Non-isolated high step-up DC DC converter adopting auxiliary capacitor and coupled inductor

Transcription

1 J. Mod. Power Sys. Clean Energy hps://doi.org/.7/s Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor Gang WU, Xinbo RUAN, Zhihong YE 2 Absrac For grid-conneced power sysem based on phoovolaic (PV) source and fuel cells, high sep-up and high-efficiency DC DC converers are needed, due o he bus volage of he grid-conneced inverer is much higher han he oupu volage of PV and fuel cells. In his paper, a novel high sep-up converer is proposed. An auxiliary capacior is inroduced ino he boos converer, which serves as a volage source. I is in series wih he inpu volage source wih he same volage polariies. Thus, he inpu volage is increased equivalenly and he volage gain is increased accordingly. To reduce he volage sresses of he swich and he diode, muliple oupu capaciors are inroduced. The volage of each oupu capacior is degraded leading o he reduced volage sress. To replenish energy for he muliple oupu capaciors, a coupled inducor is adoped. Based on his, high sep-up converer adoping auxiliary capacior and coupled inducor is derived. The operaing principles and volage gain of he proposed converers are analyzed in his paper. In he CrossCheck dae: 2 Augus 27 Received: 5 November 26 / Acceped: 2 Augus 27 Ó The Auhor(s) 27. This aricle is an open access publicaion & Gang WU wugang@nuaa.edu.cn Xinbo RUAN ruanxb@nuaa.edu.cn Zhihong YE sam.ye@lieon.com 2 College of Auomaion Engineering, Nanjing Universiy of Aeronauics and Asronauics, Nanjing 26, China Power SBG ATD-NJ R&D Cener, Lie-On Technology Corp, Nanjing 29, China end, experimen resuls are given o verify he heoreical analysis. Keywords High volage gain, High efficiency, Nonisolaed, Phoovolaic (PV), Fuel cell Inroducion Since i akes cenuries for he radiional fossil energy o be replenished, i will be exhaused wih he growing demand for energy of human sociey. Thus he energy crisis is increasingly serious. Meanwhile, he excessive usage of he radiional fossil energy has pollued he environmen and resuled in greenhouse effec on a global scale []. Therefore, i is becoming more and more imporan o opimize he energy consumpion srucure and o uilize clean and renewable energy. Solar energy and hydrogen energy are wo promising renewable energy, and have exensive applicaion prospec. As he uilizaion mehods of he wo new energy, phoovolaic (PV) and fuel cells power generaions have been applied on a large scale [2 7], such as phoovolaic power saion and elecric vehicle. In recen years, he grid-conneced power generaion based on PV source for residenial applicaion has become globally popular. Usually, an inerface uni is necessary, as he oupu volage of PV source is relaively oo low for he line volage. If he line volage is 22 V, he inpu volage needed by he grid-conneced inverer would approach 38 V. Bu he oupu volage of PV source generally varies from 25 o 45 V. To boos he oupu volage of PV source, one possible soluion o is o make series-conneced PV arrays. Bu he oal oupu power of PV arrays will be degraded due o module mismach or parial shading [8]. 23

2 Gang WU e al. Anoher promising soluion is o uilize a high sep-up DC DC converer o mach he low oupu volage of PV source and high inpu volage of he inverer. Then every PV source can realize he funcion of maximum power poin racking. For he isolaed DC DC converers, he volage gain can be increased by adjusing he urns raio of he ransformer. Bu he energy sored in he leakage inducor is difficul o be ransferred o he oupu. Thus, for he applicaion wihou galvanic isolaion requiremen, nonisolaed high sep-up DC DC converers is preferred. The boos converer is wildly used for volage sep-up. However, is duy cycle would be oo large when he inpu volage is much smaller han he oupu. And for he acual power swich and diode, a cerain delay beween urn-on and urn-off sae will probably resul ha he power swich is urned on before being cu off compleely and he diode is cu off before conducing. Thus, he reliabiliy is degraded. When he duy cycle approaches uniy, a large pulse curren will conduc hrough he diode in a shor ime, which leads o large he curren sress of he diode and severe reverse recovery problem. This will grealy affec he efficiency and brings abou a serious elecromagneic inerference problem [9 2]. By cascading anoher boos converer, a high volage gain can be easily obained. Bu he addiional swich makes he conrol scheme more complex. And i may cause insabiliy issue for cascaded sysems. The impedance source neworks are widely used in he inverers [3 6] o increase he volage boos inversion abiliy. Likewise, he impedance source neworks can also be used in high sep-up DC DC converers o achieve high volage gain [7 2]. The converers can operae wih a much smaller duy cycle, which improves he reliabiliy. By combining quasi-z-source nework and ransformer, he volage sress of he swich is reduced. Bu mos of he converers adop muliple power swiches, and have a relaively complex conrol scheme. In [2], a single power swich was adoped o simplify he conrol design. However, he volage sress of he swich is as high as he oupu volage, which brings large swiching loss. Anoher mehod of increasing he volage gain is o inroduce a coupled inducor [22 28]. However, he curren hrough he coupled inducor is disconinuous. I goes agains he lifeime of PV and fuel cell when he coupled inducor is placed on he inpu side. Especially for he low inpu volage applicaion, he inpu curren is very large. Thus, he coninuous inpu curren is preferred. To overcome he respecive disadvanages of quasi-zsource nework and coupled inducor, some isolaed high sep-up DC DC converers combining quasi-z-source nework and coupled inducor are proposed in [29, 3]. However, due o he isolaion, he energy sored in he leakage inducor of he primary winding is difficul o be ransferred o he oupu. In his paper, a non-isolaed high sep-up DC DC converer wih single swich based on quasi-z-source nework and coupled inducor is proposed. The inpu curren is coninuous and he volage sress of he swich is low. Besides, he energy sored in he leakage inducor can be absorbed by he oupu capacior, which is beneficial for he efficiency. And single swich is used o simplify he conrol scheme. The operaing principle and parameer calculaion are given in his paper, and an experimen is conduced o verify he heoreical analysis. The experimen resuls indicae ha he proposed converers can achieve a higher efficiency. 2 Derivaion of high sep-up DC DC converers adoping auxiliary capacior and coupled inducor 2. High sep-up converer adoping auxiliary capacior Figure gives he basic boos converer, where is he inpu volage, L is he boos inducor, is he swich. To increase he volage gain of boos converer, an auxiliary volage source V a can be inroduced o he inpu erminal and he volage polariy is he same as, as shown in Fig. 2. When is urned on, is in series wih V a o charge L. When is urned off, is in series wih V a and L o supply he load. And he oupu volage is he sum of, V a and he volage of L. Obviously, he auxiliary volage source increases he inpu volage equivalenly, and a high volage gain is obained. The auxiliary volage source V a in Fig. 2 can be implemened wih a capacior C a, which is defined as he auxiliary capacior. To replenish energy for he auxiliary capacior C a, he inducor L 2, and he diode D is inroduced as shown in Fig. 3a. Obviously, he larger he volage of he auxiliary capacior is, he higher he derived volage gain will be. To obain a higher volage for C a,an addiional auxiliary volage source V a can be added in he charging pah of L 2, as shown in Fig. 3b. When a is urned on, V a is in series wih he inpu volage source o charge L 2. When a is urned off, L 2 replenishes energy for C a. If V a is equal o he elecric poenial difference beween nodes a and b, he elecric poenials of he drain elecrodes are idenical and can be conneced direcly. In L D o C f Fig. Basic boos converer 23

3 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor V L a D o V C f g Fig. 2 Boos converer adoping auxiliary volage source i L2 L 2 D i D C a C a2 i L L D o i Do C f Fig. 5 High sep-up converer adoping auxiliary capacior L 2 i L2 C a D a L 2 i L2 Va C a D a Fig. 3 Derivaion process L L b C f D o (a) Sep (incomplee opology) (b) Sep 2 C f D o doing so, a can be removed o simplify he srucure. Likewise, he auxiliary volage source V a can be implemened by a capacior C a2, as shown in Fig. 4. As seen, L can be used o replenish energy for C a2. This opology has been proposed and analyzed in [9], which is called Z-source DC DC converer. As he volages of C a and in Fig. 4 are consan, he volage beween nodes c and d is also consan and equals he volage sum of C a and. Thus, a capacior can be added beween nodes C and D o serve as a new inpu source of he boos inducor L. As he new capacior charges L insead of he original one, he original auxiliary capacior can be removed as shown in Fig. 5. This srucure consising of he capacior and inducor is called quasi-zsource nework [3]. Is operaing modes when he nework is applied for DC DC converer wih single swich has no been analyzed in deail in [3]. Compared wih he converer shown in Fig. 4, he volage sress of C a in Fig. 5 is larger. Bu he inpu curren of he converer in Fig. 5 is coninuous, which is beneficial for improving he lifeime of PV and fuel cell. As shown in Fig. 5, he volage sresses of he swich and he diode are boh as high as he oupu volage which leads o a large conducion resisor of he swich and severe reverse recovery problem of he diode. Thus, he conducion loss and he swiching loss are boh large. 2.2 High sep-up converer adoping auxiliary capacior and coupled inducor To reduce he volage sress of he swich and he diode, referring o [3], muliple oupu capaciors can be used o supply he load, as shown in Fig. 6a. In doing so, he volage of C o is reduced, and he volage sress of, D and D o are reduced as well. To replenish energy for C o2, he inducor L in Fig. 5 is replaced by he coupled inducor L cp, and he secondary winding of he coupled inducor is used o charge C o2. In [3], he inducor of he boos converer is replaced by he coupled inducor, which leads o a disconinuous inpu curren. On he conrary, he inpu curren of he converer in Fig. 6b remains coninuous, which is beneficial for he lifeime of PV and fuel cell. As shown in Fig. 6b, he volage doubling recifier circui is adoped o furher increase he volage of C o2 in order o reduce he volage sresses of, D and D o. As a resul, a swich wih a lower conducion resisor can be seleced, and he conducion loss and swiching loss can be reduced. i L2 L 2 C a c D C a2 L i L C f D o 3 Analysis of high sep-up DC DC converers adoping auxiliary capacior and coupled inducor 3. Operaing principle of CCM Fig. 4 Transiion srucure (Z-source DC DC converer) d Considering he parasiic parameers of he coupled inducor, he equivalen circui is given in Fig. 7. When he 23

4 Gang WU e al. v gs i L i L L L D i D D i D v D C a L cp C a2 C o2 v Do Do i Do C o (a) Derivaion progress v D C a L cp C a2 D o2 i Do2 Co2 v Do Do i Do C o i L i i D i Llk i Lm (b) Complee opology i Do Fig. 6 High sep-up converer adoping auxiliary capacior and coupled inducor 2 3 T s 4 2T s i L L D C T a2 r_p i Tr_p i C Co3 o3 currens of L and he magneizing inducor are boh coninuous, here exis four operaing modes and he key waveforms are shown in Fig. 8, where i L is he curren of L, is he curren of he secondary winding of he coupled inducor, i Lm and i Llk are he currens of he magneizing inducor and he leakage inducor of he coupled inducor respecively, i D and i Do are he currens of D and D o. The operaing modes are shown in Fig. 9. Mode [ 2 ]: When is urned on, is in series wih C a2 o charge L, and C a charges he magneizing inducor. In his mode, he secondary winding of he coupled inducor charges hrough. D o i Do i i Llk D V Ca i Lm i Ca2 i Ca C a Fig. 7 Equivalen circui V Ca2 D o2 i Do2 C o2 C o Fig. 8 Key waveforms in CCM Mode 2 [ 2 3 ]: When is urned off, L and charge C a and C a2 hrough D respecively, and he inpu volage source is in series wih L and o charge C o.in his mode, i Lm is smaller han i Llk, where i Lm and i Llk are he currens of he leakage inducor and he magneizing inducor, respecively. Thus, he curren direcion of he secondary winding remains and he secondary winding sill charges hrough. Mode 3 [ 3 T s ]: In his mode, i Lm is larger han i Llk, leading o he curren direcion of he secondary winding changed. And he secondary winding charges C o2 in series wih hrough D o2. Mode 4 [T s 4 ]: In his mode, since i Lm is larger han i Llk, he secondary winding sill charges C o2 in series wih hrough D o Operaing principle of DCM When he curren of L is disconinuous, he key waveforms and operaing modes in DCM are shown as Figs. and, respecively. There are five operaing modes for DCM, in which Mode, Mode 2, and Mode 3 23

5 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor i L i L i L i L L C a C D T a2 o i Do r_p i i Llk D D i Ca i Lm C a D o2 i Do2 i Ca2 i Co3 i Co2 C o2 C o i Co L D C a2 D o i Do T r_p i i Llk D L C i o Lm m (a) Mode [ ~ 2 ] D o2 i Do2 (b) Mode 2 [ 2 ~ 3 ] C o2 L D C a2 D o i Do T r_p i i Llk D i L C o Lm m L C a C a (c) Mode 3 [ 3 ~T s ] C o2 D o2 i Do2 D Tr_p C a2 D i Do o i D i Llk i Lm Fig. 9 Operaing modes in CCM (d) Mode 4 [T s ~ 4 ] D o2 C o i Do2 Co2 I o v gs i L i i Llk DT s are he same wih hose in CCM. Here, only Mode 4 and Mode 5 are given in deail. Mode 4 [ 4 5 ]: When i L = i Do - i Llk, he curren hrough D decreases o zero and is cu off. Mode 5 [ 5 T s ]: The currens hrough L and L cp are zero, and C o and C o2 are in series o supply he load. 3.3 Volage gain of CCM 3 D r T s i Lm Fig. Key waveforms in DCM T s As he leakage inducor is much smaller compared wih he magneizing inducor, he duraion of Modes 2 and 4 in Fig. 8 are relaively shor. Thus, he leakage inducor is negleced here, o simplify he analysis. For seady sae, according o he vol-second relaionship of L, we have: þ V Ca2 DTs ¼ V Ca ð DÞTs ðþ where is he inpu volage; D is he duy cycle of he swich; T s is he swiching period; V a and V a2 are he average volages of C a and C a2, respecively. Similarly, he vol-second relaionship can be applied o, hen we have: V Ca DT s ¼ V Ca2 ð DÞT s ð2þ According o () and (2), V Ca, V Ca2 can be derived as: V Ca ¼ ð DÞV g ð3þ 2D V Ca2 ¼ D ð4þ 2D Referring o Fig. 9c, he volage of C o equals he volage sum of C a and C a2. 2T s 23

6 Gang WU e al. i L D o2 i Do2 Co2 i L D o2 i Do2 Co2 L D C a2 D o i Do T i r_p i Llk D C o i Lm L D C a2 D o i Do T i r_p i Llk D C o i Lm C a C a (a) Mode [ ~ 2 ] (b) Mode 2 [ 2 ~ 3 ] i L D o2 i Do2 Co2 i L D o2 i Do2 Co2 L D C a2 D o i Do T i r_p i Llk D C o i Lm L D C a2 D o i Do T i r_p i Llk D C o i Lm C a C a (c) Mode 3 [ 3 ~ 4 ] (d) Mode 4 [ 4 ~ 5 ] i L L D C a2 D o i Do T i r_p i Llk D C o i Lm C a D o2 i Do2 Co2 (e) Mode 5 [ 5 ~T s ] Fig. Operaing modes in DCM V Co ¼ V Ca þ V Ca2 ¼ ð5þ 2D The volage of can be expressed as: V Co3 ¼ N spð DÞ ð6þ 2D where N sp = N s /N p ; N s is he secondary winding urns; N p is he primary winding urns. The volage of C o2 is: V Co2 ¼ N spd 2D þ V Co3 ¼ N sp 2D Combing (5) and (7), he oupu volage is: ð7þ ¼ V Co þ V Co2 ¼ N sp þ Vg ð8þ 2D Referring o Fig. 9a and c, he volage sresses of, D and D o equal V Co, which are much smaller han he oupu volage. And i is beneficial for improving he efficiency of he converer. 3.4 Volage gain of DCM To simplify he analysis, an assumpion is made ha he leakage inducor is negleced. Thus, Mode 2 and Mode 4 23

7 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor are negleced as well. Then only Mode, Mode 3 and Mode 5 need o be considered. For seady sae, applying he vol-second balance principle o L and, we have: ð þ V Ca2 ÞDT s ¼ðV Ca ÞD r T s ð9þ V Ca DT s ¼ V Ca2 D r T s ðþ where D r T s = 4 -. Referring o Fig., we have: V Co ¼ V Ca þ V Ca2 ðþ V Co3 ¼ N sp V Ca ð2þ V Co2 ¼ V Co3 þ N sp V Ca2 ¼ N sp ðv Ca þ V Ca2 Þ ð3þ ¼ V Co þ V Co2 ¼ N sp þ VCo ð4þ Combining (9), () and (), we can derive: V Ca ¼ V Co þ 2 V Ca2 ¼ V Co 2 D r ¼ V Co þ D V Co Thus, he average curren of L can be derived: I L avg ¼ þ V Ca2 D þ D r DT s L 2 ¼ þ V Co V Co D DT s 2L V Co ð5þ ð6þ ð7þ ð8þ If he power loss is negleced, he inpu average curren is: I L avg ¼ I o ð9þ Combining (4), (8) and (9), we can derive: 2 N sp þ Io L þ D 2 T s ¼ N sp þ Vg ð2þ 2 N sp þ Io L D 2 T s 3.5 Comparison of high sep-up converers Table gives he comparison of he proposed converer wih sae-of-ar high sep-up converers adoping coupled inducor [3 35]. Fig. 2 gives he curves of he volage gains in Table, where N sp is seleced as 4. As seen, he proposed configuraion in Fig. 6b has larger volage gain han he oher high sep-up converers wih he same duy cycle and reaches a considerable value alhough he duy cycle has no been close o.5. As shown in Fig. 6b, since he coupled inducor replaces L in Fig. 5 raher han L 2 on he inpu side, he inpu curren is coninuous, which is beneficial for he lifeime of PV and fuel cell. As a consequence, he volage sress of in he proposed converer is a lile larger. 4 Experimen verificaion To verify he effeciveness of he proposed configuraions in Figs. 5 and 6b, wo prooypes are fabricaed in he lab for conras wih he following specificaions: Volage gain [34] This work D Fig. 2 Comparison of volage gain [35] [33] [32] [3] Table Comparison of high sep-up converers Parameer This work [3] [32] [33] [34] [35] Volage gain þn sp 2D þn sp D þn spþn spd D 2þN spþn spd D þ2n sp N spd D MOSFET 2 2 Diode Volage sress of MOSFET þn sp þn sp þn spþn spd 2þN spþn spd þ2n sp N spd Inpu curren Coninuous Disconinuous Disconinuous Disconinuous Disconinuous Coninuous Inpu curren ripple Small Large Large Large Large Small Magneic componen 2 2 Capacior þn sp ð DÞ 2 þn sp 23

8 Gang WU e al. ) Inpu volage : V dc ; 2) Oupu volage : 38 V dc ; 3) Swiching frequency f s : khz; 4) Maximal oupu power P o : 3 W. 4. Parameer design As he design progress of he converers in Figs. 5 and 6b are similar, he opology as shown in Fig. 6b is aken as an example o design he parameer. Prior o he design procedure of capaciors and inducors, an assumpion is made o simplify he analysis. Since he leakage inducor is relaively small compared wih he magneizing inducor, is influence can be ignored. ) Design of coupled inducor L cp As shown in Table, he volage sress of he swich decreases wih he increase of N sp. However, higher N sp would increase he curren sress of he swich. Thus, a rade-off design should be considered beween he volage sress and curren sress of he swich. Here, we prefer he volage sress lower han V, and he resulan N sp is 4. Referring o Fig. 7, according o Kirchhoff s circui laws, we have: i L ¼ i D i Ca2 ¼ i Ca þ i Lm þ i Tr p i Ca2 ¼ i Ca þ i Lm þ N sp i Tr s i Ca2 ð2þ ¼ i Ca þ i Lm þ N sp i Co3 i Ca2 Based on he charge balance principle, he average currens of capaciors, I Ca_avg, I Ca2_avg, and I Co3_avg are zero. Thus, he average curren of L equals he average curren of, and we have: I L avg ¼ I Lm avg ¼ P o = ð22þ Seing he maximum curren ripple of is 3% of he maximum average curren, hen we have: Di Lm ¼ V CaDT s ¼ ð DÞDT s 3%I Lm ð 2DÞ avg ð23þ Subsiuing (22) ino (23), yields: V2 g DÞDT s 3% ð 2DÞP o ð24þ When = 25 V, he righ par of (24) reaches he maximum value. Then we have = 5 lh. 2) Design of inducor L Likewise, he maximum curren ripple of L can be expressed as: Di L ¼ V g þ V Ca2 DTs L ¼ ð DÞDT s 3%I L avg ð 2DÞL ð25þ Subsiuing (22) ino (25), yields: L V2 g ð DÞDT s ð26þ 3% ð 2DÞP o When = 25 V, he righ par of (26) reaches he maximum value. Then we have = 5 lh. 3) Design of auxiliary capacior C a and C a2 The capacior C a and C a2 can be derived according o he volage ripple DV Ca and DV Ca2 : R DTs i Ca d C a ¼ ð27þ DV Ca R DTs i Ca2 d C a2 ¼ ð28þ DV Ca2 Referring o Fig. 9a, during he urn on inerval, we have: i Ca ¼ i Lm þ N sp i Tr s ¼ i Lm þ N sp ð29þ i Ca2 ¼ i L ð3þ Since he average currens of C o2 and are zero, he average curren hrough equals o I o. Then we have: Z DTs d ¼ I o T s ð3þ Subsiuing (29), (3) and (3) ino (27) and (28), yields: C a ¼ I Lm C a2 ¼ I L avgdt s DV Ca avgdt s DV Ca2 þ N spi o T s DV Ca ¼ P odt s DV Ca2 ¼ P odt s DV Ca þ N spi o T s DV Ca ð32þ ð33þ Seing he volage ripple is lower han 5% of he maximum average volage, we have C a = 24 lf, C a2 = 32 lf. 4) Design of oupu capacior C o, C o2 and Likewise, he oupu capaciors can be derived as: R DTs i Co d C o ¼ ð34þ C o2 ¼ DV Co R DTs i Co2 d DV Co2 ð35þ R DTs i Co3 d ¼ ð36þ DV Co3 Referring o Fig. 9a, during he urn on inerval, we have: i Co ¼ i Co2 ¼ I o ð37þ 23

9 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor i Co3 ¼ ð38þ Subsiuing (3), (37) and (38) ino (34), (35) and (36), yields: C o ¼ I odt s ð39þ DV Co C o2 ¼ I odt s ð4þ DV Co2 ¼ I ot s ð4þ DV Co3 Since C o, C o2 is placed on he oupu side, he volage ripples of C o and C o2 are limied o a smaller scale. If he volage ripples of C o and C o2 are limied o % of he respecive maximum average volage, and he volage ripple of is limied o 5% of he maximum average volage, we have C o = 4 lf, C o2 = 3 lf, = 3 lf. 5) Swich The volage sress of he swich is /(N sp? ). When is urned on, he curren of he swich i can be expressed as: i ¼ i L þ i Lm þ N sp ¼ 2ð DÞ þ 2P o ð DÞDT s þ 2N spi o ð 2DÞL ð 2DÞL DDT s ð42þ When = 25 V, he RMS curren of reaches is maximum value 9.8 A. 6) Diode D,D o,d o2 and The volage sresses of D and D o are /(N sp? ), and he volage sresses of D o2 and are N sp /(N sp? ). The currens hrough D o2 and can be expressed as: 8 >< 2½; DT s Š i Do2 ¼ 2I o ð DT s Þ ð43þ >: 2½DT s ; T s Š ð DÞð DÞT s ( 2I o 2½; DT ¼ s Š DDT s ð44þ 2½DT s ; T s Š According o Fig. 9c, we have: v Ca þ v Ca2 ¼ v Co dv Ca d 8 >< >: þ dv Ca2 d C a dv Ca d C a2 dv Ca2 d ¼ dv Co d þ C o dv Co d þ C o dv Co d þ I o ¼ i L þ N sp i Do2 þ I o ¼ i Lm ð45þ ð46þ ð47þ where v Ca, v Ca2 and v Co are he insananeous volages of C a, C a2 and C o, respecively. Combining (46) and (47), he currens hrough D and D o can be expressed as: Þ i Lm N sp i Do2 dv Ca2 ð i D ¼ i L þ C a2 ¼ C ac a2 þ C a2 C o d C a C a2 þ C a C o þ C a2 C o þðc a C a2 þ C a C o Þi L C a C a2 I o C a C a2 þ C a C o þ C a2 C o ð48þ dv Co i Do ¼ I o þ C o ¼ d C a C a2 I o þ C a C o i Lm N sp i Do2 þ Ca2 C o i Lb C a C a2 þ C a C o þ C a2 C o ð49þ According o (43), (44), (48) and (49), he curren sresses of D,D o,d o2 and can be calculaed. 4.2 Experimen resuls The main componens used in he prooypes are lised in he following. High sep-up converer adoping auxiliary capacior: ) : IPW65R45C7; 2) D : IDW2G65C5, D o : C3D6A; 3) L : 263 lh, L 2 : 263 lh; 4) C a : 5.6 lf, C a2 : 6.8 lf, C f : 22 lf. High sep-up converer adoping auxiliary capacior and coupled inducor: ) : IPPN2N3G; 2) D : STPS22C, D o : STPS2C; 3) D o2 : C3D6A, : C3D6A; 4) L :5lH, :5lH, N sp :4; 5) C a :24lF, C a2 :32lF, C f : 22 lf; 6) C o :4lF, C o2 :3lF, :3lF. where C f is used o realize he power decoupling if high sep-up converer is cascaded wih an inverer. And i is parallel wih C o and C o2 in he high sep-up converer adoping auxiliary capacior and coupled inducor. The experimenal waveforms of high sep-up converer based on quasi-z-source nework under differen inpu volages a full load are shown in Figs. 3 and 4, where v ds is he drain-source volage of he swich. As seen in Fig. 4, D and D o conducs simulaneously. I can be explained as follows. Due o he forward recovery phenomenon of D, he volage sum of C a, C a2 and he volage drop of D is larger han he oupu filer capacior when he swich is urned off. The volage difference will drop on ESR of he oupu filer capacior and cause a large curren hrough D o. As shown in Fig. 4, a he insan of urning off he swich, v ds is slighly large, and here is a large 23

10 Gang WU e al. vgs ( V/div) vds (25 V/div) v ds v gs vds (2 V/div) v ds il2 ( A/div) id ( A/div) i L2 i D ido (5 A/div) id ( A/div) i Do i D vgs ( V/div) vds (25 V/div) il2 ( A/div) id ( A/div) vgs ( V/div) vds (25 V/div) il2 ( A/div) id ( A/div) v ds v ds v gs i L2 i D v gs i D i L2 Time (2 s/div) (a) =25 V Time (2 s/div) (b) =36 V Time (2 s/div) (c) =45 V Fig. 3 Experimen waveforms of high sep-up converer adoping auxiliary capacior curren hrough D o. Thus, he curren supplied by L o replenish energy for C a2 is small, and i D is small. Wih he volage drop of D reducing gradually, he difference beween v ds and he volage of C f decreases, resuling ha i Do decreases and i D increases. As C a and C a2 are much smaller han C f, he volage ripples of C a and C a2 are larger. Thus, wih he volages of he auxiliary capaciors Time (2 s/div) Fig. 4 Experimen waveforms of high sep-up converer adoping auxiliary capacior ( = 45 V, P o = 3 W) increasing, he difference beween v ds and he volage of C f increases, leading o i Do increasing and i D decreasing. The experimenal waveforms of high sep-up converer adoping auxiliary capacior and coupled inducor under differen inpu volages a full load are shown in Figs. 5 and 6 where i cp_p is he curren of he primary winding, is he curren of, v D and v Do are he volages of D and D o. According o he heoreical analysis, should rise up from zero when he swich is urned on. However, in he real case, here exis reverse recovery problem for D o2 a he insan of urning on he swich. During he ime inerval of he reverse recovery, he volage of he secondary winding is clamped by C o2 and. The volage is refleced o he primary side by elecromagneic inducion and in series wih C a o charge he leakage inducor which leads o he curren of he leakage inducor rising up rapidly. Afer he reverse recovery of D o2 is over, he curren of he leakage inducor is larger han ha of he magneizing inducor. Thus, rises up from a posiive value. The volage sresses of he swich, D and D o shown in Fig. 6 are much smaller han he oupu volage which will reduce he power loss and improve he efficiency. The dynamic response of high sep-up converer adoping auxiliary capacior and coupled inducor is shown in Fig. 7. The oupu volage is regulaed in closed loop wih single volage compensaor. The experimenal resul shows ha he dynamic performance of he proposed converer is good. The sarup waveform ( = 36 V, P o = 3 W) is shown in Fig. 8, where v o is he oupu volage, and i L is he curren of L. As seen, he overshoo of he oupu volage is less han 3 V, which is 7.9% of he seady-sae value. The comparison experimens of he basic boos converer and he cascaded boos converer are also performed. To avoid he insabiliy issue in he cascaded boos converer, he firs sage is under open loop conrol wih 23

11 vds icp_p ido3 vds, vd, vdo (5 V/div) vds il icp_p (2 A/div) ido3 (5 A/div) vds (5 V/div) il (5 A/div) Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor vd vdo Time (4 s/div) (a) Vg=25 V vds icp_p ido3 vds, vd, vdo (5 V/div) vds il icp_p (2 A/div) ido3 (5 A/div) vds (5 V/div) il (5 A/div) Time (2 s/div) (a) Vg=25 V vd vdo Time (2 s/div) (b) Vg=36 V vds il vds icp_p ido3 vds, vd, vdo (5 V/div) icp_p (2 A/div) ido3 (5 A/div) vds (5 V/div) il (5 A/div) Time (4 s/div) (b) Vg=36 V vd vdo Time (2 s/div) (c) Vg=45 V Fig. 5 Experimen waveforms of high sep-up converer adoping auxiliary capacior and coupled inducor Time (4 s/div) (c) Vg=45 V Fig. 6 Volage sresses of he swich D and Do consan volage gain of 4. The second sage of he cascaded boos converer regulae he oupu volage. The efficiency curves of high sep-up converer adoping auxiliary capacior, high sep-up converer adoping auxiliary capacior and coupled inducor, he basic boos converer, and he cascaded boos converer are shown in Fig. 9. As he conducing period of Do in he basic boos converer is exremely shor, he curren sress is large and he reverse recovery problem is severe which leads o a large swiching loss of he swich. Thus, he efficiency of he basic boos converer is lower han ha of high sep-up converer adoping auxiliary capacior a heavy load as shown in Fig. 9. When he coupled inducor is adoped, he efficiency is furher improved. Due o he volage sresses of he swich, D and Do decreasing, he swiching loss can 23

12 Gang WU e al. vo_ac (4 V/div) io (.2 A/div) (%) 95 Esimaed Measured P o (W) Fig. 2 Esimaed efficiency and measured efficiency ( = 45 V) Time ( 2 ms/div) Fig. 7 Dynamic response of high sep-up converer adoping auxiliary capacior and coupled inducor when he load sep varies beween he full load and he half load 4 DCM CCM 3 r D vo ( V/div) Power loss raio (%) 2 r fe r _sw r _con r cu il (2 A/div) P o (W) Fig. 2 Power loss raio ( = 45 V) Time ( s/div) Fig. 8 Sarup waveform (%) P o (W) Converer in Fig. 6(b); Cascaded boos Converer in Fig. 5; Boos Fig. 9 Efficiency comparison when = 45 V be reduced effecively and he efficiency is superior o ha of he cascaded boos converer over a wide load range. According o he calculaion of he power loss in Appendix A, he esimaed efficiency is shown as Fig. 2, which maches he measured efficiency. And he power loss raios are given in Fig. 2, where r _sw = (P _on? P _off )/P in, r _con = P _con /P in, r fe = (P L_fe? P Lcp_fe )/P in, r cu = (P L_cu? P Lcp_cu )/P in, r D = (P D? P Do? P Do2? P Do3 )/P in. As seen, r _sw and r fe decrease wih he increase of he oupu power, while r _con and r cu increase wih he increase of he oupu power. Thus, he efficiency increases a ligh load and decreases a heavy load. And he presen of he maximum efficiency depends on he parasiic parameer of he componens. The experimen resuls indicae ha he proposed converers can achieve a higher efficiency and good dynamic performance as well. 5 Conclusion A novel high sep-up DC DC converer adoping auxiliary capacior and coupled inducor is proposed in his paper. The inpu curren is coninuous, and he volage sress of he power swich is low, which reduces he swiching loss. Thus, he efficiency of he converer is improved. The operaing mode of he proposed opology is analyzed and an experimen is conduced. The resuls 23

13 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor indicae ha he converers proposed in his paper can operae seadily and he performance is good. Acknowledgemens This work was suppored by Lie-On Technology Corporaion. 8 P D ¼ V f D I D avg >< P Do ¼ V f Do I Do avg P Do2 ¼ V f Do2 I Do2 avg >: P Do3 ¼ V f Do3 I Do3 avg ða4þ Open Access This aricle is disribued under he erms of he Creaive Commons Aribuion 4. Inernaional License (hp:// creaivecommons.org/licenses/by/4./), which permis unresriced use, disribuion, and reproducion in any medium, provided you give appropriae credi o he original auhor(s) and he source, provide a link o he Creaive Commons license, and indicae if changes were made. Appendix A The main power losses include he power loss of he swich, he diodes, he inducor and he coupled inducor. According o he parameer design in Secion 4, he curren sresses of he swich, he diodes, he inducor and he coupled inducor are given, and hen he power loss of each componen can be calculaed as follows. ) Power loss of he swich The power loss of he swich mainly includes he swiching loss and he conducion loss. The swiching loss can be derived as: P on ¼ f sr g V ds i on C iss ðv miller V h Þ 2 ae :5ðV miller þ V h Þ þ C rss V ds ae V miller P off ¼ f sr g V ds i off 2 ðaþ 2C iss ðv miller V h Þ V ds þ C rss V miller þ V h V miller ða2þ where f s is he swiching frequency; R g is he driving resisor; V ds is he volage sress of he swich; i _on is he curren hrough he swich when is urned on; ae is he driving volage; C iss, C rss, V miller, V h are he parasiic parameers of he swich, referring o he daashee of he swich. The conducion loss can be derived as: P con ¼ I 2 rms R dson ða3þ where I _rms is RMS curren hrough he swich; R dson is he on-sae resisor of he swich. 2) Power loss of he diodes D,D o,d o2, The volage drop of he diode can be viewed as a consan value. Then he power loss of D,D o,d o2, can be derived as: where V f_d, V f_do, V f_do2, V f_do3 are he volage drops of D,D o,d o2,, which are lised in he daashee; I D_avg, I Do_avg, I Do2_avg, I Do3_avg are he average currens hrough D,D o,d o2,, respecively. 3) Power loss of he inducor L, and coupled inducor L cp The power losses of L and L cp include he copper loss and he core loss. The copper loss of L, L cp can be derived as: 8 P L cu ¼ IL 2 dc R L dc þ IL 2 ac R L ac >< P Lcp cu ¼ ILcp 2 p dc R Lcp p dc þ ILcp 2 s dc R Lcp s dc >: þ ILcp 2 p ac R Lcp p ac þ ILcp 2 s ac R Lcp s ac ða5þ where I L_dc and I L_ac are he dc curren and ac RMS curren of L, respecively; I Lcp_p_dc and I Lcp_p_ac are he dc curren and ac RMS curren of he primary winding, respecively; I Lcp_s_dc and I Lcp_s_ac are he dc curren and ac RMS curren of he secondary winding, respecively; R L_dc, R L_ac, R Lcp_p_dc, R Lcp_s_dc, R Lcp_p_ac and R Lcp_s_ac can be measured by he impedance analyzer. The core loss of L, L cp can be derived as: ( P L fe ¼ kfs m DBn L V e P Lcp fe ¼ kfs m DBn Lcp V ða6þ e 8 DB L ¼ V g þ V Ca2 DTs >< N L A e >: DB Lcp ¼ V CaDT s N Lcp p A e ða7þ where V e is he core volume; A e is he effecive area of he core; k, m, n can refer o he daashee of he core; N L is he urns of L ; N Lcp_p is he urns of he primary winding. References [] Tseng K, Huang C, Shih W (23) A high sep-up converer wih a volage muliplier module for a phoovolaic sysem. IEEE Trans Power Elecron 28(6): [2] Leyva-Ramos J, Lopez-Cruz J, Oriz-Lopez M e al (23) Swiching regulaor using a high sep-up volage converer for fuel-cell modules. IET Power Elecron 6(8): [3] Velasco-uesada G, Guinjoan-Gisper F, Piqué-López R e al (29) Elecrical PV array reconfiguraion sraegy for energy exracion improvemen in grid-conneced PV sysems. IEEE Trans Ind Elecron 56():

14 Gang WU e al. [4] Tseng K, Huang C (24) High sep-up high-efficiency inerleaved converer wih volage muliplier module for renewable energy sysem. IEEE Trans Ind Elecron 6(3):3 39 [5] Young C, Chen M, Chang T e al (23) Cascade Cockcrof- Walon volage muliplier applied o ransformerless high sepup DC DC converer. IEEE Trans Ind Elecron 6(2): [6] Chen S, Liang T, Yang L e al (23) A boos converer wih capacior muliplier and coupled inducor for ac module applicaions. IEEE Trans Ind Elecron 6(4):53 5 [7] Ellis M, von Spakovsky M, Nelson D (2) Fuel cell sysems: efficien, flexible energy conversion for he 2s cenury. Proc IEEE 89(2):88 88 [8] Li W, He X (2) Review of nonisolaed high-sep-up DC/DC converers in phoovolaic grid-conneced applicaions. IEEE Trans Ind Elecron 58(4): [9] Tofoli F, Pereira D, Paula W e al (25) Survey on non-isolaed high-volage sep-up DC DC opologies based on he boos converer. IET Power Elecron 8(): [] Huber L, Jovanovic MM (2) Design approach for server power supplies for neworking applicaions. In: Proceedings of IEEE applied power elecronics conference and exposiion, New Orleans, USA, 6 February 2. pp [] Mosaan A, Zeinali H, Asghari S e al (24) Novel high sep up DC/DC converers wih reduced swich volage sress. In: Proceedings of Power elecronics, drive sysems and echnologies conference, Tehran, Iran, 5 6 February 24. pp [2] Evran F, Aydemir M (24) Isolaed high sep-up DC DC converer wih low volage sress. IEEE Trans Power Elecron 29(7): [3] Zhu M, Yu K, Luo F (2) Swiched inducor Z-source inverer. IEEE Trans Power Elecron 25(8): [4] Nguyen M, Lim Y, Cho G (2) Swiched-inducor quasi-zsource inverer. IEEE Trans Power Elecron 26(): [5] Li D, Loh P, Zhu M e al (23) Enhanced-boos Z-source inverers wih alernae-cascaded swiched- and apped-inducor cells. IEEE Trans Ind Elecron 6(9): [6] Li D, Loh P, Zhu M e al (23) Generalized mulicell swichedinducor and swiched-capacior Z-source inverers. IEEE Trans Power Elecron 28(2): [7] Siwakoi Y, Peng F, Blaabjerg F e al (25) Impedance-source neworks for elecric power conversion par I: a opological review. IEEE Trans Power Elecron 3(2): [8] Vinnikov D, Roaso I (2) uasi-z-source-based isolaed DC DC converers for disribued power generaion. IEEE Trans Ind Elecron 58():92 2 [9] Siwakoi Y, Blaabjerg F, Loh P e al (24) High-volage boos quasi-z-source isolaed DC DC converer. IET Power Elecronics 7(9): [2] Husev O, Liivik L, Blaabjerg F e al (25) Galvanically isolaed quasi-z-source DC DC converer wih a novel ZVS and ZCS echnique. IEEE Trans Ind Elecron 62(2): [2] Yang L, iu D, Zhang B e al (24) A modified Z-source DC DC cnverer. In: Proceedings of European conference on power elecronics and applicaions, Lappeenrana, Finland, Augus 24. pp 9 [22] Zhao, Lee F (23) High-efficiency, high sep-up DC DC converers. IEEE Trans Power Elecron 8():65 73 [23] Tseng K, Huang C, Cheng C (26) A single-swich converer wih high sep-up gain and low diode volage sress suiable for green power-source conversion. IEEE Journal of Emerging & Seleced Topics in Power Elecronics 4(2): [24] Lin T, Chen J, Hsieh Y (23) A novel high sep-up DC DC converer wih coupled-inducor. In: Proceedings of Inernaional fuure energy elecronics conference, Tainan, Taiwan, China, 3 6 November 23, 92(): [25] Wai R, Lin C, Chu C (24) High sep-up DC DC converer for fuel cell generaion sysem. In: Conference of IEEE indusrial elecronics sociey, Busan, Korea, 2 6 November 24 [26] Wai R, Lin C (25) High-efficiency, high-sep-up DC DC converer for fuel-cell generaion sysem. Proc IEE Proc Elecr Power Appl 52(5): [27] Wu T, Lai Y, Hung J e al (28) Boos converer wih coupled inducors and buck boos ype of acive clamp. IEEE Trans Ind Elecron 55():54 62 [28] Wu T, Lai Y, Hung J e al (25) An improved boos converer wih coupled inducors and buck boos ype of acive clamp. In: Proceedings of Indusry applicaions conference, Hong Kong, China, 2 6 Ocober 25 [29] Evran F, Aydemir M (23) Z-source-based isolaed high sepup converer. IET Power Elecron 6():7 24 [3] Evran F, Aydemir M (22) A coupled-inducor Z-source based DC DC converer wih high sep-up raio suiable for phoovolaic applicaions. In: Proceedings of IEEE inernaional symposium on power elecronics for disribued generaion sysems, Aalborg, Denmark, June 22. pp [3] Seong H, Kim H, Park K e al (2) Zero-volage swiching flyback-boos converer wih volage-doubler recifier for high sep-up applicaions. In: Proceedings of IEEE energy conversion congress and exposiion, Alana, USA, 2 6 Sepember 2. pp [32] Hsieh Y, Chen J, Liang T e al (23) Novel high sep-up DC DC converer for disribued generaion sysem. IEEE Trans Ind Elecron 6(4): [33] Ajami A, Ardi H, Farakhor A e al (25) A novel high sep-up dc/dc converer based on inegraing coupled inducor and swiched-capacior echniques for renewable energy applicaions. IEEE Trans Power Elecron 3(8): [34] Sahyan S, Suryawanshi H, Ballal M e al (25) Sof swiching DC DC converer for disribued energy sources wih high sep up volage capabiliy. IEEE Trans Ind Elecron 62(): [35] Liu V, Zhang L (24) Design of high efficiency Boos-Forward-Flyback converers wih high volage gain. In: Proceedings of IEEE inernaional conference on conrol and auomaion, Taichung, Taiwan, China, 8 2 June 24. pp 6 66 Gang WU (S 6) received he B.S. degrees in elecrical engineering and auomaion from Nanjing Universiy of Aeronauics and Asronauics (NUAA), Nanjing, China, in 2, where he is currenly working oward he Ph.D. degree in elecrical engineering. His curren research ineress include high sep-up DC DC converer and renewable energy generaion sysems. Xinbo RUAN (M 97-SM 2-F 6) received he B.S. and Ph.D. degrees in elecrical engineering from Nanjing Universiy of Aeronauics and Asronauics (NUAA), Nanjing, China, in 99 and 996, respecively. In 996, he joined he College of Auomaion Engineering, NUAA, where he became a Professor in 22. Since 28 o 2, he was also wih he College of Elecrical and Elecronic Engineering, Huazhong Universiy of Science and Technology, China. He is he auhor or co-auhor of seven books and more han 2 echnical papers published in journals and conferences. His main research ineress include sof-swiching power elecronics converers, power elecronics sysem inegraion and renewable energy generaion sysem. From 25 o 23, he served as Vice Presiden of he China Power Supply Sociey. Currenly, he serves as an Associae Edior for he IEEE Transacions on Indusrial Elecronics, he IEEE Journal of Emerging and Seleced Topics on Power Elecronics, he IEEE Transacions on Power Elecronics and he IEEE Transacions on Circuis and Sysems-II. 23

15 Non-isolaed high sep-up DC DC converer adoping auxiliary capacior and coupled inducor Zhihong YE (M ) received B.S. and M.S. degrees in elecrical engineering from Tsinghua Universiy, Beijing, China, in 992 and 994, respecively. He received Ph.D. degree from he Bradley deparmen of elecrical and compuing engineering, Virginia Polyechnic Insiue and Sae Universiy, in 2. From 2 o 25, he worked for General Elecric Global Research Cener as an elecrical engineer in Niskayuna, New York. From 25 o 26, he worked for Dell as a commodiy qualiy manager. Since 26, he has been working for LieOn Technology Corp., as he Direcor of Research and Developmen. His research ineress include high densiy, high efficiency power supply for compuing, communicaion and consumer elecronics applicaions, digial conrol, power converer opologies and conrols, sof-swiching echniques, ec. He holds 7 US paens, and has published more han 3 echnical papers in Transacions and inernaional conferences. 23