Yungtaek Jang, Milan M. Jovanović, Juan M. Ruiz, Misha Kumar, and Gang Liu 1, /16/$ IEEE 1292

Transcription

1 Implemenaion of 3.3-kW Ga-Based DC-DC Converer for EV On-Board Charger wih Series- Resonan Converer ha Employs Combinaion of Variable-Frequency and Delay-Time Conrol ungaek Jang, Milan M. Jovanović, Juan M. Ruiz, Misha Kumar, and Gang Liu 1, Power Elecronics Laboraory, Dela Producs Corporaion, 5101 Davis Drive, Research Triangle Park, C, USA 1 Elecrical Engineering, Fudan Universiy, Shanghai 00433, People s Republic of China Dela Power Elecronics (Shanghai) Co. Ld, 0109, People s Republic of China Absrac An isolaed dc-dc series-resonan converer ha is conrolled by a combinaion of variable-frequency and secondary-side-swich delay-ime conrol is employed as he oupu sage of he on-board charger module (OBCM) ha operaes wih a wide baery-volage range. The delay-ime conrol which is implemened by he modulaion of secondaryside swiches is used o assis he convenional variableswiching-frequency conrol of primary swiches o reduce he swiching-frequency range. By subsanially reducing he swiching-frequency range and uilizing gallium niride (Ga) swiches, he overall operaing frequency is increased o reduce he sizes of he passive componens, and hence, increase power densiy. The performance evaluaion of he proposed series-resonan converer wih delay-ime conrol was done on a 3.3-kW prooype delivering energy from 400-V bus, which is he oupu of he PFC fron end, o a baery operaing wih volage range beween 180 V and 430 V. The prooype circui exhibis he maximum full-load efficiency of 97.3% wih a swiching frequency variaion from 144 khz o 175 khz over he enire oupu-volage range. I. ITRODUCTIO To maximize he range of elecric vehicles (EVs) and plug-in hybrid elecric vehicles (PHEVs), i is necessary o uilize he maximum available energy from he baery pack. As a resul, he baery-pack volage varies in a wide range which makes he design of high-efficiency high-powerdensiy on-board charger modules (OBCMs) exremely challenging. Generally, resonan converers wih variable swiching-frequency conrol are exensively used in sae-ofhe-ar power supplies ha offer he highes power densiies and efficiencies [1]-[11]. However, variable swichingfrequency conrol is seen as a drawback of a resonan converer especially in applicaions wih a wide inpu-volage and/or oupu-volage range [1]-[15]. Specifically, as he inpu or oupu volage range increases, he conrol frequency range also increases so ha driving and magneic componen losses also increase, hereby reducing conversion efficiency. Recenly, a new conrol echnique ha significanly improves he performance of a series resonan converer ha operaes wih a wide inpu-volage range and/or a wide oupu-volage range by subsanially reducing heir swiching-frequency range has been inroduced [16]. Reducion in he swiching frequency range is achieved by conrolling he oupu volage wih a combinaion of variable-frequency feedback conrol and he open-loop delay-ime conrol. Variable-frequency conrol is used o conrol he primary swiches of he series resonan converer, while delay-ime conrol is used o conrol secondary-side recifier swiches provided in place of diode recifiers. In his paper, he inroduced conrol mehod is applied o a dc-dc series-resonan converer employed as he oupu sage of an OBCM operaing wih a wide oupu-volage range. By subsanially reducing he swiching-frequency range and uilizing gallium niride (Ga) swiches, he overall operaing frequency is increased o reduce he sizes of he passive componens, and hence, increase power densiy wihou sacrificing is performance. The performance of he proposed dc-dc converer was verified on a 3.3-kW prooype operaing wih a 400-V inpu and an oupu ha varies beween 180 V and 430 V. II. SERIES-RESOAT COVERTER WITH COMBIATIO OF VARIABLE-FREQUEC COTROL AD SECODAR- SIDE-SWITCH DELA-TIME COTROL Figure 1 illusraes he proposed conrol mehod in a series-resonan converer wih secondary synchronous recifiers. As illusraed in Fig. 1(a), oupu volage regulaion is achieved using a combinaion of variablefrequency feedback conrol and open-loop delay-ime conrol. Specifically, variable-frequency conrol is applied o primary swiches S P1 -S P4, and delay-ime conrol is applied o secondary-side swiches S S and S S3. Figure 1(b) shows ideal gae waveforms of primary swiches S P1 -S P4, drain and gae waveforms of secondary swiches S S and S S3, and resonan inducor curren in he resonan converer of Fig. 1(a). As shown in Fig. 1(b), swiches in he same leg of he primary full-bridge operae in a complemenary fashion wih a small dead ime beween heir commuaions o achieve zerovolage swiching (). The delay-ime conrol is /16/$ IEEE 19

2 S P1 S P4 V I C R S P S P3 S P1 SP S P3 S P4 L R 1 TR V SS3 n= 1 V SS S S D S1 S S D S4 C O S S3 S S3 + L O V O A - D M(, F) = = Delay Time - Q = = 0.5 BOOST MODE OPERATIO DRIVER f S VCO PHASE DELA DETECT DELA COTROL DRIVER V O(scld) V I(scld) =0 Series Resonan Converer V I SCALE V EA V I(scld) EA w/ COMP COTROL V E V O(scld) + - V O(REF) SCALE V O F = S P1 S P3 S P S P4 S S S S3 Delay Time O OFF OFF O Fig. 1(a) Ts T 0 T 1 T T 3 T 4 Fig. 1(b) Delay Time Fig. 1. Proposed series resonan converer wih addiional secondary swich conrol: (a) circui diagram, (b) conrol waveforms. implemened by delaying he urn-off of swiches S S and S S3 wih respec o corresponding zero crossings of resonan curren so ha boh swiches S S and S S3 conduc during delay-ime inervals [T 0 -T 1 ] and [T 3 -T 4 ] and shor he secondary of ransformer TR. Because of he shored secondary of he ransformer, he volage across resonan ank C R -L R during delay-ime inerval [T 0 -T 1 ] is V I insead of V I nv O which is he case wih no ime-delay conrol. Therefore, wih he delay-ime conrol, a higher volage is applied across he resonan inducor and, consequenly, a higher amoun of energy is sored in resonan inducor L R. Therefore, a he same inpu volage and swiching frequency, secondary-side delay-ime conrol provides a higher oupu volage compared o he convenional frequency conrol. This boos characerisic makes opimizing circui performance possible by selecing: (i) a OFF O O OFF D = T S Fig.. Inpu-o-oupu volage gain of proposed converer for Q=0.5 [16]. I should be noed ha converer operaes as series resonan converer when delay ime - is se o be zero. higher urns raio in he ransformer o reduce primary conducion losses and (ii) a higher magneizing inducance o reduce circulaing (i.e., magneizing) curren loss. Because of is boos propery, in ypical applicaions, he delay-ime conrol is used in he middle and high oupu-volage and/or low inpu-volage range. Dc-conversion raio M=nV O /V I of he series-resonan converer wih proposed delay-ime conrol is derived in [16] by using sae-plane analysis. For a given Q and normalized delay ime - = /T S, dc conversion raio M = nv O /V I can be numerically calculaed and ploed as funcion of normalized frequency F = f S /f O, as shown in Fig.. When delay ime is zero, he converer characerisic is he same as ha of a convenional series resonan converer. As delay ime increases, dc gain M increases and exhibis a boos characerisic. Because delay ime depends on inpu or oupu volage, a microconroller-based conrol implemenaion is preferred since he delay ime can be easily programmed. Figure 3 shows deailed conrol waveforms of he proposed series resonan converer wih delay-ime conrol shown in Fig. 1(a). In his implemenaion, as shown in Fig. 3, primary swiches S P and S P4 and secondary swich S S3 urn on ogeher a =T 0 (waveforms 1 and 7), whereas primary swiches S P1 and S P3 and secondary swich S S urn on ogeher a =T 3 (waveforms and 11 ). To implemen he delay-ime conrol, he zero crossing of resonan inducor curren a =T 1 should be deeced for gaing of swich S S3, whereas he gaing of swich S S requires zero-crossing deecion of he inducor curren a =T 4. Generally, he sensing of he zero crossings of resonan curren can be done by using a curren ransformer. However, a ligh loads, he magniude of resonan curren is oo small o be used for reliable deecion of he zero crossings. As a resul, in his paper, he drain-o-source volage waveforms of secondary- 193

3 V GS-SP V GS-SP4 1 V GS-SP1 V GS-SP3 3 V DS-SS 4 InvV DS-SS 5 ecap inpu InvV V GS-SS3 7 V DS-SS3 8 DS-SS3 9 ecap inpu 10 9 V GS-SS 11 V GS-SP, SP4 T (n) S - T (n-1) e T (n-1) S T (n-1) e1 T (n-1) S - T (n-) e1 V GS-SP3, SP1 Invered V DS-SS T (n) e T (n) S T (n) e1 T (n+1) S - T (n) e T (n) S - T (n-1) e1 T 0 T 1 T T 3 T 4 T 5 T 6 T 7 T 8 T 9 T 10 T 11 T (n+1) S Fig. 3. Deailed conrol waveforms of proposed series resonan converer shown in Fig. 1. side swiches S S and S S3 are used o indirecly deermine he zero crossings. This zero-curren-deecion mehod is based on he fac ha a he zero crossings of he secondary curren, he draino-source volage of he secondary side swich experiences an abrup change wihou commuaion delay. Specifically, for he zero crossings ha occur when he secondary curren changes from posiive o negaive, such as ha a =T 1, he drain-o-source volage of swich S S, V DS-SS (waveform 4), changes from V O o zero because of he commuaion of he secondary curren from recifier D S1 o aniparallel diode of swich S S. Similarly, for he zero crossings ha occur a negaive-o-posiive secondary-curren ransiions, e.g., a =T 4, he drain-o-source volage of swich S S3, V DS-SS3 (waveform 8), changes from V O o zero because of he commuaion of he secondary curren from recifier D S4 o aniparallel diode of swich S S3. In he digial implemenaion of he conroller, he zero crossings can be deermined by he ime differences beween he primary swich commuaion insans and he insans he drain-o-source volage of he corresponding secondary-side swich ransiions from V O o zero, i.e., by calculaing he Invered V DS-SS duraions of ime inervals [T 1 -T 0 ], [T 4 -T 3 ], [T 7 -T 6 ], ec. For he calculaion of hese ime inervals a posiive-o-negaive curren ransiions, he invered signal of drain-o-source volage V DS-SS (waveform 5) and gae-o-source volage V GS-SP (waveform 1) are processed by he AD gae as shown in he waveform of Fig. 3. The oupu signal of he AD gae is read by Enhanced Capure (ecap) Module of he microconroller (TMS30F8069) ha capures he pulse widh and sores is value as T e1. During he nex swiching cycle, he duraion of he ime inervals [T 1 -T 0 ], [T 7 -T 6 ], ec. is calculaed by subracing T e1 from one half of he curren swiching period T S, i.e., as T S [n]/-t e1 [n-1]. Finally, he gae pulse widh of swich S S3 is deermined by he sum of he calculaed ime inerval (T S /-T e1 ) and required delay ime, as shown in he waveform of Fig. 3. I should be noed ha alhough he duraion of hese ime inervals changes over he inpu volage, oupu volage, and load range, hey can be considered o be near consan during a single swiching cycle since he volage and load changes are much slower han he swiching period. For gaing of swich S S, he ime inerval beween primary swich gae ransiion a =T 3 and zero crossing of resonan inducor curren a =T 4 should be calculaed. For he calculaion of hese ime inerval he invered signal of drain-o-source volage V DS-SS3 (waveform 9) and gae volage V GS-SP1 (waveform ) are processed by he AD gae as shown in he waveform of Fig. 3. The gae pulse widh of swich S S is deermined by he sum of he calculaed ime inerval (T S [n]/-t e [n-1]) and required delay ime, as shown in he waveform 11. I should be noed ha in he conrol implemenaion in Fig. 3, secondary side swiches S S and S S3 are conducing only during ime inervals ha implemens he delay-ime conrol, i.e., hey are no used as synchronous-recifier swiches. As a resul, he body diodes of he swiches are uilized as oupu recifiers. However, he conrol mehod in Fig. 3 can also be exended o synchronous implemenaion operaion by exending he conducion of he secondary-side swiches beyond ha required by he delay-ime conrol. III. DESIG COSIDERATIOS For performance evaluaion, he proposed dc-dc converer for EV on-board charger has been designed and buil according o he following key specificaions: Inpu volage V I : 400 V DC Oupu volage V O : V DC Maximum oupu curren I O-MAX : 11 A Maximum oupu power P O-MAX : 3.3 kw Efficiency η: >96% above 50% load Dimension: 50 mm 180 mm 75 mm A. Swiching Frequency Selecion I is well undersood ha swiching frequency selecion is based on he rade-off beween efficiency and size, i.e., power densiy. In his design, he minimum frequency is se 194

4 a 140 khz, whereas he maximum frequency is limied o 350 khz o mee power densiy for he specified dimension. IITIALIZATIO Sofsarflag=0 START B. Transformer Design The urns raio n= 1 / =0/16 of ransformer TR is chosen o make inpu-o-oupu conrol characerisic M be 1 when he oupu volage is approximaely 30 V wih 400-V inpu. As a resul, he delay ime of he secondary swiching is se o zero when he converer operaes from 180 V o approximaely 30 V oupu so ha he proposed converer operaes as a series resonan converer. However when he oupu volage increases above 30 V, he conroller sars monoonically increasing he delay ime o provide he boos characerisic o mainain he oupu volage regulaion wih he seleced urns raio of ransformer TR. The ransformer has following specificaions: Core: A pair of PQ4040-PC40 ferrie cores. Primary winding: 1 = 0 urns, Liz wire (435 srands /AWG #40). Secondary winding: = 16 urns, Liz wire (435 srands /AWG #40). Air gap: 0.0 mm. The measured magneizing and leakage inducances are 1.05 mh and 1.6 μh, respecively. The maximum flux densiy a seady sae operaion is approximaely 0.3 T, which gives pleny of margin from he sauraion flux of he ferrie core. C. Resonan Capacior Design A high-frequency film capacior is a suiable candidae for resonan capacior C R because of is cos and long-erm reliabiliy. However, is maximum permissible ac volage is inversely proporional o frequency. For example, a 33-nF, 000-VDC, FKP 1 ype film capacior from WIMA has he ac-volage raing of 700-V AC-RMS a line-frequency of 50/60 Hz and only 180 V AC-RMS a approximaely 140-kHz. The peak volage of he resonan capacior can be deermined by recognizing ha during a half swiching period, he posiive resonan-inducor curren coninuously charges he resonan capacior so ha he volage across resonan capacior C R increases from is negaive o is posiive peak, i.e., changes for V CR_PK. The relaionship beween he resonan-capacior volage change and sored charge during he half swiching cycle is given by _ (1) Since he average of he resonan inducor curren over a half swiching period is equal o he oupu (load) curren refleced o he primary, sored charge during he half swiching cycle can be calculaed as () From equaions (1)-(), i follows ha _, (3) where n= 1 / is he urns raio of ransformer TR. f sl : OUTPUT POWER COTROLLER P O = V I O O PO(REF) = V I O(REF) O(REF) Lower limi of frequency for burs mode operaion f sh : Higher limi of frequency for burs mode operaion Ts Disable Swiches AALOG TO DIGITAL COVERSIO V, O VO(REF), I, O IO(REF) READ O TIMES, Te FROM ECAPTURE Sofsarflag=0 Sofsar Over? Sofsarflag=1 ED Fig. 4. Flow char of proposed conrol scheme. OUTPUT VOLTAGE COTROLLER LIMITER AD ATIWIDUP VOLTAGE COTROLLED OSCILLATOR TsH fs Te1 Curren-mode conrol? FREQUEC SOFT START OUTPUT CURRET COTROLLER f sh Enable Swiches The maximum of capacior peak volage V CR_PK occurs a minimum frequency (minimum inpu volage) and full load. The peak volage across a 33-nF capaciors is calculaed as Ts T s TsL Volage-mode conrol? DELA TIME COTROL BASED O VO(REF) UPDATE PWM REGISTER WITH Ts, TD, Te1, Te BURST MODE OPERATIO fs f sl TsH = 1 fsh TsL = 1 fsl 195

5 Since he volage waveform across he resonan capaciors is a sine wave shape, rms volage across he serially conneced wo capaciors is approximaely 336 V. To keep he maximum volage sress of capacior wihin he 180-V AC-RMS limi, wo ses of series-conneced wo 33-nF, 000-VDC, 700-V AC-RMS, FKP 1 ype film capaciors are conneced in parallel. As a resul, oal capaciance of resonan capacior C R is 33 nf. D. Resonan Inducor Design To guaranee he above-resonan-frequency operaion wih ±10% inducance olerance of L R and ±5% capaciance olerance of C R, he resonan-ank inducor value is calculaed by assuming resonan frequency of 130 khz which is 10 khz lower han he minimum specified swiching frequency. For he 130-KHz resonan frequency and 33-nF resonan capacior value, he required inducance of he resonan-ank inducor is approximaely 46 μh. To obain his inducance, he resonan inducor was buil using a pair of ferrie cores (PQ-40/40, PC40) wih a 3.8-mm gap in all hree legs. The winding was implemened wih 8 urns of Liz wire (435 srands of AWG#40) o reduce he fringingeffec-induced winding loss near he gap of he inducor core. For his inducor design, he maximum flux densiy which occurs a full load and he minimum swiching frequency is approximaely 0.8 T. E. Semiconducor Device Selecion Because he volage sresses of primary swiches S P1 - S P4 and secondary swiches S S1 - S S4 are approximaely equal o inpu volage V I and oupu volage V O, respecively, i.e., hey are below 450 V, i is necessary o use swiches ha are raed a leas 600-V o mainain he desirable design margin of 0%. In he prooype circui a TPH305WT Ga MOSFET (V DS = 600 V, R DS = Ω, C OSS =108 pf, Q rr =138 nc) from Transphorm was used for each swich. I should be noed ha he body diode of he seleced swich has relaively small reverse recovery charge. F. Conrol Implemenaion The oupu conrol of he converer was implemened by a TMS30F8069 digial conroller from TI. To implemen he baery-charging profile, a consan-curren, consan-power, and consan-volage oupu conrol is employed. The flow char of he employed conrol is shown in Fig. 4. I should be noed ha converer sars wih frequency sof sar, i.e., he swiching frequency sars from he maximum and gradually reduces unil he oupu volage reaches he desired level. Moreover, he converer eners burs-mode operaion a very ligh load. + V BULK 400 V - S P1 -S P4 TPH305WT SP1 SP CR SP4 4 x 33 nf SP3 Fig. 5. Experimenal prooype circui. PQ4040-PC44 Liz AWG# srands 8 urns, 46 uh L R 1 PQ4040-PC44 1 =0 urns, TR SS SS3 Liz AWG# srands =16 urns, Liz AWG# srands Lm = 1.85 mh, Llk = 1.6 uh V BAT V Fig. 6. Prooype circui diagram wih deails of employed power componens. I should be noed ha all primary and secondary swiches are Ga devices SS1 S S1 -S S4 TPH305WT SS4 CO 4 x. uf + - IV. EXPERIMETAL RESULTS The performance of he proposed converer wih he delay-ime conrol shown in Fig. 1 was evaluaed on a 3.3- kw prooype circui ha is designed o operae from a 400- V inpu and deliver power over V oupu volage range as described in Secion III. Figure 5 shows a view of he on-board charger module wih he cover removed. The on-board charger in Fig. 5 consiss of he proposed dc-dc sage and he fron-end PFC sage which is no discussed in his paper. Figure 6 shows he circui diagram along wih componen specificaions. I should be noed ha all primary and secondary swiches are Ga devices. Since in his implemenaion secondary swiches S S1 and S S are no operaed as synchronous recifiers, heir body diodes are uilized as oupu recifiers. Figure 7 shows he measured waveforms of gae and drain volages of primary swich S P, resonan curren, and resonan capacior volage V CR of he experimenal circui when i delivers full power a 430-V, 30 -V, and 180-V oupu. The waveforms show of primary swich S P. Alhough Fig. 7 only shows waveforms of swich S P, he waveforms of all oher primary swiches are similar o ha of swich S P and achieve as well. As shown in Fig. 7, during a half swiching period, he posiive resonaninducor curren coninuously charges he resonan capacior so ha he volage across resonan capacior C R increases 196

6 V G-SP [0 V/div] V D-SP V CR [10 A/div] V I =400 V V O =430 V P O =3.3 kw f S =174 khz V D-SS V G-SS V D-SS3 V G-SS3 V I =400 V V O =430 V = 1 μsec P O =3.3 kw f S =174 khz (a) (a) V G-SP [0 V/div] V D-SP V CR [10 A/div] V I =400 V V O =30 V P O =3.3 kw f S =144 khz (b) V D-SS V G-SS V D-SS3 V G-SS3 V I =400 V V O =30 V = 400 nsec (b) P O =3.3 kw f S =144 khz V GS-SP [0 V/div] V DS-SP V CR [10 A/div] V I =400 V V O =180 V P O = kw f S =171 khz (c) Fig. 7. Measured drain and gae volage waveforms of primary swich S P, volage waveforms of resonan capacior C R, and curren waveform of resonan inducor L R for oupu volages: (a) 430 V; (b) 30 V; and (c) 180 V. Time scale is. V DS-SS V GS-SS V DS-SS3 V GS-SS3 V I =400 V V O =180 V = 0 (c) P O = kw f S =171 khz Fig. 8. Measured drain and gae volage waveforms of secondary swiches S S and S S3 for oupu volages: (a) 430 V; (b) 30 V; and (c) 180 V. Time scale is. from is negaive o is posiive peak, i.e., changes for V CR_PK. The maximum peak capacior volage occurs a 30 V oupu as shown in Fig. 7(b), which is approximaely 400 V. As a resul, he rms volage across each 33-nF resonan capacior is approximaely 140 V a 144 khz. Figure 8 shows he measured waveforms of gae and drain volages of secondary swiches S S and S S3 of he experimenal circui when i delivers full power a 430-V, 30-V, and 180- V oupu. As shown in Fig. 8, all he secondary swiches operae wih. Figure 8 also shows delay ime. Delay ime is he period when boh drain volages of swiches S S and S S3 are zero, i.e., boh swiches conduc and he secondary winding of TR is shored. I should be noed ha he urns raio of ransformer TR is chosen o make inpu-o-oupu conrol characerisic M equal o 1 when he oupu volage is approximaely 30 V. However o properly regulae he oupu volage wih componen olerances as well as under a ransien condiion, delay-ime is inroduced from 60 V oupu. As a resul, he delay ime of he secondary swiching is se o zero when he converer operaes from 180 V o approximaely 60 V 197

7 oupu. When he oupu volage increases above 60 V, he conroller increases he delay ime o provide he boos characerisic o mainain he oupu volage regulaion wih he seleced urns raio of ransformer TR. Figure 9 shows measured efficiency of he prooype converer as a funcion of he oupu volage. I should be noed ha he converer exhibis he bes full-load efficiency when he oupu volage is beween V, which is he operaing range i mos frequenly operaes. Specifically, he converer exhibis he maximum full-load efficiency of 97.3% a 80-V oupu. Figure 10 shows he measured fullload swiching frequency of he experimenal prooype as a funcion of he oupu volage. The measured full-load swiching frequencies are in a 144-kHz o 175-kHz range over he enire oupu-volage range, which enables more effecive opimizaion of all he magneic componens and filer capaciors. As seen from Fig. 11, he delay-ime conrol is acivaed above 60-V oupu. Efficiency [%] I OUT = 11 A P OUT = 3.3 kw V IPUT = 400 V Oupu Volage [V] Fig. 9. Measured efficiencies of he experimenal prooype as funcions of oupu volage. Delay Time [nsec] I OUT = 11 A P OUT = 3.3 kw V IPUT = 400 V Oupu Volage [V] Fig. 11. Measured delay-ime of experimenal prooype as funcion of oupu volage. V. SUMMAR In his paper, an isolaed dc-dc series-resonan converer ha is conrolled by a combinaion of variable-frequency and secondary-side-swich delay-ime conrol has been inroduced. The proposed converer is designed as he oupu sage of an OBCM ha operaes wih a wide baery-volage range. The delay-ime conrol which is implemened by he modulaion of secondary-side swiches is used o assis he convenional variable-swiching-frequency conrol of primary swiches. The performance evaluaion of he proposed series-resonan converer wih delay-ime conrol was done on a 3.3-kW prooype delivering energy from 400- V bus, which is he oupu of he PFC fron end, o a baery operaing wih volage range beween 180 V and 430 V. The prooype circui exhibis he maximum full-load efficiency of 97.3% wih a full-load swiching-frequency variaion from 144 khz o 175 khz over he enire oupu-volage range. Frequency [khz] khz 175 khz I OUT = 11 A 144 khz Oupu Volage [V] P OUT = 3.3 kw V IPUT = 400 V Fig. 10. Measured swiching frequency of experimenal prooype as funcion of oupu volage. Frequency range is significanly narrowed by delay-ime conrol. REFERECES [1] M. Carrasco, E. Galvan, G. Escobar, R. Orega, and A. M. Sankovic, Analysis and experimenaion of nonlinear adapive conrollers for he series resonan converer, IEEE Trans. Power Elecron., vol. 15, no. 3, pp , May 000. [] B. ang, R. Chen, and F.C. Lee, "Inegraed magneics for LLC Resonan Converer," in IEEE Applied Power Elecronics Conf. Rec. 00, pp [3] B. Lu, W. Liu,. Liang, F.C. Lee, and J.D. Van Wyk, "Opimal design mehodology for LLC resonan converer," in IEEE Applied Power Elecronics Conf. Rec. 006, pp [4] G. Ivensky, S. Bronshein, and A. Abramoviz, Approximae analysis of resonan LLC DC-DC converer, IEEE Trans. Power Elecron., vol. 6, no. 11, pp , ov [5] H. Molla-Ahmadian, A. Karimpour,. Pariz, and F. Tahami, Hybrid modeling of a DC DC series resonan converer: Direc piecewise affine approach, IEEE Trans. Circuis Sys. I, Fundam. Theory Appl., vol. 18, no. 5, pp , Jul. 01. [6] X. Fang, H. Hu, Z. J. Shen, and I. Baarseh, Operaion mode analysis and peak gain approximaion of he LLC resonan converer, IEEE Trans. Power Elecron., vol. 7, no. 4, pp , Apr

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