Non-linear Dead-time Error Compensation Methodof Dual Active Bridge DC-DC Converter for
Variable DC-bus Voltage
Jun-ichi Itoh, Kengo Kawauchi, Hiroki Watanabe
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
Abstract— This paper proposes a transmission power error
compensation method for a Dual Active Bridge (DAB) converterwith a three-level operation when a DC-bus is varied. The nonlinear transmission power error due to a dead-time iscompensated by designing a zero current period to be longer thanthe dead-time using the three-level operation because the nonlinear transmission power error occurs when an inductor current
reaches zero during the dead-time. The proposed method adjustsa zero-voltage period according to the variable DC-bus voltage inorder to design the zero current period for compensating thenon-linear transmission power error. In addition, the three-level
operation is controlled to reduce a circulating current in order toreduce RMS value of the inductor current. The validity of the
proposed method is confirmed by a 1.9-kW prototype. As theexperimental results, the transmission power error is reduced
from 49% to 3.5%.

by designing a zero current phase to be longer than the deadtime using three-level operation. However, the compensation
method for the DC-bus voltage variation does not include theprevious consideration. In actual energy storage systems for the
DC micro-grid, the voltage fluctuation should be considered
because the DC-bus voltage is varied according to the power
generation of photovoltaic systems and load conditions.

Keywords— Dual Active Bridge converter; Dead-time error;
Three-level operation;

This paper is organized as follows; firstly, a dead-time
effect for the transmission power is introduced. Secondly, thenon-linear dead-time compensation method for the variable
DC-bus voltage is explained. Finally, experiments are
conducted in order to verify the compensation method of the
non-linear transmission power error due to the dead-time when
the DC-bus voltage is varied.

I. INTRODUCTION
In recent years, DC micro-grid systems have been actively
researched in order to solve environmental problem [1-3]. In
the DC micro-grid systems, energy storage systems isnecessary in order to compensate the power fluctuation of thehigh voltage DC-bus because the generated power depends onthe meteorological condition. In order to control power andisolate between the high voltage DC-bus and a buttery forsafety, a bi-directional isolated DC-DC converter is applied. A
dual active bridge (DAB) converter is generally employedbecause the DAB converter has a good feature in efficiency [47]. In particular, the DAB converter achieves a zero voltage
switching (ZVS) without any additional components. However,a transmission power error occurs due to a non-linear deadtime at light load to medium load although the DAB converter
has to operate at wide load range [8]. The non-linear
transmission power error occurs due to a voltage polarity
reversal phenomenon. This phenomenon is caused when the
inductor current reaches zero during the dead-time.
The authors have been proposed a non-liner transmission
power error compensation method using a three-level operation[9-10]. The voltage polarity reversal phenomenon is avoided

This paper proposes the transmission power error
compensation method corresponding to the voltage variation
on each DC-bus. By applying the proposed method, theoperation range of energy storage systems are expanded
because the transmission power error is compensated. The newcontribution of this paper is to overcome the problems of theconventional compensation method that is the transmission
power error due to the variation of the inverter input voltage.

II. DEAD-TIME EFFECT FOR TRANSMISSION POWER
Figure 1 shows the circuit configuration of the DAB
converter. The DAB converter is constructed from two fullbridge inverters and a high frequency transformer. Eachinverter outputs the square wave voltage with the duty of 0.5
and the transmission power is controlled by the phase-shift
between the primary and secondary side of the inverter output
voltage.
A-phase B-phase
S1

R-phase

S3

S5
L

Vin
vpr
S2

S4

S-phase
S7

N:1

iL

vse
S6

Fig. 1. Dual active bridge converter.

S8

Vout

Figure 2 shows operation waveforms of two-level modewith and without the dead-time. Without considering the deadtime, the transmission power is controlled by the phase-shift
without transmission power error. From Fig. 2 (a), the inductor
current is expressed as (1) taking no account of the parasitic
capacitance and the magnetizing current. Note that the turnratio N is regarded as one for simplify considering in this paper.

Voltage-polarityreversal phenomenon

vpr
0
vse
0
iL
0





(b) With non-linear dead-time error.



vse
0

Without dead-timeWith dead-time

Figure 3 shows the relationship between the phase-shift andthe transmission power when the output voltage is varied from
0% to -25%. The transmission power error is varied according
to the fluctuation of the output voltage. In Fig. 3, the non-linear
transmission error occurs when the output voltage is varied
from 0% to -15%. In contrast, the linear error is caused when
the output voltage is varied from -20% to -25%. Therefore, thedead-time compensation method corresponding fluctuation of
the DC-bus voltage is required in order to compensate two
types of dead-time effect.
Figure 4 shows the condition of occurrence of thetransmission error due to the dead-time. The non-linear
transmission power error occurs when the inductor current

Region A(c) With linear dead-time error.

Fig. 2. Operation waveforms of two-level mode.
0.7

(2).

Meanwhile, the dead-time is necessary in order to prevent
short circuit. The non-linear transmission error occurs when the
inductor current becomes zero during the dead-time. The
inductor current is clamped zero because the inductor current is
not conducted during the dead-time. Consequently, the polarityof the inverter output voltage is reversed by the clamped
inductor current. In addition, the transmission error is varied
depends on the width of the voltage polarity reversal
phenomenon. On the other hand, the linear dead-time error iscaused by current direction during the dead-time. The polarityof the inductor current at the region A becomes negative atlight load when the Vin ≠ Vout. As the result, the diodes of thesecondary side inverter does not conduct during the dead-time
because the inductor current direction is different from theforward direction of the diodes. Thus, the transmission power
has the error by the dead-time because the rise-timing of thesecondary inverter output voltage is delay by the dead-time.



Dead-timedt

iL
0Transmission power [p.u.]δ 
VinVout δ 1  

ωL 
π 

p

(a) Without dead-time.

vpr
0

where Vin and Vout are an input voltage and an output voltage, 
is a switching angular frequency, L and  are an additional
inductor and  phase-shift between the primary inverter output
voltage vpr and the inverter on the secondary side output
voltage vse. According to (1), the transmission power is givenby (2),

P

Dead-time

1
 Vin  Vout
πVin  2δ  π Vout 
θ

ωL
2ω L

for 0  θ  δ iL θ   

V

V
out
 in
θ  δ   1 2δ  π Vin  πVout 
 ωL
2ωL

δ  θ  π 
for






Without dead-time effect

0.6
0.5 Error is constant by dead-time.
-25%

0.4

-20%

0.3

-15%

0.2

-10%

Error is varied.
-5%

0.1
0

0%:Vin=Vout

0%

0

5

10

15
20
25
Phase-shift  [deg]

30

35

40

Fig. 3. Relationship between phase-shift and transmission power.
vpr
0







vse
0
iL
0


dt


Zero cross0(a) non-linear dead-time error.

Zero cross0(b) linear dead-time error.

Fig. 4. Condition of occurrence of transmission power.

becomes zero during the dead-time. Therefore, the initial pointof the voltage polarity reversal phenomenon is when the zerocross point of the inductor current equals the final point of thedead-time. This condition of the phase-shift is expressed by (3)using (1) of  ≤  ≤ ,
Vin  Vout1
πVin  2δ  π Vout   0
2ωL

V
1
δ  2δ dt  π  in  2δ dt  π 
2Vout 2ωLδ dt 

In addition, the condition of ratio between input and output
voltage is expressed by (4) form (3),Vin  Vout
ωL

1
πVin  2δdt  π Vout   0
2ωLπ  2δ dt Vout

α
π
Vin

S1

δ dt 

S3



S5
S7

where  is the rate of the fluctuation of the output voltage thatis calculated as Vout / Vin. On the other hand, the linear
transmission power error occurs when the polarity of theinductor current becomes negative as illustrated Fig. 2 (c).
Therefore, the initial point of the linear transmission error isexpressed by Fig. 4 (b). From Fig. 3 (b), the condition of theoccurrence of the linear transmission error is given by (5) using(1) of  ≤  ≤ p,1
2δ  π Vin  πVout   0
2ω LV  Voutδ  in
π
2Vin



ON

0

ON
ON

0



ON

0
0



ON

ON



vpr 0

ON
















vse 0




iL 0

vpr
0


0
p
Fig. 5. Operation waveforms of three-level mode.
With dead-time





dt

Without dead-time

iL
0

dt




Fig. 6. Dead-time effect of three-level mode.

dt

S1 0

III. NON-LINEAR TRANSMISSION POWER ERROR COMPENSATIONMETHOD

S3 0

Figure 5 shows the operation waveform of the three-level
mode. From Fig. 5, the inductor current is given by (6) under
the steady state condition,

dt



ON



dt

S5 0
S7 0

ON

dt

ON
ON




vpr 0

iL θ  

vse 0

1

 2ωL Vin π  2 ε   Vout π  2 γ  for 0  θ  ε  Vinθ  ε   1 Vin π  2ε   Vout π  2γ 

2ω L
 ωL
 for ε  θ  δ  γ  V  V out inθ  δ  γ   1 Vin 2δ  2γ  π   Vout π  2γ  
ω
L
2ωL

 for δ  γ  θ  π  ε  Vout θ  π  ε   1 V π  2 ε   V 2 ε  2δ  π 
in
out
 ωL
2ω L
 for π  ε  θ  δ  π  γ  1 2ωL Vin π  2 ε   Vout 2 γ  π 
 for δ  π  γ  θ  π 
From (6), the transmission power P is given by (7),

iL 0



2 π
v pr θ  i L θ  dθ
2π 0
V V
 in out π  2γ δ  ε  γ   δ  ε  γ δ  ε  γ  π 
2πωL

P



With dead-timeWith dead-timecompensation
Fig. 7. Duty compensation for primary inverter output voltage.

where  and  are the zero voltage period of the primary andsecondary side inverter output voltage. By applying this threelevel operation, the voltage polarity reversal phenomenon is
avoided by designing the zero current period  to be longer
than the dead-time because the voltage polarity reversal
phenomenon is caused when the inductor current reaches zero
during the dead-time. The condition of avoiding the voltage
polarity reversal phenomenon is expressed by (8),φ  γ  ε  δ  δdt Figure 6 shows the dead-time effect of three-level mode.
The duty of the inverter output voltage of the primary side 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 the primary inverter output voltage is needed to becompensated.
Figure 7 shows the duty compensation for the primary
inverter output voltage. The duty error by the dead-time iscompensated by (9) because the decrease of the duty affects thephase-shift  and the zero voltage phase ,vpr Voltage polarity
reversal phenomenon01 *δ  δ  2 δ dt1
 *
 ε  ε  δ dt 2γ *  γ









iL
0



Circulating current
Fig. 8. Operation waveforms of three-level mode by applying conventional
method.

vpr0

IV. TRANSMISSION POWER ERROR COMPENSATION METHODFOR VARIABLE DC-BUS VOLTAGE

2γ 

2 
π
δ  δ dt  1  α   
α  1 
2



δ

1
2

1  α π  δdt  (a) Mode I.

vpr
0
vse
0
iL
0





dt

(b) Mode II.





From (10) and (11), the transmission power is controlled byonly the control variable of the phase-shift . In this mode, thevoltage polarity reversal phenomenon occurs when thesecondary zero voltage period  becomes dead-time dt.
Therefore, the control limit of the three-level mode I isexpressed by (12) from (11),


 

vpr
0

A. Three-level mode I
In order to reduce the RMS value of the inductor current,
the circulating current is need to be suppressed. The circulating
current is reduced by suppressing the phase-shift angle andzero-voltage periods regarding the transmission power. The
phase-shift and zero-voltage periods are minimized when thezero-current period  is the same as the dead-time dt [10]. The
condition of  = dt is given by (11), using (8) and (10),





iL
0

Figure 9 shows the operation waveforms of the proposed
three-level modes. This compensation method is applied threetypes of the three-level operation due to avoid the voltage
polarity reversal phenomenon. In order to design the zerocurrent period in the three-level operation, the initial value of(6) for  ≤  ≤  +  need to be zero. This condition isexpressed by (10) with Vout = Vin,

2ε  2αγ  1  α π




vse
0

Figure 8 shows the operation waveforms of the three-level
mode by applying the conventional method in [9-10] when the
output voltage is varied. The voltage polarity reversal
phenomenon occurs because the zero current period is notdesigned to be longer than dead-time due to the voltage
fluctuation. In addition, the inductor current is increased by thecirculating current. Therefore, the transmission power error
compensation method for the variable voltage is required.





vse
0

where *, * and * are the phase-shift commands, the zerovoltage period command of the primary and secondary inverter.

Vin π  2ε   αVin π  2γ   0

Dead-time dt



vse0-iL0dt+b

(c) Mode III.

Fig. 9. Operation waveforms of the proposed three-level modes.

B. Three-level mode II
In the three-level mode II, the transmission power iscontrolled by the secondary zero voltage period . In order tocontrol one control variable of the secondary zero voltage
period with suppressing the circulating current, the phaseshift  is designed as fixed value of (12) in the equality
condition. In the case of controlling the zero-voltage period
with the fixed phase-shift , the phase-difference  in Fig. 6(b) needs to satisfy (13) in order to avoid the voltage-polarityreversal phenomenon,λ  ε  γ  δ  δdt 

According to (10), (12), and (13), the secondary zerovoltage-period  is limited by (14),



γ

3α
δ dt  π 
2α  1C. Three-level mode III
After the operating region of the three-level mode II, thethree-level mode III is applied. In order to avoid the voltage
polarity reversal phenomenon, the phase-difference  isdesigned to =dt+b where b is a few margin to avoid thevoltage-polarity-reversal phenomenon. The margin b is needed
to be design as small as possible because the circulating current
increases as the margin b is larger. When an FPGA is used foran experiment, the margin b is determined as one clock of the
FPGA because the phase-shift is controlled by the clock periodof the FPGA. The condition of achieving =dt+bis obtainedby (15) using (10) and (13),πδ  δ dt  β  1  α  γ   2Table I. Experimental specifications.





Figure 10 shows the flowchart of the determination ofoperation modes. The operation mode is determined as follows;in order to decide whether the operating point is in the deadtime effect area or not, the phase-shift angle  is calculatedwith the transmission power command P* by solving (2) for thephase-shift ,

Quantity

SymbolValue

Input voltage
Output voltage
Rated power
Dead time
Additional inductanceTurn ratio of transformer
Switching frequency
Margin of dead time

Vin
Vout
P
Tdt
L
N
fsw

240 V
240-180 V
1.9 kW(45 deg)
2.1 ms (15 deg)
128 mH1
20 kHz0.36 degbcompensated when the voltage ratio satisfies (4). On the other
hand, the linear transmission error is compensated when thevoltage ratio does not satisfy (4). After the decision of the kindof the dead-time effect, the operation mode is selected from thetwo-level mode or three-level modes using (3) in the non-linear
dead-time effect flow. In contrast, in the linear dead-time effectflow, the operation mode is determined by (5). The three-level
operation is applied if the phase-shift  satisfies the (3) or (5).
The three-level modes is decided by (12) and (14). The threelevel mode II is applied when the phase-shift  is not satisfy(12). In addition, the three-level mode III is used when thesecondary zero voltage period  is not satisfy (14). In the linear
dead-time effect flow, the three-level mode III is not necessary
because the secondary zero voltage period  satisfies (14) until-25% of the voltage fluctuation. Finally, the duty of the inverter
output voltage is compensated by (9) when the three-level
operation is applied.
V. EXPERIMENTAL RESULTSπ  π2 



δ

4πωLP
VinVout*2

Next, the kind of the dead-time effect is decided from thevoltage ratio  using (4). The non-linear transmission error isTable I shows the experimental specifications. A 1.9-kW
prototype of the DAB converter was tested in order to confirm
the validity of the proposed method. In this experiment, theoutput voltage is regarded as the high voltage DC-bus.
Therefore, the proposed transmission power compensation
method for the voltage fluctuation was confirmed by varying
the output voltage.

Start
input parameters
P*, Vin, Vout, , fsw, L, dt
Cal. of  : Eq.(16)(p-2dt)/p≤ 

Dead-time effect: linear error

No

Yes Dead-time effect: non-linear errorNo(p-dt)+(2dt+p)/2≤
Three-levelYes
mode(1-)(p-dt)/2≥ Mode I

Yes

Cal. of : Eq.(10-11)

Two-level mode

(Vin-Vout)p/2Vin≥ YesNo(1-)(p-dt)/2≥ Mode II
Cal. of : Eq.(10), (13)
Yes

* =

Yes
Mode I
Cal. of : Eq.(10-11)

No
Mode IIICal. of : Eq.(10), (15)(3-)dt/()+p≥Cal. of *, *, *
Dead-time comp: Eq.(9)Cal. of *, *, *
Dead-time comp: Eq.(9)FinishFig. 10. Flowchart of determination of operation modes.

Two-level mode

No

No
Mode II
Cal. of : Eq.(10), (13)

* = 

VI. CONCLUSION
This paper proposed the compensation method oftransferred power error due to the dead-time when the forvariable DC-bus voltage. The voltage polarity reversal
phenomenon was avoided by designing the zero current period
to be longer than the dead-time. In order to avoid the voltage
polarity reversal phenomenon under the voltage fluctuation,
three-types of three-level modes were proposed. From theexperimental results, the error of the transmission power was
reduced from 49% to 3.5% because the voltage-polarityreversal phenomenon was avoided.
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[3]

[4]

[5]

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0

Output voltage of secondary inverter 500V/div
0

Transformer current of primary inverter 20A/div
P* =0.72 kW
020ms/div

Fig. 11. Operation waveforms of three-level mode by applying conventional
method.
0.8
1p.u. = 1.9 kW
Transmission power P [p.u.]

Figure 12 shows the characteristics of the transmission
power regarding the transmission power command when the
output voltage is varied to -10% and -15%. According to Fig.
12 (a), by applying the proposed method, the transmissionpower error is reduced from 49% to 3.5% by avoiding thevoltage-polarity-reversal phenomenon. The transmission power
error of the proposed method at 0.2p.u. is caused by the error of
the zero-voltage phase due to a parasitic capacitor. In the
proposed method, switches S3 and S4 do not achieve zerovoltage switching (ZVS), whereas zero current switching(ZCS) is achieved at 0.2p.u. because a turn-on timing ofprimary and secondary inverter output voltages is same. Hence,
the rise time of the inverter output voltage is delay by the time
constant of the parasitic capacitor because the parasitic
capacitance is not discharged. Fig. 12 (b) shows thetransmission power characteristic when the output voltage isvaried to -15%. In the two-level mode, the dead-band occurs
due to the dead-time. In contrast, the dead-band is suppressedby proposed the transmission power compensation method.

Output voltage of primary inverter 500V/div

Transmission power P [p.u.]

Figure 11 shows the operation waveforms of the two-level
mode and three-level mode when the output voltage fluctuationis -10%. The voltage-polarity-reversal phenomenon occurs
when the conventional two-level mode is applied. In contrast,
by applying the proposed method, the voltage-polarity-reversal
phenomenon is avoided by controlling the zero voltage period
individually.

Proposed
three-level mode

0.6
0.4

Two level modewith dead-time error
Power error =3.5%
Power error =49%

0.2

P=P*
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Transmission power command P* [p.u.](a) Outout voltage condition is reduced by -10% from nominal value.
0.8 1p.u. = 1.9 kW
0

0

0.1

0.7

Two level modewith dead-time error

0.6
0.5
0.4

Proposed
three-level mode

0.3
0.2

P=P*

0.1
0

0

0.1

0.2
0.3
0.4
0.5
0.6
0.7
0.8
Transmission power command P* [p.u.](b) Outout voltage condition is reduced by -15% from nominal value.
Fig. 12. Characteristics of transmission power regarding transmission powercommand[6]

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Solid-State-Transformer", IEEJ Journal of Industry Applications, Vol. 4,
No. 4, pp.387-394, 2015.
[7] H. Higa and J. Itoh, "Extension of zero-voltage-switching range in dual
active bridge converter by switched auxiliary inductance," 2017 IEEE
Energy Conversion Congress and Exposition (ECCE), Cincinnati, OH,
2017, pp. 5324-5331.
[8] B. Zhao, Q. Song, W. Liu, Y. Sun: "Dead time Influence of the HighFrequency Isolated Bidirectional Full-Bridge DC-DC Converter:
Comprehensive Theoretical Analysis and Experimental Verification",
IEEE Trans. on Power Electronics, Vol. 29, No. 4, pp.1667-1680, 2014.
[9] J. Itoh, K. Kawauchi, H. Higa " Dead-time Compensation with DC
Offset Current Elimination Method using Three-level Operation for
Dual Active Bridge DC-DC Converter," 2018 IEEE Energy Conversion
Congress and Exposition (ECCE), Portland, OR, pp. 6299-6306, 2018.
[10] J. Itoh, K. Kawauchi, H. Watanabe, K. Kusaka " Reduction ofTransmission Power Error and Current for Dual Active Bridge DC-DC
Converter in Energy Storage Systems," 7th International Conference on
Renewable Energy Research and Applications (ICRERA 2018), 2018.