DYNAMICS ANALYSIS OF LFR MODEL FOR A SINGLE-STAGE HIGH POWER FACTOR CORRECTION DIAGONAL HALF-BRIDGE FLYBACK AC/DC CONVERTER

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1 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4, pp (9) 555 DYNMICS NLYSIS OF LF MODEL FO SINGLE-STGE HIGH POWE FCTO COECTION DIGONL HLF-IDGE FLYCK C/DC CONVETE Jong-Lck Ln*, Chen-Yang Chen, and Sung-Pe Yang STCT y means of a graf scheme, a buck-boos cell and a wde range dagonal halfbrdge flyback cell are combned o creae a noel sngle-sage hgh power facor correcon (HPFC) dagonal half-brdge flyback ac/dc conerer n hs paper. When boh of he wo cells operae n dsconnuous conducon mode, he proposed conerer exhbs hgh power facor and low bulk capacor olage sress ndependen of he load araons. ased on he Loss-Free essor (LF) model, a new echnque, referred o as ac-dc balancng mehod, s also proposed. I s useful o deermne he dc alues, olage rpples, and phase angle shfs of he bulk capacor and oupu olage of he conerer. Moreoer, he componen alues are well desgned accordng o he operaon condons and desgn specfcaons of he conerer. Fnally, a prooype of he proposed conerer wh oupu olage 48 V and power 1 W s bul o es he heorecal analyss. I s successfully aldaed by IsSpce smulaons and expermenal resuls. Key Words: dagonal half-brdge flyback conerer, sngle-sage conerer, hgh power facor correcon (HPFC), LF model. I. INTODUCTION In order o produce a DC olage supply, a fullbrdge recfer and a fler capacor are usually used beween he C power source and he oupu load. Howeer, hey resul n low power facor wh hgh lne curren harmonc dsorons. hgh power facor correcon (HPFC) crcu s herefore added beween he full-brdge recfer and he load o elmnae he oal harmonc dsoron (THD). The wo-sage conerer, ncludng a PFC sage and a dc/dc sage, can exhb hgh power facor and small oupu olage rpple. *Correspondng auhor. (Tel: ex. 6158; Fax: ; Emal: jlln@mal.njcu.edu.w) J. L. Ln s wh he Deparmen of Engneerng Scence, Naonal Cheng Kung Unersy, Tanan 71, Tawan,.O.C. and s currenly a Deparmen of Compuer Scence and Informaon Engneerng, Chang Jung Chrsan Unersy, Tanan 711, Tawan,.O.C. C. Y. Chen and S. P. Yang are wh he Deparmen of Engneerng Scence, Naonal Cheng Kung Unersy, Tanan 71, Tawan,.O.C. S. P. Yang s currenly a Deparmen of Elecrcal Engneerng, Kun Shan Unersy, Tanan 71, Tawan,.O.C. When he PFC sage operaes n CCM, mus hae a curren conrol o force he npu curren wae o follow he npu olage wae. Therefore, he wo-sage conerer causes addonal coss and rases opologcal complexy. To oercome hs defec, he sngle-sage HPFC conerer wh a PFC cell and a dc/dc cell has been proposed (Madgan e al., 199; edl e al., 1994; edl and alogh, 1995; odrguez e al., 1997; Danele e al., 1999; Qu e al., 1999; Wu and Chen, 1999; Qu e al., ; Ln e al., 5; Ln e al., 6). Whou he curren conrol, he PFC cell operang n DCM can exhb an nheren hgh power facor. The dc/dc cell operang n DCM can aod he hgh olage sress across he bulk capacor (edl e al., 1994; edl and alogh, 1995; odrguez e al., 1997; Danele e al., 1999; Qu e al., 1999). In hs work, a noel sngle-sage HPFC dagonal half-brdge flyback C/DC conerer s proposed. I s an negraon of a buck-boos cell wh a wde range dagonal half-brdge flyback cell (Gu e al., 4) by means of a graf scheme. The proposed conerer wh PFC and dc/dc cells operang n DCM

2 556 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) g D 4 D 1 S 1 : n D 3 n L f L C m D C o C L o n () C f Lm S 1 Fg. 1 Noel sngle-sage HPFC dagonal half-brdge flyback ac/ dc conerer g D 4 D a 1 S S D 1 : n 3 Lm C L Co D C C Lm 1 L o Co o C Lm S S1 1 Fg. Equalen crcu n sage 1 exhbs a uny power facor and low olage sress across he bulk capacor. In he leraure, he LF model s usually appled o analyze he power facor of ac/dc conerers (Erckson and Maksmoc, 1; Ln e al., 5; Snger, 199; Snger e al., 4). ased on he LF model, he ac-dc balancng mehod s proposed n hs work. I s useful o dere he dc alues, olage rpples, and phase angle shfs of he bulk capacor and oupu olage of he proposed conerer. aher han complcaed aeraged sae equaons, he dynamcal behaors of he proposed conerer can be well deermned. The operang prncple, LF model deraon, dynamcs analyss and desgn consderaons of he proposed conerer are presened n he work. The smulaon and expermenal resuls aldae he heorecal analyss. II. OPETING PINCIPLE The proposed noel sngle-sage HPFC dagonal half-brdge flyback ac/dc conerer s depced n Fg. 1. The wo swches (S 1, S ) are urned on or off smulaneously. The dode D s used o clamp he urn-off olage spkes for he swch S. The nducor s he magnezng nducor of he elecrcal solaon ransformer. oh PFC and dc/dc cells n he proposed conerer operae n DCM. Ths means ha boh nducor curren L and magnezng nducor curren Lm operae n DCM. Some assumpons are made n he followng o smplfy he analyss of he crcu. 1. The swches, dodes, nducors and capacors are consdered o be deal whou parasc componens n he conerer.. The full-wae recfed lne olage = m sn(ω) wh ω = π/t L can be assumed o be consan oer one swchng perod T s, because T s s much less han one half lne perod T L. 3. The bulk capacor olage and he oupu capacor olage Co can be regarded as consans because he bulk capacance C and oupu capacance C o are suffcenly large. ased on he swchng of he swches and dodes, he crcu operaon of he proposed conerer oer one swchng perod T s can be dded no four lnear sages descrbed as follows. g D 4 D 1 S S 1 : n D 3 C L D C C Co L o o Lm C o C Lm S 1 S1 Fg. 3 Equalen crcu n sage Sage 1. [, 1 ] (S 1 : On, S : On, D 1 : Off, D : Off, D 3 : Off, D 4 : On) The swches (S 1, S ) are urned on a =. The dode D 4 s forward-based and he dodes (D 1, D, D 3 ) are reerse-based. The lnear equalen crcu s depced n Fg.. In hs sage, he olages g and are respecely appled across he npu nducor and he magnezng nducor. These acons cause he npu nducor curren L and he magnezng nducor curren Lm o rse lnearly. The load recees he energy from he oupu capacor C o. Sage. [ 1, ] (S 1 : Off, S : Off, D 1 : On, D : Off, D 3 : On, D 4 : Off) The swches (S 1, S ) are urned off a = 1. The dodes (D 1, D 3 ) are forward-based and he dodes (D, D 4 ) are reerse-based. The lnear equalen crcu s presened n Fg. 3. In hs sage, he olages and Co /n are respecely appled across nducors and. These applcaons cause he nducor currens L and Lm o decrease lnearly. The bulk capacor energy s proded by he nducor curren L, and he magnezng nducor energy s ransferred a he ransformer and dode D 3 o he oupu capacor C o and he load. Sage 3. [, 3 ] (S 1 : Off, S : Off, D 1 : Off, D : Off, D 3 : On, D 4 : Off) The swches (S 1, S ) are sll off n hs sage. The sage begns a = whle he npu nducor curren L drops o zero, and hus he dode D 1 becomes reerse-based. ll dodes excep D 1 sll conduc as shown n he preous sage. The lnear equalen crcu s depced n Fg. 4, and he olage Co / n s appled across he magnezng nducor. The magnezng nducor curren Lm hereby connues o

3 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer 557 g D 4 D 1 S S 1 : n D 3 C L D C C Co L Lm o Co o C Lm S 1 S1 g D 4 D 1 S S 1 : n D 3 C L D C Co L C Lm Co o C o S 1 Lm S1 Fg. 4 Equalen crcu n sage 3 Fg. 5 Equalen crcu n sage 4 Lm () L () o n T s g () C () L () () T s Lm () S 1, S on Co n off Co () Co Co n () S 1, S S 1, S on on off off d 1 T s d T s d 3 T s d 4 T s d 1 T s d T s d 3 T s d 4 T s d 1 T s d T s d 3 T s d 4 T s 1 3 T s 1 3 T s 1 3 T s Fg. 6 Key waeforms oer one swchng perod T s lnearly decrease. The oupu energy s also proded by he magnezng nducor curren Lm n he sage. Sage 4. [ 3, T s ] (S 1 : Off, S : Off, D 1 : Off, D : Off, D 3 : Off, D 4 : Off) The swches (S 1, S ) are sll off n hs sage. The sage begns a = 3 whle he magnezng nducor curren Lm drops o zero, and hus he dode D 3 becomes reerse-based. Therefore, all dodes are off. The lnear equalen crcu s presened n Fg. 5. The load energy s proded only by he oupu capacor C o. To proceed, he operaon of he proposed conerer reurns back o he frs sage when he swches (S 1, S ) are urned on agan. ccordng o he aboe analyss, he key waeforms oer one swchng perod T s are schemacally depced n Fg. 6. III. LF MODEL DEIVTION In hs secon, he LF model s esablshed o nesgae he dynamcal behaors of he proposed conerer. y rue of he ac-dc balancng mehod n he LF model, he dc alues, olage rpples, and phase angle shfs of he bulk capacor and oupu olages of he proposed conerer can hen be dered n he followng secon. The dode D n Fg. 1 s only used o clamp he olage spkes for he swch S, and hus says off oer one swchng perod T s when he crcu s normally operang. Hence, he dode D can be remoed n Fg. 7 when he LF model of he proposed conerer s esablshed. The proposed conerer n Fg. 7 can be dded no wo pars: 1) The crcu seen o he rgh of pons and : Ineresngly, s a flyback conerer wh npu olage x, as depced n Fg. 8. ccordng o he LF model (Erckson and Maksmoc, 1), he swch S and he dode D 3 can be replaced respecely wh he emulaed ressance and he dependen power source P dep := D3 D3 as

4 558 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) g D 4 D 1 C L S 1 x S 1 : n D 3 Lm C o o S S D 1 : n 3 S Lm Lm x D3 C o o Fg. 7 emong dode D of proposed conerer Fg. 8 Equalen crcu seen o he rgh of pons and x S Lm S P dep 1 : n D3 n Lm D3 C o o x x S S P dep D3 D3 C o o Fg. 9 esulng LF model of crcu seen o he rgh of pons and D 4 D 1 L L S 1 S1 C S1 D4 P D4 D1 P D1 L e1 P e1 S1 C x D4 D1 e1 S1 P e1 (c) Fg. 1 Equalen crcu seen o he lef of pons and P D4 P D1 C C x shown n Fg. 9, where he noaon x denoes he mong aerage <x()>t s oer one swchng perod T s. The emulaed power S S of flows enrely as he emulaed power P dep. Tha s P e = P dep, where he emulaed ressance s defned as (Erckson and Maksmoc, 1) := S = S d. (1) 1 T s Snce he magnezng nducor curren Lm operaes n DCM, he aeraged nducor olage s Lm =, and hus he magnezng nducor becomes a shor-crcu. The aeraged olage of he ransformer secondary s also gen by n Lm =. Hence, Fg. 9 s reduced o Fg. 9. ) The crcu seen o he lef of pons and : Fg. 1 follows drecly from Fg. 7. ccordng o he LF model, he swch S 1 and he dodes (D 1, D 4 ) can be replaced wh he emulaed ressance e1 and he dependen power sources ( P D1 := D1 D1, P D4 := D4 D4 ), respecely. I s presened n Fg. 1. The emulaed power S1 S1 of e1 flows enrely as he sum of he emulaed powers P D1 and P D4. Tha s P e1 = P D1 P D4. Snce he npu nducor curren L operaes n DCM, he aeraged nducor olage s L =, and hus he npu nducor becomes a shor-crcu. s a resul, we hae Fg. 1(c), where he npu ressance seen o he rgh of pons and s also added. I s clear from Fg. 9. In order o deermne he emulaed ressor e1 := S1 / S1, he aeraged olage S1 mus be deermned frs. ased on he waeforms depced n Fg. 6, he

5 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer 559 D4 D1 P D4 P D1 C x D4 P D4 P D1 D1 C e x Fg. 11 LF model of crcu n Fg. 1(c) aeraged nducor olages oer one swchng perod T S are gen by L = 1 T s [d 1 T s d T s ( )], () Lm = 1 T s [d 1 T s d T s ( C o n )d 3T s ( C o n )], (3) where duy raos d 1, d, d 3, and d 4 are defned n Fg. 6, and he oupu equaon s expressed as o = Co. (4) Snce all nducors of he proposed conerer are operang n DCM, all aeraged nducor olages oer one swchng perod T s are zero, namely, L = and Lm =. Hence from Eqs. () and (3), we hae d = g() d 1, (5) d 3 =(n C Co g() )d 1. (6) Thus, yelds d 4 =1(d 1 d d 3 ) =1(1n C )d 1. (7) Co Moreoer, from Eqs. (5)-(7) and Fg. 6, we ge = d 1 T s g (), (8) Therefore, from Fg. 1(c), he aeraged olage S1 s gen by S1 = x =, (1) whch mples e1 = S 1 S1 =. (13) I also mples ha he emulaed power of he swch S 1 s gen by S1 S1 =. (14) To proceed, from Eq. (1) and Fg. 1(c), he aeraged olages of he dodes D 1 and D 4 are gen by D1 =, (15) D4 = S1 =, (16) and he aeraged curren of he dode D 4 can be expressed by = T 1 [ 1 s (d L 1 T s ) ]= d 1 T s L g () (17) from Eqs. (5)-(7) and Fg. 6. Togeher wh n Eq. (8), we hae C = d 1 T s L C d 1 T s m g (). (9) P D1 = D1 = d 1 T s g (), (18) On he oher hand, Fg. 1(c) ges = C x. (1) Subsung Eqs. (1), (8), and (9) no Eq. (1) yelds = x. (11) P D4 = D4 = d 1 T s L g (). (19) Noably, we ge D1 D1 D4 D4 = and hus S1 S1 = D1 D1 D4 D4 () s erfed from Eq. (14).

6 56 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) I follows drecly from he emulaed ressance e1 = n Eq. (13) ha Fg. 1(c) can be reduced o Fg. 11 whch s equalen o Fg. 11. Ineresngly, Eq. (19) reeals ha he dependen power source P D4 <, and hus he dode D 4 s a consumer of he emulaed power. On he oher hand, P D1 > n Eq. (18) and hus he dode D 1 s a generaor of he emulaed power. Now, le us defne he emulaed ressance g as g := g() = g P dep1 d 1 T s P D1 D1 C Fg. 1 esulng LF model of crcu seen o he lef of pons and = d 1 T s (1) from Eq. (17). The emulaed power of he emulaed ressance g s hus gen by P g := g () = d 1 T s e1 L g ()= D4 ( ) = P D4 > () from Eqs. (16) and (17). Snce P D1 = P D4 from Eqs. (18) and (19), he equalen crcu depced n Fg. 1 s fnally dered on he bass of P g = P D1 from Eq. (). Now Fg. 1 can be combned wh Fg. 9, and hus he resulng LF model of he proposed noel sngle-sage HPFC conerer s esablshed n Fg. 13. Snce T s << T L, we hae =, = and o = o oer one swchng perod T s. ased on he LF model depced n Fg. 13, we can analyze he dc alues, olage rpples, and phase angle shfs of he bulk capacor and oupu olages by rue of he ac-dc balancng mehod on he LF model n he followng secon. IV. C-DC LNCING METHOD The dynamcs analyss for bulk capacor and oupu olages can be dered n hs secon by he ac-dc balancng mehod proposed n hs work. I follows from Fg. 13 ha he dependen power sources can be expressed as P dep1 = g () g =, (3) e x P dep e D3 P dep1 D1 x C o D3 o C D1 C g Fg. 13 esulng LF model of noel sngle-sage HPFC conerer g D1 e C f( D3 g, ) g( 1s C C, o ) P dep = C = o D3. (4) e ccordngly, Eqs. (3) and (4) can be rewren as wo nonlnear equaons descrbed by g() = D1 g = f ( g, ), (5) C = o D3 D3 = g(, o ), (6) wh g n Eq. (1) and n Eq. (1). ased on he resulng LF model depced n Fg. 13, he sysem block dagram of he proposed conerer can be presened n Fg. 14. From a sysem pon of ew, each olage and curren n he crcu s smply a lnear combnaon of dc and ac componens. Tha s ()=V C C (), o ()=V o o() ()=I D1 D 1 (), D3 ()=I D3 D 3 (). (7) Noably, x() = X x(), where X and x() are used o denoe he dc and ac componens of he sgnal x(), respecely. Moreoer, we hae g ()=V m sn(ω) = V m V m cos(ω ) = V m V m ξ() (8) oer one swchng perod T s, where ω = ω and ξ() = cos(ω ). Subsuon of Eqs. (7) and (8) no nonlnear Eqs. (4) and (5) produces E 1 : V m V m ξ()v C I D1 g V C g D 1 1 sc o Fg. 14 Sysem block dagram of proposed conerer o I D1 g C g C D 1 =, (9) o

7 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer 561 I D1 V C I D3 V m E 1 DC E DC V o ξ () 1 D1 () 1 s C 1 sc o () o D3 V C V o 1 Fg. 15 Sysem block dagram of proposed conerer n dc analyss Fg. 16 Sysem block dagram of proposed conerer n ac analyss E : V C V C C C V o I D3 V o D3 I D3 o o D3 =. (3) ll erms n Eqs. (8) and (9) can be dded no hree pars: (1) dc erms: V m/, V C I D1 g, V C and V o I D3, () lnear ac erms: V mξ()/, V C g D1, I D1 g C, V C C, V o D3 and I D3 o, and (3) producs of ac erms: g C D1, C and o D3. Snce he rpples of he bulk capacor olage and oupu olage are much less han her dc alues,.e. << V C, o << V o, he producs of he ac erms can be negleced. Therefore, he dc and ac analyss can be separaed no Eqs. (9) and (3). 1. DC nalyss Seng he sum of he dc erms n Eqs. (9) and (3) o zero, we hae E 1 DC : V m V C I D1 g =, (31) E DC : V C V o I D3 =. (3) Then seng s = n Fg. 14 for dc analyss, he sysem block dagram n Fg. 14 s hereby reduced o ha n Fg. 15. I follows drecly from Fg. 15 ha I D1 = V C / and I D3 = V o /. Then subsung I D1 and I D3 no Eqs. (31) and (3) yelds V C = 1 V o = e ( 1 g V m = 1 L )V m = D 1 L V m, (33) T s V m. (34) Ineresngly, he olages V C and V o are ndependen of he urns rao n of he ransformer.. C analyss Neglecng he producs of he ac erms and dc erms n Eqs. (9) and (3), we hae V m ξ() V C g D1 I D1 g C =, (35) V C C V o D3 I D3 e o =, (36) wh I D1 = V C / and I D3 = V o / from Fg. 15. y arrangng erms n Eqs. (35) and (36), we hae D1 = 1 ξ() 1 C, (37) D3 = C o, (38) wh parameers 1, 1, and defned as V m T s 1 :=, V C 1 := d 1 = g L 1, m := V C, V o := 1 e. (39) s a resul, he sysem block dagram of he proposed conerer s presened n Fg. 16. ased on Fg. 16, ransfer funcons from npu ξ(s) o C (s) G 1 (s):= C (s) ξ(s) and npu ξ(s) o oupu o (s) G (s):= o(s) ξ(s) = = = 1 1 C C s ( 1 =, 1 ) s C C C 1 C C s ( 1 o 1 ) s ( 1 ) C C C o C o (4) 1 C C o s s C. (41) C o are dered. Snce snusodal npu ξ() = cos(ω ), we hae () = G 1 ( jω ) cos(ω G 1 ( jω )), (4) o () = G ( jω ) cos(ω G ( jω )) (43) from a sysem pon of ew. The ac olage rpples and he phase angle shfs can be hereby deermned from Eqs. (4) and (43), respecely.

8 56 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) V. DESIGN CONSIDETIONS In hs secon, o ensure he condons of he proposed conerer operang n DCM( ) DCM( ) and o sasfy he specfed olage rpple percenages across he capacors, he nducances and and capacances C and C o can be well desgned, respecely. 1. Inpu Inducance earrangng Eq. (34) yelds = T s ( D 1V m V o ). (44). Magnezng Inducance From Eqs. (5)-(7), he dependences of duy raos D () and D 3 () on D 1 a he dc operang pon are gen by D = g() V C D 1, (45) D 3 =(n V C V o g() V C )D 1, (46) wh V Co = V o. One sees from he waeforms L () and Lm () n Fg. 6 ha boh nequales D 1 D () < 1, (47) D 1 D () D 3 () < 1 (48) are requred for all me [, T L ]. In addon, snce L drops o zero earler han Lm, we hae D 3 () >. (49) Subsung Eqs. (45) and (46) no Eqs. (47)-(49) produces ( g() 1)D V 1 <1, (5) C (n V C V o 1)D 1 <1, (51) n V C V o g() V C >. (5) Snce he recfed lne olage = V m sn(ω) changes wh me, subsuon of he wors case max = V m no Eqs. (5)-(5) yelds he smulaneous nequales ( V m V C 1)D 1 <1, (53) (n V C V o 1)D 1 <1, (54) n V C V o V m V C >. (55) Subsuon of V C n Eq. (33) and V o n Eq. (34) no Eqs. (53)-(55) produces D 1 > ( ) 1D, (56) 1 < T s n (1 D 1), (57) > D 1 n T s. (58) Ths leads us o conclude ha he magnezng nducance can be deermned drecly from he smulaneous nequales Eqs. (56)-(58). For nsance, accordng o desgn specfcaons: V m = 156 V, V o = 48 V, = 3Ω, n = 1, T s = µs and D 1 =., he npu nducance = 58.8 µh s deermned drecly from Eq. (44) and hen smulaneous nequales > 9.4 µh, (59) < µh, (6) > 36. µh (61) are obaned from Eqs. (56)-(58), respecely. Hence he magnezng nducance = 1 µh s chosen n hs work. Then V C = V s deermned from Eq. (33) because of = 58.8 µh, = 1 µh and V m = 156 V. Noably, he bulk capacor C has low olage sress. fer deermnng he nducances and, he capacances C and C o can hen be deermned accordng o he specfed olage rpple percenages n he proposed conerer. 3. ulk Capacance C From Eqs. (4) and (4), he olage rpple percenage of he bulk capacor s gen by V C V C = C () max V C = G 1(jω ) V C = V C 1 C s C s = jω 1% (6)

9 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer 563 Table 1 Specfcaons and componen alues of he proposed conerer Inpu peak olage V m 156 V Duy rao D 1. Half lne perod T L 1/1 sec Inpu nducance 58.8 µh Swchng frequency f s 5 khz Magnezng nducance 1 µh Oupu olage V o 48 V ulk capacance C 47 µf Load ressance 3 Ω Oupu capacance C o µf Turns rao n 1 ulk capacor olage V C 144 V. 1. I L [] I Lm [] Tme [µs] Tme [µs] Fg. 17 Smulaon resuls of npu nducor curren L and magnezng nducor curren Lm (horzonal: 5 µs/d) wh 1 n Eq. (39), V C n Eq. (33), n Eq. (1) and ω = ω = π/t L. 4. Oupu Capacance C o From Eqs. (41), (43) and V Co = V o, he olage rpple percenage of he oupu capacor s gen by V Co V Co = C o () max V Co = G (jω o ) V Co = V Co 1 C C o (s C ) (s C o ) s = jω o 1%, (63) wh V Co = V o n Eq. (34), 1 and n Eq. (39), n Eq. (1) and ω = ω = π/t L. For desgn specfcaons: V m = 156 V, V Co = V o = 48 V, = 3 Ω, n = 1, T s = µs and D 1 =., we hae = 58.8 µh and = 1 µh as shown aboe. Hence V C = V n Eq. (33), g = Ω n Eq. (1), = 6.61 Ω n Eq. (1), and hen 1 =.6963 and =.9 n Eq. (39) are drecly deermned. If one half lne perod s gen by T L = 1/1 sec, hen ω = ω = π/t L = 4π rad/sec. Vewng hs, we hae V C V C = C (4π) C 1% (64) from Eq. (6). Hence we hae C > 56.8 µf for he specfed olage rpple percenage: V C /V C < 5%. Then, C = 47 µf s chosen n hs work. Togeher wh C = 47 µf, ges V Co V Co = C o (4π) (4π) C o 1% (65) from Eq. (63). Hence we hae C o > 93 µf for he specfed olage rpple percenage: V Co /V Co < 1%. s a resul, C o = µf s chosen n hs work. In summary, he desgn specfcaons and componen alues of he proposed conerer can be lsed n Table 1.

10 564 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) 4 15 () 4 15 () V g [V] 1 V C [V] 13 1 V g [V] 1 V C [V] Tme [ms] Tme [ms] Fg. 18 ulk capacor olage () and recfed lne olage : heorecal resuls and smulaon resuls (horzonal: 5 ms/d) o () o () V g [V] V o [V] 47.3 V g [V] V o [V] Tme [ms] Tme [ms] Fg. 19 Oupu olage o () and recfed lne olage : heorecal resuls and smulaon resuls (horzonal: 5 ms/d) VI. NUMEICL ND SIMULTION ESULTS The IsSpce smulaon resuls n Fg. 17 demonsrae ha boh PFC and dc/dc cells are operang n DCM. The npu nducor curren L and magnezng nducor curren Lm boh drop o zero oer one swchng perod T s, and L drops o zero earler han Lm as menoned n he preous secon. Wh he help of he desgn specfcaons and componen alues n Table I, he parameers 1 =.6963, 1 =.5, =.9, =.43 (66) can be compued from Eq. (39). Then, subsuon of he parameers no Eqs. (4) and (41) produces he ransfer funcons G 1 (s)= C (s) ξ(s) = s.6, (67) G (s)= o(s) ξ(s) = (s.6)(s 39.53). (68) Togeher wh s = jω = j4π, ges () = 1.964cos(ω ), (69) o () =.34cos(ω 4.57 ). (7) from Eqs. (4) and (67), and Eqs. (43) and (68), respecely. Consequenly, we hae () = V C C () = cos(ω ), (71) o () = V o o () = 48.34cos(ω 4.57 ). (7) Ths reeals ha he dc alues are V C = V and V o = 48 V, he olage rpples are V C = 3.98 V and V o =.68 V, and he phase angle shfs are θ 1

11 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer n (). 1 g () 4. 1 n () g [V] V g [V] n [V] V n [V] Tme [ms] Tme [ms] Fg. Smulaon resuls of recfed lne olage and curren g () and npu lne olage n () and curren n () (horzonal: 5 ms/d) Fg. 1 Waeform of npu nducor curren L (ercal: 5 /d, horzonal: 1 µs/d). Measuremen of power facor PF =.99 wh power lne frequency 6 Hz and npu lne olage 11 Vrms = and θ = The heorecal resuls () and o () are depced n Fg. 18 and Fg. 19, respecely. The smulaon resuls show ha he dc alue V C = 144 V and rpple V C = 4.4 V of he bulk capacor olage n Fg. 18, and he dc alue V Co = V o = 47.5 V and rpple V o =.9 V of he oupu capacor olage n Fg. 19. They are close o he heorecal resuls V C = V, V C = 3.98 V, V Co = V o = 48 V and V o =.68 V, as menoned aboe. The smulaon resuls of he olage rpple percenages V C /V C 1% =.8% < 5% and V Co / V Co 1% =.% < 1% confrm he desgn specfcaons. In addon, he smulaon resuls of he phase angle shfs of () and o () erfy he heorecal resuls from Fg. 18 and Fg. 19. Furhermore, he recfed lne olage and curren g () are presened n Fg.. Fg. reeals ha he npu lne curren n () follows he npu lne olage n (), and hus he proposed conerer has hgh power facor. The power facor s calculaed o be PF =.9995 by usng he Fourer analyss of he IsSpce sofware. VII. EXPEIMENTL ESULTS prooype of he proposed conerer depced n Fg. 1 was bul and esed o erfy he operang prncple of he proposed conerer. To compare wh Fgs. 17-, he expermenal resuls are presened n Fgs Fgure 1 presens he waeform of he npu nducor curren L and measuremen of he power facor PF =.99, whch s close o uny. Fgs. - presens he expermenal bulk capacor olage () and oupu olage o (). Ineresngly, hey are close o hose n Fg. 18 and Fg. 19, respecely. The recfed lne olage and curren g () are depced n Fg. 3 and he npu lne olage n () and curren n () are presened n Fg. 3. The harmonc specrum for he npu lne curren n () s presened n Fg. 4. I s measured by FFT sero analyzer 911. The comparson wh he IEC Class D sandards s shown n Fg. 4. The comparson reeals ha all npu lne curren harmoncs are below he requremens of IEC Class D.

12 566 Journal of he Chnese Insue of Engneers, Vol. 3, No. 4 (9) 48 V 146 V Fg. Waeforms of bulk capacor olage () and recfed lne olage g() (ercal: 5 V/d, ac, 5 V/d, horzonal: 5 ms/d) and oupu olage o() and recfed lne olage g() (ercal: 1 V/d, ac, 5 V/d, horzonal: 5 ms/d) Fg. 3 Waeforms of recfed lne olage g() and curren g() (ercal: 5 V/d, /d, horzonal: 5 ms/d) and npu lne olage n() and curren n() (ercal: 5 V/d, 5 /d, horzonal: 5 ms/d) Maxmal permssble harmonc curren per wa [m/w] IEC Class D Measuremens 7 9 Harmonc Order [n] Fg. 4 Specrum analyss: harmonc specrum for npu lne curren and comparson wh he IEC Class D sandards VIII. CONCLUSION In hs work, a noel sngle-sage HPFC dagonal half-brdge flyback C/DC conerer s proposed o achee hgh power facor correcon, low sress olage across he bulk capacor, and small oupu olage rpple. The operang prncple, LF model deraon, dynamcs analyss and desgn consderaons of he proposed conerer are presened. ased on he LF model a new echnque of ac-dc balancng, raher han he aeraged sae equaons, s proposed o successfully deermne he dc alues, olage rpples, and phase angle shfs of he bulk capacor and oupu olage. The smulaon and expermenal resuls aldae he heorecal analyss. CKNOWLEDGMENTS The auhors would lke o hank he Naonal Scence Councl of he epublc of Chna, Tawan,

13 J. L. Ln e al.: Dynamcs nalyss of LF Model for a Sngle-Sage HPFC Flyback Conerer 567 for parally supporng hs research under Conrac No. NSC96-1-E C C o d 1 D 1, D, D 3, D 4 f s n g n P dep1, P dep e1,, g S 1, S T L T s n g m o NOMECLTUE bulk capacor oupu capacor duy rao dodes swchng frequency npu curren recfed npu curren npu nducor magnezng nducor urns rao dependen power sources load ressance emulaed ressances swches me half lne perod swchng perod npu olage recfed npu olage npu peak olage oupu olage EFEENCES Danele, M., Jan P. K., and Joos, G., 1999, Sngle-Sage Power-Facor-Correced C/DC Conerer, IEEE Transacons on Power Elecroncs, Vol. 14, No. 6, pp Erckson,. W., and Maksmoc, D., 1, Fundamenals of Power Elecroncs, Second Edon, Kluwer cademc Publshers, US. Gu, Y., Gu, X., Hang, L., Lu Z., and Qan, Z., 4, Improed Wde ange Dual Swch Flyback DC/ DC Conerers, Proceedngs of IEEE ppled Power Elecroncs Conference, Sana Paula, C, US, pp Ln, J. L., Yao W. K., and Yang, S. P., 6, nalyss and Desgn for a Noel Sngle-Sage Hgh Power Facor Correcon Dagonal Half-rdge Forward C/DC Conerer, IEEE Transacons on Crcus and Sysems Par I, Vol. 53, No. 1, pp Ln, J. L., Chang, M. Z., and Yang, S. P., 5, Synhess and nalyss for a Noel Sngle-Sage Isolaed Hgh Power Facor Correcon Conerer, IEEE Transacons on Crcus and Sysems Par I, Vol. 5, No. 9, pp Ln, J. L., Yang S. P., and Ln, P. W., 5, Small- Sgnal and Conroller Desgn for an Isolaed Zea Conerer wh Hgh Power Facor Correcon, Elecrc Power Sysems esearch, Vol. 76, pp Madgan, M., Erckson,., and Ismal, E., 199, Inegraed Hgh-Qualy ecfer-egulaors, Proceedngs of IEEE Power Elecroncs Specalss Conference, Toledo, Span, pp Qu, M., Moschopoulos, G., Pnhero, H., and Jan, P., 1999, nalyss and Desgn of a Sngle Sage Power Facor Correced Full-rdge Conerer, Proceedngs of IEEE ppled Power Elecroncs Conference, Dallas, TX, US, pp Qu, W., Wu, W., Luo, S., Gu, W., and aarseh, I.,, -Flyback PFC Conerer wh Low Inermedae us Volage and Tgh Oupu Volage egulaon for Unersal Inpu pplcaons, Proceedngs of IEEE ppled Power Elecroncs Conference, Dallas, TX, US, pp edl,., and alogh, L., 1995, Desgn Consderaon for Sngle Sage Isolaed Power Facor Correced Power Supples wh Fas egulaon of he Oupu Volage, Proceedngs of IEEE Power Elecroncs Specalss Conference, Dallas, TX, US, pp edl,., alogh, L., and Sokal, N. O., 1994, New Famly of Sngle-Sage Isolaed Power-Facor Correcor wh Fas egulaon of he Oupu Volage, Proceedngs of IEEE Power Elecroncs Specalss Conference, Tape, Tawan, pp odrguez, Canales, E., F., Najera P., and rau, J., 1997, Noel Isolaed Hgh Qualy ecfer wh Fas Dynamc Oupu esponse, Proceedngs of IEEE Power Elecroncs Specalss Conference, S. Lous, MO, pp Snger, S., 199, ealzaon of loss-free resse elemens, IEEE Transacons on Crcus and Sysems, Vol. 37, No. 1, pp Snger, S., Ozer, S., and Shmloz, D., 4, pure realzaon of loss-free ressor, IEEE Transacons on Crcus and Sysems Par I, Vol. 51, No. 8, pp Wu, T. F., and Chen, Y. K., 1999, nalyss and Desgn of an Isolaed Sngle-Sage Conerer cheng Power-Facor Correcon and Fas egulaon, IEEE Transacons on Indusral Elecroncs, Vol. 46, No. 4, pp Manuscrp eceed: Mar. 13, 8 eson eceed: Sep. 3, 8 and cceped: Oc. 3, 8