A Novel Control Method Focusing on Reactive
Power for A Dual Active Bridge Converter
Jun-ichi Itoh, Hayato Higa, Tsuyoshi Nagano
Department of Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp, hhiga@stn.nagaokaut.ac.jp, ngn244@stn.nagaokaut.ac.jp
Abstract— This paper proposes a reactive current control
method focusing on a copper loss reduction for a dual active
bridge DC-DC converter. The proposed method controls thereactive current using the fundamental wave model of the
primary and secondary voltages in the dual active bridge DC-DC
converter. However, the total power factor reduced by the
harmonic component of the output voltage of the each inverter inlight load region. In order to keep the high total power factor, thepulse frequency modulation (PFM) is introduced to the proposed
method. From the experimental results which the inductor
current, total power factor, and the efficiency with the PFM
compared without the PFM. The total power factor is over 0.88
from the 40% to the rated power with the PFM. In addition, thereactive power is controlled by adjusted switching frequency inorder to achieve the minimum loss of a DAB converter prototype.
As results, the efficiency of the prototype is improved 10% at 100
W. Therefore, it is confirmed that the proposed method achieves
the minimum current value for the output power. In addition, theswitching loss can be reduced by zero voltage switching with thereactive current control. Thus, the high efficiency can beachieved in wide load region.

switching device are increased because the ratio of the reactive
current is increased in light regions. Furthermore, the ZVS areaof the DAB converter is limited due to fluctuation in voltage
such as a battery. These general approaches construct theswitching pattern focusing on the achievement of ZVS in orderto reduce the switching loss [5-7]. On the other hand, there aredifferent approaches to decide pulse pattern in the DAB
converter, which is focusing on the current reduction [8-12].
Especially, the copper loss of the transformer and conduction
loss of semiconductors are higher than the switching loss
depending on high power applications. Similarly, there is theapproach that the switching frequency is increased withincrement of the transfer power in term of the current reduction
at rated power [7].This method has drawback that the reactive
current cannot be reduced at light road. In addition, theoperation area of the DAB converter is narrow because thetransfer power is determined by impedance of the leakage
inductance in the high frequency transformer. In the case which
the voltage has a fluctuation such as a battery, the minimum
loss of the DAB converter cannot be achieved in all load region.

Keywords— Bi-directional isolated DC-DC converter; Reactive
current control; Dual active bridge DC-DC converter

This paper proposes a reactive current control method for a
DAB converter in order to reduce the copper and the
conduction loss. The proposed method controls active current
and reactive current based on the secondary side voltage. The
current is controlled to unity power factor against thesecondary side voltage keeping ZVS conditions. In order toachieve the high total power factor, the pulse frequency
modulation (PFM) is applied to the proposed method. In the
proposed method, the ratio of the reactive current in all load
region can be kept by increasing the switching frequency withdecrease of the transfer power. As a result, the transformer
current can be minimized by the proposed control. In addition,
the high efficiency is achieved in wide load range bycontrolling the switching frequency according to the active
current. This paper is organized as follows; at first, theproposed method which controls active current and reactive
current based on the secondary side voltage is introduced.
Secondary, the experimental waveforms when the proposed
method with or without PFM are applied to the DAB converter
are demonstrated. Next, the total power factors and the inductor
currents when the proposed method with or without PFM are
applied to the DAB converter are evaluated from theexperimental results. In addition, it is confirmed that the ZVS
is achieved and the ZVS area is extended by the reactive

I. INTRODUCTION
Recently, energy storage systems such as a battery haveattracted for electric vehicles and power grid systems.
Requirements of an energy storage system are a charge anddischarge of a battery and safety in the emergency. Therefore,
the battery conversion system has to need the isolation and bidirectional operation. In order to achieve the bi-directional
power transmission and isolation, a bi-directional isolated DCDC converter is used as energy storage systems [1-4]. There isa dual active bridge (DAB) converter such as a bi-directional
isolated DC-DC converter [5-10]. A DAB converter obtains
high efficiency and power density because zero voltage
switching (ZVS) is achieved by a resonance between a leakage
inductance in the high frequency transformer and a parasitic
capacitance of switching devices during dead-time period [4].
In addition, transfer power of the DAB converter is determinedby impedance of a leakage inductance in the high frequency
transformer and a phase difference between output voltages ofeach inverter. Thus, the higher power capability cannot be
achieved by higher frequency but also transformer of reduced
size. However, the copper loss and the conduction loss of the

978-1-4799-6768-1/14/$31.00 ©2014 IEEE

current control with PFM. As a result, the efficiency isimproved by the proposed method with the PFM. It is clarified
that the high total power factor is achieved in wide load region
by the proposed method.

Vin

iL
S2

Fig. 2 shows a pulse pattern of the DAB converter in Fig. 1.
In the DAB converter, output voltage waveforms of the each
inverter are three-level voltage including the zero voltage
periods or square waveform. The transfer power is determinedby a phase difference  between the primary output voltage v1
and the secondary output voltage v2, an impedance of theleakage inductance of the transformer [7]. In the dead-time
period of each inverter, the ZVS operation is achieved by aresonance between a parasitic capacitance in the switching
devices and the leakage inductance in the high frequency
transformer.
Fig. 3 shows the ideal equivalent circuit of the DAB
converter. In Fig. 3, this model consists of the square
waveform or three-level waveform voltage sources and theleakage inductance of the high frequency transformer. In thissection, the excitation inductance of the transformer isneglected because the exciting current is much smaller than theload current.

V1  V1  jV1  





V2  V2 



L

v1

Vout

v2
S6

S4

S8

Fig. 1. A configuration of A DAB converter.

g

δ

Vin
v1 0
-Vin
Vout
v2 0

t

t

-Vout
iLmax
iL 0

t

iLmin
Fig. 2. Switching pattern of the DAB converter.

L

V1

Fig. 4 shows an equivalent circuit model which isrepresented by the fundamental components of the primary sideand the secondary side voltage of the DAB converter [11]. Thismodel consists of the leakage inductance L and two sinusoidal
voltage sources which have the fundamental component of thesquare waveform or the three-level waveform including thezero voltage periods. The proposed method considers thefundamental component
Fig. 5 shows the phaser diagram of the proposed control
method which mentions relationship among the each voltages
and the current of the high frequency transformer on thecomplex plane when the primary voltage is divided into thereal part and the imaginary part based on the secondary voltage
V2. That is, the active current and the reactive current are
defined by not the primary voltage but the secondary voltage.
In Fig. 4, V1 is the real part of the primary voltage, V1 is theimaginary part of the primary voltage, V2 is the real part of thesecondary voltage, VL, IL are the inductor voltage and theinductor current,  is the phase difference between the primaryvoltage and the secondary voltage, S is an apparent power
which is considered by the fundamental component voltage andcurrent. The primary voltage V1 and the secondary voltage V2
are expressed by (1) and (2).

S7

N:1

II. CONTROL STRATEGY
Fig. 1 shows a configuration of a bi-directional isolated
DC-DC converter using DAB converter. This converter
consists of a high frequency transformer and two voltage
source inverters with H-bridge topology.

S5

S3

S1

VL
IL

fsw

V2
fsw

Fig. 3. Ideal equivalent circuit of DAB converter.

L
V1
fsw

VL

IL

V2
fsw

Fig. 4. Fundamental wave model of DAB converter.

The inductor current IL is determined by the primary voltage,
the secondary voltage, the switching frequency and the leakage
inductance in the high frequency transformer.

ΙL 

V1
(V  V1 )V1  V 2
 I L  jI L 
 j 2
(3)
j 2f sw L
2f sw L2f sw L

where, IL is the active current, IL is the reactive current basedon the secondary voltage, 2fswL is the impedance of thetransformer leakage inductance. From (2) and (3), the apparent
power is given by (4).

S  V2 I L  PDC  jQ 

V1 V2
2f sw L

jV2 (V1  V2 )2f sw L

where, the first term of (4) is the active power PDC, that is thetransmission power and the secondary term is the reactive
power Q. In order to eliminate the reactive power, it isnecessary that the real part of the primary side agrees with thatof the secondary voltage. From (4), real part of the primaryvoltage is expressed by (5).
V1  I L 2f sw L  V2
*

V1
VL

V2
IL*

 calc. 
Eq. (7)

Phase
delay

g calc.

Phase
delay

S1

PDC

*

V1 calc. V1
Eq.(4)

Eq. (8)S3S4Carrier
Command

S5 S6
S7 S8

Fig. 6. Control diagrams for the proposed method.
TABLE I EXPERIMENTAL CONDITIONS(7)

Input voltage

200V

Transformer turn ratio

1

Output voltage

100V

Leakage indactance

83µH

Rated power

700W

Dead-time

500ns

Carrier frequency
with thePFM
Carrier frequency
without the PFM

32kHz-80kHz

MOS-FET

STW75NF-30

32kHz

Output voltage of primary inverter v1[250 V/div]

1.04 rad0
Output voltage of secondary inverter v2[100 V/div]
0


2
2 
  2(V1  V1 ) cos1 


4Vin




2

V1

V1 calc.
Eq.(3)(6)

In the proposed method, a phase difference  is determined by
the real and imaginary part of the primary side voltage basedon secondary side voltage. From (5) to (7), a phase difference 
is determined by the transfer power command and reactive
current command. In order to control the reactive current of the
DAB converter by the proposed method, it is necessary that the
primary voltage is controlled in order to achieve the primaryvoltage command. The output voltage period g is given by (8)when the output voltage of the primary inverter is three-level
voltage including the zero voltage periods.
g  1

Re

0

V1

V2 s
V2
V1

S2

where,. PDC* is the active power command. From (5) and (6), in
order to control the reactive current, the primary voltage oftransformer must be higher than the secondary voltage oftransformer. Therefore, the primary voltage or the secondary
voltage should be controlled. A phase difference  between the
primary and the secondary voltage of transformer is given by
(7).

V

IL

Fig. 5. Phaser diagram with voltages and the current of transformer withcomplex notation based on fundamental wave model.

*  tan1 1

V1



(5)

where,. IL*is the reactive current command. When the reactive
current command is zero, the primary and the secondary
voltage become equal. From (4), the imaginary part of the
primary voltage is expressed by (6).
PV1  2f sw L DC
V2

Im

(4)

10 µs/div

Inductor current iL[10 A/div](8)

Fig. 7. Operation waveform at the rated power with proposed method
applying the PFM and not applying the PFM (the switching frequency is
32 kHz.) .

where, Vin is the input voltage. The amplitude of the primaryside voltage can be controlled by the output voltage period g.
Thus, the primary voltage controlled can be achieved when the
output voltage of the primary inverter is three-level operation.
In light load region, the reactive current control of thefundamental component is not effective because the total
power factor will be reduced by the harmonic component
because a narrow pulse width is used. On the other hand, from(4), when the switching frequency is increased, the impedanceof the leakage inductance in the high frequency transformer isincreased. Then, the output power can be decreased byincreasing the switching frequency while keeping on the valueof V1 and V1 because the impedance of the leakage
inductances increases. As a result, the high total power factor
operation is achieved in wide load region by controlling theswitching frequency according to the load.

Output voltage of primary inverter v1[250 V/div]

Output voltage of primary inverter v1[250 V/div]00
Output voltage of secondary inverter v2[100 V/div]

0.99 rad00
Output voltage of secondary inverter v2[100 V/div]00
10 µs/div

4 µs/div

Inductor current iL[5 A/div]

Inductor current iL[5 A/div](a) The 44% rated power without the PFM (switching frequency is 32 kHz) (c) The 44% rated power with the PFM (switching frequency is 64 kHz)
Output voltage of primary inverter v1[250 V/div]

Output voltage of primary inverter v1[250 V/div]

00.90 rad0
Output voltage of secondary inverter v2[100 V/div]00

Output voltage of secondary inverter v2[100 V/div]00
10 µs/div

Inductor current iL[5 A/div]

4 µs/div

Inductor current iL[5 A/div](b) The 26% rated power without the PFM (switching frequency is 32 kHz) (d) The 26% rated power with the PFM (switching frequency is 72 kHz)
Fig. 8 Operation wave forms with the PFM or without the PFM. The error between the phase difference of the primary side and the secondary voltage
at the 44% rated power and the 26% rated power.

Fig. 6 shows the control diagram of the proposed method.
In order to achieve the reactive current control using (5) to (8),carriers of the primary and the secondary inverter are phaseshifted. The phase shift amount of two carriers are determinedby the phase difference  and the output voltage periods g of
the three-level voltage including the zero voltage periods.
III. EXPERIMENTAL RESULTS
In this section, the experimental results are demonstrated inorder to evaluate the proposed method. In the experiment, thetotal power factor, the inductor current, the efficiency and the
ZVS area are confirmed by the proposed method applied to the
DAB converter prototype.
Table 1 shows the experimental conditions. In Table 1,
STW75NF-30 of the MOS-FETs is selected. The on resistanceof STW75NF-30 is 34 mΩ. The leakage inductance oftransformer is 83  However, the inductance is connected tothe primary side of the transformer in order to achieve theleakage inductance of the transformer in Table 1. The
switching frequency is 32 kHz with the PFM and without the
PFM at the rated power because the value of the rated power issame with the PFM and without the PFM. Note that total power
factor is determined by the inductor current and the secondaryside voltage.
Fig. 7 shows the output voltages of the primary and thesecondary inverter and the inductor current at the rated powerwith the PFM and without the PFM. In Fig. 7, the phasedifference at the rated power between the output voltage of the
primary and the secondary inverter is 1.04 rad. From inductor
current and the secondary voltage waveform, the high total
power factor is achieved because harmonic component of theinductor current is small.
Fig. 8(a) shows the operation waveform at the 44% rated
power without the PFM and Fig. 8(b) shows the operation
waveform at the 26% rated power without PFM. In Fig. 8(a),and Fig. 8(b), the transfer power can be changed by a phasedifference between the primary voltage and the secondary
voltage and the output voltage period as shown in (7). Fig. 8(c)shows the operation waveform at the 44% rated power with thePFM. The inductor current in Fig. 8(a) has more harmoniccomponent than Fig. 8(c) owing to the short output voltage
period g which the primary voltage of Fig. 8(a) has. In sameways, the inductor current in Fig. 8(b) has more harmoniccomponent than Fig. 8(d). Note that the output voltage period g
is adjusted in Fig. 8(d) because the maximum switchingfrequency is limited by the performance of the switching
device. In addition, in Fig. 8(a), the phase difference at the 44%
rated power with PFM is 0.99 rad. On the other hand, in Fig. 7,
the phase difference at the rated power with PFM is 1.04 rad.
The error between the phase difference at the rated power andthe 44% rated power with the PFM is 4.8 % (i.e. the phasedifferences at the rated power and the 44% rated power arealmost the same). Thus, the output power can be decreased
while keeping on the value of V1 and V1 by applying the PFM.

As a result, as mention below, the reactive current control canbe achieved.
Power factor [-]Without PFM

0.6
0.4
0.2

80kHz

200
400
600
800
Transfer power PDC [W]
Fig. 9. The characteristics of total power factor with the PFM
operation and without the PFM operation.

0Gate signal of S4[25 V/div]
Dead-time period of the S4
Drain to source voltage of S4[250 V/div]
Gate signal of S8[25 V/div]
Dead-time periodof the S80

Drain to source voltage of S8[100 V/div]

400ns/div(a) Rated power0

Gate signal of S4[25 V/div]
Dead-time period of the S4

0

Drain to source voltage of S4[250 V/div]
Gate signal of S8[25 V/div]0

Dead-time period of the S8

0Fig. 12 shows the efficiency of the DAB converter
prototype with the PFM, without the PFM and the adjusted
reactive current with the PFM. In the experimental results, thereactive current is eliminated by the proposed method. The

72kHz

0

Drain to source voltage of S8[100 V/div]

400ns/div(b) 30% rated power
Fig. 10. The gate signal and terminal voltage between drain andsource of the MOS-FET S4, S8 ZVS wave form at the 30% rated
power.
9
ZVS regions without PFM
7.5

Inductor current iL [A]

Fig.11 shows the inductor current and the ZVS area with
the PFM, without the PFM and adjusted reactive current with
PFM. In Fig. 11, the inductor current is reduced by 50% at 100
W because the total power factor in the light load regions is
improved by applying the PFM. In addition, the ZVS area with
the PFM is from the 40% rated power to the rated power.
However, the hard switching is achieved below the 40% rated
power. The ZVS in the light load region can be achieved by thereactive current control. On the other hand, the ZVS area
without the PFM is below the 20% rated power. This cause isthat inductor current when ZVS is not achieved is larger thanwhen the ZVS is achieved due to the low total power factor
below the 20% rated power. In order to achieve the ZVS inwide load region, the reactive current is controlled by adjusted
the switching frequency. As a result, the ZVS region isextended for 20% than the result with the PFM. However, theinductor current is increased because the reactive current isincreased in order to achieve the ZVS in wide load regions.
That is, the minimum loss of the converter loss can be achieved
when the reactive current is controlled by the ratio of theswitching loss and the copper and conduction loss.

0.8

0Fig. 10 shows the gate signal and the terminal voltage of S4and S8. Fig. 10(a) shows a result of the rated power and (b)shows a result of the 30 % rated power. In Fig. 10(a), the gate
signals turn on after the drain to source voltage is dropped by 0
V due to resonance the parasitic capacitance of the MOS-FET
and the leakage inductance of the transformer. Therefore, theZVS of the primary inverter and the secondary inverter isachieved. However, in Fig. 10(b), the ZVS of the primary
inverter and the secondary inverter is not achieved. This causethat the inductor current at the 30% rated power is smaller thanachieving the ZVS. In order to achieve the ZVS in light load
region, it is necessary to increase the reactive current using the
proposed method with the PFM.

With PFM 64kHz 56kHz 48kHz 40kHz 32kHz

0

Fig. 9 shows the total power factor with the PFM andwithout the PFM. In the result without the PFM, the total
power factor is 0.9 at rated power. However, the total power
factor at light load is decreased. This is the reason that there aremany harmonic components in inductor current owing to short
output voltage period g which the primary voltage has asshown in Fig. 8(a). On the other hand, the total power factor isover 0.88 from the 40% rated power to the rated power when
the PFM is applied to the proposed method. This is because thereactive current control can be achieved in wide load region bykeeping on the value of V1 and V1by applying the PFM.
Thus, the reactive current is reduced in wide load region by theapplying the PFM. However, the total power factor isdecreased in the light load region. Because the maximum
switching frequency is limited by the switching devices, theharmonic component of the primary voltage is increased by theoutput voltage period which is narrow width in the light load
region.

1

Adjusted reactive current with PFM

6Without PFM

4.5
With PFM

3

ZVS regions with PFM

1.5

ZVS regions adjusted reactive current with PFM

0
0

200
400
600
800
Transfer power PDC [W]
Fig. 11. The characteristics of inductor current and ZVS area with
the PFM operation and without the PFM operation.

IV. CONCLUSION
This paper proposed the reactive current control method forthe DAB converter in order to reduce the copper loss. The
voltage and the current of the transformer are discussed oncomplex plane using fundamental components. The
experimental results are demonstrated in order to confirm thevalidity of the proposed control method. From experimental
results, the total power factor with the PFM is over 0.88 from
40% to rated power. The inductor current is reduced by the
50% at 100 W with the PFM. In addition, the efficiency of
converter at 100 W is improved from 80.9% to 90.1% by the
adjusted reactive current. The ZVS area extended for 50% by
adjusted the reactive current applied to the PFM. In the future
work, relationship between the ZVS conditions and thecomponent of the each voltage on the complex notation will beclarified. The theoretical formula is derived in order to achieve
the minimum loss in all load region.
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56kHz 48kHz

40kHz 32kHz

Without PFM
72kHz
With PFM

85
80kHz

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200
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600
800
Transferred power PDC [W]
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