Design of a Highly Efficient Bidirectional Isolated LLC Resonant Converter A. Hillers, D. Christen and J. Biela Laboratory for High Power Electronic Systems ETH Zurich, Physikstrasse 3, CH-8092 Zurich, Switzerland Email: [email protected]„This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promo- tional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document you agree to all provisions of the copyright laws protecting it.”
Transcript
Design of a Highly Efficient Bidirectional Isolated LLC Resonant Converter
A. Hillers, D. Christen and J. Biela Laboratory for High Power Electronic Systems
ETH Zurich, Physikstrasse 3, CH-8092 Zurich, Switzerland Email: [email protected]
„This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of ETH Zürich’s products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promo-tional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document you agree to all provisions of the copyright laws protecting it.”
Design of a Highly Efficient Bidirectional Isolated LLCResonant Converter
A. Hillers, D. Christen and J. BielaLaboratory for High Power Electronic Systems
ETH Zurich, Physikstrasse 3, CH-8092 Zurich, SwitzerlandEmail: [email protected]
Abstract—The isolated unidirectional LLC resonant converteris known for its outstanding efficiency and high power density.Little information has however been published about the possi-bility of transferring power in the reverse direction. This paperpresents modulation schemes for making the LLC converterbidirectional. High efficiencies are predicted for both directionsof power flow, though, as the behavior of the resonant tankis substantially different in the reverse direction, some of theinherent benefits of the conventional LLC converter are lost.
Index Terms—Bidirectional, galvanically isolated, LLC series-parallel resonant converter
I. INTRODUCTION
Resonant converters are commonly selected for applicationswhich demand for a high power density and a high energy ef-ficiency. By featuring soft-switching, the switching frequencycan in general be chosen much higher than the switchingfrequency of a comparable hard-switching converter. As aconsequence, the volume required for the passive componentsis drastically reduced, enabling high power densities and highpower conversion efficiencies.
In this paper, a highly efficient battery charger is designed,which is capable of bidirectionally charging light electricvehicles (LEVs). The charger will be connected to a dc micro-grid at Vdc = 450V and will feature an output voltage rangefrom 17V to 56V. To limit the duty-cycle and/or frequencyvariation, and to provide galvanaic separation from the dc-bus,a transformer is needed.
For this type of application, the LLC resonant converter [1]promises remarkable unidirectional performance [2].
In [3], a bidirectional LLC prototype was built, but nooptimized modulation schemes were employed and the con-verter did not achieve a satisfactory power conversion effi-ciency. In [4] a symmetric fourth-order resonant converter wasbuilt based on an LLC resonant tank, featuring an additionalresonant capacitor. However, the proposed CLLC converteroperates in boost-mode in both directions and is therefore notvery suitable for use as a voltage-regulating converter.
In the following, a bidirectional LLC converter capable ofbuck-boost operation is designed. Section II summarizes the“classical” unidirectional operating principles of the converterand in Section III, modulation schemes are derived for ahighly efficient operation in the reverse direction. In Sec-tion IV, the converter is designed for use as a bidirectionalLEV charger. The analytic considerations are verified in Sec-tion V by time-domain simulations and the performance of the
sLi 2i
4S
3S
2S
1S
8S
7S
6S
5S
2v1vdcV
sL
sC1C 2CpL
n 1:
batV
sCv
Fig. 1: Circuit diagram of the LLC converter equipped with full-bridges onboth sides to allow for bidirectional power transfer.
converter is discussed. Finally, the bidirectional LLC converteris compared to the dual active full-bridge converter.
II. OPERATION IN THE FORWARD DIRECTION
Fig. 1 shows the basic circuit diagram of a bidirectionalLLC resonant converter. The resonant tank consists of a seriescapacitor Cs and a transformer with a turns-ratio of n, intowhich Ls and Lp are integrated.
The forward operation has already been analyzed com-prehensively for the classical unidirectional LLC converter(e.g. in [1] and [5]). The primary side full-bridge is usedto apply a square-wave voltage v1(t) to the resonant tank.A near sinusoidal alternating current will flow. The secondaryside switches perform synchronous rectification to increase thepower conversion efficiency [6].
As the resonant tank acts as a bandpass filter, it is commonto assume that only the fundamental components of the cur-rents and voltages in the resonant tank are responsible for thepower transfer. This is called the first harmonic approximation(FHA) [1]. In that sense, the square-wave v1 applied to theresonant tank is represented by its fundamental component
Fig. 2: Voltage gain M of the LLC converter operating in the forward directionas a function of the normalized switching frequency (a) for different valuesof h (Q = 0.8) and (b) different values of Q (h = 3).
The following substitutions are introduced:
V ′bat = nVbat, fr1 =1
2π√LsCs
,
k =fs
fr1, h =
Lp
Ls,
Z0 =
√Ls
Cs, Q =
Z0
R′2,ac.
The switching frequency is defined relative to the higherresonance frequency of the resonant tank fr1 by the parameterk. Z0 is the characteristic impedance of the resonant tank. Tomake (3) independent of the actual values of Lp, Ls and Cs,the variables h and Q are introduced. Pbat is the power that istransferred to the battery. The lower resonance frequency fr2is the frequency, at which the voltage gain M is maximal.
Fig. 2 illustrates the voltage gain for different designs(variations of h) and different loading conditions (variations ofQ) at different relative switching frequencies. At lighter loads(lower values of Q), the maximum achievable voltage gain ishigh. When operated between fr2 and fr1, the LLC converteris able to boost (M > 1). Fig. 2 implies, that a limitedcapability for voltage conversion ratios lower than one existswith switching frequencies above fr1. However, the necessaryswitching frequency variation is large because the gain curveis very flat in this region [7]. In these modes, the resonant tankbehaves inductively and zero voltage switching (ZVS) can beperformed on the primary side. Zero current switching (ZCS)is achieved on the secondary side, because the secondaryside switches are performing synchronous rectification. If theconverter was operated below the lower resonance frequency,ZVS would be lost as the resonant tank behaves capacitive inthis region [1]. Thus, this mode is typically avoided.
A. Clamped ModeBy making use of the clamped switching state available
with the primary side full-bridge, the range for voltage controlin buck mode can be expanded. This is necessary for thelater introduced bidirectional design. In terms of the FHA,the PWM reduces the fundamental component of v1 [8]:
v1,(1) =4Vdc
π· cos
((1− d)
π
2
)(4)
The duty-cycle is defined as d = 2τT . A duty-cycle of d = 1
0A
0V
t
t
btat
1vv2dcV
batV
τ
T
pLi
pLi
sLi−
sLi−
(a)
(b)
btat
0A
0V
t
tT
T
1v
v2dcV
batVτ
Fig. 3: (a) Soft switching fails on the primary side when the duty-cycle istoo small in clamped mode. (b) The asynchronous clamped mode allows forlower duty-cycles than the clamped mode.
corresponds to the block mode in which the LLC converteris typically operated. The lower limit of d is defined bythe current which is available for ZVS when the converteris leaving the clamped voltage state. The lower d gets, themore will the point in time, at which the clamped state isleft, move towards the zero-crossing of the current until theparasitic drain-source capacitances of the switches can nolonger be fully discharged. In Fig. 3, the case where ZVSfails is illustrated by a small zigzag arrow.
B. Asynchronous Clamped Mode ModulationTo further increase the possibility of voltage regulation, the
asynchronous clamped mode (ACM) [8] can be used:
v1,(1) =Vdc
π
√10 + 6 cos ((1− d)π) (5)
This time, the clamped state is only entered during thefirst conduction half-period. The voltage waveform now hasa dc-offset which is blocked from the transformer by theresonant capacitor Cs. Fig. 3 shows the currents and voltageswhen using the asynchronous clamped mode. This time, soft-switching is achieved. The limiting case for this modulationscheme is reached where v1 is only toggled between negative(resp. positive) and zero (clamped state). However, a smoothtransition to this mode is not possible because soft-switchingwould be lost with very low duty cycles.
III. OPERATION IN THE REVERSE DIRECTION
To transfer power in the reverse direction, the secondaryside switches can apply a square wave voltage v2(t) to theresonant tank. Similar to the analysis of the forward direction,the ratio of input voltage to output voltage can be expressedwith the help of the FHA. Because the resonant-tank is notsymmetric, the gain equation for the reverse direction differsfrom the gain equation for the forward direction:
Mrev =Vdc
V ′bat
1√(Qk − Q
k )2 + 1
(6)
Q is defined in an analogue manner, fr1 and k are still thesame as for the forward direction:
Q =R1,ac
Z0=
Z0π2
8
Pdc
V 2dc. (7)
DS2b.13-2
0A
0V
0V
t
t
t
T0t 1t2T
0A
1T 2T
sCv
2i−
dcVbat′V
2i−
1v
sLi
pLi′v2
sLi0sCv
Fig. 4: Characteristic currents and voltages of the LLC converter operating inbackward buck mode.
Pdc denotes the power that is fed to the dc-link.Because v′2(t) = nv2(t) is directly applied to Lp, Lp
neither participates in the resonance of Ls and Cs nor in thepower transfer. Equation (6) is thus exactly the same voltagegain relationship already known from the half-bridge seriesresonant converter (SRC), revealing a familiar drawback [1]:The inability to control the voltage in the no-load case.
This problem can be overcome by making use of theclamped voltage state available with the employed full-bridges.In the following, switching patterns are derived for both areverse buck mode and a reverse boost mode that allow forfull voltage control while transferring power in the reversedirection.
A. Reverse Operation in Buck Mode
When Vdc < V ′bat, the LLC converter can operate inbackward buck mode similar to the series resonant converteris operated in mode V in [9]. Fig. 4 shows the characteristicvoltages and currents for this mode. The switching periodis defined to begin at t0, when the primary side resonanttank current iLs is zero. The primary side switches performsynchronous rectifications, so ZVS/ZCS is achieved on theprimary side. The switching works as follows:t ∈ [t0, t1]: Before the conduction cycle starts, v′2 is still
clamped to zero by S6 and S8. v1 is negative (S2 and S3
were in the on-state to reduce the conduction losses butare now turned off to allow for the current to commutateon the primary side). At t = t0, v′2 is switched to v′2 = V ′batby turning S6 off and S5 on. iLs then begins to rise andD1 and D2 become conducting; S1 and S2 are afterwardsturned on again at zero voltage. Power is transferred to thedc-link.
t ∈ [t1,T2]: At t = t1, v′2 gets actively clamped to zero by
turning off S8 (and subsequently turning on S7). No poweris obtained from the battery anymore. The energy storedin the resonant inductor is transferred into the resonantcapacitor and to the dc-link. Hence, iLs begins to decrease.When iLs has reached zero, the first half-period of theconduction-cycle is over. At this time, vCs has reached itspeak value.
A steady-state trajectory is illustrated in Fig. 5 for a givenpower demand, a fixed dc-link voltage Vdc and a fixed batteryvoltage V ′bat. During T1 = t1 − t0, the trajectory lies on a circlearound the excitation voltage Ve = V ′bat − Vdc. For the time
2T
1t
0t
batVdcV dcV−batV sCv(0)sCv )2T(sCvdcV−batV−
1ϕ2ϕ
2r 1r
sLi0Z
Fig. 5: State-plane diagram of the resonant tank current iLs and the resonantcapacitor voltage vCs for the LLC converter operating in backward buck mode.The outer line shows the system trajectory. For reasons of symmetry, only thefirst half of the switching period is shown.
period T2 = T2 − t1, v′2 is clamped to zero and the system
trajectory lies on a circle around −Vdc. The state of Lp is notconsidered in the diagram, because Lp does not participate inthe resonance.
1) Control scheme: In order to implement the outlinedmodulation scheme, the switching times T1 and T2 can beexpressed as a function of the resonant capacitors peak voltagevCs0 = |vCs(0)|:
T1 =ϕ1
ω0=
1
ω0· cos−1
(r21 + V ′2bat − r22
2r1V ′bat
)(8)
T2 =ϕ2
ω0=
1
ω0· cos−1
(r22 + V ′2bat − r21
2r2V ′bat
)(9)
V ′bat and Vdc are assumed constant, the resonance frequencyω0 = 2πfr1 is given and r1 and r2 are marked in Fig. 5 andcan be calculated with the law of cosine:
r1 = vCs0 + V ′bat − Vdc (10)r2 = vCs0 + Vdc (11)
An analytic expression for the average power transfer isobtained from calculating the energy transferred each half-period:
WT/2 =
t1∫0
V ′batiLr(t) dt · 2 · fs = V ′bat
t1∫0
r1Z0
sin(ω0t) dt
=V ′batr1ω0Z0
[1− cos(ϕ1)]1
ω0=
2vCr0Vdc
Z0ω0
Pav is calculated as follows:
Pav = WT/2 · 2fs =2vCr0Vdc
Z0ω0· 2 1
2(T1 + T2)
=2vCr0Vdc
Z0· 1
ϕ1 + ϕ2
(12)
To control the converter, a reference power demand Pav is setand (12) is solved for vCs0. The result is plugged into (8) and(9) to obtain the switching times. A PI-controller can be used
DS2b.13-3
sCv
dcV
dcV
bat′V
1v′v2
1t
0V
0V
0A
t
t
t
T0t2T2t
sLisLi
0sCv
Fig. 6: LLC resonant converter operating in buck mode in the reverse direction.Power is transferred in small bursts between t1 and t2.
to adjust Pav to control the output voltage. Once T1 and T2
are calculated, the switching frequency is given by:
fs =1
2(T1 + T2)(13)
The switching frequency can thus not be chosen independentlyof the power-transfer and is in general above fr1. In thepresence of the non-idealities in an actual implementation,it may be necessary to measure the zero crossing of iLs toaccurately determine the switching times.
2) Switching: As the primary side performs synchronousrectification, the primary side switches are turned on and offat quasi zero current and zero voltage. On the secondary sidehowever, a superposition of the resonant tank current iLs andthe magnetizing current iLp has to be turned off when enteringthe clamped state at t = t1:
i2off =r1Z0
sin(ϕ1) +1
2
n2
LpVbat · T1. (14)
When leaving the clamped state at t = T/2, iLs is zero andonly the magnetizing current has to be turned off.
One could think of a resonant pulse mode, where one wouldwait for the resonance to complete (and thus for the iLs tocome down to zero by itself) to not switch the secondaryside current at its peak value, but a considerable magnetizingcurrent would have built up by then, leading to high turn-offlosses on the secondary side, eliminating the potential benefitsfrom this approach.
3) Quasi Burst Mode: Calculations show, that at lightload, the switching frequency is relatively high when usingthe modulation scheme discussed above. To avoid this, theconverter can be forced into a quasi inactive state with v′2 = 0when iLr has reached zero at t = t2. As long as |vCs0| < Vdc,the primary side diodes will not conduct. Power is transferredin small bursts during T1 and T2. During the newly introducedidle time T3 = T
2 − t2, the dc-link stays energized, but nopower is transferred. The two idle states are marked in Fig. 5by two stars. Fig. 6 shows the simulation results of the LLCconverter making use of the quasi burst mode. At t = t2, v′2gets clamped to zero. Notice the ringing on the diodes, as thevoltage is not clamped on the primary side. When vCs0 is notvery close to Vdc, additional power losses will occur due to theringing. These have been neglected in a first approximation.
0sCv
0A
0V
0V
t
t
t
T0t2T
0AsLi
pLi
1T 2T
sLisCv
2i−
dcV
bat′V
1v2′v
2i−
1t
Fig. 7: Characteristic Curves of the LLC converter operating in reverse boost-mode.
The idle-time can be expressed as an angle (ϕ3 = T3 · ω0)for calculating the power-transfer;
Pav = WT/2 · 2fs =2vCr0Vdc
Z0· 1
(ϕ1 + ϕ2 + ϕ3)(15)
B. Reverse Operation in Boost ModeIn case of Vdc > V ′bat, the bidirectional LLC converter
can operate in a backward boost mode similar to the modementioned in [10] for the SRC.
Fig. 7 shows the characteristic currents and voltages duringthis mode of operation. The switching period starts at t = t0where iLs is zero. In the following, the switching is explained:t ∈ [t0, t1]: Before the switching cycle starts, S3 and S2
have been conducting on the primary side (synchronousrectification), and S6 and S7 have been conducting on thesecondary side. At t = t0, v′2 is switched from v′2 = −V ′batto v′2 = V ′bat by turning S6 and S7 off and afterwardsturning S5 and S8 on. The load voltage gets clamped atv1 = 0 (see Section III-B1 for how to achieve ZVS). Theresonant tank current iLs begins to rise.
t ∈ [t1,T2]: At t = t1, v1 is switched to v1 = Vdc by turning
S3 and afterwards turning S4 on at zero voltage. Power istransferred to the dc-link. When iLs has reached zero, thefirst half-period of the switching cycle is over.
For reasons of symmetry, a discussion of the second half-period of the conduction cycle is omitted. The steady-statetrajectory is very similar to the steady-state trajectory for theboost mode and is not shown for the sake of brevity. Theswitching times T1 and T2 are calculated similar to the wayshown in Section III-A:
T1 =ϕ1
ω0=
1
ω0cos−1
(r21 + V 2
dc − r222r2Vdc
), (16)
T2 =ϕ2
ω0=
1
ω0cos−1
(r22 + Vdc − r21
2r2Vdc
). (17)
r1 and r2 describe the amplitude of the oscillation:
r1 = vCs0 + V ′bat, (18)r2 = vCs0 + Vdc − V ′bat. (19)
The switching frequency is again given by (13) and the powertransfer is derived as shown for the buck mode:
Pav =2V ′batvCs0
Z0
1
ϕ1 + ϕ2(20)
DS2b.13-4
sCv
dcV
dcV
bat′V
1v′v2
1t
0V
0V
0A
t
t
t
T0t
2T
2t
sLisLi
0sCv
3t 4t
Fig. 8: LLC resonant converter operating in boost burst mode in the reversedirection.
1) Switching: In backward boost mode, the secondaryswitches only have to turn off the magnetizing current, makingthis mode of operation far more attractive than the buck mode.Before entering the clamped switching state on the primaryside at t = t1, S2 and S3 are kept in the on-state for a shortadditional period of time. When the direction of the current haschanged, S2 is turned off and the current is used to dischargethe parasitic drain-source capacitances of S1 and S2, until S1
can be turned on at zero voltage. This way, the primary sideis switched at zero voltage. For the sake of simplicity, thedelayed switching of the primary side is not considered in thecalculation of the switching times.
2) Quasi Burst Mode: In case of Vdc > V ′bat, a quasi burstmode can be derived similar to the quasi burst mode discussedfor the backward buck mode. Fig. 8 shows the characteristiccurrents and voltages in this mode of operation. At t0, theconverter enters the quasi-inactive state by switching v′2 tozero. Before leaving the inactive state, the switches S2 and S3
are turned on at t = t3 to allow for quasi ZVS on the primary-side: a small current will build up in the resonant-tank whichis used to discharge the parasitic drain-source capacitances ofS3 and S4 when entering the clamped state at t = t4. Forthis current to be high enough, the difference between vCs0
has to be sufficiently large, which presents a trade-off. WithVdc �= vc0, the primary side will, strictly speaking, no longerswitch at zero voltage at t = t3. Simulations show, that therequired voltage difference to enable ZVS is however small.Since the switching frequency is also well below the nominaloperating frequency in burst mode, the partial loss of ZVS hasbeen neglected in a first approximation.
Because of the intermediate phase between t3 and t4, thereis no smooth transition between the burst mode and the regularbackward boost mode. Consequently, the implementation ofthe control algorithm becomes more complex.
IV. DESIGN
With the modulation schemes discussed, a bidirectionalLLC converter can be designed. To reduce the turn-off currentson the secondary side, the turns-ratio is chosen as low aspossible. Consequently, the LLC converter will have to workin buck mode in the forward direction as well. Simulationshave shown, that with n = 12.5, ZVS can still be achievedon the primary side for the whole operating area when theasynchronous clamped mode is used. With the regular clamped
TABLE I: Specification for a light electric vehicle charger. Lithium-based bat-teries with voltages of 25V, 36V resp. 48V can be charged and discharged.
Parameter Value
Battery voltage range Vbat 17V . . . 56VDC-link voltage VDC 450VMaximum output current Ibat,max ±30AMaximum output power Pbat,max ±1.65 kWNominal switching frequency fs 140 kHz
mode, ZVS is no longer possible. For n = 12.5, the LLCconverter has to operate in buck mode in the forward directionfor battery voltages of Vbat <
450 V12.5 = 36V.
In order to cope with the high turn-off currents duringreverse operation, four Infineon IPB020NE7N3 MOSFETs areparalleled for each switch on the secondary side. InfineonIPW60R045CP MOSFETs are used on the primary side. Bothare chosen for their exceptional figure of merit [11].
The conduction losses are considered for a junction tem-perature of Tj = 125 ◦C. The current is assumed to be evenlysplit up among paralleled MOSFETs. The energy dissipatedat turn-off in one of the secondary side switches is calculatedaccording to [12]:
ES,off = (LD + LS) · i2S,off ·V2,pk
V2,pk − V2(21)
iS,x denotes the current flowing through a switch Sx prior tothe turn-off. For a prototype design, it is presumed that a com-bined circuit and packaging inductance of LD+LS ≈ 12 nH isachieved per switch1. During turn-off, the voltage across theswitch will overshoot to V2,pk. This voltage is presumed to beno higher than the rated avalanche voltage Vbr of the deviceitself. Hence, Vbr of the selected switches (Vbr = 75V) hasbeen taken for the calculations. The switching losses for zerovoltage switching and the switching losses for zero currentswitching have in a first approximation been neglected.
A. Design of the Resonant Tank
According to the design method discussed in [14], Lp ismatched to the load when operating at resonance.
Lp = n2 Ro
2πfr1. (22)
In a first approximation, this minimizes the conduction lossesat the nominal operating point (36V,30A) when operating inthe forward direction [14]. Rac,2 denotes the equivalent ac-resistance in (2).
To satisfy the maximum voltage demand at maximum powerdraw, Lr = 1 · Lp is sufficient. No additional degree offreedom exists for the resonance capacitance since the nominalswitching frequency is specified.
Cr =1
(2πfr1)2 · Lr. (23)
A summary of the component values obtained is given inTable II.
1The inductance of the To-236 package is around 5 nH [13] and anadditional 7 nH have been assumed for the PCB stray inductance.
DS2b.13-5
TABLE II: Component values for the LLC converter designed for bidirectionalpower transfer
Component Value
Transformer core material EPCOS N87Transformer turns-ratio n 12.5Series capacitance Cs 7.5 nFTransformer leakage inductance Ls 172 μHLeakage layer thickness s 4.2mmTransformer magnetizing inductance Lp 172 μHAir gap length g 2.0mmPrimary side MOSFETs Infineon IPW60R045CPSecondary side MOSFETs Infineon IPB020NE7N3Resonant capacitor EPCOS 2× B32652A2332JPrimary side filter capacitance EPCOS B32522N6154JSecondary side filter capacitance EPCOS 6× B32522C106K
y-scale
(mm)
x-scale (mm)−20 −15 −10 −5 0 5 10 15 20
0
5
10
15
Fig. 9: Winding arrangement of the optimized transformer. The air gap isexemplarily drawn in the center leg but can also be realized in a distributedfashion to limit the fringing flux.
B. Transformer DesignA transformer has been designed for minimum power losses
with the help of MATLABs global optimization toolbox. AnE-core is used to allow for simple analytic calculations ofthe magnetic field. The computer performs a free variationof the geometric dimensions of the core and in each steppicks the best number of turns to realize the turns-ratio.The performance of the transformer is assessed at the threecharacteristic operating points (25V; 30A), (36V; 30A) and(48V; 30A). The target size of the transformer has been setto a box volume of Vbox = 0.05 dm3. Both the primary sidewindings and the secondary side windings are realized withlitz wire. The internal skin effect and the internal and externalproximity effect in the windings are considered accordingto [15]. The H-Field is calculated with a one-dimensionalapproach and the flux in the air-gap is assumed homogenous.The core losses are calculated with the improved generalizedsteinmetz equation (IGSE) [16].
Fig. 9 shows the optimized transformer design. A spacerwith a thickness of s = 4.2mm is inserted between thewindings to integrate the series inductance Ls. The core hasan air gap to integrate the parallel inductance Lp. To keepthe calculations simple, both have been regarded as decoupledfrom each other.
C. Filter CapacitorsThe limit for the secondary side voltage ripple has been set
to 5% of the output voltage and the filter capacitors are chosenaccordingly. The filter capacitances have been calculated asC1 > 0.24 μF and C2 > 52.1 μF. The primary side filter is
Vbat(V
)
−Ibat (A)0 10 20 30
20
30
40
50
Buck
Boost
Burst mode
Burst mode
TrTT iangular
TrTT apezoidal
TrTT iangular
0 10 20 30
20
30
40
50
Vbat(V
)
Ibat (A)(b)(a)
Fig. 10: Operating modes (a) of the LLC converter in the reverse directionand (b) of the DAB converter for both directions of power flow.
realized with two EPCOS B32522N6154J film capacitors. Onthe secondary side, six EPCOS B32522C106K are paralleled.
The resonance capacitance of Cs = 7.5 nF is realized byfive EPCOS B32652A2332J film capacitors in parallel.
V. SIMULATION
A time-domain simulation has been performed withGeckoCIRCUITS [17] to verify the analytic considerations.A PI-controller is used to control the voltage by varying theswitching frequency in forward mode. In forward buck-mode,the duty-cycle is calculated according to (5). In the reversedirection, the modulation schemes discussed in Section III areapplied. The simulation results are discussed in the following.
A. Forward OperationVery low power losses occur when operating the converter in
the forward direction. ZVS is always achieved on the primaryside, and ZCS is always achieved on the secondary side.
Fig. 11 shows the power conversion efficiency as a functionof the operating point. The efficiency surface is almost flatover the entire output voltage range. At low loads, the reactivecurrents in the resonant tank account for a large share of theoverall power losses.
Fig. 13 shows the distribution of the power losses amongthe different components. The semiconductor power losses aredivided into switching losses Psw and conduction losses Pcond.The power losses in the transformer are composed of thewinding losses Pcu and the core losses PFe. A small share ofpower Pfilt is dissipated in the filter capacitors and the resonantcapacitor PCs . The gate-drive power losses are denoted byPgate. At full load, the switching losses dominate the overallpower losses.
B. Backward OperationWhen the LLC converter is operated in the reverse direction,
large turn-off currents are observed on the secondary side.In buck mode, the full AC-link current plus the magnetizingcurrent has to be turned off. As a result, relatively highswitching losses occur and the efficiency drops towards theupper end of the output voltage range as illustrated in Fig. 11.As the switching frequency is higher than fr1, the gate drivepower losses are higher than in the forward direction. Thedifferent operating modes are illustrated as a function of theoperating point in Fig. 10.
Fig. 13 shows the distribution of the power losses amongthe different components. At full load, the switching losses
DS2b.13-6
TABLE III: Component values for the designed DAB converter
Component Value
Transformer core material EPCOS N87Leakage layer thickness s 1.6mmTransformer turns-ratio n 11.5Transformer leakage inductance Ls 68.1 μHPrimary side MOSFETs Infineon IPW60R045CPSecondary side MOSFETs Infineon 4× IPB020NE7N3Primary side filter capacitance EPCOS B32522N6154JSecondary side filter capacitance EPCOS 4× B32522C106K
dominate the overall power losses. Fig. 12 shows the current,which has to be turned off by the secondary side switches.
VI. COMPARISON WITH THE DUAL ACTIVE FULL-BRIDGE
While the unidirectional LLC converter can offer a highefficiency in configurations with only two active semicon-ductors [6], the bidirectional LLC converter has to competewith other full-bridge topologies. In [18], the dual-active full-bridge (DAB) has been found to be the most promisingisolated bidirectional converter for a very similar voltage rangeand power rating. The bidirectional LLC converter is thuscompared to the DAB converter.
The DAB converter is designed to operate with a combina-tion of the trapezoidal and triangular current mode [19]. Withthe extensions discussed in [18], ZVS is always achieved onthe primary side and ZCS is achieved on the secondary side ina large share of the operating area. To allow for a comparison,the exact same switches are chosen for both converters.
Other than the LLC converter, the DAB only needs a seriesinductance in the ac-link. The series inductance is designed toallow the converter to fulfill the maximum power requirement.A margin is included to have sufficient reservers for voltagecontrol. A turns-ratio of n = 12.5 is chosen at which theaverage power conversion efficiency at full output current ismaximal. The transformer is optimized in the same way asdone for the LLC converter. Both transformers share the sametarget volume of Vbox = 0.05 dm3. In order to have sufficientdegrees of freedom for the optimization of the transformer,the turns-ratio has been rounded to half-integers. Table IIIsummarizes the design of the DAB converter.
A. Power Conversion Efficiency
Fig. 11 shows the calculated power conversion efficiency ofthe LLC converter working in the forward direction. The peakefficiency is predicted to be ηmax,DAB = 98.3%. In the model,the currents and voltages have been calculated for the idealtriangular and trapezoidal current mode with an ideal DABconverter model. The power losses are calculated based on theso obtained voltages and currents in the transformer and theswitches. The operating point is assumed to be independent ofthe power losses. With this approximation, the power lossesare virtually the same for both directions of power flow. Thedifferent operating mode are illustrated as a function of theoperating point in Fig. 10.
When the DAB converter is operating in forward boost-mode or backward buck-mode, also relatively high currentshave to be turned off on the secondary side. This is illustrated
Vbat (V) Vbat (V)Ibat (A)10
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i
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i
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Fig. 12: Maximum turn-off current on the secondary side (a) for the LLCconverter operating in the reverse direction and (b) for the DAB converter,both times as a function of the battery voltage and charge current.
in Fig. 12. At the lower end of the output voltage range,ZCS is achieved. A reduction of the turn-off currents could beachieved by choosing n even lower, at the cost of reducing theefficiency at the lower end of the output voltage range. Recall,that this is unpractical with the bidirectional LLC converter: toreduce the turn-off currents, a further extension of the forwardbuck range would be required, which would entail the loss ofZVS on the primary side at lower battery voltages.
Fig. 13 shows the distribution of the power losses amongthe different components. At full load, the switching lossesdominate the overall power losses. Towards higher outputvoltages and higher loads, the switching losses account fora large share of those.
It becomes evident that the DAB converter outperformsthe bidirectional LLC converter in terms of power conversionefficiency. The turn-off currents in the DAB converter are lesson the secondary side and could be reduced even further. Thetransformer of the DAB converter only needs to integrate theseries-inductance. As a consequence, more degrees of freedomare available in the optimization process.
VII. CONCLUSION
Up until now, little information has been available on the ca-pabilities of operating the LLC converter in the reverse direc-tion. In this paper, possible modes of bidirectional power floware analyzed and a bidirectional LLC converter is presented.The converter is targeted towards a light electric vehiclecharger for large-quantity, small-accumulator vehicle-to-gridapplications. While the converter is predicted to achieve anoutstanding power conversion efficiency of ηmax,LLC > 97.6%for both directions of power-flow, some of the inherent benefitsof its unidirectional originator have been lost: ZCS is nolonger achieved on the secondary side when operating inthe reverse direction. At high output voltages, the turn-offcurrents are significant and high switching losses occur. Toallow for voltage control within the whole operating area, thebidirectional LLC converter needs full-bridges on both sides.Consequently, it has to compete with the DAB converter whichexhibits a better overall performance and requires less passivecomponents.
For applications with higher battery voltages and a similaroutput power, the turn-off currents on the secondary sidevoltages will be reduced. Consequently, less energy is stored inthe parasitic inductances of the switches and PCB connections,
DS2b.13-7
Vbat(V
)
−I2 (A)
ηmax = 97.6%
0.96
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ηmax = 97.6%
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Vbat(V
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LLC forward LLC reverse DAB forward / reverse
Fig. 11: Power conversion efficiency (a) of the LLC converter operating in the forward direction, (b) of the LLC converter operating in the reverse directionand (c) of the DAB converter as a function of the operating point.
Pfilt
Pcu
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Pcond
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55V48V36V25V 55V48V36V25V 55V48V36V25V
(V)batV (V)batV (V)batV(b)(a) (c)
(W)
loss
P
(W)
loss
PFig. 13: Distribution of the power losses among the different components (a) for the LLC converter operating in the forward direction (b) for the LLC converteroperating in the reverse direction and (c) for the DAB converter.
allowing the bidirectional LLC converter to achieve ZVS onboth sides in both modes (low turn-on voltages are acceptedin the backward boost burst mode), which is subject to furtherresearch.
REFERENCES
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