Reduction of Transmission Power Error and Current
for Dual Active Bridge DC-DC Converter in
Energy Storage Systems
Jun-ichi Itoh, Kengo Kawauchi, Hiroki Watanabe, Keisuke Kusaka
Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Niigata, Japan
itoh@vos.nagaokaut.ac.jp, k_kawauchi@stn.nagaokaut.ac.jp, hwatanabe@vos.nagaokaut.ac.jp, kusaka@vos.nagaokaut.ac.jp
Abstract— This paper proposes a control method for a dual
active bridge (DAB) converter, which achieves both a reduction
method of a non-linear transmission power error and an inductor
current reduction with a three-level operation. The non-linear
transmission power error is compensated by designing a zerocurrent period in the inductor current by the three-level
operation. In addition, the inductor current reduction method forthe three-level operation is also proposed. In the non-linear
transmission power error compensation method, the inductor
current is reduced by suppressing the circulating current withdetermining zero-current period to be the dead-time. The validityof the proposed method is confirmed by a 2-kW prototype. As theexperimental results, the transmission power error is reduced by
up to 85.1%. Moreover, the inductor current is reduced by up to
64.1% and loss is reduced by up to 58.6%.
Keywords— Dual active bridge converter; Dead-time error;
Current reduction; Three-level operationI.

INTRODUCTION

In recent years, a DC micro-grid system has been actively
studied in order to solve the environmental problems [1-5]. An
isolated bi-directional DC-DC converter is required for energy
storage systems in order to control power between the DC bus
and the energy storage systems with galvanic isolation. In theisolated bi-directional DC-DC converter, a dual active bridge(DAB) converter is generally employed for these applications
because the DAB converter obtains high efficiency because ofachieving zero voltage switching (ZVS) without additional
components [6-10]. However, a non-linear transmission error
occurs due to the dead-time at light load although the DAB
converter has to operate at a wide load range in energy storage
systems [11]. In order to reduce the error of the transmission
power, the dead-time compensation method has been proposed[12]. In [12], the dead-time error is compensated by thefeedforward compensation that subtracts the dead-time fromthe command of the phase-shift between the primary and thesecondary output voltage. However, this conventional method
is effective only when the transmission-power error is linear.
The non-linear error due to a voltage-polarity-reversal
phenomenon is not compensated by the compensation method
in [12].

The authors have proposed the non-linear dead-timecompensation method using a three-level operation [13]. By
applying the compensation method in [13], the non-linear
transmission error is compensated although an inductor current
is increased by a circulating current owing to the three-level
operation. The circulating current should be suppressed
because the increase in the inductor current causes the decreaseof efficiency.
This paper proposes the compensation method of the nonlinear transmission error with the current reduction method in
the three-level operation. The contribution of this proposed
method is to overcome the problems of the conventional
compensation method that is the increase in loss due to thecirculating current. The transmission power error iscompensated by avoiding the voltage-polarity-reversal. In
addition, the inductor current is reduced by suppressing thecirculating current with determining the zero-current period tobe the dead-time. By applying the proposed method, the energy
storage system is operated without the dead-time error withhigh efficiency.
This paper is organized as follows; firstly, the conventional
control method is discussed. Secondly, the reduction method of
non-linear transmission power error is introduced. Next, thecurrent reduction method for the three-level operation is
proposed. Finally, experiments are conducted in order to verify
the compensation method of the non-linear transmission power
error caused by the dead-time and the current reduction method
for the three-level operation.
II.

CONVENTIONAL CONTROL METHOD

A. Traditional two-level operation method
Fig. 1 shows the circuit configuration of the DAB converter.
The DAB converter consists of two H-bridge inverters, anadditional inductor, and a high-frequency transformer. The
primary and the secondary inverters generate the square-wave
voltage, and the transmission power is controlled by a phaseshift  between each inverter output voltage called the single
phase shift (SPS) control. The transmission power is expressedby [12],



P

δ 
NVinVout δ 1   

ωL
π 


A-phase B-phase





S5

Vin

Fig. 3 shows the influence of the voltage-polarity-reversal
phenomenon for the transmission power. The transmission
power error caused by the voltage-polarity-reversal
phenomenon is not compensated by the conventional
feedforward method because the transmission power error due
to the dead-time varies depending on the width of the voltagepolarity-reversal [11–12]. The period of the voltage-polarity
reversal is varied by the relationship between the inductor
current and the dead-time period [11]. At the period between
2dt and dt, the transmission power error is variedcorresponding the width of the voltage-polarity-reversal, wheredt is the dead-time in the radian calculated as (2) using thedead-time Tdt and switching angular frequency ,

S2

N

Vout
vse

S4

S6

S8

Fig. 1. Dual active bridge converter.
Voltage-polarityreversal phenomenon
vpr
0

q



vse
0

Dead-time

q

iL
0

q
(a) Without dead-time.
(b) With dead-time.
Fig. 2. Operation waveform with conventional two-level operation.
2δ 2 δ dt  1  dt 
π 


2V in
ωL

Without dead-time
2V in
ωL

δ 

δ dt  1  dt π With dead-time0dt

Phase-shift dtFig. 3. Influence of dead-time for transmission power.
S1
S3



S5

After dt, the transmission-power error becomes theconstant value of the dead-time without the voltage-polarity
reversal. In the area where the phase-shift  is smaller than thedead-time dt, power is not transferred because the phase-shift is canceled by the dead-time [12].

S7

B. Non-linear Transmission Power Error Compensation
Method1) Conventional operation method
Fig. 4 shows the operation waveforms of the conventional
three-level mode. In the conventional operation method, thezero voltage phases of each inverter are controlled identicallywith the phase-shift  as a constant. The three-level modes are
considered under the condition of Vin = NVout and  = . Notethat the parasitic capacitance and the magnetizing current are
not considered in this calculations. Under the steady state
condition, the inductor current iLI at the switching moment asfollows,

S7

iL

vpr

Transmission power P

Fig. 2 shows the two-level operation waveform with andwithout the dead-time. In the case of taking no account of thedead-time, the transmission power is controlled by the phaseshift  without the transmission-power error. However, in an
actual system, the dead-time is needed in order to prevent two
switching devices from the short circuit. In this case, thetransmission-power error occurs at light load when the inductor
current becomes zero during the dead-time. The inductor
current is clamped to zero because the inductor current does
not conduct primary inverter during the dead-time. As a result,the polarity of the primary inverter output voltage is reversedby the clamped inductor current. Consequently, thetransmission-power error is caused by the voltage-polarityreversal phenomenon due to the dead-time [11].

δdt  ωTdt 

S3
Lwhere  is a switching angular frequency, L is an additional
inductor, N and  are turn ratio and phase-shift between the
primary inverter output voltage vpr and the inverter on thesecondary side output voltage vse.

S1R-phase S-phase

ON

0

ON
ON

0

q

ON

0
0

q

ON

ON



ON



vpr 0



q
q


q






vse 0

q

iL 0

q
0

p
Fig. 4 Conventional operation waveform.

 Vin0  θ  δ  ε  ωL θ  δ  ε 0δ  ε  θ  ε  ViLI θ    in θ  ε 
ε  θ  π  ε  
 ωL
 Vin
π  ε  θ  δ  ε  ωL π  2 ε  Vin π  θ  ε  δ  δ  ε  θ  π 
 ωL





Fig. 5. Dead-time effect of three-level mode.
S1
S3
S5
S7
vpr
vse





2) Dead-time influence and compensation of three-level
mode
Fig. 5 shows the dead-time effect on the primary inverter
output voltage and the inductor current of the three-level mode.
The voltage-polarity-reversal phenomenon is eliminated bydetermining the zero-current period  to become longer thanthe dead-time because the voltage-polarity-reversal
phenomenon occurs when the inductor current becomes zero
during the dead-time. The condition of  ≥ dt is given byφ  2ε  δ  δdt However, the duty of the primary inverter output voltage isdecreased by the dead-time because diodes of the B-phase leg
is not conducted during the dead-time instead of designing thezero-current period  to be longer than the dead-time.
Therefore, the duty of primary inverter output voltage isneeded to be compensated.
Fig. 6 shows the dead-time compensation for the three-level
operation. The duty error by the dead-time is compensated by(7) because the decrease of the duty affects the phase-shift and the zero voltage phase ,δ *  δ  δdt / 2 *ε  ε  δdt / 2  *γ  ε

dt
q

dt

0

q

ON

q

dt

0
0

ON

dt

0

ON

dt

q

ON

q
q

0
0

q

With dead-timeiL
0

2ε  π  δ Without dead-timeiL
0

In order to be operated by the conventional three-levelmode, PWM pulses of each inverter output voltage are notoverlapped. The condition of the conventional three-level modeis expressed by


q

dt



According to (3), the transmission power PI is calculated byVin22 ππ  2 ε 2 PI v pr θ  i LI θ  dθ 

2π 0
2πωL

With dead-time

vpr
0

q

With dead-timecompensation

Fig. 6. Dead-time compensation mehod for three-level operation.

where *, * and * are the phase-shift commands, the zerovoltage phase command of the primary inverter, and the zerovoltage phase command of the secondary inverter.
3) Decision of phase-shift In this chapter, the phase-shift  is determined astransferring maximum power in order to compensate the entire
range of transmission power error. According to (4) and (5),the maximum transmission power is given by minimizing thezero voltage phase . Therefore, the phase-shift  of the
maximum transmission power max_I is given by (8) using (5)and (6),δ m axI 

1π  δdt  
2



Therefore, the range of the zero voltage phase  and thetransmission power of PI are expressed by (9) and (10) using(4), (5), and (6),1

0  PI 

4π  δdt   ε  1 π 



2

Vin2
π  δdt 2 
4πωL0

In addition, RMS value of the inductor current is expressedby (11) from (3),
iLI _ RMS 

2 π
2iLI θ  dθ
2π 0

V
 in
ωL

1
2ε  π 2 3δ  π  2ε 
3πIII.

CURRENT REDUCTION METHOD FOR THREE-LEVELOPERATION

Figure 7 shows the circulating current of the conventional
three-level operation. In the conventional three-level operation,
the circulating current accounts for more than half of theinductor current. Therefore, conduction loss increases because
the inductor current against the transmission power is bigger
than the two-level mode. Hence, the circulating current isrequired to reduce in order to achieve high efficiency.


q




vse
0
iL


q
q

0
Circulating current

Fig. 7. Circulating current of conventional three-level mode.

Figure 8 shows waveforms of the proposed three-level
operation. In the proposed operation method, the zero voltage
phases of each inverter and the phase-shift are controlled in adifferent manner of the conventional three-level operation. The
proposed three-level modes is considered under the conditionof Vin = NVout and  = . Note that, the parasitic capacitance andthe magnetizing current are not considered in this calculations.
Under the steady state condition, the inductor current iLII at theswitching moment as follows,0  θ  ε 
0

 Vin
θ  ε ε  θ  ε  δ 

ω
L

V
iLII θ    in δε  δ  θ  π  ε  
 ωL
 Vin
 ωL π  ε  δ  θ  π  ε  θ  π  ε  δ 0π  ε  δ  θ  π 




vpr
0

S1
S3
S5
S7

ON

0

ON

ON






q

ON





q



q


vse 0

q

iL 0

q
0

vpr
0
vse
0
ise

Then, the transmission power PII is given by (13) using (12),

q

ON

0
0

q

ON

0

vpr 0



ONpFig. 8. Proposed operation waveform.




q




q

dtq0
Circulating current



PII 

2

 v pr θ iLII θ  dθ 
π

2π 0

Vin2
2πωL

δ 2π  4 ε  δ   

In order to be operated by the proposed three-level mode,
pulses of each inverter output voltage are overlapped. The
condition of the proposed three-level mode is expressed by2  p   

In addition, the RMS value of the proposed three-level
operation is given by (15), from (12),iLII _ RMS 

2i θ  dθ
2π 
π

0

Fig. 9. Circulating current of proposed three-level operation.

regarding the transmission power. The phase-shift and zerovoltage periods are minimized when the zero-current period 
is the same as the dead-time. Therefore, the inductor current isreduced by controlling the zero-current period  to be the deadtime period dt. The condition of  = dt is given by


ε

1
2

δ  δdt  

Substituting (16) for (13), the transmission power PIII isexpressed by

2

LI

Vin

1

ωL

3π





2ε  π  3δ  π  2ε 
2Figure 9 shows the circulating current of the proposed
three-level operation. In order to reduce the inductor current in
the three-level mode, the circulating current is suppressed byminimizing the phase-shift angle and zero-voltage periods

PIII 

Vin22πωLδ 2π  2δdt  3δ  

The command of the phase-shift * is given by solving (17)for the phase-shift  as



δ 
*

2π  2δdt   2π  2δdt 2  24 πωLP * Vin2
6

Start





where P* is the command of the transmission power. Using(16) and (18), the inductor current is reduced because thecirculating current is suppressed.
Figure 10 shows the flowchart for the determination ofoperation modes. The operation mode is determined as follows;
the phase-shift angle  is calculated with the transmission
power command P* by solving (1) for the phase-shiftδπ  π 2  4πωLP * Vin22

Cal. of  : Eq.(19)Cal. of *, *, *
Dead-time comp: Eq.(7)The operation mode is decided by the phase-shift commandε

12πωLP * 
2π  δdt  α  δdt  α Vin2 
2

Vout
fsw
L

dt
* =

FinishFig. 10. Flowchart of determination of operation modes.
Table I. Experimental condition.
mH
Input voltage Vin
240 V
Additional inductance L
Margin of dead-time 
0.36deg
Output voltage Vout 240 V
2 kW
1Rated power P
Transformer turn ratio Nms
20 kHzDead time Tdt
Switching frequency fsw

* and the dead-time dt. Under the condition of * > 2dt, theVinTwo-level modeNo2dt >
Three-level
Yes
mode
No
Controlling≥dt+
, Controlling
Yes
Cal.
of

,

:
Eq.(20) , , Cal. of : Eq.(16), (18)

conventional two-level operation is used. In contrast, thetransmitted power is determined by the phase-shift  and thezero-voltage period  given by (16) and (18) when the threelevel operation is used. The voltage-polarity-reversal
phenomenon occurs when the phase-shift angle  reaches dt
because the inductor current reaches zero during the dead-time.
Therefore, the phase shift angle is limited by dt + where  isa few margin to avoid the voltage-polarity-reversal
phenomenon. The margin  is needed to be design as small as
possible because the circulating current increases as the margin is larger. When an FPGA is used for an experiment, themargin  is determined as one clock of the FPGA because thephase-shift is controlled by the clock period of the FPGA.
After the operation range of dt + , the transmission power iscontrolled by the zero-voltage periods with the phase-shift ofdt +. The zero-voltage command is given by (20) form (17)and dt +,

INPUT
Pref

CircuitSpecifications

Output voltage of primary inverter 500V/div0

Output voltage of secondary inverter 500V/div0

P* =1.11kW, P=0.582 kW, Error=47.6 %Inductor current of primary inverter 20A/div
0

20ms/div(a) Two-level mode.
Output voltage of primary inverter 500V/div0

Output voltage of secondary inverter 500V/div00

Finally, the dead-time error due to avoiding the voltagepolarity-reversal phenomenon is compensated by (7).

P* =1.11kW, P=1.14 kW, Power error=2.70 %, iL=11.3A
Inductor current of primary inverter 20A/div
0

20ms/div(b) Conventional three-level mode.

IV.

EXPERIMENTAL RESULTS

Table I shows the experimental parameters. A 2-kW
prototype of the DAB converter is tested in order to confirm
the validity of the proposed method.
Figure 11 shows experimental waveforms of the two-level
mode and three-level modes. Fig. 11(a) shows operation
waveforms of two-level mode. The transmission error of 47.6%
occurs because the voltage-polarity-reversal phenomenon iscaused. By applying the conventional non-linear dead-timecompensation method, the transmission error is reduced by
44.9%. However, the inductor is 11.3 A due to the circulating
current. In contrast, using the proposed current reduction
method, the inductor current against the transmission power is

Output voltage of primary inverter 500V/div0

Output voltage of secondary inverter 500V/div0

P* =1.11kW, P=1.10 kW, Power error=0.90 %, iL=5.52A
Inductor current of primary inverter 20A/div
0

20ms/div(c) Proposed three-level mode.
Fig. 11. Experimental waveforms of two-level operationand three-level operation.

Figure 13 shows the characteristics of the inductor current
regarding the transmission power. By applying theconventional method, the inductor current is increased by morethan twice that of the two-level mode. On the other hand, theinductor current is reduced by up to 64.1% because thecirculating current is reduced with the proposed method.
Figure 14 shows the efficiency characteristics of the twolevel mode, the conventional method, and the proposed method.
In the conventional method, the efficiency is decreased owing
to the increase in conduction loss. By applying the proposed
method, loss is reduced by up to 58.6% because the increase in
the inductor current is suppressed.
V.

CONCLUSION

This paper proposed the compensation method of thetransferred power error due to the dead-time with the reduction
method for the inductor current. The error of the transmission
power is reduced by up to 85.1% because the voltage-polarityreversal phenomenon is avoided. Moreover, the inductor
current is reduced by up to 64.1%. In the future work, thecompensation method for the non-linear dead-time error under
the condition of Vin ≠ NVout will be considered.

Transmission power P [kW]Proposed method: controlling , , 

1.3
Proposed method: controlling , 

0.8Reducedby 85.1%

0.3
0

0

[1]

[2]

[3]

[4]

[5]

[6]

[7]

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0.2

0.4

Power error=86.3%

Two level modewith dead-time error

0.6
0.8
1
1.2
1.4
Transmission power P[kW]

1.6

1.8

Fig. 12. Charactarisitics of transmission power.
14
12

Conventional
method10

Reducedby 64.1%

8
6

Proposed method: controlling , 

40Proposed method: controlling , , 
Two level modewith dead-time error

2
0

0.5

1.0
1.5
Transmission power P [kW]2.0

Fig. 13. Charactaristics of inductor curretn regarding transmission power.
100
95
90
85
80
75 0

REFERENCES

Power error=1.22%

P=P*

Inductor current iL [A]Figure 12 shows the characteristics of the transmission
power against the transmission power command. In the twolevel mode, the transmission power has the non-linear error due
to the voltage-polarity-reversal phenomenon. By applying the
proposed method, the transmission-power error is reduced by
up to 81.5% by avoiding the voltage-polarity-reversal
phenomenon.

1.8

Efficiency h[%]reduced by 51.2% by controlling the zero-current period to thedead-time dt.

Proposed method: controlling , Maximum eff. 94.5%

Two level modewith dead-time error
Loss is reduced Proposed method: controlling , , 
by 58.6%
Conventional method
0.5

1.0
1.5
2.0
Output power Pout [kW]Fig. 14. Efficiency charactaristics of conventional method and proposed
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