Voltage Control Method in
Non-linear Dead-time Effect Region for
Dual Active Bridge DC-DC Converter
Jun-ichi Itoh1, Kengo Kawauchi1, Hayato Higa1, Hiroki Watanabe1 and Keisuke Kusaka1
1

Nagaoka University of Technology, Japan

Abstract-- This paper proposes a voltage control method
for a Dual Active Bridge (DAB) converter with three-level
operation in the dead-time effect region. The non-linear
transmission power error is reduced by controlling the zerocurrent phase to the dead-time or more because the nonlinear error of the transmission power occurs when the
inductor current reaches zero during the dead-time. In
addition, the voltage control is operated under the linear
region which is decided from the output current and the zerovoltage period. The validation of the proposed method is
confirmed by a 2.3-kW prototype. In the experiments, thenon-linear error in the transmission power is reduced by
76.3%. The linearity between a control variable and an
output current is confirmed. In addition, a load step between
two modes of three-level operation is achieved without the dc
offset in the inductor current. Moreover, the RMS value ofthe inductor current is reduced by 50.2% compared with theconventional triangular modulation.
Index Terms—Dual Active Bridge converter, Voltage
control, Non-linear, Dead-time

I. INTRODUCTION
Recently, DC micro-grid systems have been studied[1]-[5]. A power conversion efficiency is improved byapplying DC micro-grid systems because the number of
power conversion times is reduced. In order to compensate
power variation of the high voltage DC-bus, an energy
storage systems is applied [6]-[9]. The isolatedbidirectional DC-DC converter is used for the energy
storage systems to control power between battery and highvoltage DC-bus safely. A dual active bridge (DAB)
converter is applied to the energy storage systems because
the DAB converter obtains high efficiency [10]-[15].
Especially, the zero voltage switching (ZVS) is achievedat the turn on state of switching devices. However, theDAB converter has several drawbacks; one is the error of
the transmission power caused by the dead-time at medium
load to light load which prevents the DAB converter fromoperating over wide load range. Compensation methods
for the transmission power error have been proposed [16][17]. In [16]-[17], the error of the transmission power iscompensated by the feedforward control which subtracts
the dead-time from the command value of the phase-shift.
However, this compensation method does not compensate
an error of the transmission power due to voltage polarity
reverse phenomenon [18]. The compensation method forthe non-linear error of the transmission power has been
proposed to solve this problem [19]. The non-linear errorof the transmission power is suppressed by the zerocurrent period designed to dead-time or more in three-levelmode.
On the other hand, the relationship between the control
variable of the phase-shift and an output current is nonlinear in the voltage control. Therefore, the gain of the PI
controller is varied depending on the operation point. As
the result, the controller design is complicated because thenon-linear compensation in the voltage control is neededto achieve the desired response. In order to compensate
non-linear effect in the voltage control, compensation
methods have been proposed [17], [20]. In [17], the valueof proportional gain of the PI controller is calculated every
control cycle to vary the proportional gain dependently on
the operating point. In addition, the error compensation of
the transmission power owing to the dead-time isconducted by the feedforward control. Nevertheless, thismethod does not consider the non-linear dead-time effect.
Meanwhile, the linearization method in the voltage control
have been proposed for the DAB converter [20]. In [20],non-linear factor in the plant of the DAB converter iscompensated by applying the linearization control [21].
However, the RMS value of the inductor current isincreased because the inductor current is needed to becontrolled by the triangular modulation (TRM).
This paper proposes a voltage control method in the
non-linear dead-time effect region for the DAB converter.
The voltage control is operated by three-level mode, where
the relationship between the output current and control
variable is linear. In particular, the non-linear error of thetransmission power because of the dead-time iscompensated by the three-level operation. The originalityof this paper is to overcome two non-linear problem of the
DAB converter to achieve the desired response in thevoltage control.
This paper is organized as follows; the effect of thedead-time on the transmission power is explained in
section II. Next, the compensation method for the
nonlinearity in the transmission power is introduced in
section III. In section V, the voltage control method in theregion with non-linear dead-time effect is presented.
Finally, the effectiveness of the voltage control method inthe dead-time effected region is confirmed by theexperiments.
II. DEAD-TIME EFFECT ON TRANSMISSION POWER
Figure 1 shows the DAB converter configuration. The
DAB converter consists of an auxiliary inductor, a highfrequency transformer, and two H-bridge inverters. Two
H-bridge inverters generate a square wave voltage with aduty ratio of 50%. In the DAB converter, the phase-shift
between primary and secondary transformer voltage
controls the transmission power.
Figure 2 shows the typical operation waveforms
without and with the dead-time effect, and figure 3 shows
the state of the circuit in the voltage polarity reverse
phenomenon. Without the dead-time effect, the phase-shift
controls the transmission power introducing no error of thetransmission power. According to Fig. 2 (a), the inductor
current is introduced by (1) ignoring the magnetizing
current and the parasitic capacitance. Moreover, the turnratio of the high frequency transformer N is designed as
one for simplifying the consideration.

1
 Vin + Vout
{πVin + (2δ − π )Vout }
θ−

2ωL
ωL


for (0 ≤ θ ≤ δ )
iL (θ ) = (1),
Vin − Vout (θ − δ ) + 1 {(2δ − π )V + πV }
in
out
 ωL
2ωL


for (δ ≤ θ ≤ π )where δ and L are a phase-shift between the primarytransformer voltage vpr and the secondary transformer
voltage vse and an auxiliary inductor value, ω is a switchingangular frequency, Vout and Vin are output voltage and input
voltage. According to (1), the transmission power isintroduced by following;P=

Fig. 1. Dual active bridge converter.

Fig. 2. Traditional operation waveforms.


δ
V V
2 π
v pr (θ )iL (θ )dθ = in out δ 1 −  (2).
02πωL  π 

In contrast, the dead-time is necessary to avoid shortcircuit in the actual system. The non-linear error of thetransmission power is caused when the inductor current
reaches zero during the dead-time. Then, the inductor
current is clamped to zero because two H-bridge inverters
does not flow the current. In particular, all switching
devices in the primary H-bridge inverter are turned off due
to the dead-time. As the result, the secondary transformer
voltage occurs in the primary side of the transformer. Thisphenomenon is called voltage polarity reverse
phenomenon [18].
Figure 4 shows the boundary condition of the nonlinear transmission power error. The non-linear error of thetransmission power is caused by the voltage polarity
reverse phenomenon when the inductor current reaches
zero during the dead-time. Hence, the initial point of thevoltage polarity reverse phenomenon is when the end pointof the dead-time equals the zero cross timing of theFig. 3. Circuit in the voltage polarity reverse phenomeon.

Fig. 4. Boundary condition of non-linear transmission power error.

inductor current. This condition of the phase-shift is givenby (3) using (1) of 0 ≤ θ ≤ δ,

Vin + Vout1
{πVin + (2δ − π )Vout } ≥ 0
δdt −
ωL
2ωL
(3)
Vin
1
δ ≤ (2δdt − π )+ (2δdt + π )2Vout 2where δdt is the dead-time in the radian calculated as (4)using the dead-time Tdt and switching angular frequencyω,δdt = ωTdt

2Vin
 2δ 
2δdt 1 − dt 
ωL
π 


Without dead-time
2Vin  δdt 
δdt 1 − ωL π With dead-time(4).

Figure 5 shows the effect of the voltage polarity reverse
phenomenon on the transmission power when the input
voltage Vin is same as output voltage Vout. According to (3),the starting point of the voltage polarity reverse
phenomenon is δ = 2δdt. The error of the transmission
power is increased accordingly to the decrease of the phaseshift command because the width of the voltage polarity
reverse is varied corresponding to the zero cross timing of
the inductor current. The voltage polarity reverse
phenomenon is stopped when the phase-shift command δ *equals to the dead-time δdt. In this state, diodes does notconduct at the turn on timing of the IGBT, causing thedead-zone. The phase-shift command is canceled because
the phase-shift command is smaller than the dead-time δdt.

dt

Phase-shift

dt

Fig. 5. Effect of the voltage polarity reverse phenomenon fortransmission power.

III. NON-LINEAR ERROR COMPENSATION METHOD FOR
TRANSMISSION POWER
Figure 6 shows the proposed three-level operation. In
the three-level operation, the transmission power iscontrolled by the three-variables: the zero voltage periodof the primary side ε, the zero voltage period of thesecondary side γ and the phase-shift δ. According to Fig. 6(b), the zero voltage period is generated by circulating
current. The three-level mode is considered under thecondition of Vin = NVout. In addition, the zero voltage
period of each inverter are controlled as ε = γ to generate
the zero current phase φ. Note that the magnetizing current
and the parasitic capacitance are not considered. At thesteady state, the inductor current iL at the switching
moment is given by (5),(0 ≤ θ ≤ ε )
0

 Vin
(ε ≤ θ ≤ ε + δ ) ωL (θ − ε )ViL (θ ) =  in δ
(ε + δ ≤ θ ≤ π − ε )
(5).
 ωL
 Vin (π − ε + δ − θ ) (π − ε ≤ θ ≤ π − ε + δ ) ωL(0 ≤ θ ≤ ε )0According to (5), the transmission power is calculated
as follows;
2 πv pr (θ )iL (θ ) dθ
2π 0
V2= in δ (2π − 4 ε − δ )
2πω L

P=

(6).

(a) Operation waveforms.

(b) Current flow during zero voltage period.
Fig. 6. Proposed three-level operation.

In order to control the three-level operation, pulses ofeach transformer voltage are needed to be overlapped. The
condition of the three-level mode is expressed as follows;
2ε < π − δ(7).

In addition, the RMS value of the inductor current in
the three-level mode is given by (8), derived from (5),i L _ RMS =2 π
2i LI (θ ) dθ
2π 0

(8).
Vin
1
2
(2ε − π ) (3δ − π + 2 ε )=ωL 3π
The voltage polarity reverse phenomenon is eliminatedby controlling the zero current period φ to the dead-time
δdt or more using the three-level operation because thevoltage polarity reverse phenomenon is caused when the
inductor current becomes zero during the dead-time. The

condition to avoid the voltage polarity
phenomenon is given by (9) shown in Fig. 6,
φ = 2 ε − δ ≥ δdt

reverse(9)

Figure 7 shows the effect of the dead-time in the threelevel operation. The duty of the transformer voltage of the
primary side is decreased by the dead-time δdt because theinductor current does not flow the diode on the B-phaseleg during the dead-time thanks to the zero- current period
being longer than dead-time. Hence, duty compensation isnecessary for the primary transformer voltage.
Figure 8 shows the compensation method of thedecrease in the duty for the three-level operation. The
decrease in the duty affects not only the phase-shift but
also the zero voltage period of the primary side. Therefore,
the duty compensation is needed for both phase-shift andthe zero voltage period of the primary side. The duty
compensation is introduced as follows;δdt *δ = δ + 2δdt*ε = ε −2γ* = εFig. 7.Dead time effect for three-level operation.

(10)

where ε*, γ*, and δ* are the zero voltage period commandof the transformer voltage of the primary side, the zerovoltage period command of the transformer voltage of thesecondary side, and the phase-shift command.

Fig. 8. Duty compensation method for three-level operation.

δ 
V in 
δ 1−π ω L 

IV. VOLTAGE CONTROL METHOD IN NON-LINEAR DEADTIME EFFECT REGION
A. Conventional voltage control method
Figure 9 shows the conventional voltage control
principle. The phase-shift command δ * is generated by the
PI controller in the conventional method. However, theplant of the DAB converter GDAB has the non-linear factor.
The relationship between the phase-shift δ and DAB
output current iDAB is expressed as (11) from (2) and P =dI DAB: SmalldδdI DAB: LargedδVoutiDAB,iDAB =

δVin 
δ 1 − 
ωL 
π

(11)

According to (11), the relationship between the phaseshift δ and the DAB output current iDAB is non-linear.
Therefore, the control variable is not in proportion to the
output current in the PI controller. Especially, the designof the gain is complicated because the non-linear error of
the transmission power is caused at light load. Moreover,the DAB output current is varied by the voltage polarity
reverse phenomenon. As the result, two types of the nonlinearity occur at light load.
B. Conventional voltage control operation
Figure 10 shows the operation waveforms of the
trapezoidal modulation (TRM). In the condition of Vin =Vout, the phase-shift δ is same as each zero voltage period

Fig. 9. Conventional voltage control method.

ε and γ. At the steady state condition, the inductor current

iL at the switching moment as follows; Vin ωL (θ − π + 3ε )0
iL (θ ) =  Vin (θ − ε )
 ωL
 Vin
(2π − 3θ ) ωL

(0 ≤ θ ≤ π − 3ε )(π − 3ε ≤ θ ≤ ε )(ε ≤ θ ≤ π − ε )(π − ε ≤ θ ≤ π )(12).

According to (12), the transmission power in the TRM
is given by (13),2 πv pr (θ )i L (θ ) dθ
2π 0
(13).
Vin2
=
(π − 2ε )2πω LIn addition, the RMS value of the TRM is introduced asfollows;P=

i L _ RMS =2 π
2i LI (θ ) dθ

0
2π

V
= in
ωL

(

2 3
π − 6 επ 2 + 12 ε 2 π − 8ε 3
3π

)

(14).

C. Proposed voltage control method
Figure 11 shows the proposed voltage control method.
In order to eliminate the non-linear dead-time effect, thethree-level operation is used. In the three-level operation,
the relationship between control variables and the output
current iDAB is given by (15) from (6) and P = Vout iDAB,
i DAB =V in
δ (2π − 4 ε − δ )
2πω L

(15).

According to (15), the relationship between the zerovoltage period ε and the output current iDAB is linear
considering the phase-shift δ as constant value.
Next, the determination method of the phase-shift δ forthe three-level mode is explained. In order to transfer the
power with the non-linear error compensation method on
the transmission power, multiple values of phase-shift δ
are necessary to compensate entire region with the deadtime effect. In this paper, two phase-shifts are selected forachieving the maximum and minimum transmission power
to reduce the operation modes. The maximum power isachieved when the zero voltage period is the shortest: (9)is established. By substituting (9) into (6), the transmission
power is expressed by (16),

{

}

Vin
(16).
− δ 2 + (− δdt + 2π )δ
2πωLIn (7), the maximum power is obtained when the phaseshift δ becomes minimum. Therefore, the phase-shift forachieving the maximum power δ max is given by (17)derived from (16),
P=

{

}

Fig. 10. Operation waveform of trapezoidal modulation.

d− δ 2 + (− δdt + 2π )δ = 0
dδ
(17)
1
δmax = (π − δdt )3
In contrast, the minimum transmission power isobtained when δ = δdt + α, where α is a margin to preventthe voltage polarity reverse phenomenon because thisphenomenon occurs at δ = δdt. The margin α is needed to
be design as small as possible because the circulating
current increases as the margin α is larger. The margin α
is determined as one clock of an FPGA (fieldprogrammable gate array) when an FPGA is used for an
experiment. The phase-shift is controlled by the clock

Fig. 11. Proposed voltage control method.

period of FPGA. Therefore, the phase shift for achieving
the minimum transmission power δ min is given by (18),δmin = δdt + α(18).

In the proposed method, the three-level mode I isapplied with the phase-shift for achieving the maximum
transmission power δ max. On the other hand, the threelevel mode II is applied with the phase-shift for achieving
the minimum transmission power δ min. The changing
mode is conducted at the maximum transmission power inthe three-level mode I PI_max from mode I to mode II.
Meanwhile, the mode changing from mode II to mode I is
conducted at the minimum transmission power in thethree-level mode II PII_min. The maximum transmission
power in the three-level mode I PI_max is given by (19) from
(6), (7), and (18),Vin2(α + δdt )(2π − 5δdt − 3α ) (19).
2πω L
The minimum transmission power in the three-level
mode II PII_min is given by (20) from (6), (7), and (17),PI _ max =2

PII _ min =Vin(π − δdt )218πω L

Transformer voltage of primary side vpr 250V/div(20).

Figure 12 shows the control block diagram of the
proposed method. The operation mode is decided by thetransmission power calculated by the detected output
current and the detected output voltage. The duty
compensation is applied for the primary transformer
voltage vpr. Next, the phase-shift carriers of each leg is
generated using the zero voltage period of eachtransformer voltage ε, γ and the phase-shift to operate thethree-level operation.

0

Transformer voltage of secondary side vse 250V/div
0

Inductor current iL 20A/div0

P* = 1.50 kW, P =1.12 kW
Error = 21.5%

20 s/div(a) Two-level mode.

V. EXPERIMENTAL RESULTS
Table I shows parameters for the experiment. In order
to confirm the validity of the proposed method, a 2.3-kW
prototype of the DAB converter was tested.
Figure 13 shows the operation waveforms of theconventional two-level mode and the proposed three-level
mode. In the conventional two-level mode, the error of thetransmission power of 21.5% occurs owing to the voltage
polarity reverse phenomenon. In contrast, in Fig. 13 (b),the error of the transmission power is reduced by 20.8% byapplying the proposed method because the voltage polarity
reverse phenomenon is eliminated. Furthermore, thevoltage polarity reverse phenomenon is also avoided in thethree-level mode I. The error of the transmission power isreduced to 2.0% in the three-level mode I.
Figure 14 shows the transmission power characteristic.
The non-linear error of the transmission power occurs due(b) Three-level mode II.

Table I . Experimental parameters.

(c) Three-level mode I.
Fig. 13. Operation waveforms of two-level mode andproposed three-level mode.

Fig. 12. Control block diaglam of proposed method.

to the voltage polarity reverse phenomenon when the twolevel mode is used. On the other hand, the error of thetransmission power is reduced by up to 76.3% using the
proposed method.
Figure 15 shows the RMS value of the inductor current
in the TRM and the TZM when the transmission powercommand is 0.50 kW. In the TRM, the RMS value of theinductor current is 6.12 A. As the result, the efficiency of
the TRM is 85.3%. In contrast, using the TZM, the RMS
value of the inductor current is reduced to 3.05 A, resulting
the efficiency improvement to 93.8%. In the other words,
the efficiency is improved by 8.5% because the RMS valueof inductor current is reduced by 50.2%.
Figure 16 shows the characteristics between thetransmission power and the RMS value of the inductor
current in the TRM and the proposed TZM. By applying
the proposed method, the RMS value of the inductor
current is reduced by up to 54.0%. In the proposed threelevel operation, the peak value of the inductor current
depends on the phase-shift δ which is expressed by (5) of
the interval ε + δ ≤ θ ≤ π - ε. Therefore, the RMS value ofthe inductor current in the three-level mode II is larger than
the three-level mode I.
Figure 17 shows the characteristics between the zerovoltage period ε and the transmission power P. The
transmission power fits with 2.3% of maximum error bycontrolling the zero current period to the dead-time ormore. In addition, the DAB converter is controlled by thezero voltage period ε without the non-linear effect because
the relationship between the zero voltage period ε and theoutput current is linear.
Figure 18 shows the load step dynamic response of
proposed three-level operation with the voltage control
when the load is changed from 0.43p.u. to 0.22p.u. Thischanging mode is conducted between two modes. In Fig.
18, the changing mode is achieved without the dc offset in
the inductor current.
VI. CONCLUSION
This paper proposed the voltage control method for the
DAB converter in the dead-time effect region with thethree-level operation. This paper overcome two types of
the non-linear effect in the DAB converter. Firstly, thenon-linear error on the transmission power due to thevoltage polarity reverse phenomenon was reduced by thethree-level mode. The voltage polarity reverse
phenomenon was eliminated by controlling the zerocurrent period to the dead-time or more because thevoltage polarity reversed phenomenon occurred when the
inductor current reached zero during the dead-time.
Secondly, the non-linearity between the manipulated
variable and the DAB output current improved using thethree-level operation. The three-level operation was
operated by the zero voltage period with the constant valueof the phase-shift. From the experimental results, the nonlinear transmission power error was reduced by 76.3%
because the voltage polarity reverse phenomenon waseliminated. In addition, the RMS value of the inductor
current was reduced by 50.2% compared with theFig. 14. Transmission power characteristic.
Transformer voltage of primary side vpr 250V/div
0

Transformer voltage of secondary side vse 250V/div
0

Inductor current iL 20A/div0

iL_RMS = 6.12 A, Efficiency= 85.3%20 s/div(a) TRM.
Transformer voltage of primary side vpr 250V/div
0

Transformer voltage of secondary side vse 250V/div
0

Inductor current iL 20A/div0

iL_RMS = 3.05 A, Efficiency= 93.8%20 s/div(b) TZM.
Fig. 15. RMS value of inductor current in TRM and TZM.

Fig. 16. Characteristics between transmission power andRMS value of inductor current.

conventional TRM. As the results, the efficiency was
improved by 8.5% because the conduction loss was
reduced. Furthermore, the linearity between a control
variable and an output current was confirmed. The
transmission power fitted with the maximum error of
2.3%. Moreover, the load step between two three-level
operations was achieved without the dc offset in the
inductor current. In the future work, voltage control

method in the condition of Vin ≠ Vout will be considered.
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0.8

1p.u.=2.3kW( =45deg)

0.7

Mode II
max. error = 1.47%
Mode II=54.72deg

0.6
0.5
Experimental
value

0.4
0.3

Mode I
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0.1
0

Theoretical value

Mode I=16.1deg

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Zero-voltage phase command [deg]Fig. 17. Characteristics between zero-voltage period
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