DECENTRALIZED MULTI STRING PV SYSTEM WITH INTEGRATED ZVT CELL RAFAEL C. BELTRAME, MATHEUS I. DESCONZI, HÉLIO L. HEY

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1 DECETRALIZED MULTI STRIG PV SYSTEM WITH ITEGRATED ZVT CELL RAFAEL C. BELTRAME, MATHEUS I. DESCOZI, HÉLIO L. HEY Power Elecronics and Conrol Research Group, Federal Universiy of Sana Maria , Sana Maria, RS, BRAZIL s: MÁRIO L. DA SILVA MARTIS, HELDER T. CAMARA Power Analysis and Processing Research Group, Federal Universiy of Technology Parana , Pao Branco, PR, BRAZIL s: Absrac This paper explois he advanages and limiaions of using a cascaded connecion of DC-DC sep-up sages for a series sring of PV panels, in a single-phase residenial/commercial grid conneced insallaion. I is demonsraed ha when mulisring PV sysems are adoped in order o minimize shadowing problems, i is required o employ some approach o reduce he swiching losses (urn-on losses of MOSFETs and diode reverse recovery losses) of he DC-DC sep-up sages. As a muli-sring PV sysem is normally comprised by several DC-DC sep-up sages, inegraed sof-swiching opologies are aracive due o heir compacness, reliabiliy and low cos. Thus, his work proposes he use of an inegraed ZVT cell, which assiss all he DC- DC sep-up sages and employs a very compac circui, enabling o minimize he swiching losses, improving he sysem efficiency. The proposed cell makes use of a magneically-coupled auxiliary volage source implemened by adding a secondary winding on he inpu inducors. In order o validae he proposed opology, experimenal resuls are presened. Keywords Muli-sring PV sysem, DC-DC sep up converer, zero-volage-ransiion. Inroducion Recen advances in power elecronics and semiconducor echnology associaed wih favorable incenives, such as low-ineres loans and ax incenives, has led o growh of he PV marke mosly due o he proliferaion of grid conneced PV sysems, Cory (008). PV sysems conneced o he uiliy do no require back-up sysem and charge regulaor, i.e., hey are commonly simpler, cheaper and more reliable when compared o a sand alone one. oneheless, he wide uilizaion of PV is sill limied by he iniial insallaion cos. Likewise oher inermien renewable sources, o opimize he PV array area and make he implanaion of grid conneced PV sysems economically viable, i is essenial o drain he maximum power produced by he PV array. I can be done by means of a maximum power poin rack algorihm, Femia (005) and Yu (00), commonly applied o he fron-end DC-DC sage. Indeed, PV modules canno produce idenical energy levels in a PV array for several reasons, including dissimilariies of panel producion, differen emperaures and irradiaions due o panel orienaion, aging and, in some cases, shading, Carannane (009). As he PV panels in a series sring are consrained o all conduc he same curren, he leas efficien panel ses he sring curren. In long sring arrays, his siuaion resuls in he los of he maximum power poin of he array, which reduces he overall efficiency of he array and, in exreme cases, i can also cause he degeneraion of he panels due o he ho spo phenomenon. To overwhelm hese problems, and also ensure he maximum producion of elecriciy even when shading or oher dissimilariies are presen, decenralized PV sysems have been proposed in he lieraure. Some works presened demonsrae ha a gain of up o 6% of generaed energy could be achieved on decenralized PV sysems, Imhoff (008). In general, decenralized PV sysems spli he maximum power poin racker (MPPT) sage, which can be dedicaed exclusively o a single or a group of PV panels. They can be grouped in hree caegories, namely module inegraed sysems, Meinhard (999), and sring and muli-sring sysems, Meinhard (00). The curren, volage and power raings of DC-DC sep-up MPPT semiconducors, as well as heir volage gains are quie differen for each decenralized sysem. Depending on he semiconducor echnology and he required volage gain, he conducion and swiching losses can be paricularly disinc from one decenralized sysem DC-DC sep-up sage o anoher. As a muli-sring PV sysem can be comprised by several DC-DC sep-up sages, o reduce he urnon losses of MOSFETs and diode reverse recovery losses of all DC-DC sage is a quie complex ask since he auxiliary circuiry may increase significanly he converer size, weigh and cos. Addiionally, a large semiconducor coun could reduce he reliabiliy of he PV sysem. This paper explois he advanages and limiaions of using a cascaded connecion of DC-DC sep-up sages for a series sring of PV panels, in a singlephase residenial/commercial grid conneced insallaion wih an inegraed sof-swiching opology, Schuch (009). The proposed Zero-Volage Transiion ACC which assiss all he DC-DC sep-up sages and employs a very compac circui, enabling o

2 minimize boh he urn-on losses of MOSFETs and diode reverse recovery losses. In order o validae he proposed opology heoreical analysis and experimenal resuls are presened. Loss Analysis of Muli-sring Grid-Conneced PV Sysem Table. Parameers for he Hypoheical Sandard Module. Parameer Value V OC (I SC ).9 V (8.0 A) Peak power volage (curren) 7.6 V (7.39 A) Peak power (o. of panels of he array) 30 W (3) Table. Parameers for he inpu DC-DC sep-up sages. Parameer Swiching frequency, f s Inpu filer inducor, L ( of urns) Value 00 khz 85 μh ( urns) Ferrie core EE 65/6 Maximum flux densiy, B Max Copper wire Oupu capacior, C Main swich (MOSFET) Main diode 0. T 3 x 63 x 37 AWG (Liz) 470 μf IRFP460 8ETH06 Muli-sring PV sysem combines he advanage of higher energy yield of a sring PV sysem wih he lower coss of a cenral inverer PV sysem, as shown in Figure, allowing he use of individual MPPT algorihm for each one, Myrzik (003), reducing he possibiliy of shadowing mismaches ha may occur in a single long sring PV module configuraion. From he efficiency perspecive, he series connecion of he DC-DC sages reduces heir volage gain and, consequenly, relaed conducion losses. In addiion, he DC-DC sage oupus conneced in series may provide a DC bus volage ha maches direcly wih hose used o feed sandard inverer sages. Figure shows he efficiency comparison of muli-sring PV sysems wih one, wo, hree and four inpu DC-DC sep-up sages. I can be seen he efficiency is proporional o he number of inpu sages. I occurs because he larger he number of sages is, he lower he inpu DC-DC converer gain is for he same DC bus volage (defined as 50 V), reducing he RMS curren hrough he ransisor and he relaed conducion losses. Addiionally, he swiching losses (urn-on losses of MOSFET and diode reverse recovery losses) are minimized because he volage applied on semiconducor devices is reduced. For he heoreical curve, he efficiency was esimaed by using he loss models presened in Appendix A. To simplify he analysis, he sysems make use of he Hypoheical Sandard Module (HSM) specified in Table. The sep-up sage parameers and componens are defined in Table. I is also considered ha he sep-up sage is operaing in he maximum power poin (MPP) of he PV arrays. A MOSFET is employed in sep-up converer because i allows he increase of he converer swiching frequency, and associaed volume, weigh and, mainly, cos reducion of he enire sysem. The MOSFET uilized were he -Channel Sandard Power MOSFET IRFP460 (500V/0A). The diode uilized was he Ulrafas Swiching Mode Power Recifier 8ETH06 (600V/8A). Also in Figure experimenal daa from a laboraory prooype is depiced, i can be seen by he ploed curves ha he esimaed losses presens a good agreemen wih he daa measured from he laboraory prooype. The disribuion of he losses in he DC-DC sep-up semiconducors for a muli-sring PV sysem composed by wo sages (93.6%, vide Figure ) is shown in Figure 3. I can be concluded ha in he MOSFET based PV sysem, he ransisor urn-on and urn-off losses represens abou 3% of he semiconducor losses, and he diode swiching losses represens 35%, confirming he imporance in reducing swiching losses. 3 Proposed Muli-Sring Grid-Conneced PV Sysem wih Inegraed ZVT Cell As he swiching frequency of he sep-up sages increases, he large reverse-recovery currens of he diodes affec he sysem efficiency and also produce elecromagneic inerference (EMI) noise. To overcome Efficiency (%) Experimenal Esimaed umber of Inpu Sages Figure. Decenralized muli-sring PV sysem wih a cascaded connecion of DC-DC sep-up sages. Figure. Efficiency comparison of hard swiched muli-sring PV sysem.

3 6% 7% Trans. Cond. Trans. T-on Trans. T-off Diode Swi. Diode Cond. 35% 7% 4% Figure 3. Semiconducor power loss balance in he PV sysem. hose problems, various passive, Tseng (007), Li (009), and acive approaches have been proposed for he DC-DC sep-up converer, Jovanovic (005), Marins (005) and Wang (005). Among hese echniques, he zero-volage-ransiion (ZVT) echnique is especially suiable o overcome he aforemenioned drawbacks because i reduces he diode reverse recovery losses by conrolling he di/d slope of he curren during he urn-off of he diode. Furhermore, i effecively minimizes he swiching losses and also promoes he absorpion of he parasiic capaciances energy of semiconducor devices, Marins (004), minimizing he urn-on capaciive losses when majoriy carrier devices such as MOSFETs are employed. There are several ways o implemen he ZVT auxiliary commuaion circui (ACC), depending on how he auxiliary volage source of he ACC is synhesized. In converers ha presen a filer inducor, as he DC- DC sep-up converer, an auxiliary volage source implemened by a magneic coupling wih he inducor filer, as proposed by Lee (994), is advanageous because he volage source is implemened in he same magneic core as he filer inducor, and he auxiliary inducor can be implemened by means of he leakage inducance of hese inducors, Russi (008). This way, hese feaures resul in a very compac opology in ha here are no exra magneic componens. 3. The Inegraion Concep The inclusion of ACCs increases he number of addiional componens, and herefore he cos and he complexiy of he overall sysem. I is a criical problem for sysems wih several power conversion sages, such as decenralized PV muli-sring sysems, as can be seen in Figure. In hese sysems, i would be necessary o include an independen ACC for each power conversion sage, decreasing he usefulness of hese circuis. Aiming o reduce he number of addiional auxiliary devices, he inegraion concep of ACCs can be employed, which is suiable o sysems wih several power conversion sages. This concep is based on sharing an ACC among differen converers or sages, aiming o reduce he number of addiional auxiliary devices, Schuch (009). Therefore, i is proposed he use of he unpublished inegraed ZVT cell shown in Figure 4, which employs a very compac circui and can assis all he DC-DC sep-up sages. The proposed ACC makes use of a magneically-coupled auxiliary volage source implemened by adding a secondary winding on he inpu inducors. As he ACC is galvanic isolaed from he main power circui, i can be shared by all he DC- DC sep-up converers wih none shor-circui risk. The ZVT cell presened in Figure 4 makes possible o minimize diode reverse recovery losses of D o D n by conrolling he di/d slope of heir currens and o assis he urn-on of S o S n simply by using a phase difference of 360º n among heir command signals, where n is he number of DC-DC sep-up sages, or by synchronizing heir urn-on insans. 3. Inegraed ZVT Cell Operaion In order o explain he ACC operaion, for simpliciy i is considered only one DC-DC sep-up converer, as presened in Figure 5, where he coupledinducor was replaced by is canilever model, Maksimovic (000). Furhermore, he inpu inducor (L ) was approximaed by a consan curren source (I L ). This approximaion can be made if he magneizing inducance of he coupled-inducor (L m ) is much larger han he leakage inducance ( ) and he ripple of he curren hrough L in a swiching period is small. Mode ( 0 ) : previous o he ACC operaion, S is urned off and D is conducing I L, as presened in Figure 5 (a) and in Figure 6 for 0. During his mode, he volage on C s (v S ) and he curren hrough ( ) are V o and zero, respecively. Mode ( ) < : aiming o commuae I L 0 from D o S, he auxiliary swich is urned on a 0. The circui configuraion during his mode is represened in Figure 5 (b) and he main heoreical waveforms in Figure 6 for 0 <. The volage on C s is V o and he curren hough increases linearly wih a slope given by ( Vo Vi) Lx. I is imporan o noice ha he urns raio () mus be posiive in order o apply a posiive volage on. This mode ends a, when () reaches I L and D urns off wih a conrolled di/d slope. The ime duraion of his mode, defined as Δ = 0, can be calculaed by (). D xn D x PV sring V in L in L i C in V i S n a n a D n C i S C s C sn C on D C o V on V o V BUS Figure 4. Proposed muli-sring PV sysem wih inegraed ZVT.

4 Mode 3 ( ) Lx IL Δ = V V ( ) o i () < : his mode begins a, when D urns off, and boh C s and go o a resonan process. The circui configuraion during his mode is represened in Figure 5 (c) and he main heoreical waveforms in Figure 6 for <. The volage on C s goes zero during he resonan process. The curren peak hough can be calculaed by (). Where V V I Z o i L Lx( max) = + () i Z L x =. (3) Cs In order o achieve he zero-volage-swiching (ZVS) condiion o S, i is mandaory ha v S () reduces o zero vols. I can be demonsraed ha he resricion (4) mus be observed in order o saisfy he aforemenioned ZVS condiion. The resricion (4) implies ha he converer gain mus be always higher han wo. Vo V (4) i This mode ends a, when v S () reduces o zero and is clamped by he aniparallel diode of S. Thus, he ime duraion of his sage, defined as Δ =, can be calculaed by (5). V i arccos ω n V i V o Δ = (5) Where Mode 4 ( ) 3 ω n =. (6) LC x s < : afer v S () reaching zero a, he aniparallel diode of S sars conducing, as presened in Figure 5 (d). The volage on C s remains clamped a zero vols and he curren hough decreases linearly wih a slope given by Vi Lx. I is imporan o noice ha mus be posiive in order o apply a negaive volage over. The main heoreical waveforms are presened in Figure 6 for < 3. This mode ends a 3, when () reduces under I L and S sars assuming gradually I L. The ime duraion of his mode, defined as Δ =, can be calculaed by (7). 3 3 Where ( ( ) ) L i I Δ = (7) x Lx L 3 Vi ( ) V o i L ilx = V sin( ωn Δ ) + I. (8) Z Mode 5 ( ) 3 4 < : a 3, when S sars assuming gradually I L, he circui goes o he configuraion represened in Figure 5 (e). The circui operaion is similar o ha in he previous mode. The main heoreical waveforms are presened in Figure 6 for 3 < 4. This mode ends a 4, when () reduces o zero and D x urns off under a conrolled di/d slope. I is imporan o highligh ha afer he urn-off of D x, can be urned off under zero-curren-swiching (ZCS). Thus, an IGBT can be employed as auxiliary D x D x D x D x v L v L v L v L V i S v S D x L x v i L Lx I L / i S i D D D D a D a a a G S I L I L I L I L v V o V i V o L v V i C L v V o V i s vs S C L v s vs S C L s vs S G Sx (a) Mode ( ) v L ~ ~ ~ ~ ~ ~ ~ ~ ~ 0. (b) Mode ( ) D i L D x 0 V o V ( -V) I L a a a I L I L I L V i v V o V i L v V o V i S C L v V o V i s vs S C L v s vs S C L s vs S Figure 6. Theoreical waveforms Figure of he 5. proposed Single DC-DC opology. sep-up sage wih ZVT cell operaion modes. C s vs <. (c) Mode 3 ( < ). (d) Mode 4 ( ) o Ci Sx D D x D x v L v L D I L a <. 3 D (e) Mode 5 ( < ). (f) Mode 6 ( < ). (g) Mode 7 ( < ). (h) Mode 8 ( ) C s vs <. 6 7 V o V o

5 swich. The ime duraion of his mode, defined as Δ =, can be calculaed by (9) Mode 6 ( ) 4 5 L I x L Δ 4 = (9) Vi < : afer D x urning off a 4, S conducs I L. Thus, v S () and () are boh zero. During his mode, represened in Figure 5 (f), he PWM modulaion is implemened. This mode ends a 5, when S is urned off. The main heoreical waveforms are presened in Figure 6 for 4 < 5. < : his mode begins a 5, when Mode 7 ( ) 5 6 S is urned off and I L is ransferred o he snubber capacior C s. This way, C s is charged linearly wih a slope given by I L C s. The circui configuraion during his mode is represened in Figure 5 (g) and he main heoreical waveforms are presened in Figure 6 for 5 < 6. This sage ends a 6, when vs( ) = Vo and D sars conducing I L, clamping v S () a V o. Addiionally, he ime duraion of his mode, defined as Δ =, can be calculaed by (0) Mode 8 ( ) 6 7 C V s o Δ 5 = (0) I L < : his mode only exiss due o G S G Sx I is possible o find a se of and combinaions ha comply wih he specificaions of he conv S i S i D ~ ~ ~ ~ ~ ~ ~ ~ ~ I L / i L V o V ( -V) I L Figure 6. Theoreical waveforms of he proposed opology. o i he inrinsic capaciance of ( ). In he following analysis, i is assumed ha he linear charge of C s (snubber commuaion) was finished. Thus, he volage applied over L is V i V o a 6. This volage, refleced o he ACC side, urns D x on and enables and o sar a resonan process. The circui configuraion during his mode is represened in Figure 5 (h) and he main heoreical waveforms in Figure 6 for 6 < 7. This mode ends a 7, when () reduces o zero and is D x urned off. This way, he circui reurns o he configuraion of Figure 5 (a) (mode ). The volage over a 7 has he level expressed in (). ( ) ( ) v = V V () Sx 7 o i 4 Design Mehodology The design mehodology for he auxiliary ZVT circui is based on he selecion of and in order o saisfy he resricions ha guaranee he proper ACC operaion and also limi he volage and curren sresses in he DC-DC sep-up sage semiconducor devices. 4. Selecion of As menioned during he analysis of he operaion modes and 4, mus be posiive in order o guaranee he magneizing and demagneizing condiions o, as expressed in (). Furhermore, in order o comply wih he maximum volages of D x (v Dx(max) ) and ((max) ), which occur during mode, (3) and (4) mus be saisfied. = > () ( min) ( min) 0 Mag Des ( max) vsx( max) 4. Selecion of ( max) vdx( max) v = = Sx( max) ( V V ) v o i Dx( max) ( V V ) o i (3) (4) The minimum value of ha comply wih he maximum di/d slope during he urn off of D (di/d D ) can be calculaed from (), as expressed in (5). In he same way, he minimum value of ha comply wih he di/d slope of D x (di/d Dx ) can be calculaed by (6). Furhermore, he minimum value of ha limis (max) o he levels of auxiliary semiconducor devices (i ACC(max) ) can be calculaed by (7). On he oher hand, he maximum value of ha guaranees ha he magneizaion ime will no be larger han a fracion of he swiching ime ( (max) ), offseing he duy cycle of he converer, can be calculaed by (8). L L ( ) Vo Vi x( min) did D didd = (5) V i Lx( min) = (6) did Dx diddx Vo V i x( min) = C ilx( max) s (7) iacc ( max) IL L xmax ( ) Δ( max) 4.3 Design Abacus ( ) Vo Vi Δ( max) = (8) I L

6 Table 3. Converer specificaion and semiconducor limiaions. Parameer Value Inpu power (P in ) 390 W Swiching frequency (f s ) 00 khz Inpu volage (V i ) / Oupu volage (V o ) 5.8 V / 50 V Maximum volage over ((max) ) / D x (v Dx(max) ) 480 V / 480 V Maximum curren hrough he ACC (i ACC(max) ) 3 A Maximum di/d hough D (di/d D ) and D x (di/d Dx ) 00 A/μs verer and he limiaions (maximum volages and currens) of he semiconducor devices. Thus, he resricions () o (8) are ploed in Figure 7 using he specificaions summarized in Table 3. This way, from Figure 7 was seleced L x = 7.μH and =. in order o saisfy he resricions defined in Table 3. 5 Sysem Implemenaion and Experimenal Resuls In order o verify he reliabiliy of he proposed sysem, an experimenal analysis is carried ou for a single DC-DC sep-up converer employing he inegraed ZVT cell presened in Figure 4. The semiconducors employed in he prooype are summarized in Table 4, as well as some addiional ACC specificaions. For his analysis he PV panels were emulaed by a consan volage source wih a volage level equal o he MPP volage, and he MPP curren was drained from he volage source by adjusing he DC-DC sep-up converer duy-cycle. Figure 8 presens he experimenal waveforms of he converer operaing a nominal power. In Figure 8 (a)-(b) are presened he sead-sae waveforms of he command signals of boh main (v GS ()) and auxiliary swiches (v GSx ()), as well as heir volage (v S () and (), respecively), and he curren hrough he auxiliary inducor ( ()). I is possible o see in Figure 8 (a)-(b) ha he ACC inervenion demands a small porion of he swiching period. I mus be noed ha he linear rising of () (wih di/d conrolled by ) corresponds o a linear falling of he curren hough Auxiliary Inducor, ( μ H) Snubber capacior (C s ) - C OSS Mag Des i ACC(max) (max) Δ (max) di/d D Projec di/d Dx v Dx(max) Turns Raio, Figure 7. Design abacus. 480 pf Table 4. Semiconducor devices and ACC specificaions. Parameer Value oe Main swich (S ) IRFP460 Discree MOSFET Main diode (D ) 8ETH06 Discree Diode Auxiliary swich ( ) IRG4BC0UD Discree IGBT Auxiliary diode (D x ) 8ETH06 Discree Diode Ferrie core EE 65/6 Cooper Wire 63 x 37 AWG Liz Inpu inducor (L ) 85μH Auxiliary inducor ( ) 7.μH Leakage D, reducing is reverse recovery losses. I is possible o see in Figure 8 (b) ha is urned off afer () reaching zero, characerizing a ZCS commuaion. Furhermore, Figure 8 (c) presens he deails of he urn-on commuaion of S. As can be seen in Figure 8 (c), he main swich S is urned on afer v s () v GS v S 3 Turns raio (). Ch: 00 V/div Ch3: 5 A/div Ch: 00 V/div Ch3: 5 A/div v S Ch: 00 V/div Ch3: 5 A/div v GSx Ch4: 0 V/div Ch4: 0 V/div v GS Ch4: 0 V/div (a) (b) (c) Time: us/div Time: us/div Time: 500 ns/div (pri) = x 3 (sec) = 7 x ZVS Figure 8. Experimenal resuls. (a) Main circui in sead-sae operaion. (b) Auxiliary circui in sead-sae operaion. (c) ZVS commuaion deail.

7 Efficiency (%) Sof-Swiched Hard-Swiched MPP Power (W) Figure 9. Converer efficiency in funcion of solar irradiaion. In a range from 600 o 000 W/m. reaches zero, characerizing a ZVS commuaion. Figure 9 shows he measured efficiency of he DC-DC sep-up prooypes evaluaed experimenally as a funcion of PV modules power for a se of irradiances defined a priori. I can be observed ha he efficiencies are inversely proporional o he PV module power, since he conducion losses increase wih he module curren. In spie of i, he Inegraed ZVT DC- DC prooype presened higher efficiency for he enire module power range. The real efficiency gain of he ZVT DC-DC prooype can be seen in Figure 0. 6 Conclusions 0,4 0,35 0,3 0,5 0, 0,5 0, 0,05 0 Efficiency Gain Irradiaion Figure 0. Inegraed ZVT efficiency gain in funcion of he irradiaion in W/m. This paper presened and analyses an inegraed ZVT ACC ha uses a magneically-coupled auxiliary volage source implemened by adding a secondary winding on he inpu inducors. The proposed ACC assiss all he DC-DC sep-up converers of a decenralized muli-sring PV sysem employing a very compac circui, reducing he cos and size of he overall sysem, and improving is performance by reducing he urn-on capaciive losses of he main swiches and he diode reverse recovery losses. Thus, he benefis of using muli-sring PV sysems, such as reducing he possibiliy of shadowing mismaches and increasing he generaed energy are kep wihou penalizing he sysem reliabiliy and cos. The proposed inegraed ZVT was analyzed heoreical and experimenally. A design procedure o deermine is auxiliary componens have been presened and discussed. The proposed opology was validaed by experimenal resuls obained from a single DC- DC sep-up converer operaing a 390 W and 00 khz. The experimenal resuls proved he effeciveness of he converer. Appendix A The forward volage drop on boh main ransisor and main diode can be esimaed by (9), where he coefficiens A, B and C, summarized in Table 5, can be obained using he daa exraced from he device daashee, and i dev is he insananeous curren hrough he device. ( ) B vdev idev = Aidev + C (9) This way, he ransisor and diode conducion losses can be calculaed by (0), where T s is he swiching period, Belrame (009). Ts cnd dev dev dev Ts 0 ( ) ( ) P = v i i d (0) The ransisor swiching losses can be divided in urn-on and urn-off losses. The urn-on losses are composed by he overlap beween he volage and curren hough he ransisor, McMurray (980), and by he urnon capaciive losses, Belrame (009). On he oher hand, he urn-off losses are mainly due o he overlap beween he volage and curren. Thus, he urn-on capaciive losses can be calculaed by (), where V o is he oupu volage of he DC-DC sep-up converer. Addiionally, he urn-off losses can be calculaed by (). The parameers C oss, f and r are defined in Table 5. Pon = idevvo r fs + CossVo fs () Poff = idevvo f fs () The swiching losses of he diode are basically due o he reverse recovery phenomenon. Then, he swiching losses of he diode can be esimaed by (3), Schönberger (008), where Q rr is defined in Table 5. Prr = QrrVo (3) Finally, he losses observed in he inducor can be esimaed by (4), where I Lrms is he RMS curren hough he inducor and R L is he DC resisance of he cooper wire. I is imporan o noice ha only he cooper losses Table 5. Parameers employed o esimae he converer losses. Device Parameer Value A; B; C 0.083;.380; Main swich C oss 480 pf (IRGP460) r ; f 8 ns; 65 ns Main diode A; B; C 0.969; 0.9; 0.35 (8ETH06) Q rr 5 nc Inducor R L 39.6 mω

8 were ake ino accoun o calculae he inducor losses. P = I R (4) L Lrms L Acknowledgmen The auhors would like o express heir graiude o Coordenação de Aperfeiçoameno de Pessoal de ível Superior CAPES and Conselho acional de Desenvolvimeno Cienífico e Tecnológico CPQ (proc. nº /009-7 and proc. nº 47854/009-7) for financial suppor. References Belrame, R.C., Candido, D.B., Marins, M.L.S., Pinheiro, J.R. and Hey, H.L., Comparison beween inegraed and simplified ZVT opologies for hree-phase volage-source inverers, in Proc. IEEE Indusrial Elecronics Sociey Conf., 009, pp. 7-. Carannane, G., Fraddanno, C., Pagano, M. and Piegari, L., Experimenal Performance of MPPT Algorihm for Phoovolaic Sources Subjec o Inhomogeneous Insolaion, IEEE Trans. on Indusrial Elecronics, Vol. 56, o., pp , 009. Cory, K., Coughlin, J., Jenkin, T., Paer, J. and Swezey, B., Innovaions in Wind and Solar PV Financing, Technical Repor REL/TP , 008. Femia,., Perone, G., Spagnuolo, G. and Vielli, M., Opimizaion of Perurb and Observe Maximum Power Poin Tracking Mehod, IEEE Trans. on Power Elecronics, Vol. 0, o. 4, pp , July 005. Imhoff, J., Pinheiro, J.R., Russi, J.L., Brum, D., Gules, R. and Hey, H.L., DC-DC Converers in a mulisring configuraion for sand-alone phoovolaic sysems, in Proc. IEEE Power Elecronics Specialiss Conf., 008, pp Jovanovic, M.M. and Jang, Y., Sae-of-he-Ar, Single- Phase, Acive Power-Facor-Correcion Techniques for High-Power Applicaions An Overview, IEEE Trans. on Indusrial Elecronics, Vol. 5, o. 3, pp , June 005. Li, R.T.H., Chung, H.S.H. and Sung, A.K.T., Passive lossless snubber wih minimum volage and curren sress for boos PFC, in Proc. IEEE Energy Conversion Congress and Exposiion, 009, pp Maksimovic, D., Erickson, R.W. and Griesbach, C., Modeling of cross-regulaion in converers conaining coupled inducors, IEEE Trans. on Power Elecronics, Vol. 5, o. 4, pp , 000. Marins, M.L.S. and Hey, H.L., Self-commuaed auxiliary circui ZVT PWM converers, IEEE Trans. on Power Elecronics, Vol. 9, o. 6, pp , ov Marins, M.L.S., Russi, J.L. and Hey, H.L., Zerovolage ransiion PWM converers: a classificaion mehodology, in Elecric Power Applicaions, IEE Proceedings, Vol. 5, o., pp , 005. McMurray, W., Selecion of Snubbers and Clamps o Opimize he Design of Transisor Swiching Converers, IEEE Trans. on Indusry Applicaions, Vol. IA-6, o.4, pp , July 980. Meinhard, M., O Donnell, T., Schneider, H., Flannery, J., Mahuna, C.O., Zacharias, P. and Krieger, T., Miniaurised low profile module inegraed converer for phoovolaic applicaions wih inegraed magneic componens, in Proc. IEEE APEC, Vol., 999, pp Meinhard, M., Wimmer, D. and Cramer, G., Mulisring-converer: The nex sep in evoluion of sring-converer, in Proc. IEEE EPE, 00. Myrzik, J.M.A. and Calais, M., Sring and module inegraed inverers for single-phase grid conneced phoovolaic sysems a review, in Proc. IEEE Power Tech Conf., 003. Russi, J.L., Marins, M.L.S. and Hey, H.L., Coupled-filer-inducor sof-swiching echniques: principles and opologies, IEEE Trans. on Indusrial Elecronics, Vol. 55, o. 9, pp , Sep Schuch L., Rech C., Pinheiro J.R., Inegraed auxiliary commuaion circuis: a generalised approach, Power Elecronics, IET, Vol., pp. 4-5, 009. Schonberger, J., Feix, G., Modelling urn-off losses in power diodes, in Conrol and Modeling for Power Elecronics, 008, pp. -6. Tseng, S.-Y., Shiang, J.-Z., Chang, H.H., Jwo, W.-S. and Hsieh, C.-T., A ovel Turn-On/Off Snubber for Inerleaved Boos Converers in Proc. IEEE Power Elecronics Specialiss Conf., 007, pp Wang, C.M., A novel zero-volage-swiching PWM boos recifier wih high power facor and low conducion losses, IEEE Trans. Indusrial Elecronics, Vol. 5, o., pp , Apr Yu, G.J., Jung, Y.S., Choi, J.Y., Choy, I., Song, J.H. and Kim, G.S., A novel wo-mode MPPT conrol algorihm based on comparaive sudy of exising algorihms, in Phoovolaic Specialiss Conf., 00, pp