Consan Duy Cycle Sinusoidal Oupu Inverer wih Sine Ampliude Modulaed High Frequency Link Gusavo C. Knabben, Dominik Neumayr and Johann W. Kolar Power Elecronic Sysems Laboraory ETH Zurich, Swizerland {knabben,neumayr,kolar}@lem.ee.ehz.ch Absrac Despie he increasing performance of power semiconducors and passives componens, limied iming resoluion in off-he-shelf available digial conrol hardware ofen prevens he swiching frequency in kw-scale dc/ac power conversion o be increased above several MHz for he sake of exreme power densiies. In his paper an alernaive approach o generae a sinusoidal oupu volage, based on consan duy cycle frequency shif conrol of a high frequency resonan inverer sage and a subsequen synchronous cycloconverer, is analyzed. The design of he presened converer is faciliaed by means of a derived mahemaical model. A novel closed-loop conrol sysem is proposed which achieves igh regulaion of he oupu volage by means of conrolling he swiching frequencies of he involved bridge legs operaed in resonan mode. Characerisic waveforms of he dc/ac converer during seady-sae and load ransiens are presened. Two disinc implemenaions of he resonan inverer sage, consiuing an inermediae volage or inermediae curren link, are analysed and compared. Index Terms Dc/Ac Inverer, Sof-Swiching, Resonan Converer, Cycloconverer, Frequency Shif, Phase Shif. I. INTRODUCTION Exremely compac power conversion sysems are a key echnology in he auomoive and elecom indusry and he design of compac power elecronics has recenly been promoed by Google and IEEE in he Lile Box Challenge, an open compeiion o build he world s smalles kw PV inverer. As can be seen from he echnical documenaion of he LBC finaliss [], [], he majoriy of approaches relied on a singlesage full-bridge based PWM inverer opology wih imevarying duy cycle for sinusoidal oupu volage generaion. A consan or variable swiching frequency in he range of. MHz MHz was seleced by he finaliss, where several eams employed sophisicaed riangular curren mode (TCM) conrol o enable sof-swiching and push he frequency up o he MHz. Apar from he residual swiching loss, despie employing laes GaN semiconducor echnology and zero volage swiching (ZVS) [3], and he limied performance of magneics a high frequency (HF), oday s exising offhe-shelf digial conrol hardware (microconrollers, FPGAs, PWM conroller ICs) prevens he swiching frequency o be increased above MHz 3 MHz due o unaccepably low ω ω HF v /i inverer v V HF 3 /i 3 v r /i r dc inverer v /i (c) f (d) ω v f /i f ω ω HF v /i inverer HF /i 3 Cycloconverer v r /i r inverer v /i ω V dc f /i 3 v /i v /i φ() v /i /i 3 v /i Fig. : Generic concep of a volage- or curren-based sine ampliude modulaion (SAM) high frequency (HF) link dc/ac converer wih diode recificaion, low-pass filer and unfolding sage. The diode recifier and LF unfolding sages can also be replaced wih a cycloconverer. The HF inverer sages are conrolled by means of eiher (c) sine-wave frequency shif (ω, FS = ω s±ω o) or (d) phase shif (ω, PS = ω s ± φ()), generaing an inermediae HF volage or curren link (depending on he seleced inverer implemenaion) wih sinusoidally varying ampliude (SAM). duy cycle resoluion. Now, keeping he expeced performance improvemen of WBG semiconducors and magneic core maerials [4] in mind, a dc/ac conversion opology which suppors swiching frequencies up o en MHz, while achieving boh a low THD and igh regulaion of he ac volage wih reasonable digial conrol effor, is needed. Two alernaive conceps o generae a low frequency (LF) sinusoidal volage from a dc source are schemaically shown in Fig.. Two resonan inverer sages, HF inverer and, are conrolled such ha he respecive sinusoidal oupu volages, v and v, exhibi eiher (i) a sligh difference in ac ac
frequency or (ii) a ime-varying phase-shif. The volage difference of v and v consiues he volage of a HF volage link which exhibis a sine ampliude modulaion (SAM), i. e. he envelope of changes over ime and resembles a recified sinusoid wih he desired oupu frequency. As shown in Fig. he SAM volage link is recified and he HF conen removed by a subsequen low-pass filer. The sinusoidal oupu volage is hen obained by means of a ac /ac unfolding sage. This hree-sage approach has been proposed in [5] [7]. The diode recifier and LF unfolder can also be replaced wih a cycloconverer as depiced in Fig.. This wo-sage approach wih resonan link has been sudied by he auhors in [8] []. I should be noed ha, depending on he seleced opology o implemen he HF inverer sages, he generaed HF link can also feaure impressed currens (i,i,i 3 ) raher han volages (v,v, ). A similar dc/ac conversion approach including a HF curren link wih fixed ampliude and a halfwave cycloconverer is described in []. By means of phaseconrol of he cycloconverer wih respec o he resonan curren a very efficien power delivery o he mains is achieved. The modulaion concep of operaing he HF resonan inverers wih consan 5 % duy cycle bu slighly differen frequency, ermed sine-wave frequency shif (FS) in lieraure [9], is depiced in Fig. (c) showing wo sine waves v and v of same ampliude ˆV bu differen angular frequencies, v = ˆV sin (ω ) = ˆV sin (ω s + ω o ), v = ˆV sin (ω ) = ˆV sin (ω s ω o ). The difference beween v and v hen forms he SAM HF volage link, () = v v = ˆV sin (ω o ) cos (ω s ), () wih cener frequency ω s = πf s and wih ω o = πf o sinusoidally varying ampliude, where f o is he desired frequency of he ac oupu. Alhough he duy cycle can be kep consan in case of FS, here is sill a high requiremen on he available resoluion of he modulaor. Given he raio of swiching frequency and clock frequency of he implemened modulaor (microconroller or FPGA), N = f clk f s, (3) he smalles difference in frequency which can be se is f s = f clk N(N + ). (4) For a clock frequency of 5 MHz and f s =.5 Hz Eq. (4) can be solved o find N = 73. Thus, a frequency resoluion of.5 Hz can only be achieved if he swiching frequency of he HF inverer sage is kep below roughly 8.7 khz. However, his apparen limiaion o use FS modulaion for above MHz operaion can be resolved if dedicaed clock generaion or direc digial synhesis (DDS) ICs are employed in addiion o sandard microconroller or FPGA hardware. By means of such frequency and/or phase shif programmable ICs, conrol signals up o hundreds of MHz wih frequency resoluion beer han. Hz can be generaed [], [3]. Anoher opion o generae a volage link wih sinusoidally varying envelope is o operae boh HF inverers wih idenical frequency bu apply a ime-varying phase shif (PS), φ(), beween he respecive conrol signals such ha, v = ˆV sin (ω s + φ()), v = ˆV sin (ω s φ()), =v v = ˆV sin (φ()) cos (ω s ), as analyzed horoughly in [8]. Compared o FS, sine-wave PS is a more generic mehod which allows o generae envelopes of arbirary shape and frequency and is he preferred echnique by he auhors in [6], [7], [4] []. Neverheless, since PS modulaion a very high frequency also requires dedicaed ICs for conrol signal generaion and because he phase shif beween he conrol signals mus be coninuously updaed over ime, sine-wave FS is he preferred choice in his work. In his paper a wo-sage HF resonan link based dc/ac converer employing sine-wave FS conrol is analysed in deail. Two varians of he HF inverer sage, a SAM volage and curren link, are inroduced in Sec. II and he basic operaion of he opology is explained. A comprehensive mahemaical model of he converers is derived in Sec. III in order o idenify opimal values for he passive componens. Moreover, a novel conrol sysem is proposed for igh regulaion of he oupu volage by means of FS. Secion IV presens ypical waveforms of he converer wih proposed FS conrol a saionary operaion and during load ransiens obained from simulaions. Furhermore, he sudied HF volage and curren link converers are compared o a single-sage TCM inverer by means of several performance indicaors, highlighing he benefis and drawbacks of he respecive opologies. II. SAM HF LINK CONVERTER The dc/ac converer opologies analyzed in his paper are shown in Fig.. The SAM volage link based converer is depiced in Fig., where he HF inverer sage is implemened by means of wo parallel resonan converers (PRC). Each PRC is formed by a bride-leg wih a LC resonan ank conneced beween he respecive swich node (A or B) and he spli dc-link midpoin O. Bridge-leg A and B are operaed wih 5 % duy-cycle and frequencies ω and ω slighly above he resonance frequency of he resonan ank o reduce load dependency of he volage gain, as discussed in Sec. III-A, and o enable ZVS. (5)
V dc O V dc V dc O V dc S S S S A A S 3 S 4 S 3 B L,p L,p C,p v i L i L C,p i C,s L,s B L S,s i 4 C,s v i 3 i 3 S 5 S 6 S 7 S 8 S 5 S 6 S 7 S 8 i r C o,s L o,p v r C o,p Fig. : Volage- and curren-based SAM HF link converer opologies wih isolaion ransformer and cener-apped cycloconverer. As described in he inroducion, ω and ω differ precisely by wice he oupu frequency in order o esablish he SAM volage link which is consiued by he difference of v and v. For increased conversion efficiency and o suppor reacive power ransfer, a wo-sage approach wih cyclcoconverer (cf. Fig. ) is preferred. Alhough galvanic isolaion migh no be required by he applicaion, he ransformer urns-raio inroduces an addiional degree of freedom in he design of he respecive inverer sage which helps o reduce he currens in he resonan ank (cf. Sec. III-A). Among several opions o implemen he cycloconverer, he double-winding cenerapped realizaion allows full-wave cycloconversion (power ransfer in he posiive and negaive half-wave of ) wih only wo four-quadran power swiches. Zero curren swiching (ZCS) applies o he cycloconverer (synchronous cycloconversion) as long as he conrol signals are well synchronized o he volage link. The oupu inducor behaves as a curren source, which requires a commuaing sraegy o ensure a pah for he impressed curren in L o,p during swiching sage ransiions. One possible sraegy is o keep S 6 and S 8 urnedoff when he curren in L o,p is posiive and o operae S 5 and S 7 a high frequency. During he pos. half-wave of, S 5 is urned-on and S 7 is off. Slighly afer he zero-crossing of, S 7 is urned-on, iniiaing a curren commuaion beween S 5 and S 7 and allowing S 5 o be urned on subsequenly wih zero curren. The swiching frequency of he cycloconverer is se o he cener frequency obained from he oupu volage conroller (cf. Sec. III-B) and, in order o synchronize, he carrier signal of he modulaor is rese a he sar of every new period. This can be achieved in pracice by deecing he zero-crossing of by means of a high-bandwidh comparaor circui. To faciliae swif curren commuaion beween he swiches, he rese of he carrier signal is slighly delayed wih respec o he zero crossing. The second analysed opology in his paper is shown in Fig. where he HF inverer sage is implemened by means of wo series resonan converers (SRC) which consiue a SAM curren link i 3 and require an impressed volage a he oupu of he cycloconverer (C o,s ). The SRCs are also operaed slighly above resonance frequency o achieve ZVS in all operaing poins. Now, he conrol of he cycloconverer mus be synchronized o he curren link i 3 o achieve ZVS in S 5 -S 8. Since deecing he zero crossing of a curren is more challenging a very high frequency, he SAM curren link based opology wih cycloconverer has a clear downside compared o he volage link based opology. In he nex secion a mahemaical model of he converers is presened which allows o idenify opimal values for he resonan ank elemens and ransformer urns-raio. III. CONVERTER DESIGN AND CONTROL STRATEGY A. Mahemaical Model and Converer Design Procedure Applying he firs harmonic approximaion (FHA), he cycloconverer and he low-pass filer (cf. Fig. and ) can be represened by a single resisor R 3 as indicaed in Fig. 3 and [], [3]. R 3 is calculaed according o = π 8n R, R 3,s = 8 p π n R, (6) s where subscrips (p) and (s) denominae he parallel (volage HF link) and series (curren HF link) resonan circuis, R = Vo /P o represens he load conneced o he oupu of he converer and n p /n s is he urns-raio of he employed ransformer. The equivalen circuis depiced in Fig. 3 and are furher simplified as shown in Fig. 3 (c) and (d) by means of inroducing a ime-varian resisance R (). In case of he v PRC, he insananeous power p,p = v i 3 = provided o he oupu can be wrien as p,p = ˆV cos (ω o ) sin (ω s ) sin (ω s + ω o ), (7) subsiuing wih Eq. (). The ime varian resisance shown in Fig. 3 (c) is calculaed by means of averaging p,p over he resonan period P,p = p,p Ts = Ts T s and hen subsiuing (8) in R,p = ˆV P,p R,p () = p,p d = ˆV sin (ω o ), (8) which leads o sin (ω o ). (9) I can be inferred ha R,p () varies periodically wih he oupu frequency f o beween a nominal value / and opencircui.
v AO, v AO, L,p L,p v v BO, v AO, v C,p C C,p,p (c) L C,s C,s,s L,s i R i i 3,s 3 v BO, v AO, (d) Z i Z i L,p L,s C,s R,p v R,s i Fig. 3: Simplified circuis ha faciliae mahemaical analysis and passive componen design. Equivalen resisance /R 3,s represens boh cycloconverer and load resisor R. Circuis in and can be furher simplified as shown in (c) and (d) by inroducing a ime-varian resisance R,p()/R,s(). Following he same line of hough, Eq. () resuls for he equivalen resisance of he SRC model shown in Fig. 3 (d), p,s = i i 3 R 3,s = Î R 3,s cos (ω o ) sin (ω s ) sin (ω s + ω o ), P,s () = p,s Ts = Ts p,s d = T Î R 3,s cos (ω o ), s R,s () = R 3,s cos (ω o ). () Using he basic expression for qualiy-facor and naural frequency of he series and parallel resonan circui, he componen values of he resonan ank elemens are given by Eq. () for he PRC and by Eq. () for he SRC, where in a wors-case consideraion, he minimum value of R,p and R,s over ime was seleced, L,p = π R = ω n Q p 6n, pω n Q p C,p = Q p ω n = 6n pq p ω n π R, L,s = Q sr 3,s = 6Q sr ω n π n, s ω n C,s = = π n s ω n Q s R 3,s 6ω n Q s R. () () Now, he required ransformer urns-raio o mee he oupu volage requiremen for given dc inpu volage and resonan ank parameers is calculaed for he HF volage link dc/ac converer (cf. Fig. ). The peak value of he envelope of he recified HF volage a he oupu of he cycloconverer is relaed o he oupu volage according o Reflecing ˆV r ˆV r = π V o. (3) o he primary side of he ransformer and observing from Eq. () ha ˆV = ˆV 3 yields ˆV = π 4n p V o. (4) Inroducing he volage gain of he parallel resonan ank, H p = [ ( ) ], (5) ( ) ωs ω n + ωs ω nq p and considering he expression for he firs harmonic of v AO, V AO, = π V DC, allows o relae he peak value of he resonan capacior volage o he dc-link volage, ˆV = H p ˆV AO, = H p V dc π. (6) Subsiuing Eq. (4) in Eq. (6) and rearranging resuls in an expression for he urns-raio, n p = π V o 8 H p V dc. (7) The same analysis is applied o find n s, in which Î = n sπ I o, 4 and he series resonan ank gain is wrien as Î = H s V dc π, (8) H s = ω s ω nq s R [ ( ) ], (9) ( ) ωs ω n + ωs ω nq s resuling in he desired urns-raio expression n s = 8 H s V dc π I o. () Now according o he echnical specificaion given in Tab. I (P o,v o,v dc,f o,f s ), he resonan ank parameers L,p /L,s and C,p /C,s can be compued depending on he design-space variables f n and Q. In a nex sep, he occurring resonan ank curren and volage are compued depending on f n and Q. Then, for a maximal allowed volage across he resonan capacior, he opimal value of f n and Q is deermined by minimizing he resonan ank curren. Based on he equivalen circuis in Fig. 3 and, analyical expressions for he peak capacior volage and peak inducor curren ( ˆV C,ÎL) of boh parallel and series resonan converers can be derived. For he PRC, volages v and v can be relaed o he sinusoidal exciaions v AO, and v BO, according o Eq. () and Eq. (), [ ] [ ] [ ] k k v vao, =, () k k v v BO, k = ω s L C + jω sl and k = jω sl. ()
ˆ V C,p /V C,s (V) 5 5 4.5 3.5.5.5.5 35 Q ˆ 4 f n (khz) 4 f n (khz) I L,p (A) 35.5.5.5 3.5 Q 4.5 3 I II I,II I II 9 9 6 6 3 3 35 4.5 V C (V) ˆ ˆ f n (khz) V ˆ C (V).5 Q ˆ I L,s (A) Fig. 4: Resonan ank capacior peak volage ˆV C and inducor peak curren Î L as a funcion of f n and Q for boh volage (p) and curren (s) SAM HF links. ˆVC surfaces for boh opologies are idenical ( ˆV C,p = ˆV C,s = ˆV C). The curren-based link presens less inducor peak curren if compared o he volage-based link for he same capacior peak volage. Inersecion curves where (I) ˆV C = Ω ÎL,p and (II) ˆV C = 5.6 Ω ÎL,s, exhibiing a common opimum poin of f n = 38.9 khz and Q =.8. Solving he linear sysem for v and v resuls in [ ] [ ] [ ] v k3 k = 4 vao,, (3) v k 4 k 3 where k 3 = k k k v BO, 4.5 and k 4 = k k. (4) k This allows o express he capacior volage and he inducor curren, v C = k 3 v AO, + k 4 v BO,, (5) i L = v AO, v C jω s L = v AO, k 3 jω s L v BO, k 4 jω s L, (6) which can be rewrien using ˆV AO, = ˆV BO, = V dc /π in order o find he maximum value of he involved quaniies, and ˆV C,p = V DC π ( k 3 + k 4 ) (7) Î L,p = V DC π ( ) k 3 jω s L + k 4 jω s L. (8) The same analysis is applied o compue he peak capacior volage ˆV C,s = V ( ) DC k 3 π jω s C + k 4 jω s C, (9) R R R - - - - -3-4 -5 9 - -9-35 - -8-9 Frequency (khz) (c) Frequency (khz) Mag (db) Pha (deg) 4 5 3 4 3 9 9 - - -9-9 Frequency (khz) (d) Frequency (khz) Mag (db) Pha (deg) Fig. 5: Transfer funcion (a,c) and inpu impedance (b,d) Bode plos of he parallel (a,b) and he series (c,d) resonan converer depending on he equivalen resisance R. and peak inducor curren Î L,s = V DC π ( k 3 + k 4 ) (3) of he SRC. The derived expressions allow o plo ˆVC,p / ˆV C,s and Î L,p /ÎL,s for several values of f n and Q. The plo of Fig. 4 reveals he rade-off beween ˆV C and ÎL for he volage and he curren link based opology and shows ha he peak curren is subsanially lower in he curren link based converer. Mag (db) Pha (deg) Mag (db) Pha (deg) TABLE I: Technical specificaions. Oupu power (P o ) Oupu RMS volage (V o ) DC-link volage (V dc ) Oupu frequency (f o ) Swiching frequency (f s ) Nominal oupu load resisance (R) kw 3 V V 5 Hz 5 khz 6.5 Ω The opimal resonan ank parameer f n and Q are lised in Tab. II and have been obained from he inersecion curves ploed in Fig. 4. The shown inersecion curves are ˆV C = Ω ÎL,p in case of he PRC and ˆV C = 5.6 Ω ÎL,s in case of he SRC, where he scaling facors for boh opologies were chosen such ha he max. allowed 5 V across he resonan capacior is aained for he opimal values of f n and Q in order o minimize resonan ank curren. TABLE II: Opimal resonan ank parameer. Maximum ank capacior volage ( ˆV C,p / ˆV C,s ) 5 V Resonan ank naural frequency (f n ) 38.9 khz Resonan ank qualiy facor (Q).8
SOGI v α v β θ o S S αβ dq v d v q ω ω MOD v d * C v C pll ω s * S 3 S 4 S 5 S 6 S 7 S 8 ω ω o ω ω o * Cω ω o * ω sc ω oc MOD.5 MOD 3 Fig. 6: Combined ampliude and frequency conrol loop. A second-order generalized inegraor (SOGI) phase locked loop (PLL) measures he oupu frequency ω o and feeds a conroller C ω o impose he correc desired frequency-shif beween ω and ω. A second conroller C v changes boh frequencies ω and ω simulaneously o compensae oupu volage ampliude variaions. The block diagram of deails he SOGI block inernal srucure. ω ω k v β ω o v α Once opimum values for f n and Q are found, he quaniies n, L and C are calculaed wih Eq. (6)-() according o he specificaions in Table I. The opimized circui parameers are summarized in Table III. TABLE III: Volage (p) and curren (s) based links main parameers. Transformer urns raio (n p ).86 Tank inducance (L,p ) 49.9 µh Tank capaciance (C,p ) 336 nf Oupu inducance (L o,p ) 5 µh Oupu capaciance (C o,p ) µf Transformer urns raio (n s ).96 Tank inducance (L,s ) 8.4 µh Tank capaciance (C,s ) 3 nf Oupu capaciance (C o,s ) 4 µf The inpu impedance (Z i ) and ransfer funcions (v /v AO and i /v AO ) Bode plos of boh parallel and series resonan converers wih opimized circui parameers are depiced in Fig. 5. An increase in he equivalen ank resisance R represened by dashed lines in he plos reveals how he magniude and he phase changes wih varying load. The PRC ransfer funcion gain near he naural frequency f n increases for higher R values, while he opposie behaviour is found in he SRC. Since R () varies over he oupu period (cf. Eq. (9) and Eq. ()) i is no feasible o operae he converers wih f s = f n where he magniude varies srongly wih R. The operaion above resonance is he preferred opion (posiive phase of Z i ) since i also enables ZVS of he half-bridge MOSFETs. The Bode plo of he PRC and SRC ransfer funcions in Fig. 5 and Fig. 5 (c) also exhibi a difference in he slope of he magniude above resonance frequency. In case of he PRC he magniude decreases wih 4 db/dec while he SRC feaures a slope of jus db/dec. The seleciviy (qualiy facor) of he PRC improves wih increasing resisance R while i decreases in case of he SRC. Thus, he PRC feaures beer harmonic aenuaion and more sinusoidal HF-link waveforms. This renders he PRC beer suied for applicaions ha require very low THD in he oupu volage, paricularly a ligh loads. B. Proposed conrol sraegy Using FS modulaion, he resonan links are excied by square-wave volage waveforms wih frequency ω = (ω s +ω o ) and ω = (ω s ω o ), respecively. The cener frequency of boh resonan links, ω s = (ω + ω )/, (3) ses he prevailing gain of he PRC and SRC ransfer funcions (cf. Eq. (5) and Eq. (9)) and allows o adjus he ampliude of he oupu volage. The angular frequency of he oupu volage, ω o = (ω ω )/, (3) can be conrolled by precisely adjusing he difference beween ω and ω. Fig. 6 depics he developed conrol sysem o regulae he oupu volage. A phase-locked-loop (PLL) [4] algorihm is applied o deermine he angular frequency ω o of he oupu volage. A deviaion of ω o from is reference value ωo is compensaed by means of PI conroller C ω wih addiional feed-forward erm (ωo ). The ampliude of he oupu volage is obained from he dq-ransformaion (v d ) and conrolled o mee he ampliude reference vd by means of compensaor C v wih addiional feed-forward of he angular swiching frequency value (ωs ). The exciaion frequencies of he respecive bridge-legs, ω and ω, are hen compued according o Eq. (3) and Eq. (3). The conrol signals of he HF link MOSFETs, S -S 4, are hen obained from PWM wih 5 % duy cycle and he respecive frequency. The PWM uni generaing he conrol signals for he cycloconverer sage, S 5 -S 8, is paramerized wih ω s in order o synchronize he cycloconversion o HF volage, as explained in Sec. II.
IV. SIMULATION RESULTS AND PERFORMANCE COMPARISON Fig. 7 illusraes circui simulaion resuls of he volage based SAM HF link converer designed in Sec. III for saionary operaion a raed oupu power. The characerisic volage waveforms are shown in Fig. 7 over a mains period and in Fig. 7 over wo resonan periods. Considering Fig. 7, i can be seen ha he individual resonan ank volages, v and v, exhibi a flucuaing ampliude wih wice he oupu frequency which can be explained by he ime-varying equivalen resisance R () (cf. Sec. III-A) which essenially alers he ransfer characerisics of he resonan ank over ime (cf. Fig. 5 ). Noe, ha his flucuaion would become more severe if he resonan ank would be operaed closer o is resonance frequency. Volage presens he desired SAM shape, which is hen cycloconvered (v r ) and low-pass filered o generae. The waveforms wih respec o he resonan period are depiced in Fig. 7. Exciing he resonan ank above he resonance frequency, he inpu impedance becomes inducive (posiive phase) and an increasingly riangular raher han sinusoidal shape of he currens i L and i L can be recognized. Noe, ha he resuls of he HF curren link based converer are omied since he waveforms are very similar o he volage link based converer and he main discrepancies are highlighed in he performance comparison presened a he end of his secion. The performance of he volage link based converer subjec o several sepwise load changes is shown in Fig. 8, demonsraing he excellen performance of he proposed FS conrol sysem described in Sec. III. A = 5 ms a sepwise decrease o 5 % of he load is iniiaed followed by anoher 5 % reducion a 85 ms. A = ms, a sepwise increase of he load back o kw raed power is shown. I can be seen ha even under severe load changes, he oupu volage is conrolled ighly. Also shown in Fig. 8 are he compued conrol variables, swiching (f sc ) and oupu (f oc ) frequencies, required o ensure he correc oupu frequency and ampliude. The low values of converer passive componens explain he fas dynamic response of he circui, which leads o spikes during abrup load ransiens. Also noe, how he ampliude flucuaion of v and v depends on he prevailing load. TABLE IV: TCM inverer parameers. Inducance 6. µh Capaciance 6.6 µf Lower curren boundary 5 A Lower swiching frequency 5 khz In order o compare he performance of he volage and curren SAM HF link converers, several performance indicaors were compued. The performance of a wo-level fullbridge inverer operaing in riangular curren mode (TCM) 6 4 - -4-6 8 4-4 -8 6 4 - -4-6 3 - - -3 3 - - -3 6 4 - -4-6 6 4-6 v r v 4 8 ime (ms) v AO v r i L v BO i L 8.5 8.6 8.7 8.8 ime (ms) v 6 4 - -4-6 6 4 - -4-6 8 4-4 -8 - Fig. 7: Seady-sae simulaion resuls of he volage-based SAM HF link inverer a raed oupu power for a mains period and wo resonan periods. [5] is included as a benchmark, designed for he echnical specificaions shown in Table I which resuls in he parameer values summarized in Table IV. Since TCM feaures a variable swiching frequency, he inducance value is chosen such ha he minimum swiching frequency corresponds o he 5 khz of he SAM converer for a similar size of he passives. Fig. 9 shows he performance indicaors wih respec o oupu power and in he form of a radar char. The indicaors were chosen in order o easily recognize feaures and drawbacks of each i 3 Curren (A) Curren (A) Curren (A)
Freq. (khz) Freq. (Hz) 6 4 - -4-6 8 4-4 -8 4 - -4 58 56 54 5 5 48 5 5 5 49 48 v v i o 4 6 8 4 6 8 ime (ms) f sc f oc - - Fig. 8: Transien response simulaion resuls for a 5 % sepwise load reducion afer 5 ms followed by anoher 5 % reducion a 85 ms and a final sepwise increase o he kw raed power a ms, demonsraing he performance of he proposed conrol sraegy. opology. The inducor RMS curren (I L /I L ), he swiching frequency (f s ) and he oupu volage THD (THD vo ) provide a gauge of he conducion losses, swiching losses and harmonic disorions, respecively. The average swiching frequency over a period was compued in case of he TCM inverer. Concerning conducion losses, he curren link inverer presens a beer figure of meri compared o he volage link due o he lower ank inducor RMS currens (I L /I L ). The oupu volage THD is around % a raed power, bu increases drasically in case of he curren link converer if P o is reduced below kw, exceeding ypical THD limis when operaing a ligh loads. This is explained by he huge dependency of he SRC ank gain on he oupu load (cf. Fig. 5), which requires a large increase of f s o keep he ampliude of a is nominal value under ligh load. In conras, he THD vo in case of he volage link converer is almos independen of he oupu power. Finally, regarding he f s indicaor, i can be seen ha he average swiching frequency of he TCM inverer is clearly above boh SAM converers. Curren (A) V. CONCLUSIONS In his paper an alernaive approach o convenional PWM wih varying duy cycle o generae a low frequency sinusoidal oupu volage in dc/ac converer applicaions is sudied in deail. By means of consan duy cycle frequency shif (FS) conrol of a HF inverer sage a he dc side, an inermediae HF volage or curren link is esablished which exhibis a sinusoidally varying ampliude a he desired oupu frequency. A second cycloconversion sage wih subsequen low-pass filer yields he desired ac oupu. Two varians of he HF inverer sage, a volage or curren link implemened by means of parallel or series resonan converers, respecively, have been analyzed. Based on a derived mahemaical model of he converer, he resonan ank passives and ransformer urns-raio were chosen considering a minimizaion of he curren sress for a given maximum resonan capacior volage in a kw 4 V dc/ac applicaion. A novel close-loop conrol sysems is proposed which allows o ighly regulae he frequency and ampliude of he ac volage. A dqransformaion based PLL and wo individual PI conrollers are implemened o compensae boh ampliude and frequency deviaions by adjusing he swiching frequency of he respecive HF inverers. The presened simulaion resuls show excellen ransien performance of he converer. In case of he PRC-based HF inverer, an abrup load sep of 75 % of nominal power seles wihin an oupu period and requires a shif of he cener frequency (avg. frequency of boh HF inverers) by roughly 4 khz. Moreover, he performance of PRC and SRC implemenaions were compared o a singlesage TCM inverer regarding curren sress, THD of he oupu volage and swiching frequency. Ineresingly, he resonan inducor curren is significanly higher in case of he PRC implemenaion compared o he SRC which exhibis values jus slighly above he TCM inverer. As a consequence high conducion losses mus be expeced in case of he PRC implemenaion which leads o reduced efficiency paricularly a ligh loads since he curren sress in he resonan sage remains high. A nominal oupu power boh HF inverer implemenaion show low oupu volage THD values in he same range as he TCM inverer. Unforunaely, in case of he SRC implemenaion he THD increases significanly a ligh loads. I can be concluded ha he HF curren link based converer wih FS conrol is a viable opion o realize above MHz, kw-scale dc/ac power conversion. However, dedicaed iming ICs are needed o realize FS conrol and he exac synchronizaion of he cycloconverer o he HF curren link by means of curren zero-crossing deecion is crucial. REFERENCES [] Google, Lile box challenge, www.lileboxchallenge.com, 6, accessed: 7-7-6.
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