Abstract — This paper proposes a new LLC resonant DC-DC
topology with bidirectional power flow capability. All the
switches in the proposed topology can achieve zero voltage
switching (ZVS) at turn on, and zero current switching (ZCS) is
achieved for the output side switches at turn off. Compared with
the traditional bidirectional dual active bridge (DAB) converter,
the turn off current is greatly reduced, and the frequency
modulation control scheme can almost eliminate the large
circulating energy. Therefore, the conversion efficiency can be
much improved, which makes it quite attractive in energy
storage applications. The output characteristic of the proposed
LLC converter is different from the conventional unidirectionalLLC resonant converter. A new analytical model is also
proposed in this paper. The detailed operating principle and
performance of the proposed topology are analyzed. And a 1 kW
prototype is built to verify the theoretical analysis. Over 98%
efficiency is achieved base on the prototype.
I. INTRODUCTION
As energy saving and environment protection becomemore and more important, lots of research efforts have beencarried out in order to use the energy in a clean and efficientway. The distributed generation (DG) and smart gridtechnologies are emerging with the rapid application growthof renewable energy resources. However, the intermittent
nature of these resources introduces issues with systemstability, reliability, and power quality. Energy storagesystems (ESSs) are required to against such intermittentoutages for grid-tied and off-grid applications [1]-[3].Batteries and super capacitors are the most popular energystorage components considering the price and performance.Fig. 1 shows a typical DG system with renewable energyresources and ESSs. The ESSs should have the bidirectional power flow capability to store the excess energy and release itduring peak times of energy consumption [4]-[6]. And the bidirectional DC-DC converter is a key component in theseapplications to enable the bidirectional power flow.
Bidirectional DC-DC converters for ESSs should have thecharacters like high power density, high efficiency and high
reliability. Various kinds of bidirectional DC-DC topologieshave been proposed [7]-[9]. Among these topologies, the dualactive bridge (DAB) converter has attracted a lot of researchinterests in recent years, due to its simple structure, wide rangesoft switching capability and high efficiency. Though DABtopology is widely adopted as an interface for ESSs and solidstate transformers [10]-[12], it suffers from high circulatingenergy and high turn off current which causes high power lossand deteriorates the efficiency. A lot of methods have been
proposed to further improve its efficiency and performance.An improved DAB topology with the reduced circulatingenergy and simple control scheme was proposed in [13], butthe topology loses the bidirectional power flow capability.Several Dual-Phase-Shifted control methods were proposed tominimize the circulating energy and increase the efficiency in[14][15], but the control methods are complex and the turn offloss is still high.
The turn off power loss is related to the turn off current,which can be reduced by operated the DAB topology in series
resonant mode with an extra resonant capacitor, i.e. dual bridge series resonant converter (DBSRC) [16][17]. However,it can be only operated under buck mode which is not suitablefor wide output range applications like ESSs. A new bidirectional SRC for wide voltage range application withclamped capacitor voltage was studied in [18], but thetopology itself is quite complex due to the auxiliary circuits.
Among the resonant converters, the LLC resonantconverter has superior performance compared to the SRC,especially for buck/boost operation capability, narrowswitching frequency variation and higher efficiency [19]. Butvery little research works on bidirectional LLC resonantconverter is reported in literature. A bidirectional LLCresonant topology for vehicular applications was proposed in
[20]. However, the topology is still a conventional SRC during backward mode, which is still not preferred for wide voltagerange application. In [21], a bidirectional CLLC resonantconverter with two resonant tanks in the transformer primaryside and secondary side was proposed. The extra resonant tank
Figure 2. The proposed bidirectional LLC resonant converter.
increases the cost and volume of the converter, and the voltagegain is reduced compared to the traditional LLC converter.Furthermore, the current in output side has to flow through the body diodes of switches which may cause high reverserecovery current.
This paper proposes a new bidirectional LLC resonantconverter for ESSs applications. In order to achieve bidirectional power flow and maintain the buck/boostoperation capability in any mode, an extra inductor is added
between the midpoints of two switches legs in transformer primary side as shown in Fig. 2. The switches in the input sideare switched with 50% duty cycle as traditional LLC resonantconverter and the switching frequency modulation is used toregulate the output power. All the switches in the proposedtopology can achieve ZVS. And ZCS is achieved for theswitches in the output side. The switches in output side arealso operated with same switching frequency as the input sideswitches to prevent current from flowing through the bodydiodes, thus the current in the proposed topology are always incontinuous conduction mode (CCM). In order analyze theoutput characteristic of the proposed bidirectional LLCresonant topology, a new analysis method based on thefundamental harmonic approximation (FHA) method is also
introduced in this paper. The detailed operating principle ofthe proposed bidirectional LLC resonant converter is presented in Section II. The theoretical analysis based on the proposed FHA method is given in Section III. Theexperimental verification from a 1 kW prototype is given inSection IV. Efficiency over 98% is achieved at full lad basedon the prototype.
II. PRINCIPLE OF OPERATION
The proposed bidirectional LLC resonant converter isshown in Fig. 2. The primary side and secondary side are bothfull-bridge structures consisting 4 MOSFETs. It should benoted that a half-bridge structure can also be used. An extrainductor Lm2 is added between point A and point B as shown
in Fig. 2. In forward mode, the resonant inductor Lr , resonantcapacitor C r and transformer magnetizing inductor Lm1 formthe LLC resonant tank, and the extra inductor Lm2 is used tohelp achieve ZVS of primary side switches. In backwardmode, Lm2 is served as the resonant inductor, which makes theoperation of the proposed converter exactly the same as that inforward mode. And the transformer magnetizing inductor Lm1 is used to help achieve ZVS for secondary side switches. If Lm2 is equal to Lm1, the proposed topology is a symmetricalLLC resonant converter both for forward mode and backward
mode. For simplification, only the operating principle inforward mode is discussed in the paper.
The steady state operation waveforms are shown in Fig. 3.Fig. 3(a) to Fig. 3(c) show the waveforms when the switchingfrequency is below, equal and above the resonant frequency f r respectively.
The gate drive signals for M1, M4, M5 and M8 are the
same and with 50% duty cycle, which is complementary to thegate signals for M2, M3, M6 and M7 without considering thesmall dead time. Thus the conduction of body diodes ofMOSFETs in secondary side can be minimized, which helpsto reduce conduction loss and avoid severe reverse recovery problem. And the current in the output side will always be inCCM, which is different from traditional LLC converter.
A. f s < f r
There are three operating modes in a half switching cyclewhen the switching frequency is below the resonant frequency.
Mode 1 (t0 - t1): M1, M4, M5 and M8 turn on at t0, ir andcurrent of Lm2 are both negative at the moment, so currentthrough M1 and M4 is negative and they can be turned on
with ZVS. Since ir is higher than i Lm1 at t0, thus i s > 0, M5 andM8 turn on with ZVS. The voltage across point C and point Dis equal to the output voltage and the voltage across Lm1 isequal to nV o, so i Lm1 increases linearly during this mode.Voltage across Lm2 is equal to the input voltage and its currentincreases linearly, too. This mode ends when ir is equal toi Lm1at t1.
Mode 2 (t1 – t2): i s is zero at t1, as M5 and M8 are still on,i Lm1 will keep increasing and is will drop to below zero.Current through M5 and M8 will be positive (from drain tosource). This mode ends when M1, M4, M5 and M8 turn offat t2. Though turn off current of MOSFETs in the secondaryside is not zero, it’s much smaller than the turn off current in
DAB converter.Mode 3 (t2 – t3): M1, M4, M5 and M8 turn off at t3. In the
secondary side i s is negative and current in secondary begins tocharge the parasitic capacitors of M5 and M8 and dischargethe parasitic capacitors of M6 and M7. After the voltage of the parasitic capacitors of M5 and M8 are charged to Vo, current begin to flow through the body diodes of M6 and M7. In thisway, M6 and M7 can be turned on with ZVS. Then thevoltage across Lm1 changes to -nV o, and i Lm1 begins to decrease.
In primary side, ir plus the auxiliary inductor current i Lm2 will charge the parasitic capacitors of M1 and M4, anddischarge the parasitic capacitors of M2 and M3 until thevoltage across the parasitic capacitors of M1 and M4 equal tothe input voltage, then current in the primary side begin toflow through the body diodes of M2 and M3. The auxiliaryinductor current ilm2 helps to charge and discharge the parasiticcapacitors and the zero voltage switching is easier to beachieved.
In the next half switching cycle, the operation is almost thesame, which will not be elaborated here.
B. f s = f r
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When the switching frequency is equal to the resonantfrequency, there are only two operating modes in halfswitching cycle. The Mode 2 described above is not existedanymore, which means that no energy is fed from output side back to the input side.
C. f s > f r
When the switching frequency is higher than the resonant
frequency, there are also three operating modes in halfswitching cycle.
Mode 1 (t0 - t1): This operating mode is exactly the same asMode 1 we described when f s < f r , which is not repeated here.
(a) (b)
(c)
Figure 3. Waveforms of the proposed topology
Mode 2 (t1 – t2): M1, M4, M5 and M8 turn off at t1, the parasitic capacitors of M1 and M4 are charged to the inputvoltage by i Lm2 and ir , and then current in primary side willflow through the body diodes of M2 and M3. The current of Lm2 helps to achieve ZVS. In secondary side, since i s is stillabove zero, the body diode of M5 and M8 keep on, which willdrop quickly to zero at t2, then this mode ends.
Mode 3 (t2 – t3): ir is equal to i Lm1 at t2, and then i s will
change its direction. Since M5 and M8 are already off, thecurrent will flow through the body diodes of M6 and M7.Then M6 and M7 can be turned on with ZVS.
As described above, the auxiliary inductor Lm2 doesn’tinfluence the operating principle in forward mode, and it onlyhelps to achieve the ZVS of the switches in the primary side.All the switches in the topology can achieve ZVS. Soft currentcommutation of the switches in the output side can beachieved as conventional LLC resonant converter when theswitching frequency is above or equal to the resonantfrequency. When the switching frequency is lower than theresonant frequency, there is small circulating energy and theturn off current of secondary side MOSFET is very small.
III.
PERFORMANCE ANALYSIS
The FHA method is widely used to analyze the outputcharacteristics of LLC resonant converter. And the load alongwith the diode rectifier is usually represented by an equivalentAC resistor .But the results like voltage gain derived by thismodel is not accurate especially when the switching frequencyis below the resonant frequency due to some assumption toderive the equivalent AC resistance is not maintained anymore.
However in the proposed topology, since the secondaryside current is always in CCM even when f s< f r . There is a phase difference φ between the transformer secondary sidevoltage and current as shown in Fig. 3(a), the impedance of
the transformer secondary side is not resistive anymore, whichmeans the conventional equivalent AC resistor method is notapplicable. A new analysis model using equivalent AC voltageis proposed. The equivalent circuit is shown in Fig. 4.
In Fig. 4, vCD1(t ) represents the fundamental component ofthe equivalent output voltage vCD(t ) referred to the primaryside, and the expression is given in (1) based n Fourierdecomposition. The equivalent AC output current (transformersecondary side current referred to the primary side) is iCD1(t )and it can be expressed as in (2), where A is the amplitude ofiCD1(t ) and φ is the phase angle between iCD1(t ) and vCD1(t ).The output power can be expressed as in (3), and then A can be derived and iCD1(t ) is given in (4). The equivalent outputimpedance is given in (5).
Figure 4. The equivalent circuit.
ϕ
M1,M4
M5,M8
v AB
M2,M3
M6,M7
vCD
V Cr
ir
i Lm1
M1,M4
M5,M8
i s
im5
t0 t1t2t3
io
t4t5
i Lm2
M1,M4
M5,M8
v AB
M2,M3
M6,M7
vCD
V Cr
ir
i Lm1
M1,M4
M5,M8
i s
im5
t0 t1t2t3
io
t4t5
i Lm2
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The voltage gain “G” is the ratio of the equivalent outputvoltage and the equivalent input voltage as given in (6):
o
in
nV G
V = (6)
According to the equivalent circuit, the voltage gain can be
expressed as follows:
1
11
e m
e m r
r
Z j LG =
Z j L j L j C
ω
ω ω ω
+ +
(7)
Then the voltage gain can be solved and is shown in (8).The voltage gain of traditional unidirectional LLC resonantconverter derived by using the equivalent AC resistance isshown in (9). It is seen that when f s ≤ f r , the voltage gain of the proposed topology is lower than the traditional unidirectionalLLC converter with the existence of φ. When f s ≥ f r , φ will bezero, then the voltage gain of the proposed topology is same
In a half switching cycle, inductor current ir can beexpressed as in (10), where θ is the initial phase of ir . Butmethods to calculate the exact value of θ will be complicated,so ir can be approximately expressed as in (11), where I r (0) isseen as the initial value of ir .
1sin( )
o inr
r r r
r
nV V i t
L L C
C
θ −
= − (10)
1sin( ) (0)
o inr r
r r r
r
nV V i t I
L L C
C
−≈ + (11)
The current of magnetizing inductance i Lm1 can beexpressed as in (12).
1
1 14
o o Lm
m m s
nV nV i t
L L f = − (12)
1o
r Lmi
i in
− = (13)
According to equation (13), the average value of the outputcurrent can be expressed in (14). Then the initial phase of ircan be solved as in (15).
2
1 10
1[ sin( ) (0) ]4
2
Ts
o in o o
r
m m sr r r
or o
s o
nV V nV nV n t I t dt L L f L L C
V C I
T R
−
+ − +
= =
∫
(14)
( )(1 cos )
(0)
o ino
r
o r
x V V V x I nR Z
π
π
− −
= − (15)
When ir is equal to i Lm1, io is equal to zero, then (13) can bederived into (16).
2
( )(1 cos )8sin( ) ( ) 0
2
o ino in o o
r r r r
x V V nV V nV Q nV x
Z x Z kxZ Z
π
π ϕ π ϕ
π π
− −− −+ − − − =
(16)
Taking (8) into (16), it will be an equation of x and φ, andthe left side of the equation can be regarded as a function of xand φ, which is f (x, φ). Then taking different value of x into f (x, φ) and depict its curve, so the intersection of f (x, φ) andy=0, is the value of φ at the corresponding switchingfrequency. Fig. 5 shows the value of φ corresponding to xwhere k is set to 4. It is seen that φ will increase when Q decreases of the switching frequency get lower.
C. Reverse energy
When f s is higher than f r , φ is equal to zero, therefore theoutput voltage and output current are in phase and there is noreverse energy. When f s is lower than f r the ratio of reverse power P b and output power P o can be solved as follows:
1 1
1 10
( ) ( )
( ) ( )
CD CDb
oCD CD
v t i t dt P
P v t i t dt
π
π ϕ
π
−
•
=
•
∫
∫ (17)
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For a traditional DAB converter with the voltage gainequals to 1, the ratio of reverse energy and output energy can be shown as follows [14]:
4( )
b
o
P
P
α
π α
=−
(19)
Where α is the phase shift angle between the switches in primary side and secondary side.
A comparison of reverse energy between the proposedconverter and the traditional DAB converter is shown in Fig.7. It is obviously that though reverse energy in the proposedtopology is much smaller than that of the traditional DABconverter.
Figure 5. The value of φ at different switching frequency
Figure 6. Ratio of turn off current and the amplitude of the
output current when k=4. From the bottom to top are curves
when Q=0.3, Q=0.4 and Q=0.5
(a)
(b)
Figure 7. (a) reverse energy of the proposed bidirectionalLLC converter; (b) reverse energy of DAB converter.
IV. EXPERIMENTAL RESULTS
A 1kW prototype system is built up to verify the analysisabove. The input voltage V in is 400V and output voltage V o ranges from 160V to 220V; transformer turns ratio n is equalto 2; the resonant frequency f r is 100 kHz.
It is expected that the switching frequency shouldn’t be toolow to cause additional loss, in this way the lowest switchingfrequency is set to70 kHz. Full load output resistor R f is set to50Ω. k shouldn’t be too large to avoid high conducting loss,and neither too small which will make the voltage gain lessthan 1 when f s < f r , so k is set to 4. Lr is set to 115uH, C r is setto 22nF, and Lm1 and Lm2 are set to 460uH.
For operation in backward mode is symmetry to forwardmode, only waveforms in forward mode is shown. Fig. 8shows the waveforms when f s is lower than f r , and Fig. 9shows the waveforms when f s is higher than f r . It is seen thatZVS is achieved and turn off current in secondary side is verysmall when the switching frequency is lower than the resonantfrequency, and the turn off current will be zero when the
switching frequency is higher than the resonant frequency.
Fig. 10 compares the voltage gain in experimental results,voltage gain derived by traditional method and voltage gainderived by the proposed method. When the switchingfrequency is lower than the resonant frequency, voltage gainderived by traditional voltage gain formula is much higherthan the experimental results and is obviously not accurate,while voltage gain solved by the proposed voltage gain
formula is a little lower than the experimental results but ismuch closer to them.
When the switching frequency is higher than the resonantfrequency, voltage gain derived by each method is the sameand are both approximate to the experimental results. So thevoltage gain derived by the proposed method will be moreadaptable in theoretical analysis.
Fig. 11 compares the efficiency of the proposed converterand DAB converter with same output voltage. The efficiencyof the DAB converter with traditional control strategy is testedwith the same voltage gain (G=1) and the same power rate(1000w). It is seen that the maximum efficiency of proposedconverter is about 98.2% at 70% load, which is 5% higherthan DAB converter. The efficiency of the proposed topologyat full load is about 98%, and it will be higher than 97% inmost load conditions. It is obvious that the efficiency of bidirectional LLC resonant converter improves a lot comparesto the traditional DAB converter.
Figure 8: full load test results with V o=210V when f s < f r .
Figure 9: Full load test results with V o =190V when f s > f r .
Figure 10 Voltage gain of experimental results and calculated by traditional and proposed method when Q=0.5.
Figure 11. Efficiency of the proposed topology and the DABconverter when the voltage gain is equal to 1.
V. CONCLUSIONS
This paper proposed a LLC resonant topology which hasan improved circuit structure to achieve the bidirectional power flow capability. It can achieve ZVS for all theMOSFETs with and soft current commutation in the output
side when f s ≥ f r , while the turn off current when f s < f r is also
very small. Besides, the proposed converter has very littlecirculating energy compared to traditional DAB converter.These characters contribute to the high efficiency and it can beabove 98% at full load. So the proposed bidirectional topologywill be popular in energy storage applications like batteriesand super-capacitors.
The control scheme of the proposed topology is differentfrom the unidirectional LLC resonant converter that theMOSFETs in secondary side also turn on and off according tothe related primary side, in this way the reverse recoverycurrent at turning off is limited. A new analyze model is also proposed based on the FHA method, and the correspondingcircuit performance like voltage gain, ZVS region, and reverseenergy are all analyzed in detail, which is more accurate than
the traditional analyze method. A prototype of 1 kW is builtand confirms the theoretical analysis well.
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