φ. RM upu olage sin sin β + ( β ) RM The Average Thyrisor Curren β T Avg id T ( ω) β R ( ω ) ω sin ( ) sin T Avg ω φ ( φ) e d( ω) Z β β R ( ω ) ω sin ( ). d( ) sin T Avg ω φ ω ( φ) e d( ω) Z Maxiu value of T ( Avg ) occur a. The hyrisors should be raed for axiu T ( Avg ), where. Z RM Thyrisor Curren T ( RM ) β T RM id T ( ω) Maxiu value of T ( RM ) occurs a. Thyrisors should be raed for axiu T ( RM ) When a Triac is used in a single phase full wave ac volage conroller wih R ype of load, hen and axiu T Avg T ( RM ) TU NTE 39

40 TU NTE QUETN PAPER NEW REUT PRBEM. A single phase full wave ac volage conroller supplies an R load. The inpu supply volage is 3, RM a 5Hz. The load has H, R Ω, he delay angle of hyrisors T and T are equal, where. Deerine 3 a. Conducion angle of he hyrisor T. b. RM oupu volage. c. The inpu power facor. Coen on he ype of operaion. Given 3, f 5Hz, H, R Ω, 6, s radians, ( ω ) ( ω ) oad pedance Z R ( f) ω Ω Z Ω A Z.488 ω oad pedance Angle φ an R φ an an (.3459) Trigger Angle > φ. Hence he ype of operaion will be disconinuous load curren operaion, we ge β < + β < ( 8 + 6) ; β < 4 Therefore he range of β is fro 8 degrees o 4 degrees. 8 < β < 4 TU NTE 4

41 TU NTE QUETN PAPER NEW REUT Exincion Angle β is calculaed by using he equaion sin ( β φ) sin ( φ) e R ( β ) ω n he exponenial er he value of and β should be subsiued in radians. Hence R ( βrad Rad ) ω sin ( β φ) sin ( φ) e ; Rad 3 Assuing Assuing ( φ) ( ) ( β ) sin 7.44 sin e ( β ) 3.83( β ) sin e 8 radians, β 9 ; β Rad β Rad β 9 β H.: R.H.: ( β ) sin sin e 4.94 β 83 ; β Rad β ( β ) sin β φ sin sin h.: 4 R.H.: e Assuing β 8 β Rad β β TU NTE 4

42 TU NTE QUETN PAPER NEW REUT.H.: ( β φ) R.H.: sin sin e Assuing β 96 β Rad β H.: ( β φ) R.H.: sin sin e Assuing β 97 β Rad β sin β φ sin H.: R.H.: e Assuing β 97.4 β 97.4 β Rad sin β φ sin H.: R.H.: e 3.79 Conducion Angle δ ( β ) RM upu olage sin sin β ( RM ) ( β ) + RM RM sin 6 sin RM TU NTE 4

43 TU NTE QUETN PAPER NEW REUT npu Power Facor P PF RM ( RM ) A Z.488 P R W RM 3, RM P PF A single phase full wave conroller has an inpu volage of (RM) and a load resisance of 6 oh. The firing angle of hyrisor is. Find a. RM oupu volage b. Power oupu c. npu power facor d. Average and RM hyrisor curren. oluion 9,, R 6Ω RM alue of upu olage sin + sin8 + RM upu Curren ols A R 6 oad Power P R P was TU NTE 43

44 TU NTE QUETN PAPER NEW REUT npu Curren is sae as oad Curren Therefore 4.4 Aps npu upply ol-ap A Therefore oad Power npu ol-ap npu Power Facor.77( lag ) Each Thyrisor Conducs only for half a cycle Average hyrisor curren T ( Avg ) RM hyrisor curren T ( RM ) d T Avg R sin ω. ( ω ) ( + cos ) ; R [ + cos9 ] 4.5 A 6 sin ω d T RM R ( ω ) ( cos ω ) R d ( ω) sin R + sin R + sin8 + Aps 6 TU NTE 44

45 TU NTE QUETN PAPER NEW REUT 3. A single phase half wave ac regulaor using one CR in ani-parallel wih a diode feeds kw, 3 heaer. Find load power for a firing angle of 45. power oluion 45, 3 ; P KW W 4 A sandard rs supply volage of 3, he heaer dissipaes KW of oupu Therefore P R R Resisance of heaer 3 R 5.9Ω P RM value of oupu volage sin + ; for firing angle 45 sin ols 4 RM value of oupu curren Aps R 5.9 oad Power P R Was 4. Find he RM and average curren flowing hrough he heaer shown in figure. The delay angle of boh he CRs is 45. CR + i o -φ ac CR kw, heaer TU NTE 45

46 TU NTE QUETN PAPER NEW REUT oluion 4 45, Resisance of heaer R 48.4Ω R Resisance value of oupu volage sin + sin ols 4 RM curren flowing hrough heaer Aps R 48.4 Average curren flowing hrough he heaer Avg 5. A single phase volage conroller is eployed for conrolling he power flow fro, 5 Hz source ino a load circui consising of R 4 Ω and ω 6 Ω. Calculae he following a. Conrol range of firing angle b. Maxiu value of RM load curren c. Maxiu power and power facor d. Maxiu value of average and RM hyrisor curren. oluion For conrol of oupu power, iniu angle of firing angle is equal o he load ipedance angle θ θ, load angle ω 6 θ an an 56.3 R 4 Maxiu possible value of is 8 Therefore conrol range of firing angle is 56.3 < < 8 TU NTE 46

47 TU NTE QUETN PAPER NEW REUT Maxiu value of RM load curren occurs when θ A his value of he Maxiu value of RM load curren Aps Z Maxiu Power P R W npu ol-ap W Power Facor P npu A Average hyrisor curren will be axiu when θ and conducion angleγ 8. Therefore axiu value of average hyrisor curren + sin T Avg ( ω θ) d( ω) Z Noe: sin ( ω θ) sin ( θ) A, i it e Z it i sin Z ( ω θ) Z cos( ω θ) T Avg + R ( ω ) ω Bu θ, Z cos( + θ) + cos( θ) T Avg Z + Z Z cos( ) cos( ) [ ] T Avg Aps T Avg Z iilarly, axiu RM value occurs when and γ. Therefore axiu value of RM hyrisor curren + TM sin d Z ( ω θ) ( ω ) TU NTE 47

48 TU NTE QUETN PAPER NEW REUT ( ω θ) + cos TM d Z ( ω ) TM TM ( ω θ) sin ω 4 Z 4 Z + [ ] + TM.5777 Aps Z TU NTE 48

49 TU NTE QUETN PAPER NEW REUT CNTRED RECTFER (ine Couaed AC o DC converers) NTRDUCTN T CNTRED RECTFER Conrolled recifiers are line couaed ac o power converers which are used o conver a fixed volage, fixed frequency ac power supply ino variable oupu volage. AC npu olage ine Couaed Converer + DC upu (d c ) - Type of inpu: Fixed volage, fixed frequency ac power supply. Type of oupu: ariable oupu volage The inpu supply fed o a conrolled recifier is ac supply a a fixed rs volage and a a fixed frequency. We can obain variable oupu volage by using conrolled recifiers. By eploying phase conrolled hyrisors in he conrolled recifier circuis we can obain variable oupu volage and variable (average) oupu curren by varying he rigger angle (phase angle) a which he hyrisors are riggered. We obain a unidirecional and pulsaing load curren wavefor, which has a specific average value. The hyrisors are forward biased during he posiive half cycle of inpu supply and can be urned N by applying suiable gae rigger pulses a he hyrisor gae leads. The hyrisor curren and he load curren begin o flow once he hyrisors are riggered (urned N) say a ω. The load curren flows when he hyrisors conduc fro ω o β. The oupu volage across he load follows he inpu supply volage hrough he conducing hyrisor. A ω β, when he load curren falls o zero, he hyrisors urn off due o AC line (naural) couaion. n soe bridge conrolled recifier circuis he conducing hyrisor urns off, when he oher hyrisor is (oher group of hyrisors are) urned N. The hyrisor reains reverse biased during he negaive half cycle of inpu supply. The ype of couaion used in conrolled recifier circuis is referred o AC line couaion or Naural couaion or AC phase couaion. When he inpu ac supply volage reverses and becoes negaive during he negaive half cycle, he hyrisor becoes reverse biased and hence urns off. There are several ypes of power converers which use ac line couaion. These are referred o as line couaed converers. Differen ypes of line couaed converers are Phase conrolled recifiers which are AC o DC converers. AC o AC converers AC volage conrollers, which conver inpu ac volage ino variable ac oupu volage a he sae frequency. Cyclo converers, which give low oupu frequencies. TU NTE 49

50 TU NTE QUETN PAPER NEW REUT All hese power converers operae fro ac power supply a a fixed rs inpu supply volage and a a fixed inpu supply frequency. Hence hey use ac line couaion for urning off he hyrisors afer hey have been riggered N by he gaing signals. DFFERENCE BETWEEN DDE RECTFER AND PHAE CNTRED RECTFER The diode recifiers are referred o as unconrolled recifiers which ake use of power seiconducor diodes o carry he load curren. The diode recifiers give a fixed oupu volage (fixed average oupu volage) and each diode recifying eleen conducs for one half cycle duraion (T/ seconds), ha is he diode conducion angle 8 or radians. A single phase half wave diode recifier gives (under ideal condiions) an average oupu volage ( ) and single phase full wave diode recifier gives (under ideal condiions) an average oupu volage ( ), where is axiu value of he available ac supply volage. Thus we noe ha we can no conrol (we can no vary) he oupu volage or he average load curren in a diode recifier circui. n a phase conrolled recifier circui we use a high curren and a high power hyrisor device (silicon conrolled recifier; CR) for conversion of ac inpu power ino oupu power. Phase conrolled recifier circuis are used o provide a variable volage oupu and a variable (average) load curren. We can conrol (we can vary) he average value ( value) of he oupu load volage (and hence he average load curren) by varying he hyrisor rigger angle. We can conrol he hyrisor conducion angle δ fro 8 o by varying he δ rigger angle fro o 8, where hyrisor conducion angle APPCATN F PHAE CNTRED RECTFER DC oor conrol in seel ills, paper and exile ills eploying oor drives. AC fed racion syse using racion oor. Elecro-cheical and elecro-eallurgical processes. Magne power supplies. Reacor conrols. Porable hand ool drives. ariable speed indusrial drives. Baery charges. High volage DC ransission. Uninerrupible power supply syses (UP). oe years back ac o power conversion was achieved using oor generaor ses, ercury arc recifiers, and hyraorn ubes. The odern ac o power converers are designed using high power, high curren hyrisors and presenly os of he ac- power converers are hyrisorised power converers. The hyrisor devices are phase conrolled o obain a variable oupu volage across he oupu load erinals. The TU NTE 5

51 TU NTE QUETN PAPER NEW REUT phase conrolled hyrisor converer uses ac line couaion (naural couaion) for couaing (urning off) he hyrisors ha have been urned N. The phase conrolled converers are siple and less expensive and are widely used in indusrial applicaions for indusrial drives. These converers are classified as wo quadran converers if he oupu volage can be ade eiher posiive or negaive for a given polariy of oupu load curren. There are also single quadran ac- converers where he oupu volage is only posiive and canno be ade negaive for a given polariy of oupu curren. f course single quadran converers can also be designed o provide only negaive oupu volage. The wo quadran converer operaion can be achieved by using fully conrolled bridge converer circui and for single quadran operaion we use a half conrolled bridge converer. CAFCATN F PHAE CNTRED RECTFER The phase conrolled recifiers can be classified based on he ype of inpu power supply as ingle Phase Conrolled Recifiers which operae fro single phase ac inpu power supply. Three Phase Conrolled Recifiers which operae fro hree phase ac inpu power supply. DFFERENT TYPE F NGE PHAE CNTRED RECTFER ingle Phase Conrolled Recifiers are furher subdivided ino differen ypes Half wave conrolled recifier which uses a single hyrisor device (which provides oupu conrol only in one half cycle of inpu ac supply, and i provides low oupu). Full wave conrolled recifiers (which provide higher oupu) o Full wave conrolled recifier using a cener apped ransforer (which requires wo hyrisors). o Full wave bridge conrolled recifiers (which do no require a cener apped ransforer) ingle phase sei-converer (half conrolled bridge converer, using wo CR s and wo diodes, o provide single quadran operaion). ingle phase full converer (fully conrolled bridge converer which requires four CR s, o provide wo quadran operaion). Three Phase Conrolled Recifiers are of differen ypes Three phase half wave conrolled recifiers. Three phase full wave conrolled reciriers. o ei converer (half conrolled bridge converer). o Full converer (fully conrolled bridge converer). PRNCPE F PHAE CNTRED RECTFER PERATN The basic principle of operaion of a phase conrolled recifier circui is explained wih reference o a single phase half wave phase conrolled recifier circui wih a resisive load shown in he figure. TU NTE 5

52 TU NTE QUETN PAPER NEW REUT R R oad Resisance Fig.: ingle Phase Half-Wave Thyrisor Converer wih a Resisive oad A single phase half wave hyrisor converer which is used for ac- power conversion is shown in he above figure. The inpu ac supply is obained fro a ain supply ransforer o provide he desired ac supply volage o he hyrisor converer depending on he oupu volage required. v P represens he priary inpu ac supply volage. v represens he secondary ac supply volage which is he oupu of he ransforer secondary. During he posiive half cycle of inpu supply when he upper end of he ransforer secondary is a a posiive poenial wih respec o he lower end, he hyrisor anode is posiive wih respec o is cahode and he hyrisor is in a forward biased sae. The hyrisor is riggered a a delay angle of ω, by applying a suiable gae rigger pulse o he gae lead of hyrisor. When he hyrisor is riggered a a delay angle of ω, he hyrisor conducs and assuing an ideal hyrisor, he hyrisor behaves as a closed swich and he inpu supply volage appears across he load when he hyrisor conducs fro ω o radians. upu volage v v, when he hyrisor conducs fro ω o. For a purely resisive load, he load curren i (oupu curren) ha flows when he hyrisor T is on, is given by he expression v i, for ω R The oupu load curren wavefor is siilar o he oupu load volage wavefor during he hyrisor conducion ie fro o. The oupu curren and he oupu volage wavefor are in phase for a resisive load. The load curren increases as he inpu supply volage increases and he axiu load curren flows a ω, when he inpu supply volage is a is axiu value. The axiu value (peak value) of he load curren is calculaed as i( ax). R TU NTE 5