Derivation of Operation Mode for Flying Capacitor
Topology Applied to Three-level DAB converter
Hayato Higa and Jun-ichi Itoh
Department of Electrical Engineering
Nagaoka University of Technology
Niigata, Japanhhiga@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
Abstract— This paper discusses a Dual Active Bridge (DAB)

DC-DC converter utilizing to three-level flying capacitor
topology for a battery conversion system. With applying toa multi-level topology, the voltage stress is reduced in all
switches. In addition, the low order harmonic components
are reduced due to five-level waveform. In a two-level DAB
converter, the efficiency becomes low when the input
voltage is not closed to the nominal voltage. In order toimprove the efficiency at the input voltage fluctuation, thispaper also proposes the operation mode of the three-level
DAB converter at the input voltage fluctuation. The output
voltage waveform of the inverter is determined by the
relationship among the efficiency of the two modes which
are so called the full-bridge mode and the half-bridge mode.
In this paper, the changing point between the half-bridge
and the full-bridge mode is derived using the loss
calculation. In the simulation, the ZVS range and theinductor current are compared with the two-level and thethree-level inverter. It is confirmed that the ZVS range is
extended by 60%. In addition, the fundamental operationof the proposed DAB converter is confirmed by theexperimental results.
I.

INTRODUCTION

Recently, energy storage systems have attracted forelectric vehicles and smart grid systems. A bi-directional
isolated DC-DC converter is used as the battery interface
system. A dual active bridge (DAB) converter has been studied
actively as a bi-directional isolated DC-DC converter [1-3].
The DAB converter obtains the high efficiency and the highpower density because zero voltage switching (ZVS) is
achieved during the dead-time using an additional capacitor ora parasitic capacitance of the switching devices [4]. However,the ZVS range of the DAB converter is limited by the error
between the ratio of the input/output voltage and thetransformer turn ratio [5]. Furthermore, reactive current is also
increased at light load for the same reason. When the ratio of

the input /output voltage fluctuates in the system, theefficiency of the DAB converter decreases at light load. Inorder to solve these problems, Pulse Width Modulation(PWM) is added to the phase shift control in order to extend
the ZVS range and reduce the circulating current in [6-7].
However, it is not always possible to achieve the ZVS for all
switches due to the error between the input/output voltages
including the turn ratio of the transformer.
On the other hand, the multi-level DAB converter inwhich a multi-level inverter is applied to the high voltage sidehas been proposed. The multi-level inverter can reduce thevoltage stress of switching devices [8]. In [9], a three-level
DAB converter with a neutral-point-clamped topology has
been proposed in order to improve the total harmonic distortionof the inductor current. However, ZVS is not achieved because
the drain-to-source voltage is clamped by clamped diodeduring dead-time period. Moreover, the voltage balance
control is required. On the other hand, a three-level DAB
converter applied with T-type topology has been proposed inorder to achieve the minimum inductor current [10]. The
switching pattern of the three-level inverter is determined by
the relationship among the turn ratio of the transformer and the
input/output voltage. However, this literature has not discussed
the ZVS operation though the voltage stress of the bidirectionalswitch is reduced by the T-type three-level inverter.
This paper proposes the three-level DAB converter
applied with a flying capacitor topology. With the three-level
flying capacitor topology, the voltage stress is reduced in all
switches in the high voltage side. The switching patterns are
determined by the loss calculation. This paper is organized asfollows; first, the circuit configuration of the three-level DAB
converters is introduced. Second, the operation mode of thethree-level DAB converter is explained. Thirdly, the operation
mode of the three-level DAB converter is determined by theloss calculation results. Fourth, the three-level DAB converter
and the two-level DAB converter are demonstrated from thesimulation. From the simulation results, the ZVS range and theinductor current are compared with the three-level DAB
converter and the conventional two-level DAB converter.
Finally, the fundamental operation is confirmed by the
prototype of the proposed DAB converter.
II.

Cds

N:1

Vin

Vout

L

PROPOSED CIRCUIT

Fig. 1 shows the configuration of the two-level DAB
converter. This converter consists of the high frequency
transformer and the two voltage source inverters with H-bridge
topology. If the voltage fluctuation occurs. The ZVS range islimited and the circulating current is increased.
Fig. 2 shows the configuration of the three-level DAB
converter with a flying capacitor topology. The three-level
DAB converter comprises a flying capacitor three-level
inverter at the primary side of the transformer and a two-level
inverter at the secondary side of the transformer. It should be
noted that the three-level inverter is applied to the high voltage
side. Thus, the voltage stress of the switching devices isreduced compared to two-level inverter. Therefore, a highperformance MOSFET can be used.
Fig. 3 shows the switching pattern of the three-level DAB
converter when the output voltage of the three-level inverter isthe five-level waveform (five-level mode). In Fig. 2, the eachvoltage level period is determined by the half voltage period ofarm voltage  and the phase difference between each arm
voltage . In addition, the output voltage of the three-level
inverter is square waveform which has the voltage level; ±Vin
(Full-bridge mode) when , are zero. Similarly, the output
voltage of the three-level inverter is the square voltage
waveform which has voltage levels; ±1/2Vin (Half-bridgemode) when the half voltage period of the arm voltage  iszero and the phase difference between each arm voltage is/2 rad. (1)A. Output power of full-bridge mode and half-bridge mode
When the primary side of the transformer is operated as thefull-bridge converter, the output power to the secondary side
Pout_FB is expressed by (1) [1]

Fig. 1. Configuration of two-level DAB converter. The primary side (highvoltage side) and the secondary side (low voltage side) is applied with thetwo-level inverter.

N:1

Vin

v1

L

iL

v2

Vout

v1v

v1u

Fig. 2. Configuration of three-level DAB converter. The primary side (highvoltage side) is applied with flying capacitor three-level inverter. thesecondary side (low voltage side) is applied with the two-level inverter.
Vin2

v1u 1/2Vin

q

0
Vin
v1v 1/2Vin



q

0
v1

Vin
1/2Vin0-1/2Vin
-Vin
NVout

v2

/2
q

-2

q0-NVout

iL

q

0
0



VinVout 2  (1)
( 
)
NL


Fig. 3. Switching pattern of three-level DAB converter. The each voltage

Where  is switching angular frequency, N is a turn ratio of
the high frequency transformer. is aphasedifference
between the primary side voltage and the secondary side
voltage of the transformer.

From (2), the output power at the full-bridge mode is smaller
than the output power at the half-bridge mode.

Pout _ FB 

When the secondary side of the transformer is operated as
the half-bridge converter, the amplitude of the secondary
voltage of the transformer becomes Vin/2. In the half-bridgemode, the output power to the secondary side Pout_HB isexpressed by (2).
V V
 2 ................................................. (2)Pout _ HB  in out ( 
)
2 NL


level is determined by the half of the input voltage level period and thephase difference of the each arm voltage 

B. Inductor current of full-bridge mode and half-bridgemode
The inductor current of the full-bridge mode IL_FB against
the phase difference is obtained by (3) [1].
I L _ FB 

VinVoutNL



4 3
 2 N (Vin  NVout )2 .............. (3) 2 312
VinVout

From (3), the inductor current is increased by the error between
the turn ratio of the transformer N and the output/primaryvoltage Vout/Vin. On the other hands, the inductor current of thehalf-bridge mode IL_HB is obtained by (4).
I L _ HB 

VinVout
2 NL



4 3
 2 N (Vin / 2  NVout ) 2 .......... (4) 2 36
VinVout

secondary side MOSFET Ron_pr. Thus, the power loss per
secondary MOSFET Pcondloss_se can be obtained by (8) using theon-resistance of the secondary side MOSFET
Pcondloss_ pr  4Ron _ pr ( I L / 2) 2....... .......................................... (7)From (4), the inductor current is minimum when the value of
NVout/Vin is close to 0.5.

Pcondloss_ se  2Ron _ se ( NI L / 2) 2

C. ZVS range of full-bridge mode and half-bridge mode
In order to achieve ZVS for all switching devices, thecondition of the output power is presented by (5)[5].

In the half-bridge mode, the inductor current is double
compared to the full-bridge mode at same load.

2
VinVout  
VinVout   NVout  



1


  Pout _ FB 
NL 4   Vin  NL 4  (5)

In general, the operation range of the DAB converter is/2/2Hence, the right side of (5) is the rated power.
From (5), the lower limit of the output power to achieve theZVS increases due to the ratio of the primary and the secondary
voltage including the turn ratio of the transformer NVout/Vin .
On the other hands, the condition of the output power ispresented by (6) in order to achieve the ZVS in the half-bridgemode.
2
 NVout  
VinVout  
V V 


   Pout _ HB  in out (6)1  4
NL 4 NL 8
 Vin  From (6), The ZVS range at the half-bridge mode is wider
than the full-bridge mode at light load when NVout/Vin is close to
0.5. At the half-bridge mode, the ZVS is achieved at light load
compared to full-bridge mode. On the othrer hand, the ZVS isachieved at a heavy load at the full-bridge mode. As a result,the ZVS range is extended due to changing operation between
half-bridge mode and full-bridge mode.
In the proposed circuit, the efficiency can be improved forwide load variation by designing the ZVS range and adjusting
the ratio among the conduction loss, the copper loss and theiron loss of the transformer. Therefore, it is necessary to
calculate the each loss in order to derive the changing point theoperation mode.
III.

DERIVATION OF OPERATION MODE FROM LOSSCALCULATIONThis section explains the power loss expression of the
proposed circuit. The switching loss is ideally zero, because theswitching devices can achieve the ZVS. The power loss of the
proposed circuit consists of the conduction loss and the constantloss. The conduction loss is generated in the on-resistance of
MOSFET, the wire resistance of the transformer. The constantloss is generated within the iron loss of the transformer and the
no load loss.
A. Mathmatical loss expression
The power loss of the MOSFET consists of the conduction
loss. In the secondary voltage side inverter of Fig. 1, theconduction loss of the secondary voltage side MOSFET
Pcondloss_pr can be obtained by (7) using the on-resistance of the... .......................................... (8)The power loss of the transformer consists of the iron loss
and the copper loss. The iron loss occurs because of the fluxchange in the core. The copper loss occurs in the winding
resistance of transformer. At first, when the square wave isinput to the transformer, the flux density ΔB is obtained by (9).
B 

V1  t on(9)............................. .......................................
2 N1 Ac

where V1 is the input voltage of the transformer, N2 is thesecondary wire turns, Ac[m2] is the effective cross-section of thecore. Therefore, the iron loss of the transformer Ptrans_fe is
obtained by (10) using the characteristics of the flux density core loss value Pcv[W/m3] and the effective volume of the coreVe[m3]. In the half-bridge mode, the iron loss is decreased bydecrement of the flux density.
Ptrans _ fe  PcvVe(10)........................ ......................................
The copper loss of the transformer is obtained from thewinding resistance with the skin effect. The primary winding
copper loss Pcopper_pr in the main circuit is obtained by (11) using
the primary winding resistance of the main circuit with skineffect Rwire_pr. The secondary winding copper loss Pcopper_se in
the main circuit is obtained by (12) using the primary winding
resistance of the main circuit with skin effect Rwire_se.
Pcopper _ pr  Rwire _ pr I L

2................ ........................................

Pcopper _ se  Rwire _ se NI L 

2............. ........................................

(11)
(12)

The power loss of the additional inductor consists of thecopper loss and the iron loss. In order to neglect the saturationof the flux in the core, the air coil is used. Thus, the copper loss
occurs only in the additional inductor. The copper loss of theadditional inductor is obtained by similarly to (9).
The root mean square value of the inductor current ischarged or discharged to the output and the input capacitor.
Therefore, the output capacitor loss Ploss_C_out, Ploss_C_in are
obtained by (13), (14) using the equivalent series resistanceRC_out, RC_in.
Ploss _ C _ in  RC _ in I L2..................... .....................................

Ploss _ C _ out  RC _ out NI L2(13)

............... ........................................

(14)

B. Derivation of changing pointAt the changing point, the loss of the full bride mode isequal to the half-bride mode. The relationship between the loss
and the inductor current is is presented by (15).
22( I L _ HB  I L _ FB ) 

Ptrans_ fe _ FB  Ptrans_ fe _ HB ....................... (15)N R  R 
2

se

pr

where Ptrans_fe_FB is the iron loss at the full-bridge mode,
Ptrans_fe_HB is the iron loss at the half-bridge mode, Rpr is the sumof the on-resistance of the primary side MOS-FETs, equivalent
series resistance of the input capacitance, the primary side wire
resistance of the transformer, Rse is the sum of the secondaryside resistance. In order to derive the output power of thechanging point, the derivation of the phase difference is neededfrom (1) or (2). At the changing point, the phase difference ofthe half-bridge mode is about the half of the phase difference
the full-bridge mode. Therefore, it is possible to derive thechanging point using the only phase difference of the fullbridge mode. On the other hand, the each mode of the inductor
current is varied by NVout/Vin from (3). Therefore, the phasedifference at the changing point is derived using the two
conditions according to NVout/Vin. At the first condition of
0.75NVout/Vin, the equation (4) is approximated. The phasedifference at the changing point HB-FB is presented by (16) at
the first condition using (15), (3) of approximation and (4).
Half bridge mode

98.0

 _ HB  FB 

 _ HB  FB   7 ( NL) 2 Ptrans_ fe _ FB  Ptrans_ fe _ HB
5  4 VinVout( N Rse  R pr )2

13 (Vin  NVout ) 2 2   
10 NVinVout
5 

The output power at the changing point is derived by (16) or(17), (1).
IV.

LOSS CALCULATION RESULTS

Fig. 4 shows the loss calculation results against the output
power at the fluctuation of the primary and the secondary
voltage. From the results, the maximum efficiency of over 95%
is achieved against the voltage fluctuation. From Fig. 4, thechanging point between the half-bridge mode and the fullbridge mode is decided by the primary/the secondary side
voltage including the turn ratio of the transformer.

Half bridge mode

Full bridge mode

Half bridge

96.0

Efficiency [%]Efficiency [%]13 (Vin / 2  NVout ) 2 2 

 
10
NVinVout
5




98.0

94.0
92.0

Full bridge

94.0
92.0

Full bridge

90.0
88.0

88.0
0

200

400

600

Output power [W]

800

0

1,000

(a) Vin =480 V Vout=36 V NVout/Vin=0.6
Half bridge
Full bridge mode
mode

200

400

600

Output power [W]

800

1,000

(b) Vin =380 V Vout=36 V NVout/Vin=0.76

98.0

Full bridge mode

98.0

96.0

96.0

94.0
92.0

Full bridge

90.0
88.0

200

94.0

Full bridge

92.0
90.0

Half bridge
0

Efficiency [%]Efficiency [%]( N Rse  R pr )2(17)

Full bridge mode

Half bridge

5
 4 VinVout(16)At the second condition of 1NVout/Vin>0.75, the equation (3)is approximated. Therefore, the phase difference at thechanging point HB-FB is presented by (17) using (15), (4) ofapproximation and (3).

96.0

90.0

  7 ( NL) 2 Ptrans_ fe _ FB  Ptrans_ fe _ HB

400

600

Output power [W]

800

1,000

Half bridge

88.0
0

200

400

600

Output power [W](c) Vin =380 V Vout=48 V NVout/Vin =1(d) Vin =380 V Vout=60 V NVout/Vin =1.26
Fig. 4. Efficiency calculation results of proposed circuit.

800

1,000

V.

SIMULATION RESULTS

Fig. 6 shows the characteristics of the inductor current withthree-level DAB converter and the two-level DAB converter.
Fig. 6(a) shows the results when NVout/Vin is set to 0.76. Fig.
6(b) shows the results when NVout/Vin=0.5. At 33% load (300W), the characteristic of the inductor current is sharply
increased because the changing point between the full-bridge
mode and the half-bridge mode at the 33% load (300 W). In Fig.
6(a), the inductor current is increased maximum 20% at 10%
load (100 W). However, the iron loss is decreased by the halfbridge mode. In the loss calculation results, the efficiency isimproved compared to the conventional DAB converter.
Moreover, In Fig. 6(b), the inductor current is also reduced
maximum 84% at 10% load (100 W) because the amplitude of
the primary voltage is equal to the secondary voltage.
Fig. 7 shows the ZVS range against the inductor current
between the three-level DAB converter and the two-level DAB
converter. In Fig. 7, the ZVS is achieved at light load comparedto the two-level DAB converter when the ratio of the input andthe output voltage including the turn ratio of the transformer is0.3>NVout/Vin>1. Especially, the output power for achievementof ZVS is from 5% load to 50% load in the case of NVout/Vin=0.5
because the error between the ratio of the input/output voltage
and the turn ratio of the transformer is zero. In addition, the ZVS
range is extended by 60% compared to the two-level DAB
converter. Therefore, the copper loss and the switching loss are
reduced.
VI.

EXPERIMENTAL RESULTS

In this section, the fundamental operation of the proposed
DAB converter is verified by the prototype.

Vin
Vin/2
0
-Vin/2-Vin
NVout
0-NVout1.4
1.3

NVout/Vin

1.2
1.1
1

Half bridge mode

Vin
Vin/2
0
-Vin/2-Vin
NVout
0-NVoutFull bridge mode

0.9
0.8

Calculation results by (15)0.7

Loss analysis
by simulation results

0.6
0.5

0

100 200 300 400 500 600 700 800 900 1000
Output power Pout[W]Fig. 5. Changing point between full-bridge mode and half-bridge modeby loss calculation.

Full bridge mode

Half bridge mode

4

Inductor current iL [A]

Fig. 5 shows the changing point against NVout/Vin. In orderto derive the changing point against NVout/Vin, equations (16) or(17), (1) is calculated using the specifications which are theinput and the output voltage, the switching frequency, theleakage inductor and the turn ratio of the transformer. From Fig.
5, the good agreement with the simulation results. Moreover,the maximum error between the calculation and the simulation
result is 4.3%. This is because the inductor current is varied by
the dead-time. Therefore, the validity of changing point
calculation is confirmed.

1.5

3

2

Simulation result of
3-level DAB converter

1

Simulation result of
2-level DAB converter
0
0

200

400

600

800

1000

Output power Pout[W](a)NVout /Vin=0.76

Half bridge mode

10

Inductor current iL [A]

Fig.4 (a) shows the efficiency against the output power
when Vin is 480 V, Vout is 36 V. the efficiency of the half-bridge
mode is much higher than the full-bridge mode at the light load.
This is because the iron loss is decreased compared to the fullbridge mode. However, the efficiency at the full-bridge mode
is low. This is cause that the reactive current is large due to theerror between the primary voltage and the secondary voltage
including the turn ratio of the transformer. For the same reasons,the efficiency of the full-bridge mode becomes low at close to
NVout/Vin=0.5 (In Fig.4 (b) and (c)). On the other hand, In Fig.
4 (d), the efficiency of the full-bridge mode is increased when
the ratio of the primary and the secondary inverter voltage
including the turn ratio is close to 1.

Full bridge mode

Simulation result of
2-level DAB converter

864

Simulation result of
3-level DAB converter

2
0

0

200

400
600
Output power Pout [W]

800

1000

(b) NVout/Vin=0.5
Fig. 6. Characteristic of the inductor current with three-level DAB
converter and DAB converter

Fig. 8 shows the operation waveform of the proposed DCDC converter. The input voltage Vin is 100 V. The output
voltage Vout is 20 V. the switching frequency fsw is 100 kHz. It
is clear that the five-level waveform is output by the primary
inverter. However, the output voltage of the primary inverter is
not 1/2Vin. This is because that the gate signals in the primaryside switching devices are delayed by the gate drive circuit.

This paper proposed the DAB DC-DC converter utilizing to
the three-level flying capacitor topology for the battery
interface system. The operation mode of the three level DAB
converter is determined by the loss calculation results. The
theoretically with the maximum efficiency of over 95% in the
full-bridge mode and the half-bridge mode. In addition, thevalidity of the changing point calculation is also confirmed.
From the simulation results, the ZVS range is extended by 60%.
In addition, the fundamental operation is validity.
In the future work, the operation mode including the fivelevel waveform will be derived using the loss calculation.
Moreover, the validity of the proposed DAB converter is also
confirmed by the experimental results.
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Imakubo, Yuuji Imakubo, Yuuji Sasaki, Takehiro Jikumaru:「Improvement of Efficiency of Dual Active Bridge DC-DC Converter
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4, pp. 724-738 (2002)[9] Moonem, M.A, Krishnaswami, H., Fang Zheng Peng: 「Control andConfiguration of Three-Level Dual-Active Bridge Converter as a Frontend Interface for Photovoltaic System」, APEC2014, pp. 3017-3020(2014)[10] P. A. M. Bezerra, F. Krismer, R, M. Burkart, J. W. Kolar: 「Bidirectional
Isolated Non-Resonant DAB DC–DC Converter for Ultra-Wide Input
Voltage Range Applications」, PEAC2014, pp. 1038-1044 (201

NVout/Vin

VII. CONCLUSTION

1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

ZVS boundary lineof 3-level DAB converter ZVS boundary lineof 2-level DAB converter

010Inductor current [A]20

Fig. 7.Characteristic of ZVS range with three-level DAB converter andtwo-level DAB converter.

Output voltage of three-level inverter 100V/div
0

[1]

0
Output voltage of two-level inverter 20V/div
0
Primary current of transformer 100 mA/div
4 ms/div
Fig. 8. Fundamental operation of proposed DAB converter.