A 1-MHz Series Resonant DC-DC Converter With a Dual-Mode Rectifier for PV Microinverters

Transcription

1 Aalbog Univesitet A -MHz Seies Resonant DC-DC Convete With a Dual-Moe Rectifie fo PV Micoinvetes Shen, Yanfeng; Wang, Huai; Shen, Zhan; Yang, Yongheng; Blaabjeg, Fee Publishe in: I E E E DOI (link to publication fom Publishe):.9/TPEL Publication ate: 9 Document Vesion Accepte autho manuscipt, pee eviewe vesion Link to publication fom Aalbog Univesity Citation fo publishe vesion (APA): Shen, Y., Wang, H., Shen, Z., Yang, Y., & Blaabjeg, F. (9). A -MHz Seies Resonant DC-DC Convete With a Dual-Moe Rectifie fo PV Micoinvetes. I E E E, PP (99). Geneal ights Copyight an moal ights fo the publications mae accessible in the public potal ae etaine by the authos an/o othe copyight ownes an it is a conition of accessing publications that uses ecognise an abie by the legal equiements associate with these ights.? Uses may ownloa an pint one copy of any publication fom the public potal fo the pupose of pivate stuy o eseach.? You may not futhe istibute the mateial o use it fo any pofit-making activity o commecial gain? You may feely istibute the URL ientifying the publication in the public potal? Take own policy If you believe that this ocument beaches copyight please contact us at vbn@aub.aau.k poviing etails, an we will emove access to the wok immeiately an investigate you claim.

2 A -MHz Seies Resonant DC-DC Convete With a Dual-Moe Rectifie fo PV Micoinvetes Yanfeng Shen, Stuent Membe, IEEE, Huai Wang, Senio Membe, IEEE, Zhan Shen, Stuent Membe, IEEE, Yongheng Yang, Senio Membe, IEEE, an Fee Blaabjeg, Fellow, IEEE Abstact The photovoltaic (PV) output vaies ove a wie ange epening on opeating conitions. Thus, the PVconnecte convetes shoul be capable of hanling a wie input ange while maintaining high efficiencies. This pape poposes a new seies esonant c-c convete fo PV micoinvete applications. Compae with the conventional seies esonant convete (SRC), a ual-moe ectifie (DMR) is configue on the seconay sie, which enables a twofol gain ange fo the popose convete with a fixe-fequency phase-shift moulation scheme. The zeo- switching () tun-on an zeo-cuent switching (ZCS) tun-off can be achieve fo active switches an ioes, theeby minimizing the switching losses. Moeove, a vaiable c-link contol scheme is intouce to the popose convete, leaing to a futhe efficiency impovement an input--ange extension. The opeation pinciple an essential chaacteistics (e.g., gain, soft-switching, an oot-mean-squae cuent) of the popose convete ae etaile in this pape, an the powe loss moeling an esign optimization of components ae also pesente. A -MHz 5-W convete pototype with an input ange of 7 V 43 V is built an teste to veify the feasibility of the popose convete. Inex tems PV micoinvete, c-c convete, seies esonant convete, wie input ange, -MHz fequency. I. INTRODUCTION Compae with cental an sting photovoltaic (PV) invetes, micoinvetes ae favoable in low-powe applications, ue to the capability of moule-level maximum powe point tacking (MPPT), low installation effots, easy monitoing an failue etection, an low maintenance cost []-[3]. Nevetheless, cetain challenges emain fo PV micoinvetes: ) the efficiency pefomance of micoinvetes is elatively low compae with sting invetes (e.g., the peak efficiency is aoun 99. % in [4]); ) thee is a ten that micoinvetes will be incopoate into PV moules in the futue [5], [6], which implies that micoinvetes shoul be moe compact (i.e., high powe ensity an low pofile); 3) panel-embee mico- Manuscipt eceive June, 8; evise August 4, 8; accepte Octobe 8, 8. (Coesponing autho: Yanfeng Shen). This wok was suppote by the Innovation Fun Denmak though the Avance Powe Electonic Technology an Tools (APETT) poject. The authos ae with the Cente of Reliable Powe Electonics (CORPE), Depatment of Enegy Technology, Aalbog Univesity, Aalbog 9, Denmak ( yaf@et.aau.k, hwa@et.aau.k, zsh@et.aau.k, yoy@et.aau.k, fbl@et.aau.k). PV Moule Focus of this pape DC-DC Convete DC Link Invete AC Gi Fig.. Configuation of a two-stage gi-connecte PV micoinvete system. invetes may be inevitably heate up by the PV panels, acceleating the egaation [7], [8]. Impoving the powe convesion efficiency an eucing powe losses can be an effective way to enhance the enegy yiel an eliability of PV micoinvetes [3], [9]. In the liteatue, thee powe convesion stuctues can be foun fo PV micoinvetes, i.e., the high-fequency-link (single-stage) micoinvete [], pseuo-c-link micoinvete [], an c-link (two-stage) micoinvete [], [3]. The clink micoinvetes have the avantages of simple stuctue, lowe powe ecoupling capacitance, an easie pefomance optimization fo each stage; theefoe, ecently, they attacte much inteest [6], [9], []-[6]. Fig. shows the configuation of a two-stage gi-connecte PV micoinvete system. Typically, the font-en c-c convete is contolle to achieve the MPPT of the PV moule. Depening on the moule chaacteistics an the opeating conitions (i.e., the sola iaiance an ambient tempeatue), the output s of PV moules at maximum powe points vay ove a wie ange (e.g., -4 V). Theefoe, the c-c convete shoul be able to hanle a wie input ange while maintaining high efficiencies. It is also equie that the c-c convete shoul boost the low- (< 5 V [6]) PV moule output to a esie high (at the c link) in oe to fee a giconnecte o stanalone invete [7]. Pefeably, a highfequency tansfome is insete into the font-en c-c stage to achieve the galvanic isolation, leakage cuent elimination, an a high -boost atio [3]. Futhemoe, in oe to euce the system pofile, it is equie to incease the switching fequency an/o aopt low-pofile passive components (e.g., plana magnetics [8] an low-pofile ecoupling capacitos [9]). Taitional flyback convetes with snubbes o active clamping cicuits ae simple in topology an low in cost; theefoe they ae aopte as the font-en c-c stage in some micoinvetes [], []. Howeve, the stess of the

3 pimay switches is high an thus low- MOSFETs with low on-state esistances cannot be use [], [3]. In the phaseshift full-bige c-c convete, the pimay switches can achieve zeo--switching (); howeve, it is challenge when opeating in a wie gain ange, e.g., the naow ange fo the lagging leg switches, uty cycle loss, lage ciculating cuent, an spikes acoss the output ioes [4]. The LLC esonant convete is a pomising topology in tems of high efficiency an high powe ensity [4]-[7]. Howeve, the pimay concen fo this topology is that the gain ange is not wie an thus hybi contol schemes [8]-[3] have to be applie, which inceases the ealization complexity of the MPPT. Fo instance, a full-bige LLC esonant convete is esigne fo PV applications in [8]; howeve, the bust moe contol has to be use in aition to the vaiable fequency contol. In [9], a hybi contol combining the pulse-fequency moulation (PFM) an phase-shift pulse-with moulation (PS-PWM) is employe to a full-bige LLC esonant convete to impove the efficiency, but the contol complexity is significantly incease as well. In aition to the hybi contol schemes, many moifie LLC esonant convete topologies have been popose [7], [3]-[4]. Stuctual moifications can be mae to the pimaysie invete [3]-[35], the seconay-sie ectifie [36]-[38], an the tansfome/esonant tank [39]-[4]. Instea of the conventional half-bige o full-bige stuctue, a vaiable fequency multiplie is applie to the LLC esonant tank to exten the gain ange while maintaining high efficiencies [3]. In [33], the pimay-sie full-bige invete is eplace by a ual-bige invete; thus, a multi-level ac can be applie to the esonant tank, an a twofol gain ange can be achieve; howeve, the pimay-sie switches have high tun-off cuents, an may suffe fom high off-switching losses when opeating in high step-up applications (e.g., PV micoinvetes). By combining a boost convete with an LLC esonant convete, two cuent-fe LLC esonant convetes ae popose in [34], [35]. Nevetheless, the pimay-sie switches shae uneven cuent stesses, which may lea to high conuction losses as well as high off-switching losses. To avoi the high off-switching losses on the highcuent pimay-sie switches, [36]-[38] popose seconayectifie-moifie LLC esonant convete topologies. Specifically, in [36] an [37], two ioes in the full-bige ectifie ae eplace with two active switches, yieling a contollable ectifie. In [38], two active switches ae utilize to obtain a econfiguable multiplie ectifie, leaing to a squeeze switching fequency ange an impove efficiencies ove a wie input ange; notably, the numbe of ectifie components is high (8 ioes active switches 6 capacitos), an thus this topology may not be cost-effective fo PV micoinvete applications. Futhemoe, [39]-[4] moify the tansfome an esonant tank to exten the gain ange of the LLC esonant convete. In [39], an auxiliay tansfome, a biiectional switch (implemente with two MOSFETs in an anti-seies connection), an an exta full-bige ectifie ae ae to the conventional LLC esonant convete. Thus, the equivalent tansfome tuns atio an magnetizing inuctance can be aaptively change in oe to achieve a wie gain ange; howeve, the component count is high an the tansfomes utilization atio is elatively low. To aess the issues in [39] as well as to maintain high efficiencies ove a wie input ange, Sun et al [4] poposes a new LLC esonant convete with two split esonant banches; in this way, two opeation moes, i.e., the low- an meium-gain moes, ae enable, an the gain ange fo moe tansition is.5 times, leaing to a smoothe efficiency cuve ove the gain ange. Moeove, in [4], a new tansfome plus ectifie stuctue with factional an econfiguable effective tuns atios is popose fo a wiely vaying gain. As afoementione, thee is a ten to incease the switching fequency an lowe the convete pofile such that the micoinvete can be mechanically an physically integate with a PV moule [5], [6]. Theefoe, the MHz opeation an esign optimization of esonant c-c convetes [4]-[48] ae becoming attactive to achieve so. Notably, the epote peak efficiency of a -MHz LLC esonant convete has eache 97.6 % with an optimal esign of the integate plana matix tansfome [46]. Howeve, the convesion atios in these systems ae fixe [43]-[48] o vay within a naow ange (± 5%) [4], which is not suitable fo PV micoinvete applications whee the c-c stage shoul hanle a wie gain ange. In light of the above, this pape poposes a new ual-moe ectifie (DMR) base seies esonant c-c convete fo PV micoinvete systems. A twofol gain ange can be achieve with a fixe-fequency phase-shift moulation scheme. The active switches can tun on une zeo- switching () an the ectifie ioes can tun off une zeo-cuent switching (ZCS), leaing to minimize switching losses. Also, a vaiable c-link contol is applie, yieling a significant efficiency impovement an input-ange extension. The expeimental tests on a -MHz micoinvete pototype show that the popose convete can achieve high efficiencies ove a wie input ange, i.e., 7 V 43 V. This pape is an expansion of ou pevious confeence publication in [49] by aing two topology eivatives, etaile chaacteistics analysis, powe loss moeling an esign optimization of components, an -MHz expeimental veifications. The contibutions of this pape ae summaize as: i) thee DMR-base seies esonant c-c convete topologies ae popose fo PV micoinvete systems; ii) the opeation pinciple, citical chaacteistics (incluing gain, ootmean-squae cuent, an soft switching), an esign optimization of the basic DMR seies esonant convete ae analyze in etail; iii) a vaiable c-link contol is intouce to the popose convete; iv) a -MHz micoinvete pototype is built an teste to veify the feasibility of the popose convete. The emaine of this pape is oganize as follows. Section II pesents the opeation pinciples of the popose convete. In Section III, the key opeating chaacteistics ae analyze an paamete esign guielines ae pesente. Then, the powe loss moeling an esign optimization of main components ae pefome in Section IV. Afte that, the contol stategy, moulation implementation an extensive expeimental tests ae povie in Section V. Finally, conclusions ae awn in Section VI.

4 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS V in S C in S a Pimay sie S 3 S 4 b i p T x :n Seconay sie D L i Lm L m v C C D c D 3 D 4 C o S 6 S 5 Fig.. Schematic of the popose ual-moe ectifie base seies esonant cc convete. V in V in S C in S S C in S a a S 3 S 4 S 3 S 4 b b i p i p T x :n T x :n i Lm L m i Lm L m L C L C S 5 S 6 S 5 S 6 c c D 5 C o Fig. 3. Schematics of the extene seies esonant convete topologies with ual-moe ectifies fo high- output applications: extene topology A an extene topology B. II. OPERATION PRINCIPLES OF THE PROPOSED CONVERTER A. Topology Desciption an Opeation Moes The popose DMR-base seies esonant convete (DMR- SRC) is shown in Fig.. The DMR is implemente by aing a pai of anti-seies tansistos (S 5-S 6) between the mipoints of the ioe leg (D 3-D 4) an the output capacito leg (C o an C o). Thus, two ectifie moes can be achieve by contolling the anti-seies tansistos S 5-S 6: ) Half-Bige Rectifie (HBR) moe: when the anti-seies tansistos S 5-S 6 ae tiggee on, a half-bige ectifie ( ouble) consisting of D, D, S 5, S 6, C o an C o pesents on the seconay sie; ) Full-Bige Rectifie (FBR) moe: when S 5-S 6 ae isable, thee is a full-bige ectifie (D -D 4) on the seconay sie. Inspie by the ual-moe ectification concept, two extene seies esonant c-c convetes ae eive fo high output applications, as shown in Fig. 3. All the seconay ioes an tansistos only nee to withstan half of the output. By contolling the seconay-sie active switches S 5 an S 6, a ual-moe ectifie can be fome on the seconay sie, an theefoe a wie gain can be achieve. Nevetheless, this pape will only focus on the basic topology shown in Fig.. A fixe-fequency phase-shift moulation is applie to the popose DMR-SRC, as illustate in Fig. 4. The pimay-sie iagonal switches ae iven synchonously, an the uppe an lowe switches of each leg ae phase-shifte by. On the D6 D 5 D 6 C o C o C o C o R o R o R o seconay sie, the tun-on instant of S 5 is synchonize with that of S an S 3, but the tun-off of S 5 is lagge by a phase of with espect to that of S an S 3. The gate signal of S 6 is shifte by a phase of with that of S 5. It is note that the fixefequency phase-shift moulation scheme is also applicable to the two extene topologies shown in Fig. 3 an. With this moulation scheme, the acoss the mipoints of the two pimay-sie switch legs, i.e.,, is an ac squae wave (with an amplitue of V in) which applies to the tansfome. In aition, the switching fequency f s is equal to the seies esonant fequency of the esonant inucto L an capacito C, i.e., fs f / ( LC ). The pimay-sie tansfome cuent i p is the sum of the magnetizing cuent i Lm an the esonant cuent efee to the pimay sie, i.e., ip n( ilm i L ) () whee n epesents the tansfome tuns atio. The wavefom of capacito v C has half-wave symmety, i.e., vc ( t) vc ( t T s / ). Thus, the chage vaiation of the esonant capacito ove half a switching cycle [, T s/] can be obtaine as q [ v ( T / ) v ()] C V C hs C s C C i () t i ( t)t t i ( t)t n i () t T P Ts / Ts / p Ts / L Lm Ts/ p T / s s t [ V ( )] inip t t n nvin Ts nf Vin () whee V C enotes the initial esonant capacito at t = (see Fig. 4), an P is the tansfee powe. The gain of the convete an the inuctos atio of L m to L ae efine as G = /(nv in), an m = L m / L, espectively. The quality facto is enote as Q = Z /R o = P/( /Z ), in which the chaacteistic impeance Z L / C. Thus the quality facto Q is also teme as the nomalize powe. The initial capacito V C can be obtaine fom () as P GQVo VC (3) 4nf C V in The magnetizing cuent i Lm can be expesse as nv i I I nv in in Lm() Lm Lm m L mz whee t with (4) f being the esonant angula fequency, an I Lm epesents the initial magnetizing cuent at =. The peak magnetizing cuent I Lmpk is eache at =, i.e., I Lmpk = i Lm(). Due to the half-wave symmety of the magnetizing cuent i Lm, we have ILm ilm() ilm( ) I Lmpk (5) Substituting (5) into (4) yiels the peak an initial magnetizing cuents, i.e., I Lmpk I Lm nv in mz mz G V o (6)

5 S &S 4 S &S 4 S &S 3 S &S 3 S 5 S 5 S 5 S6 S 6 a π ( ) I Lmpk / nv in i p i m V in V in S C in S S C in S a a S 3 S 4 S 3 S 4 b b i p i p T x :n T x :n D L i Lm L m C v C D D L i Lm L m C v C D c c D 3 D 4 D 3 D 4 C o S 6 S 5 C o C o S 6 S 5 C o R o R o V C v C S a S 3 i p T x D L i Lm c D 3 C o ip()=ilm =-ILmpk ZCS-off ZCS-off i S &i S4 i D i D4 i S &i S3 i D i D3 V in C in S S 4 b :n L m C v C D D 4 S 6 S 5 (c) Fig. 5. Equivalent cicuits of the popose convete ove the fist half switching cycle [, ]. Stage I: [, ], Stage II: [, a], an (c) Stage III: [a, ]. C o R o -il() HBR FBR HBR FBR : a π π πa π t: T s / T s Fig. 4. Fixe-fequency phase-shift moulation fo the popose convete shown in Fig. an key opeating wavefoms. B. Opeation Pinciple The key opeating wavefoms of the popose DMR-SRC ae shown in Fig. 4. Neglecting the eatime, six stages can be ientifie ove one switching cycle. Due to the symmety of opeation, only stages I-III ove the fist half switching cycle [, ] ae escibe. Stage I ( [, ], see Figs. 4 an 5): Befoe the time instant, S, S 3 an S 5 ae conucting. At =, S an S 3 ae tune off, the negative magnetizing cuent I Lm begins to chage/ischage the paasitic output capacitos (C oss-c oss4) of pimay-sie switches, such that S an S 4 can achieve -on. Duing this stage, S 5 is tune on, an a half-bige ectifie is fome on the seconay sie. The is clampe by half of the output /. The esonant inucto L an capacito C esonate, an the esonant cuent stats inceasing fom zeo. When the paasitic output capacito of S 6, i.e., C oss6, is fully ischage, the antipaallel ioe of S 6 begins to conuct. Thus, -on of S 6 can be achieve subsequently by applying the tun-on gate signal. The govening iffeential equations in this stage ae obtaine as i S5 i S6 il( ) L nv ( ) v ( ) v ( ) nv V / v ( ) ab c C v ( ) C C il in o C () Consieing the initial conitions vc () V C an i L (), (7) can be solve as i ( ) ( / Z )sin A sin L v ( ) cos nv V / C in o whee nvin Vo / V C, an A / Z. Stage II ( [, a], see Figs. 4 an 5): At =, S 5 is tune off, the esonant cuent is ivete fom S 5-S 6 to D 4, an a full-bige ectifie is pesente on the seconay sie. Thus, the ac is equal to the output, causing the esonant cuent to ecease sinusoially. The govening iffeential equations in this stage ae il( ) L nvab( ) vc ( ) vc ( ) nvin Vo vc () (9) vc( ) C il() The inucto cuent an capacito at =, i.e., i L( ) an ( ) C v, can be obtaine fom (8). Then, (9) can be solve as (7) (8)

6 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS Fig. 6. Analytical an simulate esults fo the nomalize gain G with espect to the phase shift at iffeent quality factos. Voltage gain G Voltage gain G.5 Q =..8 f n [, 5] Q =. Q = Q =.6 Q =..4 Q =. Q =.3 f n [.48, ]. Q =.6.5 Q = Nomalize fequency f n Nomalize fequency f n.8.6 D [.4,.5].4 Q =..4 Q =. Q =. Q =.. Q =.3. Q =.3 Q =.6 Q = Duty cycle D Duty cycle D.4.5 (c) () Fig. 7. Voltage gain chaacteistics of the full-bige seies esonant c-c convete an the full-bige LLC esonant c-c convete: SRC with PFM, LLC esonant convete with PFM, (c) SRC with PWM o PSM, an () LLC esonant convete with PWM o PSM. In Fig. 7 an, the nomalize switching fequency f n is base on the seies esonant fequency of the esonant tank..8.6 D [.5,.5] il ( ) sin( ) il ( )cos( ) A sin( ) Z vc ( ) cos( ) il ( ) Z si n( ) nvi n Vo () whee nvin Vo v C ( ), A ( / Z ) i ( ), an accos[( / Z ) / A ]. Stage III ([a, ], see Figs. 4 an 5(c)): When the esonant cuent falls to zeo at = a, D an D 4 tun off une ZCS. Thus, the esonant tank is pevente fom esonance an the esonant cuent an ae kept at an V C, espectively. The output capacitos ae ischage to supply the loa. III. CHARACTERISTICS OF THE PROPOSED CONVERTER In this section, the chaacteistics of the popose convete ae analyze in etail in tems of the DC gain, RMS cuents, an the soft-switching pefomance. Aitionally, basic esign guielines ae also pesente. L A. DC Voltage Gain Because of the half-wave symmety of both the esonant inucto cuent an the capacito v C, we have il ( ) il () () v ( ) v () V C C C Solving (3), (8), (), an () yiels the expessions fo the gain G an phase angle α as Vo G nvin Q(3 cos ) 3 4 Q(4 Q sin ) cos 3 cos K 4 Q cos cos 4(sin ) ( cos ) () whee cos K[3 8 Q cos cos( )] 7 4 Q 3 Q 4( 4 Q) cos (3 8 Q) cos( ) K 8 Q( Q cos cos ) ( cos ). Accoing to (), the gain can be epicte in Fig. 6. It can be seen that the ange of the gain is always between an iespective of the quality facto (i.e., the loa). It shoul be note that the inuctos atio m = L m/l oes not affect the gain. Theefoe, the magnetizing inuctance can be esigne as a lage value une the conition that the -on of pimay-sie switches can be achieve. Cicuit simulations of the popose convete ae conucte, an the esults ae also pesente in Fig. 6, which valiates the obtaine analytical gain moel (). To compae, the gain chaacteistics of the fullbige seies esonant convete (SRC) [5] an the full-bige LLC esonant convete [5] ae shown in Fig. 7. Fo the PFM contolle SRC, the light-loa gain ange is naow (e.g.,.85- at a light loa Q =.) even within a wie nomalize switching-fequency ange f n [, 5]. The PFM-contolle LLC esonant convete has impove gain chaacteistics. Howeve, the heavy-loa gain ange is still naow (e.g., -.47 at a heavy loa Q =.3). In oe to have a high full-loa gain peak, the chaacteistic impeance Z has to be ecease, esulting in a wie fequency ange an/o incease conuction losses. With the fixe-fequency PWM o phase-shift moulation (PSM) contol, the gain anges of the SRC an the LLC esonant convete ae extene. Howeve, the vaiation of the uty cycle D is also wie. When the uty cycle D is small, the conuction losses will ise an the soft-switching conition will be lost, because the peak magnetizing cuent is euce amatically in this case. In aition, when contolle with the PWM o PSM scheme, the pimay-sie (low- an highcuent sie) switches of the SRC an LLC convete have to tun off at a lage cuent, an thus the off-switching loss is lage. By contast, the peak magnetizing cuent of the popose esonant convete oes not vay significantly with espect to the gain G: the vaiation ange of I Lmpk is twofol accoing to (6). Theefoe, the -on of the pimay-sie switches can be achieve while keeping the magnetizing

7 Components Pimaysie active switch Seconaysie active switch Dioe TABLE I COMPARISON OF BILL OF MATERIALS OF FIVE TOPOLOGIES Fullbige SRC [5] Fullbige LLC esonant convete [5] Popose DMRbase SRC (Fig. ) Popose DMR- SRC eivatives A an B (Fig. 3) Count Voltage stess Input Input Input Input Count Half of Half of Voltage output output stess Count Voltage stess Output Output Output Half of output Tansfome Resonant inucto Resonant capacito in in Output capacito Count Voltage stess Output Output seies Half of output seies Half of output Fig. 8. Pimay an seconay tansfome RMS cuents with espect to the gain at m = 6. inuctance lage. Moeove, the pimay-sie switches in the popose convete ae tune off at the small peak magnetizing cuent; thus, the off-switching loss is small as well. Futhemoe, the bill of mateials (BOM) of the five topologies, i.e., the full-bige SRC [5], the full-bige LLC esonant convete [5], the popose DMR-base SRC (see Fig. ), an the eivatives A an B of the DMR-base SRC (see Fig. 3), is shown in Table I. The iffeences between the popose an conventional topologies ae highlighe in e. Compae with the conventional SRC an LLC esonant convete, the popose DMR-base SRC (see Fig. ) has a highe component count. Moe specifically, two active switches withstaning half of the output ae ae on the seconay sie, an the output capacito is split into two low- ones. Likewise, the popose DMR-SRC eivatives A an B (see Fig. 3) also employ two seconay-sie switches an two output capacitos in seies. Howeve, the seconay-sie ioe count is euce fom 4 to, an the stess of the ioes is only half of the output, which is beneficial to cost euction. B. RMS Cuents The seconay an pimay tansfome RMS cuents can be obtaine by I i () L, ms L I i ( ) i ( ) p, ms L Lm (3) The final expessions of I L,ms an I p,ms ae given in Appenix as (39). Fig. 8 shows the nomalize RMS cuents at iffeent quality factos. The cuent nomalization base is /Z. It can be seen in Fig. 8 that at heavy loas, the RMS esonant cuent I L,ms inceases with espect to the gain. The eason is that when the gain inceases, the input eceases an thus the RMS cuent inceases if the powe is fixe. Howeve, at light loas, the RMS cuent fistly inceases an then Fig. 9. Full-loa RMS cuents with espect to the chaacteistic impeance Z at iffeent gains. Seconay-sie RMS cuent I L,ms; Pimaysie RMS cuent I p,ms. eceases. This is because the angle a (see Fig. 4) is small at light loas when the gain is in the mile aea. A smalle a means a lage RMS cuent if the powe is fixe. Fo the pimay tansfome RMS cuent I p,ms, it is oveall ising as the gain G inceases. Howeve, at light loas, I p,ms becomes flat with espect to G. When compaing the two RMS cuents, it can be obtaine that the iffeence between them is small. It is because the inuctos atio m = L m/l can be esigne to be lage fo the popose convete.

8 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS V in S C in S a Coss Coss S 3 S 4 b i p () Coss3 Coss4 T i Lm L m D L D D 3 C ( ) D 4 C ossd3 C oss6 C o S 6 S 5 C ossd4 C o HB leg HB leg HB leg 3 T-type leg Fig.. mechanism of pimay an seconay tansistos (see Fig. ): tun-on of S an S 4 at t =, an tun-on of S 6 at t =. C oss-c oss4, C ossd-c ossd4, an C oss5-c oss6 ae the paasitic capacitances of tansistos an ioes. V s V D V s6 i p t,p,s /w /w S 5 V in -gv c, q eq,s / q eq,p / q eq,p / S &S 4 i Lm S 6 c CossD CossD S &S 3 t,m t,p t,s /w α/w /w Fig.. Opeating wavefoms of the popose convete consieing the eatime an output capacitances of tansistos an ioes. Fo the popose convete, the chaacteistic impeance Z has a significant impact on the RMS cuent chaacteistics when the loa is fixe. Fig. 9 shows the full-loa RMS cuent cuves une iffeent chaacteisitc impeances Z an gains G. As can be seen, the full-loa RMS cuents ecease with espect to the incease of the chaacteistic impeance Z except fo G = an G = in Fig. 9. Consieing the conuction losses, the chaacteistic impeance Z shoul be esigne as lage as possible. Moeove, when the esonant fequency is fixe, a lage Z means a lage L, which is beneficial to the shot-cicuit cuent suppession. Howeve, a lage Z also leas to a lage ac ipple an a highe peak ove the esonant capacito C. Theefoe, a taeoff shoul be mae in pactice. C. Soft-Switching Ieally, the pimay an seconay MOSFETs can achieve the tun-on if i p() an -( ) (see Fig. 4) ae negative, as analyze in Section II-B. This ieal conition always S 5 R o t t t t t t t t t hols, as inicate by (6) an (8). In pactice, howeve, thee ae paasitic output capacitances in paallel with MOSFETs an ioes. Theefoe, a cetain amount of chage is equie to fully ischage the output capacitance of the MOSFET uing the eatime inteval, such that its antipaallel ioe will conuct befoe the tun-on signal is applie [5]. Fig. shows the mechanism of the pimay an seconay tansistos, an Fig. illustates the opeating wavefoms consieing the eatime an output capacitance of tansistos. Duing the eatime intevals, the output capacitances of the tansistos ae chage o ischage with i p, i Lm an/o. It is assume that C oss = C oss = C oss3 =C oss4 =C oss,p, C oss5 = C oss6 = C oss,s, an C ossd = C ossd = C ossd3 = C ossd4 =C oss,d. Then, the change an chage equie fo the -on can be obtaine, as summaize in Table II. Pimay-Sie : The -on ealization of S equies a complete chaging of C oss an a complete ischaging of C oss uing the eatime inteval t,p, as shown in Fig. an Fig.. The total equie chage q eq.p (see Table II) can be ivie into q eq.p/ within [, t,m] an q eq,p/ within [t,m, t,p], as illustate in Fig.. Due to the high nonlineaity of the paasitic output capacitance with espect to the ain-souce, the cuent wavefoms i Lm an i p will not be istote significantly uing the eatime inteval [5]. To achieve the complete chaging an ischaging of output capacitances, the chage povie by the cuents i Lm an i p (see Fig. ) uing the eatime inteval [, t,p] shoul satisfy t, m t, m nv q in eq, P i ( ) Lm t t I Lm t t mz t t t t i ( t) t [ A sin( t) i ( t)] t, P, m, P, m p Lm t, P t, m nv q in eq, P I Lm A tt mz (4) Fom (4), it is obtaine that the inuctos atio m shoul be esigne accoing to m L nt V ( t ) m in min 8 qeq, PZ nvin t[ G( L GQ ) ] (5) Seconay-Sie : Befoe the output ectifie conucts, e.g., befoe t = in Fig., a capacito netwok compose of C ossd-c ossd4 an C oss6 pesents on the seconay sie, as shown in Fig.. By applying the Kichhoff s an cuent laws to the capacito netwok, the steay-state capacito s (i.e., the s at t = ), can be obtaine as V V / ( ) V whee D, o c, V V / ( ) V D, o c, V V / V D3, o c, V V / V V V D4, o c, ss 5, V ss 6, c, (6)

9 Commutation moe Pimay sie (see Fig. 9) Seconay sie (see Fig. 9) Cuent to achieve ilm an ip il HB leg HB leg HB leg 3 T- type leg Output capacito TABLE II REQUIRED MINIMUM CHARGE TO ACHIEVE FOR DIFFERENT SWITCH LEGS. Initial capacito at t = Final capacito at t = t,p o t,s Absolute chage vaiation of a capacito Coss Vin VinCoss,P Coss Vin VinCoss,P Coss3 Vin VinCoss,P Coss4 Vin VinCoss,P Chage vaiation of an HB/T-type leg VinCoss,P VinCoss,P CossD.5Vo ( g)vc [.5Vo ( g)vc]coss,d [.5Vo ( CossD.5Vo ( g)vc Vo [.5Vo ( g)vc]coss,d Coss D3.5Vo gvc.5vo gvccoss,d Coss D4.5Vo gvc.5vo gvccoss,d Coss5 Coss6 gvc gvccoss,s g)vc]coss,d gvc(coss,d Coss,S) Minimum chage qeq fo -ON of all switches qeq,p = VinCoss,P qeq,s = max{[.5vo ( g)vc]coss,d, -gvc (Coss,D Coss,S)} Bounay between complete an incomplete -on Aea of incomplete -on Aea of complete -on Fig.. Ranges of complete -on an incomplete -on fo S 5 an S 6. The shae aea epesents the ange of incomplete -on, an the soli e line is the bounay between the complete an incomplete -on anges. 4C C oss, D C oss, D oss, S V nv V V c, in C o GQ G (7) The tun-on of S 6 lags the tun-off of S &S 3 with a eatime t,s =,s / w, an the tun-on of S 5 lags the tun-off of S &S 4 with the same eatime t,s =,s / w, as shown in Fig.. At t = t,s, the seconay-sie capacitos each new steay states with the final s showing in Table II. Then, the absolute chage vaiation of each capacito an the minimum chage q eq,s equie fo the seconay-sie -on can be obtaine, as liste in Table II. To achieve the -on opeation fo the seconay tansistos S 5 an S 6, the chage povie by the esonant cuent shoul be lage than the equie one q eq,s, i.e., /( t) /( t) i ( t) t A sin( t) t L /( t) /( t) A sin( t ) t q eq, S (8) Simplifying (8) yiels the pactical complete -on conitions fo S 5 an S 6, i.e., A ( cos ) A [cos( ) cos( )] q eq, S (9) If (9) is not satisfie, S 5 an S 6 will withstan incomplete -on. Nevetheless, the ain-souce of S 5 an S 6 is low, i.e., /. Theefoe, the tun-on losses ae not significant even opeating une an incomplete -on conition. Base on (9), the aeas fo the complete -on an incomplete -on of S 5 an S 6 can be obtaine, as shown in Fig.. It is seen that the incomplete -on occus only when the quality facto Q (i.e., the loa) is vey low (e.g., Q <.7 at G = ). D. Design Guielines The flowchat of the esign pocess fo the main components of the popose convete is shown in Fig. 3. Befoe the esign, system specifications, e.g., the most possible PV ange, nominal output (c-link), an maximum output powe, ae etemine. Then, the stesses of semiconucto evices an output capacitos can be obtaine base on Table I. Afte that, the component paametes, e.g., output capacitances C o-c o, tansfome tuns atio n, magnetizing inuctance L m, an esonant tank (L an C ) can be etemine. Subsequently, the cuent stesses of the main components can be calculate base on the mathematic moels built in Sections II an III. Finally, the component selection an esign optimization can be pefome. The paamete etemination pocess is etaile as follows. ) Output (DC-Link) Capacitances The output capacitos of the popose c-c convete also act as an enegy buffe in the two-stage PV micoinvete. The instantaneous feeing powe to the gi contains a fluctuating powe at twice the line fequency, wheeas the Putput is c powe. Thus, the output (c-link) capacitos ae use to ecouple the powe mismatch. The electical stesses ove the c-link capacitos can be calculate as [53] Vo P / ( fc ov o) () I P / ( V ) Co, ms whee f epesents the line fequency, P is the aveage powe injecte to the gi, the equivalent output (c-link) capacitance C o = /(/C o /C o), Δ is the peak-to-peak ipple of the output, an I Co,ms is the RMS cuent flowing though the output (c-link) capacitos. Consieing a 6%- ipple on the c-link, the equie minimum capacitance output capacitance equals 83 F. In this esign, two low-pofile (height:.5 cm) 5-V 8-F electolytic capacitos ae aopte an connecte in seies. ) Tansfome Tuns Ratio an Magnetizing Inuctance The tansfome tuns atio n is etemine by o

10 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS System Specifications Most pobable PV ange V in [ V, 4 V]; Nominal output (c-link) = 4 V; Maximum output powe P = 5 W; GS665B N unit = GS6654B N unit = 4 Voltage stess of S -S 4 : V in Output capacitances C o -C o GS6656T N unit = 6 Voltage stess of S 5 -S 6 : / Tansfome tuns atio n GS6658B N unit = 8 Voltage stess of D -D 4 : Voltage stess of C o -C o : / Voltage stesses of components Magnetizing inuctance L m Resonant inuctance L an capacitance C Paamete etemination Cuent stesses of components Component selection an esign optimization Pice (Euo) Fig. 3. Flowchat of the esign pocess fo the main components of the popose convete. n N N V o s : p GVin () whee N p an N s ae the numbes of pimay an seconay wining tuns. Consieing the anges of the gain G (see Fig. 6) an the input V in (see Fig. 3), the tansfome tuns atio n is chosen as. Fo the magnetizing inuctance L m, it is use to assist the pimay-sie switches achieve the -on. A smalle L m leas to a highe magnetizing cuent, theeby being beneficial to -on. Howeve, the conuction loss will be incease ue to the highe ciculating cuent (i.e., magnetizing cuent). Theefoe, the esign pinciple of L m is that it shoul be possibly lage une the pemise that the -on of S -S 4 can be achieve, as illustate by (5). 3) Resonant Inuctance an Capacitance As analyze in Section III-B, a tae-off between the RMS cuents an the esonant capacito ipple (o peak ) shoul be mae fo the esign of the chaacteistic impeance Z. Meanwhile, it is seen fom Fig. 9 that the RMS cuent cuves become flat when Z excees a cetain value (e.g., 75 ~ 5 ), which means that inceasing Z cannot futhe euce the conuction losses. Theefoe, the esign of L an C follows fs f MHz LC () L 75 Z 5 C Solving () an consieing the availability of esonant capacitos yiel L = 34 H an C = 7.5 nf. Numbe of ie units N unit Fig. 4. Micoscopy images of fou 65-V GaN ies [58]; The total ie aea of GS6658P (.3 mm [59]) is almost twice of GS6654B (6. mm [6]). Maket pice of GaN Systems 65-V GaN ehemts with iffeent numbes of ie units; the suvey was conucte at Mouse Electonics TM in 7. IV. POWER LOSS MODELING AND DESIGN OPTIMIZATION A. Powe Semiconuctos ) Pimay-Sie Switches S -S 4 All the pimay-sie switches can achieve the -on an ae tune off at the small peak magnetizing cuent I Lm. Theefoe, the switching losses of the pimay-sie switches ae small an can be neglecte. The total conuction losses of the fou switches S -S 4 can be calculate as P 4 R ( I / ) (3) S4, con S4, on p, ms whee R S4,on is the on-state esistance of the pimay-sie switches S -S 4. As analyze in Section III, the stess of S -S 4 equals the input V in which is etemine by the PV moule popeties (e.g., numbe of cells an mateial) an envionmental conitions (i.e., sola iaiance an ambient tempeatue). In this pape, a maximum input of 43 V is consiee fo the popose convete, an thus, the 8-V egan FETs [54] fom Efficient Powe Convesion (EPC) Copoation ae chosen fo a sufficient magin. The maximum RMS cuent flowing though S -S 4 is about 4. / A (see Fig. 9). Consieing the availability of 8-V GaN tansistos, EPC9 is finally selecte fo the implementation of S -S 4.

11 Fig. 5. Double-pulse test on the GaN ehemt GS6654B: measue tunoff wavefoms of GS6654B, compaison between the measue tun-off enegy loss an the enegy stoe in the output capacitance of GS6654B at V s = V. ) Seconay-Sie Switches S 5-S 6 The stess of the seconay-sie switches S 5-S 6 is half of the output. The maximum output is 43 V in this pape, an the maximum withstaning of S 5-S 6 is about 5 V. Consieing a.5- times magin, the ating of S 5-S 6 shoul be V. Howeve, the available atings of GaN tansistos on the maket wee eithe below above 6 V when the PV micoinvete was esigne in 7. To the best of ou knowlege, the 35-V an 4-V GaN tansistos [55], [56] has not been commecialize until 8. Fo a seies of GaN tansistos with the same ating, thei cuent atings an ain-souce on-state esistances ae achieve by employing iffeent numbes of stana ie units in paallel. Fo instance, the numbes of ie units insie the 65- V GaN ehemts, GS665B, GS6654B, GS6656T an GS6658B [57] ae, 4, 6, an 8, espectively, as shown in Fig. 4. Thei ain-souce on-state esistances ae invesely popotional to the numbe of ie units, wheeas the paasitic input an output capacitances of a GaN tansisto ae popotional to the total ie aea. Thus, the lowe the ainsouce on-state esistance, the highe the paasitic input an output capacitances. In this case, the gate ive loss an incomplete loss [6] will be incease. Fo the popose convete, the incomplete ange of S 5-S 6 is vey small, as inicate in Fig.. Hence, the conuction loss an cost ae the main factos affecting the selection of GaN tansistos. Fig. 4 V gs I L V s I s V s I s shows the maket pice of the 65-V GaN ehemts of GaN Systems. It can be seen that the pice of a GaN tansisto inceases with espect to the numbe of ie units insie. As mentione befoe, the on-state esistance an conuction loss can be euce with a highe numbe of ie units, but the implementation cost will be incease as well. Theefoe, as a tae-off between the cost an the powe convesion efficiency, GS6654B with N unit = 4 is selecte fo S 5 an S 6. The seconay switches S 5-S 6 can achieve the -on opeation, but ae tune off with a elatively lage cuent, as shown in Fig. 4. Theefoe, thee may be an amount of tun-off losses if the tun-off spee is not fast enough. A ouble-pulse testing setup has been built up in oe to exploe the tun-off powe losses of GS6654B evices. The tun-off wavefoms at V s = V an I s =.43 A ae shown in Fig. 5. When the gate V gs falls to below the theshol, the channel is cut off quickly, but the ain-souce V s has not significantly incease. Theefoe, the ain-souce cuent is ivete to the output capacito of the GaN ehemt, causing V s to ise fom to V. The measue tun-off enegy loss is appoximately equal to the enegy stoe in the output capacito C oss, as shown in Fig. 5. It shoul be note that the calculate tun-off enegy loss E off ( E oss) is not tuly issipate uing the tun-off peio. If the switch is subsequently tune on une ha switching, then the enegy stoe in the output capacito C oss, i.e., E oss, will be issipate on the channel. Howeve, the switch in this convete can achieve the -on, which means that the enegy stoe in the output capacito is tansfee instea of being issipate. Theefoe, fo the popose convete, the seconay-sie switches implemente with GaN HEMTs can achieve a quasi-lossless tun-off. Fo the conuction loss of S 5-S 6, it can be calculate as S56, con S56, on S56, ms P R I (4) whee R S56,on is the on-state esistance of S 5 an S 6, an I S56,ms is the RMS cuent flowing though S 5 an S 6. 3) Seconay-Sie Rectifie Dioes The ectifie ioes D -D 4 ae opeating in the iscontinuous conuction moe (DCM), an theoetically, the ZCS-off can be achieve fo D -D 4, as shown in Fig. 4. In pactice, howeve, the ZCS conition (i.e., = ) cannot be always guaantee ue to the esonance of the paasitic output capacitos of ectifie ioes, esonant capacito C, an seies inucto L. If D -D 4 ae implemente with silicon ultafast ecovey ioes, the evese ecovey losses will be high at the -MHz switching fequency espite of a quasi-zcs opeation. Hence, fou 6-V SiC Schottky ioes, C3D6E, ae utilize in oe to ensue a negligible evese ecovey loss at the -MHz switching fequency. The conuction loss of the ectifie ioes can be calculate as D, con ( D, avg D34, avg ) F ( D, ms D34, ms ) D P I I V I I R (5) whee V F an R D ae the op at the zeo cuent an the esistance of the ioe, espectively; I D,avg an I D34,avg epesent the aveage cuents of D -D an D 3-D 4, espectively; an I D,ms an I D34,ms enote the RMS cuents of D -D an D 3-D 4, espectively.

12 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS Fig. 6. Powe loss ensity of ML9S mateial une sinusoial excitation. P ( tun) Insulato P ( tun) Insulato S ( tun) Insulato S ( tun) MMF I I m L = m L = m L3 = m L4 = P ( tun) Insulato S ( tun) Insulato P ( tun) Insulato S ( tun) MMF I m L = m L = m L3 = m L4 =.5P ( tun) Insulato S ( tun) Insulato P ( tun) Insulato S ( tun) MMF -.5I.5I m L = m L =.5 m L3 =.5 m L4 =.5 Insulato.5P ( tun) m L5 = (c) Fig. 7. MMF istibution of iffeent wining aangements in the case of Np = : non-inteleaving wining aangement: P-P-S-S, inteleaving wining aangement: P-S-P-S, (c).5p-s-p-s-.5p. P epesents the pimay wining an S enotes the seconay wining. B. Magnetic Components Plana tansfomes an inuctos ae use in this eseach, an the magnetic coe mateial is ML9S fom Hitachi Metal, which has the lowest coe loss ensity at the -MHz fequency among all available mateials [46], [47]. Fig. 6 pesents the powe loss ensity ata of the ML9S mateial une the sinusoial excitation. With cuve fitting, its Steinmetz paametes k, α an β can be obtaine, as shown in Fig. 6. Fo the popose convete, the magnetic coes ae excite with nonsinusoial s, an theefoe, the coe loss ensity can be calculate with the impove genealize Steinmetz equation (igse) [6] whee T s B Pv k ( ) i B t T t s (6) k k i (7) ( ) cos (c) Fig. 8. Calculate powe losses of plana tansfomes with iffeent wining aangements an iffeent numbes of pimay tuns Np: non-inteleaving wining aangements: P-S fo Np =, P-P-S-S fo Np =, P-P-P-S-S-S fo Np = 3, inteleaving wining aangement: P- S fo Np =, P-S-P-S fo Np =, P-S-P-S-P-S fo Np = 3, (c).5p-s-.5p fo Np =,.5P-S-P-S-.5P fo Np =,.5P-S-P-S-P-S-.5P fo Np = 3. The ac esistance of the wining inceases amatically with espect to the fequency ue to the skin effect an poximity effect, an it can be calculate with the Dowell equation [63], [64]: Rac sinh sin sinh sin (m ) (8) R cosh cos cosh cos c whee h / s, h is the thickness of PCB taces, s is the skin epth of the conucto, an m is a magnetomotive foce (MMF) atio

13 A A I I L,pk L,pk A I L, A I L, δ π/δ π/ π/ π π/ π A A I L,pk wt δ π/δ π/ δ wt π/δ π/ π/ π (c) Fig. 9. Positions of the peak esonant cuent I L,pk in iffeent opeating conitions: < / δ, / δ < /, (c) /. Fig.. Calculate powe losses of plana inuctos with iffeent numbes of tuns NL. I L, Fh ( ) m (9) F ( h ) F () in which F() an F(h) ae the MMFs at the boes of a laye. The wining loss calculation equies the RMS values of the hamonics of the esonant cuent. Theefoe, the esonant cuent is expane base on Fouie seies, as shown in the Appenix. ) Tansfome Fo the tansfome in the popose convete, applying the Faaay s law to (6) yiels a simplifie coe loss ensity equation: Vin Pv ki( fs ) NA p e wt (3) whee N p is the numbe of pimay tuns, an A e is the effective sectional aea of the magnetic coe. The plana coe ER3/6/5 an -laye PCB winings (7- m coppe thickness fo each laye) ae aopte to fabicate the tansfome. Fo the PCB wining layout, thee aangements ae exploe, as illustate in Fig. 7. As can be seen, iffeent wining aangements lea to iffeent MMF istibutions, which affect the ac esistance an powe loss of winings. Compae with the non-inteleaving (see Fig. 7) an inteleaving (see Fig. 7) wining aangements, the aangement.5p-s-p-s-.5p (see Fig. 7) enables the minimum MMF atio fo winings, an theefoe the ac esistance can be euce. In aition to the powe loss, the inta- an inte-wining capacitances of plana tansfomes will affect the convete opeation, an they shoul be contolle as low as possible fo the popose convete. It is pove in [65] an [66] that the aangement.5p-s-p-s-.5p can achieve the minimum stay capacitance while maintaining the lowest esistance. Fig. 8 shows the calculate powe losses of the plana tansfomes with iffeent wining aangements an iffeent numbes of pimay tuns N p. As can be seen, the wining aangement.5p-s-p-s-.5p can achieve the minimum powe losses compae with the othe two aangements. Fom Fig. 8, it can also be obseve that with the incease of the numbe of pimay tuns N p, the coe loss eceases, wheeas the wining loss ises ue to the incease esistance. The case when N p = allows the tansfome to achieve the minimum powe loss. ) Resonant Inucto The acoss the esonant inucto can be obtaine as vl ( t) vab ( t) vc ( t) vc ( t ) (3) Substituting (8) an () into (3) yiels v L ove half a switching cycle [ ], i.e., B t vl() t NLAe, L A Z cos( t), t [, / ] (3) AZ cos( t ), t ( /, / ] NLAe, L, t ( /, / ] whee accos 4 QG( G ) G( QG) (33) Fo the magnetic flux ensity swing of the esonant inucto, it is elate to the peak esonant cuent, which has thee iffeent cases, as illustate in Fig. 9. Then, the flux ensity swing can be obtaine as B L L I L L N A N A L e, L L e, L whee A / Z, A, i ( ), L A, ( / ) L, (34) A Z I, actan[( / Z ) / A ], an IL, ( / Z )sin. The coe loss can be subsequently calculate base on (6). The magnetic coe ER6/6/5 an -laye PCB winings (7-m coppe thickness fo each laye) ae use to implement the plana esonant inucto. The calculate powe losses of plana inuctos with iffeent numbes of tuns N L ae shown in Fig.. It is seen that N L = enables the inucto to achieve the minimum powe loss.

14 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS DC-link(output) Vo (V) A B C D E [ V, 4 V] Fixe DC-link contol Vaiable DC-link contol [7 V, 43 V] Input V in (V) Fig.. Opeation pofile of the PV micoinvete with fixe an vaiable DClink contol schemes. The pofile of the Putput powe P PV is etemine by iffeent PV panels as well as the envionmental conitions (i.e., the sola iaiance an ambient tempeatue). Output PV simulato DC powe supply Switch state MPPT Voltage Reg. I in V in V in Popose DC-DC Convete F R o Moulato PI,ef Vaiable PI c-link V in MPPT algoithm DSP Fig.. Contol iagam of the popose c-c convete with two opeation moes: output (c-link) egulation o MPPT. C. Capacitos The powe losses in capacitos ae geneally compose of ielectic losses an themal losses [67]. The ielectic losses associate with the cycle of chaging an ischaging of ielectics ae calculate as PC C VC f s tan (35) whee tan δ is the ielectic loss facto of the chosen capacito. The themal losses ae eive as P R I (36) Cth e L, ms whee Re is the equivalent seies esistance of the esonant capacito C. V. CONTROL STRATEGY, MODULATION IMPLEMENTATION, AND EXPERIMENTAL VERIFICATIONS A. Contol Stategy Depening on the PV panel popeties an the envionmental conitions (i.e., the sola iaiance an ambient tempeatue), the Putput an powe at the maximum powe points (MPPs) may change significantly. Fig. epicts a typical opeation pofile, i.e., the maximum powe with espect to the input, fo PV micoinvete systems. In this case, the maximum powe P max is 5 W when V in is within [5 V, 38 V], but P max eclines when V in is out of this ange. Six opeating points ae ientifie, as shown in Table III. Maximum powe Pmax (W) Table III IDENTIFIED SIX OPERATING POINTS WITH FIXED AND VARIABLE DC- LINK VOLTAGE CONTROL STRATEGIES Opeating point PV V PV PV powe P PV DC-link une the vaiable DC-link contol DC-link une the fixe DC-link contol A 7 V 7 W 34 V NaN B 5 V 5 W 34 V 4 V C 3 V 5 W 34 V 4 V D 34 V 5 W 34 V 4 V E 38 V 5 W 38 V 4 V F 43 V W 43 V NaN CTR EPWMA EPWMB PHS EPWMA EPWMB S 5 PRD ZRO ZRO Z P Z P Dea ban CTR CTR Z EPWMA EPWMB EPWMA EPWMB Z S &S 4 S &S 4 P Dea ban ZRO CAU PRD CMPA S &S 3 S &S 3 CBD CMPB S 5 S 5 S 6 S 6 PRD Z ZRO P CAU P S &S 4 S &S 4 P Dea ban S 6 S 6 Z PRD CMPA PRD ZRO ZRO Z P Z P Dea ban PHS Z,s CTR CMPA ZRO CAD Z,s CMPB CBU PRD Z P CBD CMPB S &S 3 S &S 3 ZRO CMPA P CAD P S 5 S 5 Z PRD P CMPB CBU PRD Fig. 3. Moulation wavefoms base on TMS3F875 DSP >,s,,s. PRD an PRD epesent the peio egistes of the two epwm moules (epwm an epwm), PHS is the phase egiste of epwm, CMPA an CMPB ae the counte-compae A an B egistes of epwm. CAU inicates the event when the counte CTR equals the active CMPA esiste an CTR is incementing. CAD inicates the event when the counte CTR equals the active CMPA esiste an CTR is ecementing. CBU inicates the event when the counte CTR equals the active CMPB esiste an CTR is incementing. CBD inicates the event when the counte CTR equals the active CMPB esiste an CTR is ecementing. Z an P epesents the events when the counte equals zeo an the peio, espectively.

15 Input Tansfome & esonant tank D-D4 DC-link capacitos S -S 6 Invete stage Length: 4.8 cm Fig. 4. Photo of the PV micoinvete pototype. TABLE IV PARAMETERS OF THE CONVERTER PROTOTYPE Paametes Values Input V inn 7-43 V Nominal input V inn 34 V Most pobable PV (input) -4 V ange Output V Rate powe P N 5 W Tansfome tuns atio n = N s : N p Magnitizing inuctance L m 5 H Resonant inucto L 34 H Resonant capacito C.75 nf Switching fequency f s MHz Pimay-sie switches S -S 4 egan FET, EPC9 R s,on = 3. m Seconay-sie switches S 5-S 6 GaN ehemt, GS6654B R s,on = m Rectifie ioes D -D 4 SiC Schottky Dioe, C3D6E DC-link capacitos C o& C o LGJE8MELB5, 8 F/5 V In the PV micoinvete systems (see Fig. ), the c-link can be egulate eithe by the font-en c-c stage o by the c-ac invete stage. If the MPPT is implemente with the c-c stage, then the c-link will be egulate by the invete stage, an vice vesa. Howeve, it is not necessay to always keep the DC-link constant [9]. In this pape, a vaiable DC-link contol is popose, as shown in Fig.. When the input PV V in is lowe than 34 V, the clink (output) will be always egulate to 34 V; howeve, when V in is highe than 34 V, then the c-link (output) efeence will ise with the incease of V in. Thus, the input ange can be extene fom [ V, 4 V] with the conventional fixe c-link contol to [7 V, 43 V] with the new contol. In the meanwhile, the RMS cuents une the vaiable c-link contol ae also euce which is beneficial to efficiency impovement. As afoementione, the popose c-c convete can be contolle eithe to achieve the MPPT of the PV panel o to egulate the c-link. In oe to emonstate the feasibility of the popose convete in both cases, a flexible contol scheme is applie, as shown in Fig.. If opeation moe is enable, the popose c-c convete will be connecte to a PV simulato an it will be contolle to achieve the MPPT; if opeation moe is selecte, then the popose With: 9.8 cm convete will be powee by a c powe supply an it will be use to egulate the output to the efeence,ef. B. Moulation Implementation Two enhance pulse with moulato (epwm) peipheals of TMS3F875 igital signal pocesso (DSP), i.e., epwm an epwm, ae utilize, an thei output signals ae EPWMA/EPWMB an EPWMA/EPWMB, espectively. EPWMA an EPWMB ae the gate signals of S &S 4 an S &S 3, espectively. EPWMA an EPWMB ae use to contol S 5 an S 6, espectively. Each time-base counte CTR of the epwm moules is unning in the count-up-an-own moe, an the peio egistes of epwm an epwm ae the same. The ea time of EPWMA (S &S 4) an EPWMB (S &S 3) is achieve by using the ea-ban submoule of epwm. Thee is a phase shift PHS between the two countes (CTR an CTR) of epwm an epwm. The phase shift is use to geneate the tun-on elay of S 5 an S 6 with espect to the tunoff events of S &S 4 an S &S 3, as inicate by,s in Fig.. The values of the peio egistes PRD an PRD ae etemine by PRD PRD f / ( f ) (37) whee f cpu is the clock fequency of the micocontolle. Fo the two counte-compae egistes CMPA an CMPB, thei values an actions geneate by the CTR = CMPA/B event ae iffeent in two cases: PRD ( s, ) /, s, Action : EPWMA cleas at CAU CMPA PRD ( s, ) /, s, Action : EPWMA cleas at CAD CMPB s cpu PRD ( s, ) /, Action : EPWMB cleas at CBD PRD (, s )/, Action : EPWMB cleas at CBU (38) The moulation scheme enables the convete contol vaiable, i.e., the phase shift, to be ajuste fom to. C. Expeimental Veifications A 5-W convete pototype with the imension of 4.8 cm 9.8 cm cm has been built up, as shown in Fig. 4. The etaile paametes ae liste in Table IV. The steay-state pefomance at the six opeating points (see Table III) ae shown in Fig. 5. As can be seen, the steay-state wavefoms ae in close ageement with the theoetical analysis in Section II. As state in Section V-A, thee ae two contol options fo the c-c stage in micoinvete applications, i.e., the c-c convete can be use eithe to achieve the MPPT o to egulate the c-link. Fig. 6 pesents the ynamic expeimental wavefoms of the popose convete with the output close-loop contol (i.e., opeation moe is enable in Fig. ). As can be seen, the output can be egulate to the efeence being 34 V afte the loa changes. A goo ynamic pefomance is achieve: the tansition time is less than ms an the oveshoot an uneshoot ae quite small, i.e., less than 5 V. s, s,

16 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS (5 V/iv) (5 V/iv) (5 V/iv) (5 V/iv) i p / ( A/iv) ( A/iv) i p / ( A/iv) ( A/iv) i Lm / ( A/iv) v C (5 V/iv) Time (4 ns/iv) i Lm / ( A/iv) v C (5 V/iv) Time (4 ns/iv) (5 V/iv) (5 V/iv) (5 V/iv) (5 V/iv) i p / ( A/iv) ( A/iv) ( A/iv) i p / ( A/iv) i Lm / ( A/iv) v C (5 V/iv) Time (4 ns/iv) i Lm / ( A/iv) -v C (5 V/iv) Time (4 ns/iv) (c) () (5 V/iv) (5 V/iv) (5 V/iv) (5 V/iv) ( A/iv) i p / ( A/iv) i p / ( A/iv) i Lm / ( A/iv) i Lm / ( A/iv) v C (5 V/iv) Time (4 ns/iv) v C (5 V/iv) Time (4 ns/iv) (e) Fig. 5. Steay-state pefomance of the popose convete une iffeent conitions (see Fig. an Table III): opeating point A: V in = 7 V, = 34 V, P o = 7 W; opeating point B: V in = 5 V, = 34 V, P o = 5 W; (c) opeating point C: V in = 3 V, = 34 V, P o = 5 W; () opeating point D: V in = 34 V, = 34 V, P o = 5 W; (e) opeating point E: V in = 38 V, = 38 V, P o = 5 W; (f) opeating point F: V in = 43 V, = 43 V, P o = W. (f) Then, the MPPT contol moe (i.e., opeation moe in Fig. ) is selecte fo the popose c-c convete, an the expeimental ynamic pefomance is teste, as shown in Fig. 7. It is seen that the popose convete with the MPPT contol enables the PV simulato to tack its maximum powe points une iffeent conitions. The soft-switching pefomance of the popose convete is teste at iffeent opeating points, as shown in Fig. 8. Due to the symmety of the topology an the moulation scheme, only the wavefoms of S 4 an S 6 ae given. As can be seen, the ainsouce has fallen to zeo befoe the coesponing gatesouce ises to its theshol. That is, the

17 P = 5 W P = 5 W P = 5 W (5 V/iv) V s4 V gs4 ( V/iv) ( V/iv) I o (.5 A/iv) V gs6 (5 V/iv) (5 V/iv) V s6 ( V/iv) Time (4 ns/iv) ( A/iv) Time ( ms/iv) V s4 V gs4 ( V/iv) ( V/iv) V s6 V gs6 ( V/iv) (5 V/iv) Time (4 ns/iv) Time (4 ns/iv) Time (4 ns/iv) (5 V/iv) (5 V/iv) I o (.5 A/iv) (5 V/iv) I o (.5 A/iv) (5 V/iv) V s4 V gs4 ( V/iv) ( V/iv) ( A/iv) Time (4 ns/iv) ( A/iv) Time (4 ns/iv) V s6 V gs6 ( V/iv) (5 V/iv) Time (4 ns/iv) (c) Fig. 6. Tansient pefomance of the popose convete with the output close-loop contol (the input V in = 3 V an the output efeence _ef = 34 V): tansition between P = 5 W an P = 5 W, zoome-in wavefoms at P = 5 W, (c) zoome-in wavefoms at P = 5 W. V s4 V gs4 ( V/iv) ( V/iv) Time (4 ns/iv) (c) Time (4 ns/iv) P PV ( W/iv) V s6 V gs6 ( V/iv) (5 V/iv) Time (4 ns/iv) V PV ( V/iv) I PV (A/iv) Powe off P PVmax = 5 W P PVmax = 5 W Time ( s/iv) t (s) Fig. 7. Measue PV MPPT wavefoms of the popose convete powee by a PV simulato. At t = s, the PV simulato is connecte with the convete pototype, an the PV simulato opeates at its maximum powe point being 5 W afte a shot tansition; at t = 5 s, the maximum powe of the PV simulato steps to 5 W, an the MPPT contolle convete allows the PV simulato to tack its maximum powe point at 5 W. antipaallel ioe conucts befoe the gate signal is applie. Thus, the -on is achieve, leaing to a negligible tun-on loss fo the switches. The measue efficiency cuves of the popose convete with the vaiable c-link contol (see Fig. ) at iffeent input s ae shown in Fig. 9. As can be seen, Time (4 ns/iv) Time (4 ns/iv) () Fig. 8. Soft-switching wavefoms of the popose convete at iffeent opeating points: opeating point A: V in = 7 V, = 34 V, P o = 7 W; opeating point B: V in = 5 V, = 34 V, P o = 5 W; (c) opeating point E: V in = 38 V, = 38 V, P o = 5 W; () opeating point F: V in = 43 V, = 43 V, P o = W. peak efficiencies ove 95% ae achieve fo a wie input ange, i.e., V in = 5 V, 3 V, 34 V, 38 V an 43 V. The measue full-loa (5-W) efficiency inceases with espect to the input. This is ue to the fact that the RMS cuents an conuction losses euce as the input ises. When the popose convete is contolle to have a constant c-link (output) 4 V, the efficiency is measue at iffeent input s V in = 5 V, 34 V an 38 V, as shown in Fig. 9. It can be seen that the vaiable c-link contol enables a significant efficiency impovement fo the popose convete. Moeove, the popose vaiable c-link contol allows

18 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS Efficiency (%) Efficiency (%) Vin = 7 V Vin = 5 V 84 Vin = 3 V Vin = 34 V 83 Vin = 38 V Vin = 43 V PV powe (W) Vin = 5 V, Vo = 34 V Vin = 5 V, Vo = 4 V Vin = 34 V, Vo = 34 V Vin = 34 V, Vo = 4 V Vin = 38 V, Vo = 38 V Vin = 38 V, Vo = 4 V PV powe (W) Fig. 9. Measue efficiency of the convete pototype: efficiency cuves at iffeent input s with the vaiable c-link contol; efficiency compaison between the vaiable an fixe c-link contol schemes; soli lines epesent the efficiencies with the vaiable c-link contol an ashe lines ae the esults with the fixe c-link contol. the convete to cope with a moe wie input ange V in [7 V, 43 V] than the conventional fixe c-link contol (V in [ V, 4 V]). The powe losses of the main components ae calculate at iffeent input s an contol schemes, as shown in Fig. 3. Oveall, the powe semiconuctos evices (S -S 4, S 5-S 6, D - D 4) an magnetic components (tansfome T x an esonant inucto L ) epesent the majo powe loss souces. The powe losses of S -S 4, S 5-S 6, D -D 4 an L ecline with espect to the incease of V in, wheeas the powe loss of T x ises ue to the incease coe loss at a highe input V in. Meanwhile, it is seen fom Fig. 3 that the powe losses of D -D 4 become highe with the vaiable c-link contol; it is because D -D 4 suffe fom a highe ectifie cuent in compaison with the fixe c-link ( = 4 V) contol. Nevetheless, the new contol scheme enables to euce the powe losses of othe main components S -S 4, S 5-S 6, T x, an L. Theefoe, highe powe convesion efficiencies can be achieve fo the popose convete. VI. CONCLUSION In this pape, a new ual-moe ectifie base seies esonant c-c convete is popose fo PV micoinvete applications. The moulation, opeation pinciples, an key chaacteistics ae analyze. A etaile powe loss moeling an esign optimization of main components ae pefome, an a vaiable c-link contol scheme is intouce to the popose (c) Fig. 3. Powe loss beakown of the popose convete with iffeent input s an contol schemes. V in = 5 V, P = 5 W. V in = 34 V, P = 5 W. (c) V in = 38 V, P = 5 W. convete. A -MHz 5-W convete pototype is teste an the expeimental esults have veifie the theoetical analysis. The popose convete with the vaiable c-link contol can cope with a wie input ange, e.g., fom 7 V to 43 V. The active switches an ioes can achieve -on an ZCS-off, espectively. Compae with the conventional constant c-link contol, the popose vaiable c-link contol enables a emakable efficiency impovement. High powe convesion efficiencies (peak efficiency = 95.5 %) can thus be achieve ove the wie input ange fom 7 V to 43 V, as teste on the 5-W pototype. Theefoe, the popose topology is a pomising convete caniate fo PV micoinvete systems.

19 ACKNOWLEDGMENT The authos woul like to thank Hitachi Metals, Lt. fo poviing magnetic coes to the pototype. APPENDIX The seconay an pimay tansfome RMS cuents ae expesse as I I L, ms p, ms 3 A A ( sin cos ) ( sin cos ) Vo 6 ( ) 3 ( ) 4( ) 4 3 mgz ma G A Gm ( sin cos ) ( ) cos 4 sin Z / Vo A ( ) cos sin ( AGm cos Z / V 4) ( ) o (39) whee. The esonant cuent in (8) an () can be expane into its Fouie seies: whee i ( t ) a sin( n t ) b cos( n t ) (4) L n s n s n,3,... a A[( )cos sin( )cos( )] A( sin cos ) b A[ sin [cos( ) cos( )] / sin ] A sin (4) ( n )sin[ ( n ) ] ( n )sin[ ( n ) ] an A A [ n sin cos( n ) cos sin( n )], n 3,5,... ( n ) [ nsin( )cos( n ) cos( )sin( n )] ( n )cos[ ( n ) ] ( n )cos[ ( n ) ] bn A A[ n sin sin( n ) cos cos( n ) ], n 3,5,... ( n ) [ n sin( )sin( n ) cos( )cos( n )] Then, the RMS value of the n th hamonic of the esonant cuent can be obtaine as n bn a I (4) L, ms, n REFERENCES [] H. Olenkamp, an I. e Jong, The etun of the ac-moule invete, in Poc. 4th Eu. Conf. Photovolt. Sola Enegy, Hambug, 9, pp [] S. B. Kjae, J. K. Peesen, an F. Blaabjeg, A eview of single phase gi-connecte invetes fo photovoltaic moules, IEEE Tans. In. Appl., vol. 4, no. 5, pp. 9 36, Oct. 5. [3] D. Leuenbege an J. Biela, PV-Moule Integate AC Invetes (AC Moules) with Subpanel MPP-Tacking, IEEE Tans. Powe Electon., vol. 3, no. 8, pp , 7. [4] Y. Shi, L. Wang, R. Xie, Y. Shi, an H. Li, A 6-kW 3-kW/kg five-level T-type SiC PV invete with 99.% peak efficiency, IEEE Tans. In. Electon., vol. 64, no., pp , Nov. 7. [5] B. Gu, Powe convete an contol esign fo high-efficiency electolyte-fee micoinvetes, Ph.D. issetation, Blacksbug, VA, Nov. 3. [6] D. Dong, M. S. Agamy, M. Hafman-Tooovic, X. Liu, L. Gaces, R. Zhou, an P. Cioffi, A PV Resiential Micoinvete With Gi-Suppot Function: Design, Implementation, an Fiel Testing, IEEE Tans. In. Appl., vol. 54, no., pp , Jan./Feb. 8. [7] J. Flicke, G. Tamizhmani, M. K. Moothy, R. Thiagaajan, an R. Ayyana, Acceleate testing of moule-level powe electonics fo long-tem eliability, IEEE J. Photovolt., vol. 7, no., pp , Jan. 7. [8] P. Hacke, S. Lokanath, P. Williams, A. Vasan, P. Socho, G. TamizhMani, H. Shinohaa, an S. Kutz, A status eview of photovoltaic powe convesion equipment eliability, safety, an quality assuance potocols, Renewable an Sustainable Enegy Reviews, pp. 97-, Feb. 8. [9] Y. Shen, A. Chub, H. Wang, D. Vinnikov, E. Liivik, an F. Blaabjeg, Wea-out Failue Analysis of an Impeance-Souce PV Micoinvete Base on System-Level Electo-Themal Moeling, IEEE Tans. In. Electon., to be publishe, 8. oi:.9/tie [] N. Kummai, S. Chakaboty, an S. Chattopahyay, An Isolate High- Fequency Link Micoinvete Opeate with Seconay-Sie Moulation fo Efficiency Impovement, IEEE Tans. Powe Electon., vol. 33, no. 3, pp. 87-, Ma. 8. [] M. Gao, M. Chen, C. Zhang, an Z. Qian, Analysis an implementation of an impove flyback invete fo photovoltaic AC moule applications, IEEE Tans. Powe Electon., vol. 9, no. 7, pp , Jul. 4. [] Z. Zhang, J. Zhang, S. Shao, an J. Zhang, A High Efficiency Single- Phase T-type BCM Micoinvete, IEEE Tans. Powe Electon., to be publishe, 8. oi:.9/tpel [3] Q. Li an P. Wolfs, A eview of the single-phase photovoltaic moule integate convete topologies with thee iffeent c link configuations, IEEE Tans. Powe Electon., vol. 3, no. 3, pp , May 8. [4] H. C. Chiang, F. J. Lin an J. K. Chang, Novel Contol Metho fo Multimoule PV Micoinvete With Multiple Functions, IEEE Tans. Powe Electon., vol. 33, no. 7, pp , July 8. [5] S. M. Tayebi an I. Bataseh, Mitigation of Cuent Distotion in a Thee- Phase Micoinvete With Phase Skipping Using a Synchonous Sampling DC-Link Voltage Contol, IEEE Tans. In. Electon., vol. 65, no. 5, pp , May 8. [6] L. Chen, C. Hu, Q. Zhang, K. Zhang, an I. Bataseh, Moeling an Tiple-Loop Contol of Gi-Connecte DC/AC Convetes fo Thee-Phase Balance Micoinvete Application, IEEE Tans. Powe Electon., vol. 3, no. 4, pp. -3, Apil 5. [7] T. LaBella, W. Yu, J.-S. Lai, M. Senesky, an D. Aneson, A biiectional-switch-base wie-input ange high-efficiency isolate esonant convete fo photovoltaic applications, IEEE Tans. Powe Electon., vol. 9, no. 7, pp , Jul. 4. [8] Z. Ouyang an M. Anesen, Oveview of plana magnetic technology Funamental popeties, IEEE Tans. Powe Electon., vol. 9, no. 9, pp , Sep. 4. [9] Nichicon, Aluminum Electolytic Capacitos, available online [8], [] M. A. Rezaei, K. J. Lee an A. Q. Huang, A High-Efficiency Flyback Mico-invete With a New Aaptive Snubbe fo Photovoltaic Applications, IEEE Tans. Powe Electon, vol. 3, no., pp , Jan. 6. [] T. Loh, N. Pagallapati, an V. Agawal, Novel Contol Scheme fo Inteleave Flyback Convete Base Sola PV Micoinvete to Achieve

20 SHEN et al: -MHZ SERIES RESONANT DC-DC CONVERTER WITH DUAL-MODE RECTIFIER FOR PV MICROINVERTERS High Efficiency, IEEE Tans. In. Appl.,.to be publishe, 8. oi:.9/tia [] W. Yu, B. Yok, an J.-S. Lai, Inuctoless fowa-flyback softswitching convete with ual constant ON-time moulation fo photovoltaic applications, in Poc. IEEE Enegy Conves. Cong. Expo. (ECCE), Sep., pp [3] H. Wu, L. Chen, an Y. Xing, Seconay-sie phase-shift contolle ual-tansfome-base asymmetical ual-bige convete with wie gain, IEEE Tans. Powe Electon., vol. 3, no., pp , Oct. 5. [4] Z. Guo, D. Sha, X. Liao, an J. Luo, Input-seies-output-paallel phaseshift full-bige eive DC DC convetes with auxiliay LC netwoks to achieve wie zeo- switching ange, IEEE Tans. Powe Electon., vol. 9, no., pp , Oct. 4. [5] U. Kunu, K. Yenui an P. Sensama, Accuate Analysis fo Magnetic Design an Efficiency Impovement of Full-Bige LLC Resonant Convete, IEEE Tans. Powe Electon., vol. 3, no. 3, pp , Ma. 7. [6] G. Yang, P. Dubus, an D. Saanac, Double-phase high-efficiency, wie loa ange high- /low- LLC DC/DC convete fo electic/hybi vehicles, IEEE Tans. Powe Electon., vol. 3, no. 4, pp , Ap. 5. [7] C. Shi, H. Wang, S. Dusmez, an A. Khaligh, A SiC-base, high efficiency, isolate onboa PEV chage with ulta-wie DC link ange, IEEE Tans. In. Appl., vol. 53, no., pp. 5 5, Jan./Feb. 7. [8] S. Abel-Rahman, Resonant LLC Convete: Opeation an Design, Infineon Technologies Noth Ameica, available online [], Design_example_esonant_LLC_convete_opeation_an_esign-ANv_-EN.pf?fileI=b3a3433a47ba3a4a6e3be64a [9] X. Mao, Q. Huang, Q. Ke, Y. Xiao, Z. Zhang, an A. E. Anesen, Giconnecte Photovoltaic Mico-invete with New Hybi Contol LLC Resonant Convete, in Poc. 4n Annual Confeence of the IEEE Inustial Electonics Society, pp , 6. [3] M. M. Jovanovic, an B. T. Iving, On-the-Fly Topology-Mophing Contol Efficiency Optimization Metho fo LLC Resonant Convetes Opeating in Wie Input- an/o Output-Voltage Range, IEEE Tans. Powe Electon., vol. 3, no. 3, pp , Ma. 6. [3] M. Chen, K. K. Afii, S. Chakaboty, an D. J. Peeault, Multitack powe convesion achitectue, IEEE Tans. Powe Electon., vol. 3, no., pp , Jan. 7. [3] W. Inam, K. Afii, an D. Peeault, Vaiable Fequency Multiplie Technique fo High-Efficiency Convesion Ove a Wie Opeating Range, IEEE J. Emeg. Sel. Top. Powe Electon., vol. 4, no., pp , Jun. 6. [33] X. Sun, X. Li, Y. Shen, B. Wang, an X. Guo, A ual-bige LLC esonant convete with fixe-fequency PWM contol fo wie input applications, IEEE Tans. Powe Electon., vol. 3, no., pp. 69 8, Jan. 7. [34] Y. Jeong, J. K. Kim, J. B. Lee an G. W. Moon, An Asymmetic Half- Bige Resonant Convete Having a Reuce Conuction Loss fo DC/DC Powe Applications With a Wie Range of Low Input Voltage, IEEE Tans. Powe Electon., vol. 3, no., pp , Oct. 7. [35] X. Sun, Y. Shen, Y. Zhu, an X. Guo, Inteleave boost-integate LLC esonant convete with fixe-fequency PWM contol fo enewable enegy geneation applications, IEEE Tans. Powe Electon., vol. 3, no. 8, pp , Aug. 5. [36] H. Wu, T. Mu, X. Gao, an Y. Xing, A seconay-sie phase-shift contolle LLC esonant convete with euce conuction loss at nomal opeation fo hol-up time compensation application, IEEE Tans. Powe Electon., vol. 3, no., pp , Oct. 5. [37] X. Zhao, L. Zhang, R. Bon, an J.-S. Lai, A High-Efficiency Hybi Resonant Convete With Wie-Input Regulation fo Photovoltaic Applications, IEEE Tans. In. Electon., vol. 64, no. 5, pp , May 7. [38] M. Shang, H. Wang, an Q. Cao, Reconfiguable LLC Topology With Squeeze Fequency Span fo High-Voltage Bus-Base Photovoltaic Systems, IEEE Tans. Powe Electon., vol. 33, no. 5, pp , May 8. [39] H. Hu, X. Fang, J. Shen, F. Chen, Z. J. Shen, an I. Bataseh, A Moifie High-Efficiency LLC Convete With Two Tansfomes fo Wie Input-Voltage Range Applications, IEEE Tans. Powe Electon., vol. 8, no. 4, pp , Ap. 3. [4] M. K. Ranjam, I. Moon, an D. J. Peeault, Vaiable-Invete-Rectifie- Tansfome: A Hybi Electonic an Magnetic Stuctue Enabling Ajustable High Step-Down Convesion Ratios, IEEE Tans. Powe Electon., vol. 33, no. 8, pp , Aug. 8. [4] W. Sun, Y. Xing, H. Wu, an J. Ding, Moifie High-efficiency LLC Convetes with Two Split Resonant Banches fo Wie Input-Voltage Range Applications, IEEE Tans. Powe Electon., to be publishe, 8. oi:.9/tpel [4] X. Wu, H. Chen, an Z. Qian, -MHz LLC Resonant DC Tansfome (DCX) With Regulating Capability, IEEE Tans. In. Electon., vol. 63, no. 5, pp. 94-9, May 6. [43] D. Huang, S. Ji, an F. C. Lee, LLC Resonant Convete With Matix Tansfome, IEEE Tans. Powe Electon., vol. 9, no. 8, pp , Aug. 4. [44] W. Zhang, F. Wang, D. J. Costinett, L. M. Tolbet an B. J. Blalock, Investigation of Gallium Nitie Devices in High-Fequency LLC Resonant Convetes, IEEE Tans. Powe Electon., vol. 3, no., pp , Jan. 7. [45] H. P. Pak an J. H. Jung, Powe Stage an Feeback Loop Design fo LLC Resonant Convete in High-Switching-Fequency Opeation, IEEE Tans. Powe Electon., vol. 3, no., pp , Oct. 7. [46] C. Fei, F. C. Lee an Q. Li, High-Efficiency High-Powe-Density LLC Convete With an Integate Plana Matix Tansfome fo High-Output Cuent Applications, IEEE Tans. In. Electon., vol. 64, no., pp , Nov. 7. [47] M. H. Ahme, C. Fei, F. C. Lee an Q. Li, 48-V Voltage Regulato Moule With PCB Wining Matix Tansfome fo Futue Data Centes, IEEE Tans. In. Electon., vol. 64, no., pp , Dec. 7. [48] Y. Guan, Y. Wang, W. Wang an D. Xu, A High-Fequency CLCL Convete Base on Leakage Inuctance an Vaiable With Wining Plana Magnetics, IEEE Tans. In. Electon., vol. 65, no., pp. 8-9, Jan. 8. [49] Y. Shen, H. Wang, Z. Shen, Y. Yang, an F. Blaabjeg, Seies Resonant DC-DC Convete with Dual-Moe Rectifie fo PV Micoinvetes, in Poc. Int. Powe Electon. Conf. (IPEC), May 8, pp [5] S. Tian, F. C. Lee an Q. Li, A Simplifie Equivalent Cicuit Moel of Seies Resonant Convete, IEEE Tans. Powe Electon., vol. 3, no. 5, pp , May 6. [5] J. Evets, F. Kisme, J. V. en Keybus, J. Diesen, an J. W. Kola, Optimal moulation of single-phase single-stage biiectional DAB ac-c convetes, IEEE Tans. Powe Electon., vol. 9, no. 8, pp , Aug. 4. [5] C. Maxgut, F. Kisme, D. Botis, an J. W. Kola, Ultaflat inteleave tiangula cuent moe (TCM) single-phase PFC ectifie, IEEE Tans. Powe Electon., vol. 9, no., pp , Feb. 4. [53] H. Wang, Y. Yang, an F. Blaabjeg, Reliability-oiente esign an analysis of input capacitos in single-phase tansfome-less photovoltaic invetes, in Poc. of APEC 3, pp , Ma. 3. [54] Pouct Selecto Guie fo egan FETs an ICs, Efficient Powe Convesion (EPC), 8. [Online]. Available: [55] EPC5: 35 V, 6 A Enhancement-Moe GaN Powe Tansisto, Efficient Powe Convesion (EPC), 8. [Online]. Available: [56] CoolGaN 4V an 6V e-moe GaN HEMTs, Infineon, 8. [Online]. Available: [57] GaN Tansistos 65 V E-HEMT, GaN Systems, 8. [Online]. Available: [58] E. Babaini, Revese Technology an Cost Repot. [Online]. Available: [59] S. Song, S. Munk-Nielsen, C. Uhenfelt, an I. Tintis, Pefomance assessment of commecial gallium nitie-on-silicon iscete powe evices with figue of meit, in IECON 6-4n Annual Confeence of the IEEE Inustial Electonics Society, Oct. 6, pp [6] E. Babaini, Si, SiC o GaN: technology an cost compaison. [Online]. Available: lectonics/_elena%babaini_systemplusconsulting.pf

21 [6] M. Kaspe, R. M. Bukat, G. Deboy an J. W. Kola, of Powe MOSFETs Revisite, IEEE Tans. Powe Electon., vol. 3, no., pp , Dec. 6. [6] K. Venkatachalam, C. R. Sullivan, T. Aballah, an H. Tacca, Accuate peiction of feite coes loss with nonsinusoial wavefoms using only Steinmetz paametes, in Poc. IEEE Wokshop Comput. Powe Electon.,, pp [63] X. Nan an C. R. Sullivan, An impove calculation of poximity-effect loss in high-fequency winings of oun conuctos, in Poc. IEEE Powe Electon. Spec. Conf., 3, pp [64] J. Feeia, Impove analytical moeling of conuctive losses in magnetic components, IEEE Tans. Powe Electon., vol. 9, no., pp. 7 3, Jan [65] Z. Ouyang, O. C. Thomsen, an M. A. E. Anesen, Optimal esign an taeoff analysis of plana tansfome in high-powe DC-DC convetes, IEEE Tans. In. Electon., vol. 59, no. 7, pp. 8 8, Jul.. [66] M. A. Saket, N. Shafiei, an M. Oonez, LLC convetes with plana tansfomes: Issues an mitigation, IEEE Tans. Powe Electon., vol. 3, no. 6, pp , Jun. 7. [67] T. B. Soeio, J. Muhlethale, J. Linne, P. Ransta, an J. W. Kola, Automate esign of a high-powe high-fequency LCC esonant convete fo electostatic pecipitatos, IEEE Tans. In. Electon., vol. 6, no., pp , Nov. 3. Yanfeng Shen (S 6) eceive the B.S. an M.S. egees in electical engineeing an powe electonics fom Yanshan Univesity, Qinhuangao, China, in an 5, espectively. He is cuently woking towa the Ph.D. egee in powe electonics at the Cente of Reliable Powe Electonics (CORPE), Aalbog Univesity, Aalbog, Denmak. He woke as an Inten at ABB Copoate Reseach Cente, Beijing, China, fom Aug. to Oct., 5. His eseach inteests inclue the eliability of powe electonics, c-c convetes an PV invetes. Zhan Shen (S 6) eceive the B.E. egee in electical engineeing an automation fom Nanjing Univesity of Aeonautics an Astonautics in 3, an M.E. egee in electical engineeing fom Southeast Univesity in 6, both in Nanjing, China. He is a Ph.D. stuent at the Cente of Reliable Powe Electonics(CORPE), Aalbog Univesity, Aalbog, Denmak. He was a eseach assistant an pusue his maste thesis at the RWTH Aachen Univesity, Aachen, Gemany, fom 4 to 6, an a Visiting Scientist with the Massachusetts Institute of Technology (MIT), Cambige, MA, USA, in 8. He was with the ABB Copoate Reseach Cente, Beijing, China, in 6. His eseach inteests inclue the electomagnetic-themal-eliability moeling an esign of magnetic components in powe electonic convetes. Yongheng Yang (S M 5 SM 7) eceive the B.Eng. egee in electical engineeing an automation fom Nothwesten Polytechnical Univesity, Shaanxi, China, in 9 an the Ph.D. egee in electical engineeing fom Aalbog Univesity, Aalbog, Denmak, in 4. He was a postgauate stuent at Southeast Univesity, China, fom 9 to. In 3, he spent thee months as a Visiting Schola at Texas A&M Univesity, USA. D. Yang is cuently an Associate Pofesso with the Depatment of Enegy Technology, Aalbog Univesity. He has been focusing on the gi integation of enewable enegies, in paticula, photovoltaics, powe electonic convete esign, analysis an contol, an eliability in powe electonics. D. Yang seve as a Guest Associate Eito of the IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS. He is an Associate Eito of the CPSS an Applications an the Electonics Lettes. D. Yang eceive the 8 IET Renewable Powe Geneation Pemium Awa. Huai Wang (M SM 7) Huai Wang (M', SM 7) eceive the B.E. egee in electical engineeing, fom Huazhong Univesity of Science an Technology, Wuhan, China, in 7 an the Ph.D. egee in powe electonics, fom the City Univesity of Hong Kong, Hong Kong, in. He is cuently an Associate Pofesso at the Cente of Reliable Powe Electonics (CORPE), Aalbog Univesity, Aalbog, Denmak. He was a Visiting Scientist with the ETH Zuich, Switzelan, fom Aug. to Sep. 4, an with the Massachusetts Institute of Technology (MIT), USA, fom Sep. to Nov. 3. He was with the ABB Copoate Reseach Cente, Switzelan, in 9. His eseach aesses the funamental challenges in moelling an valiation of powe electonic component failue mechanisms, an application issues in system-level peictability, conition monitoing, cicuit achitectue, an obustness esign. D. Wang eceive the Richa M. Bass Outstaning Young Powe Electonics Enginee Awa fom the IEEE Powe Electonics Society in 6, an the Geen Talents Awa fom the Geman Feeal Ministy of Eucation an Reseach in 4. He is cuently the Awa Chai of the Technical Committee of the High Pefomance an Emeging Technologies, IEEE Powe Electonics Society, an the Chai of IEEE PELS/IAS/IE Chapte in Denmak. He seves as an Associate Eito of IET POWER ELECTRONICS, IET ELECTRONICS LETTERS, IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS, an IEEE TRANSACTIONS ON POWER ELECTRONICS. Fee Blaabjeg (S 86 M 88 SM 97 F 3) was with ABB-Scania, Ranes, Denmak, fom 987 to 988. Fom 988 to 99, he got the PhD egee in Electical Engineeing at Aalbog Univesity in 995. He became an Assistant Pofesso in 99, an Associate Pofesso in 996, an a Full Pofesso of powe electonics an ives in 998. Fom 7 he became a Villum Investigato. He is honois causa at Univesity Politehnica Timisoaa (UPT), Romania an Tallinn Technical Univesity (TTU) in Estonia. His cuent eseach inteests inclue powe electonics an its applications such as in win tubines, PV systems, eliability, hamonics an ajustable spee ives. He has publishe moe than 6 jounal papes in the fiels of powe electonics an its applications. He is the co-autho of fou monogaphs an eito of ten books in powe electonics an its applications. He has eceive 8 IEEE Pize Pape Awas, the IEEE PELS Distinguishe Sevice Awa in 9, the EPE-PEMC Council Awa in, the IEEE William E. Newell Powe Electonics Awa 4 an the Villum Kann Rasmussen Reseach Awa 4. He was the Eito-in-Chief of the IEEE TRANSACTIONS ON POWER ELECTRONICS fom 6 to. He has been Distinguishe Lectue fo the IEEE Powe Electonics Society fom 5 to 7 an fo the IEEE Inusty Applications Society fom to as well as 7 to 8. In 8 he is Pesient Elect of IEEE Powe Electonics Society. He was nominate in 4, 5, 6 an 7 by Thomson Reutes to be between the most 5 cite eseaches in Engineeing in the wol.