[SiC-En-2013-23] High-Efficiency Isolated Bidirectional AC–DC Converter for a DC Distribution System

1642 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 4, APRIL 2013

High-Efficiency Isolated Bidirectional ACDCConverter for a DC Distribution System

Ho-Sung Kim, Member, IEEE, Myung-Hyo Ryu, Ju-Won Baek, Member, IEEE, and Jee-Hoon Jung, Member, IEEE

AbstractA high-efficiency isolated bidirectional acdc con-verter is proposed for a 380-V dc power distribution system tocontrol bidirectional power flows and to improve its power con-version efficiency. To reduce the switches losses of the proposednonisolated full-bridge acdc rectifier using an unipolar switchingmethod, switching devices employ insulated-gate bipolar transis-tors, MOSFETs, and silicon carbide diodes. Using the analysisof the rectifiers operating modes, each switching device can beselected by considering switch stresses. A simple and intuitive fre-quency detection method for a single-phase synchronous referenceframe-phase-locked loop (SRF-PLL) is also proposed using a filtercompensator, a fast period detector, and a finite impulse responsefilter to improve the robustness and accuracy of PLL performanceunder fundamental frequency variations. In addition, design andcontrol methodology of the bidirectional full-bridge CLLC resonantconverter is suggested for the galvanic isolation of the dc distribu-tion system. A dead-band control algorithm for the bidirectionaldcdc converter is developed to smoothly change power conversiondirections only using output voltage information. Experimental re-sults will verify the performance of the proposed methods using a5-kW prototype converter.

Index TermsACDC boost rectifier, bidirectional isolated con-verter, CLLC resonant converter dc distribution system.

I. INTRODUCTION

DC DISTRIBUTION system is one of important futurepower systems to save energy and to reduce CO2 emis-sion because it can improve the efficiency of systems due tothe reduction of the number of power conversion stages [1][3].Especially, the dc distribution system for a residential houseusing dc home appliances can allow the flexibility of mergingmany renewable energy sources because most of the output ofrenewable energy sources is dc. The overall system configura-tion of the proposed 380-V dc distribution system is shown inFig. 1. In order to balance the power flow and to regulate thedc-bus voltage, the dc distribution system requires an isolatedbidirectional acdc converter to interface between dc bus and

Manuscript received March 31, 2012; revised July 12, 2012; accepted August6, 2012. Date of current version October 26, 2012. Recommended for publica-tion by Associate Editor M. Veerachary.

H.-S. Kim is with the Department of Electrical Engineering, Pusan NationalUniversity, Busan 609-735, Korea, and also with the Power Conversion andControl Research Center, HVDC Research Division, Korea ElectrotechnologyResearch Institute, Changwon 642-120, Korea (e-mail: [email protected]).

M.-H. Ryu, J.-W. Baek, and J.-H. Jung are with the Power Conversionand Control Research Center, HVDC Research Division, Korea Electrotechnol-ogy Research Institute, Changwon 642-120, Korea (e-mail: [email protected];[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2213347

Fig. 1. 380-V dc distribution system with an isolated bidirectional acdcconverter.

ac grid. It usually consists of a nonisolated bidirectional acdcrectifier [4][9] for grid-connected operation and an isolatedbidirectional dcdc converter to interface dc bus and dc link ofthe rectifier [10][18].

The single-phase nonisolated bidirectional rectifier typicallyconsists of a conventional full-bridge structure. It has two si-nusoidal pulsewidth modulation (SPWM) methods such as thebipolar and the unipolar switching modes. One of the disad-vantages of the bipolar switching mode is the need of a largeinductor to reduce the input current ripple because the peak-to-peak voltage of the inductor is more than twice the unipolarswitching mode. If the full-bridge rectifier operates in the unipo-lar switching mode, inductance for a continuous current mode(CCM) power factor correction (PFC) operation can be reduced.One of full-bridge rectifier legs in the unipolar switching modeis operated at a line frequency while the other one is modu-lated at a switching frequency. However, the unipolar switchingmode rectifier using conventional switching devices including anormal antiparallel diode causes high reverse recovery currentand turn-on switching noise. The switching and the conduc-tion losses in the bidirectional rectifier are the main cause ofdecreasing power conversion efficiency.

The phase estimation, so-called phase-locked loop (PLL),is required to control the bidirectional acdc rectifier; espe-cially, the phase information of supply voltage is mandatoryto generate a current reference. One of the popular PLL meth-ods is synchronous reference frame (SRF-PLL) which uses a

0885-8993/$31.00 2012 IEEE

KIM et al.: HIGH-EFFICIENCY ISOLATED BIDIRECTIONAL ACDC CONVERTER FOR A DC DISTRIBUTION SYSTEM 1643

AC

Single-phase Bidirectional Rectifier for Grid Interface

Bidirectional Full-bridge CLLC Resonant Converter for Isolation

L1

S1 S3

S2 S4

Q1 Q3

Q2 Q4

Q5 Q7

Q6 Q8

DS1 DS3

CDL

TrLr1 Lr2

Cr1 Cr2Co

+Vo-

+VDL

-

DSP Controller (TMS320F28335)

Voltage & CurrentSensing Circuit

RectifierDriving Circuit

Bidirectional CLLC Driving CircuitOutput voltageSensing Circuit

VAC IAC VDL S1 S2 S3 S4 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Vo

Fig. 2. Circuit configuration of the proposed isolated bidirectional acdc converter.

rotating reference frame for tracking a phase angle. However,the conventional SRF-PLL has a weak point of frequency track-ing performance because it uses the constant angular frequencyof a fundamental component. It can cause a tracking error inthe PLL operation when the fundamental frequency changesto the different value of the constant angular frequency. Nu-merous methods for improved PLL have been presented andintroduced in the literature [19][23]. Even though they havegood performance against the frequency distortion, their algo-rithms are complicated to be implemented for various applica-tions. Another PLL method has been proposed using a simplefrequency detector and trigonometric calculations without anylinear phase detector; however, this method requires the half-cycle data acquisition of the fundamental frequency to detect theexact line frequency [24]. Therefore, a more simple, faster, andmore intuitive frequency detection method should be upgradedfor improving the performance of the single-phase bidirectionalrectifier.

Some isolated full-bridge bidirectional dcdc convertertopologies have been presented in recent years. A boost full-bridge zero-voltage switching (ZVS) PWM dcdc converter wasdeveloped for bidirectional high-power applications. However,it needs extra snubber circuits to suppress the voltage stress ofthe switches [25][28]. A bidirectional phase-shift full-bridgeconverter was proposed with high-frequency galvanic isolationfor energy storage systems [29], [30]. This converter can im-prove power conversion efficiency using a zero-voltage tran-sition feature; however, it requires input voltage variations toregulate constant output voltage because this topology can onlyachieve the step-down operation. A bidirectional full-bridgeLLC resonant converter was introduced for a UPS system with-out any snubber circuits [17]. This topology can operate undersoft-switching conditions of primary switches and secondaryrectifier. In addition, the topology confines voltage stresses with-out any clamp circuits. However, application of this convertershowed different operations between transformers turn ratioand the difference of resonant networks. Therefore, the novel

design guides suitable for a 380-V dc distribution system shouldbe proposed.

In this paper, the high-efficiency isolated bidirectional acdcconverter system with several improved techniques will be dis-cussed to improve the performance of a 380-V dc distributionsystem. In order to increase the efficiency of the nonisolatedfull-bridge acdc rectifier, the switching devices are designedby using insulated-gate bipolar transistors (IGBTs) without anantiparallel diode, MOSFETs, and silicion caribde (SiC) diodes.Through the analysis of operational modes, each switch is se-lected by considering switch stresses. The major novelty of theproposed PLL is the suggestion of a simple and intuitive fre-quency detection method for the single-phase SRF-PLL usingan advanced filter compensator, a fast quad-cycle detector, anda finite impulse response (FIR) filter. Finally, design guides andgain characteristics of the bidirectional full-bridge CLLC res-onant converter with the symmetric structure of the primaryinverting stage and secondary rectifying stage will be discussedfor a 380-V dc distribution system. Experimental results willverify the performance of the proposed methods using a 5-kWprototype converter.

II. CIRCUIT CONFIGURATION OF THE PROPOSED ISOLATEDBIDIRECTIONAL ACDC CONVERTER

Fig. 2 shows the circuit configuration of the proposed iso-lated bidirectional acdc converter. It consists of the single-phase bidirectional rectifier for grid interface and the isolatedbidirectional full-bridge CLLC resonant converter for galvanicisolation. To control the proposed converter, a single digitalsignal processor (DSP) controller (TMS320F28335) was used.The power flow directions in the converter are defined as fol-lows: rectification mode (forward direction of power flow) andgeneration mode (backward direction of power flow).

The switching method of the proposed single-phase bidi-rectional rectifier is unipolar SPWM. In order to reduce theswitching losses caused by the reverse recovery current in the


rectification mode, the high-side switches of the proposed rec-tifier are composed of two IGBTs without antiparallel diodes(S1 and S3) and two SiC diodes (DS1 and DS3). The low-side switches are composed of two MOSFETs (S2 and S4) forreducing conduction loss and for using ZVS operation in thegeneration mode. The detailed circuit operation of the proposedbidirectional rectifier and advanced PLL method will be dis-cussed in Section III.

The proposed bidirectional full-bridge CLLC resonant con-verter has the full-bridge symmetric structure of the primaryinverting stage and secondary rectifying stage with a symmet-ric transformer. Using the high-frequency transformer, the con-verter can achieve galvanic isolation between the primary sideand the secondary side. The transformer Tr is modeled with themagnetizing inductance Lm and the transformers turn ratio of1:1. The leakage inductance of the transformers primary andsecondary windings is merged to the resonant inductor Lr1 andLr2 , respectively. The resonant capacitors Cr1 and Cr2 makeautomatic flux balancing and high resonant frequency with Lr1and Lr2 . The detailed analysis and design guides of the proposedconverter will be discussed in Section IV.

III. NONISOLATED ACDC BIDIRECTIONAL RECTIFIERHigh-power rectifiers do not have a wide choice of switch-

ing devices because there are not many kinds of the switch-ing devices for high-power capacity. Generally, the full-bridgerectifier in high-power applications consists of the same fourdevices: IGBT modules or intelligent power modules (IPMs)are chiefly used. This modular devices have antiparallel diodes,which have fast recovery characteristics. A fast recovery diode(FRD) has a small reverse recovery time trr . When the full-bridge rectifier operates, the time trr causes a reverse recoverycurrent which increases power loss and EMC problems. There-fore, soft-switching techniques using additional passive or ac-tive snubber circuits have been proposed [31][33]. Even thoughthese methods require a relatively large number of passive oractive components, which decrease the reliability of the rectifiersystem and increase system cost, the soft-switching techniquesin the high-power rectifier are a unique solution for reducing thereverse recovery problems. On the other hand, a medium-powerrectifier system around 5 kW for a residential house or buildinghas a wide selection of switching devices such as discrete-typeIGBTs and MOSFETs. Especially, commercial IGBTs with-out the antiparallel diode can be selected to replace antiparallelFRDs to SiC diodes. In theory, the SiC diode does not have trr .Therefore, the combination of IGBTs without the antiparalleldiode and the SiC diodes is another viable solution to reducethe reverse recovery problems.

In the bidirectional rectifier using the unipolar switchingmethod, the turn-on period of low-side switches increases oneand half times more than the turn-on period of the high-sideswitches. Therefore, the low-side switches should be chosento consider low conduction losses for increasing the powerconversion efficiency. The latest generation of MOSFETs em-ploying superjunction technology can achieve extremely lowon-resistance RDS.on . It is better than the latest very low VCE

AC

L1

S1 S3

S2 S4

DS1 DS3

CDL

AC

L1

S1 S3

S2 S4

DS1 DS3

CDL

IL1

IL1 AC

L1

S1 S3

S2 S4

DS1 DS3

CDLIL1

(b)

(c) (d)

AC

L1

S1 S3

S2 S4

DS1 DS3

CDLIL1

(e)

AC

L1

S1 S3

S2 S4

DS1 DS3

CDLIL1

Irr-c

(a)

Fig. 3. Operating modes of the proposed bidirectional acdc rectifier in therectification mode: (a) Mode 1, (b) Mode 2, (c) Mode 3, (d) Mode 4, and(e) Mode 5.

IGBTs in the view point of the conduction loss when the samecurrent flows into the switching devices. Therefore, MOSFETsare suitable for the low-side switches in the unipolar switchingmethod.

A. Consideration for Reverse Recovery Lossesin a Rectification Mode

In the rectification mode, the bidirectional rectifier has fiveoperating modes in a single switching cycle. The circuit opera-tions in the positive half period of the input voltage are shownin Fig. 3. The dark lines denote conducting paths for each state.The theoretical waveforms of the proposed rectifier are given inFig. 4.

At time t0 , the low-side switch S2 turns ON. At this time,if DS1 is FRD, DS1 cannot immediately turn OFF becauseof its reverse recovery process. This simultaneous high reverserecovery current causes an additional switching loss on S2 . Thereverse recovery current increases the current stress on the low-side switches and decreases the EMI performance of the rectifier.To solve this reverse recovery problem, the high-side switchesof the proposed circuit should use IGBTs without antiparalleldiodes and SiC diodes as antiparallel diodes of the IGBTs. Eventhough the reverse recovery current is not completely zero in a


t 1 t 2t 0 t 3

VS2.gs

VS2.ds

IS2

t

ID

VS1.gs

VS1.ds

t 4 t 5

Irr-c

Irr-c

Fig. 4. Theoretical operating waveforms of the proposed bidirectional acdcrectifier in the rectification mode.

practical manner, it is significantly reduced as compared withthe FRD operation.

At t3 , the gate signal VS1.gs turns ON. Since the IGBTs cannotconduct in the reverse direction, the energy in the input voltagesource and the inductor L1 is still discharged through SiC diodeDS1 . In the rectification mode, the high-side SiC diodes in-stead of the IGBTs are fully operated during entire rectificationmodes. Therefore, the conduction loss of the high-side switchesdepends on the forward voltage drop of the SiC diodes. Otheroperation modes are not different from the conventional full-bridge rectifier using a unipolar switching method.

B. Consideration for Switching Losses in a Generation ModeIn the generation mode using the same switching pattern as

the rectification mode, the proposed bidirectional rectifier hasfive operating modes in a single switching cycle. The circuitoperations in the positive half period of the input voltage areshown in Fig. 5. After the discharge operation of dc-links en-ergy, the antiparallel diode including the low-side switch S2 willbe conducted by freewheeling operation using inductors energyas shown in Mode 2. During this period, the energy stored inthe output capacitance of S2 can be fully discharged. In Mode3, S2 turns ON under the ZVS condition. Through these oper-ation modes, the turn-on losses in the low-side switches can bereduced. When the high-side switch S1 turns ON in Mode 5,the antiparallel diode of S2 cannot immediately turn OFF be-cause of poor reverse recovery performance of the MOSFETsantiparallel diode. It causes an additional switching loss on S1through the reverse recovery current. Therefore, the genera-tion mode using the same switching pattern of the rectificationmode has advantages of soft switching and disadvantages ofreverse recovery loss. The MOSFETs losses in the generationmode depend on the MOSFETs RDS.on and the reverse recov-ery characteristics of the antiparallel diode. The selection ofthe MOSFET can determine the significant loss factor between

(b)(a)

(d)

(e)

(c)

Fig. 5. Operating modes in the rectifiers generation mode using the sameswitching pattern as the rectification mode: (a) Mode 1, (b) Mode 2, (c) Mode3, (d) Mode 4, and (e) Mode 5.

switching and conduction losses. However, if IGBTs are usedfor the low-side switches, the ZVS operation is not significantto reduce their switching loss. There are also reverse recoverylosses through the reverse recovery characteristics of the an-tiparallel diode. They can increase the turn-off switching lossesthrough the IGBTs tailing current.

If the reverse recovery loss through the MOSFETs is sig-nificant, it can be overcome employing the inverted switchingpattern in the generation mode. The operation mode of the in-verted switching pattern is shown in Fig. 6. In this operation,the switching pattern is perfectly inverted and the turn-on periodof the high-side switches is one and half times longer than theturn-on period of the low-side switches. In Mode 5, the low-sideswitch S4 turns ON. At the same time, the reverse recoverycurrent should be limited by the SiC diode DS3 . Using thisswitching pattern in the generation mode, there are no benefitsof the ZVS operation. However, the reverse recovery losses canbe significantly reduced as compared with the same switchingpattern of the rectification mode. The modified switching patterndoes not affect the power conversion and control performancesof the acdc rectifier.

C. Consideration for Conduction LossesIn the unipolar switching method, the turn-on period of low-

side switches is one and half times longer than the turn-on


(b)(a)

(d)

(e)

(c)

Fig. 6. Operating modes in the rectifiers generation mode using the invertedswitching pattern against the rectification mode: (a) Mode 1, (b) Mode 2, (c)Mode 3, (d) Mode 4, and (e) Mode 5.

period of high-side switches. To analyze the conduction lossof MOSFETs as the low-side switches, the circuit operation ofthe proposed bidirectional rectifier assumes that inductor L1 issufficiently large to operate CCM and the ac input current is aperfectly sinusoidal waveform. Generally, the conduction lossin MOSFETs can be calculated using the rms current passingthrough MOSFETs RDS.on . Since the turn-on period of thelow-side switches is 75% of the fundamental period of the acinput current, the rms current of the low-side switches can becalculated using the following equation:

Irms.low =

12

32

o

(Iin.P sint)2dt. (1)

Through the aforementioned assumptions, the peak current Iin .Pand the average current Iin.av of the ac input can be derived asfollows:

Iin.P =

2Pout

Vin.rms(2)

Iin.av =2Iin.P (3)

where is the power conversion efficiency.Using the aforementioned equations, the total conduction

losses of the rectifiers switches in the rectification can be

Output Power [W]

P[W

]

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

20

40

60

80

100

120

140

160

180

IXKR47N60C5IXKR47N60C5 2IGW75N60T

Fig. 7. Calculated conduction loss of rectifier switches in the rectificationmode.

calculated as follows:

Pcon-rec 2(Irms.low )2RDS.on + 2(

14Iin.av

)VF

=34I2in.P RDS.on +

1Iin.P VF (4)

where the conduction loss in the rectification mode is Pcon-recand VF is the forward voltage drop of the high-side SiCdiode, respectively. In comparison to using IGBTs for thelow-side switches, Fig. 7 shows the calculated conductionlosses using (4). The low-side switches use MOSFETs, whichhave extremely low RDS.on (IXKR47N60C5) and the latestIGBTs (IKW75N60T), which have the very low collectoremitter threshold voltage VCE . The high-side switches use SiCdiodes (C3D20060D) as the antiparallel diode and IGBTs with-out antiparallel diode (IGW75N60T). The typical values ofRDS.on , VF , and VCE are obtained from their datasheets. SinceVF and VCE are almost the same value, the conduction loss inthe generation mode is expected to be nearly the same as theconduction loss in the rectification mod, Pcon-rec . In Fig. 7, theconduction losses of MOSFETs are less than the conductionlosses of IGBTs under the load condition of 6.5 kW or less.Under the light-load condition, MOSFETs is better than IGBTsin the view point of the power conversion efficiency. At the ratedload (5 kW), the difference of the conduction losses betweenMOSFETs and IGBTs is about 12 W. If two MOSFETs areused in parallel, the conduction losses in the rated load will bereduced about 30 W.

D. SRF-PLL With Enhanced Frequency EstimatorFor the application of the grid-interactive power converters,

the phase estimation of the supply voltage is required to controlthe entire power system; especially, the phase information of thesupply voltage is mandatory to generate the current reference.The phase estimation method requires robustness to noise anddisturbance from grid, accuracy to the fundamental frequencyvariation and harmonic distortion, and easy implementation us-ing analog or digital platforms. The SRF-PLL is one of thepopular methods. It has a weak point of a frequency trackingperformance. In Fig. 8, the constant angular frequency of thefundamental component s is used as a feedforward term forcompensating the phase angle tracking. It can cause a track-ing error in the PLL operation when the fundamental frequency


Fig. 8. Block diagram of a conventional single-phase SRF-PLL.

changes to the different value of the constant s . To track un-expected fundamental frequencies, the SRF-PLL requires a fre-quency estimator instead of the constant angular frequency.

The SRF-PLL method uses the /2 phase-shifted wave ofthe supply voltage using the all-pass filter (APF). Therefore,the PLL has four zero crossing points in a period of the supplyvoltage and they are located at every /2. It means that thefrequency information can be obtained at every quarter of theperiod. However, the conventional research has updated the fre-quency information at every half of the period. Consequently, theproposed frequency detection algorithm illustrated in Fig. 9(a)can update the variation of the supply frequency two times fasterthan the conventional one. In the algorithm, there are two timezones to calculate the supply period: Tc and Td where Tc is thetime duration between two zero crossing points and Td is thetime duration near the zero crossing point. Td is introduced toimplement a practical PLL system using the proposed algorithmsince noises in the power stage and sensors make the exact de-tection of the zero crossing points imperfect. In Fig. 9(a), thesupply frequency can be estimated as shown in

fs =1

4(Tc + Td). (5)

The FIR low-pass filter (LPF) illustrated in Fig. 9(b) isadopted to the proposed frequency detector instead of a movingaverage (MA). The filtered output can be calculated as follows:

sf [n] =7

k=0

bks[n k] (6)

where s[n] is the nth input signal, sf [n] is the nth filteredsignal, and bk is the kth-order filter coefficient. This filter hasseventh order and uses the Blackman window to enhance thesharpness of the filter at the cut-off frequency and to suppresssidelobe components. It can improve the transient dynamics andreduce the steady-state error of the frequency detector. Fig. 9-(c)shows the block diagram of the single-phase SRF-PLL using theproposed frequency detector. The frequency detector calculatesthe fundamental frequency using (5) and it is added to the PIvalue of Vde instead of the constant value to generate an accurateangle value with respect to frequency variations. In addition,the calculated frequency is used in the voltage generator whichmakes the orthogonal waveform to the supply voltage.

Fig. 10 shows the comparison of the frequency detectionspeeds of three methods: half-cycle detection (HD) with MA,

(a)

(b)

(c)

Fig. 9. Proposed single-phase PLL method: (a) frequency detection algorithmusing zero crossing and APF, (b) block diagram of the seventh-order FIR filter,and (c) block diagram of the PLL using the proposed frequency estimator.

quad-cycle detection (QD) with MA, and QD with FIR filterusing the Psim simulation software. The simulation result ofthe HD with MA, which is the conventional one, shows highfluctuation and long settling time in the fundamental frequencydetection. However, the simulation result of QD with MA showslow fluctuation and short settling time because of the shorterupdate duration than the case of HD. In addition, QD with FIR


70

65

60

75

55

50Fun

dam

enta

l Fre

quen

cy (

Hz)

Time (100ms/div)

Real Frequency

Estimated: HD with MA

Estimated: QD with MA

Estimated: QD with FIR

Fig. 10. Simulation results of the proposed single-phase PLL for comparisonof frequency detection speed.

filter has higher transient dynamics and faster convergence thanthe case of QD with MA because of the seventh-order FIR filterusing the Blackman window instead of MA.

IV. ISOLATED BIDIRECTIONAL CLLC RESONANT CONVERTERIn this section, the design methodology of the power stages of

the proposed bidirectional CLLC resonant converter will be dis-cussed. The new control schemes are proposed to decide powerflow directions and to regulate output voltage under bidirectionalpower flows. In addition, the dead-band control algorithm is pro-posed to smoothly change the power conversion direction onlyusing output voltage information. This algorithm is based on ahysteresis control method to decide the power flow direction ofbidirectional converters.

A. Gain Analysis Using the FHA modelThe first harmonic approximation (FHA) model and opera-

tion mode in the proposed CLLC resonant converter are alreadyintroduced in [18]. Fig. 11 shows the equivalent circuit of theproposed full-bridge bidirectional CLLC resonant converter us-ing the FHA method. The resonant network of the converter iscomposed of the series resonant capacitor Cr = Cr1 = Cr2 , theequivalent series resonant inductance Leq , and the magnetizinginductance Lm . Since the turn ratio of the transformer is 1:1,it does not affect the circuit model and Leq equals the twice ofthe series resonant inductance Lr = Lr1 = Lr2 . The forwardtransfer function Hr of the resonant network can be derived asshown in

Hr (s) =Vo,FHA(s)Vi,FHA(s)

=Zo(s)Zin(s)

Ro,e(sCr )1 + Ro,e

(7)

Zin(s) =1

sCr+ sLeq(s) + Zo(s) (8)

Leq(s) =Lr

s2LmLr [Ro(sLm + sLr + Ro)]1 + 1(9)

Zo(s) =LmC

1r + sLmRo,e

sLm + (sCr )1 + Ro,e, Ro,e =

82

Ro. (10)

1:1Cr1

Ro VoVi,FHA Lm

Lr1 Ir,FHA

Io

Ii vCr1

Ro,e Vo,FHA

Hr

Cr2

Lr2 vCr2

Fig. 11. FHA model of the proposed bidirectional CLLC resonant converter.

Therefore, the gain of converter Hr can be derived asfollows:

VoVin

= Hr (fn ) = f3n

f 2nA2(fn ) + Q2B2(fn )

(11)

where A(fn ) and B(fn ) are the function components as follows:

A(fn ) = f 2n (1 + k) + k (12)B(fn ) = f 4n f 2n (2 + k) + k. (13)

In addition, fn can be described using the resonant frequencyfr ,Q is the quality factor, and k is the inductance ratio betweenthe magnetizing and leakage inductance, respectively, given by

fn =fsfr

, fr =1

2

LrCr,Q =

ZrRo,e

, Zr =

LrCr

, k =LrLm

.

(14)Fig. 12 (a) shows the gain curve according to load current

and normalized frequency at Lm = 130 H. The gain has apeak value at low resonant frequency which contains the mag-netizing inductance as a resonant component. At high resonantfrequency, the gain of the converter is slightly higher than unitygain. Under the light-load condition, the gain is high and theslope of the gain curve is sharp. However, the overall value ofthe gain curve is decreasing under the heavy-load condition. Thehigher load induces the lower gain in the proposed bidirectionalCLLC resonant converter.

B. Soft-Switching ConditionsThe ZVS operation of the primary power MOSFETs and the

soft commutation of the output rectifiers are significant factorsfor the efficiency-optimal design of the bidirectional full-bridgeCLLC resonant converter. The lower operating frequency thanthe resonant frequency can guarantee the soft commutation ofthe output rectifiers because the difference between the switch-ing frequency and the resonant frequency makes discontinu-ous rectifying current. In addition, during the dead time of theswitches, the primary current should discharge the output capac-itance of four primary switches for their ZVS turn-on. There-fore, the magnetizing inductance is limited by the maximumoperating frequency as shown in

fs fr (15)

Lm tdt16CSfs,max =tdt

16CSfr. (16)


(a)

(b)

Fig. 12. Theoretical gain curves according to normalized frequency. (a) Ac-cording to load current (Lm =130 H). (b) According to magnetizing inductanceat full load (5 kW).

Inequality (16) shows that small Lm can guarantee the ZVSof main switches. However, small Lm also increases the con-duction loss of MOSFETs, transformer windings, and outputrectifiers in the primary and secondary sides. On the other hand,the large magnetizing inductance satisfied with (16) can reducethe conduction loss and improve the power conversion efficiencyof the converter. However, large Lm can make a gain reductionbelow the unity gain in the proposed bidirectional CLLC reso-nant converter. Fig. 12(b) shows the gain curve according to themagnetizing inductance and normalized frequency. At highermagnetizing inductance than 160 H, the gain curve does notmonotonically decrease. Under this condition, when the loadincreases or the input voltage decreases, the conventional PIcontroller cannot regulate the output voltage.

C. Design Guide for a Limited Gain CurveIn order to obtain the monotonic gain curve according to the

operating frequency, the resonant components of Lm ,Lr , andCr should be selected considering proper fr for the operatingfrequency, and proper Q and k for the available gain curve higherthan the unity gain. The resonant network in the proposed bidi-rectional CLLC resonant converter should be designed to keepthe gain of the converter higher than the unity gain with respectto entire load range. The monotonic gain curve can regulate the

output voltage employing a linear feedback controller. Usingthe polarity of the gain functions derivative with respect to fn ,the gain can be decided to whether a monotonically decreasingfunction or not. The derivative of (11) can be derived follows:

d

dfnHr (fn ) = 2kf

4nA(fn )Q2f 2nB(fn )C(fn )[f 2nA

2(fn ) + Q2B2(fn )]1.5 (17)

where C(fn ) is the function component as shown in

C(fn ) = f 4n + f2n (2 + k) 3k. (18)

The derivative of the gain curve has to be negative if thegain is a monotonically decreasing function within the operatingfrequency. The polarity of (17) is decided by only the value of itsnumerator because the denominator of (17) is always positive.For the quality factor Q, an inequality can be derived using thenumerator of (17) as shown in

Q /JPEG2000ColorImageDict > /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 150 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages false /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict > /GrayImageDict > /JPEG2000GrayACSImageDict > /JPEG2000GrayImageDict > /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 600 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False

/Description >>> setdistillerparams> setpagedevice

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[SiC-En-2013-23] High-Efficiency Isolated Bidirectional AC–DC Converter for a DC Distribution System