Closed-Loop Black Start-Up of Dual-Active-Bridge Converter With Boosted Dynamics and Soft-Switching Operation

Abstract

This article proposes a closed-loop black start-up control for the dual-active bridge (DAB) converter. With a simple combination of the extended phase-shift and triple phase-shift modulation schemes, the DAB converter can start up with the maximum allowable pre-charge current while realizing soft-switching operation in the trapezoidal current mode simultaneously. Compared to the conventional start-up procedure that usually requires multiple steps of operation and parameter fine-tuning, the proposed start-up method can be implemented simply into the existing closed-loop controller and can shorten the start-up transients of the DAB converter significantly. The presented methods are validated experimentally on a downscaled DAB converter prototype.

Full text

IEEE TRANSACTIONS ON POWER ELECTRONICS
Closed-Loop Black Start-up of Dual-Active Bridge Converter
with Boosted Dynamics and Soft-Switching Operation
Jingxin Hu, Member, IEEE, Shenghui Cui, Member, IEEE, Rik W. De Doncker, Fellow, IEEE
Abstract—This article proposes a closed-loop black start-up
control for the dual-active bridge (DAB) converter. With a simple
combination of the extended phase-shift and triple phase-shift
modulation schemes, the DAB converter can start up with the
maximum allowable pre-charge current while realizing soft-
switching operation in the trapezoidal current mode simulta-
neously. Compared to the conventional start-up procedure that
usually requires multiple steps of operation and parameter fine-
tuning, the proposed start-up method can be implemented simply
into the existing closed-loop controller and can shorten the start-
up transients of the DAB converter significantly. The presented
methods are validated experimentally on a downscaled DAB
converter prototype.
Keywords—Dual-active bridge, black start-up, closed-loop con-
trol, soft switching, inrush current.
I. INTRODUCTION
The dual-active bridge (DAB) is a popular dc-dc converter
topology to transfer a bidirectional power flow over a wide
voltage range with galvanic isolation and soft-switching op-
eration [1]. Since the DAB converter is widely used as a dc
transformer in grid and industrial applications, the black start-
up is a crucial function to restore the system after faults or
maintenance and enhance the system stability and availability
[2].
In the black start-up procedure, the fully discharged output
dc capacitor of the DAB converter needs to be pre-charged
from the input side. However, when directly applying the
steady-state switching pattern, e.g. the single phase-shift (SPS)
modulation [1], a high inrush current occurs in the ac link
which results in excessive thermal stress and potential failures
in the power semiconductor devices [3]. To address this
issue, soft start-up procedures are proposed in [4]–[6] which
first operate the output bridge only as a diode rectifier and
increase the inner phase-shift of the input bridge gradually
in an open-loop manner. When the output dc capacitor is
naturally charged to the maximum rectification voltage, the
output bridge starts switching, and the closed-loop control is
enabled to regulate the output voltage to the final reference
value gradually. To ensure a suppressed inrush current in the
whole start-up procedure, the aforementioned method requires
a careful manual fine-tuning of the parameters under different
load conditions [5], [6], i.e. the ramp slope-rate of both the
inner phase-shift and the reference voltage. This makes such
methods less generic and difficult to optimize. Moreover, as
This work is supported by European Union’s Horizon 2020 research
and innovation programme under grant agreement No. 957788, project HY-
PERRIDE, and the Federal Ministry of Education and Research (BMBF,
FKZ03SF0490), Flexible Electrical Networks (FEN) Research Campus. (Cor-
responding author: Shenghui Cui.)
J. Hu, S. Cui and R. W. De Doncker are with the Institute for Power
Generation and Storage Systems at E.ON ERC and the FEN Research Cam-
pus, RWTH Aachen University, Aachen, Germany. (e-mail: jhu@eonerc.rwth-
aachen.de; scui@eonerc.rwth-aachen.de; post pgs@eonerc.rwth-aachen.de).
ip
S1
ABCD
Lσ
S2
S3
S4
Q1
Q2
Q3
Q4
is,dc
isC
iload
Fig. 1: Circuit diagram of single-phase DAB converter.
Vs - case 1 Vs - case 2
ip - case 1
ip - case 2
12
open-loop ramp closed-loop ramp
vAB
vCD
ip
Fig. 2: Key waveforms of the state-of-the-art soft start-up procedure (case 1:
high slope ramp-rate; case 2: low slope ramp-rate).
the maximum peak value of the inrush current is only limited
but not fully utilized in the whole procedure, those multi-step
approaches have an inherent limitation in the start-up speed.
In [3], the dual phase-shift (DPS) modulation is proposed to
reduce the inrush current during start-up, but further analysis
and evaluation are still needed. In [7], the extended phase-
shift (EPS) modulation is also considered to increase the pre-
charge current at the start-up in an open-loop manner, but the
mode selection and parameter calculation are rather complex.
Besides, multiple steps of operation are also required in the
start-up procedure.
In this article, a dedicated EPS mode is proposed which is
particularly suitable for a low output voltage operation with
a high output current. Combined with the triple phase-shift
(TPS) modulation [8], the DAB converter can realize a closed-
loop start-up control with a fully regulated inrush current, a
boosted start-up speed and soft-switching operation.
II. STATE-OF-THE-ART SOFT START-UP PROCEDURE
The single-phase DAB consists of two H-bridges with ac
voltages denoted by vAB,vCD and a high-frequency trans-
former with a leakage inductance Lσand a turns ratio Ntr as
depicted in Fig. 1. As illustrated in Fig. 2, the state-of-the-art
soft start-up procedure is generally divided into two steps.
The first step is known as the open-loop ramp phase, where
only the gate signals of S1−S4in the input bridge are
activated. The inner phase-shift ratio of the input H-bridge
Dpincreases from 0 to 0.5 linearly with a slope ramp-rate

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0Ts/2 Ts
0
0
0Ts/2 Ts
ip
DpTs
DsTs
DφTs
(a) (b)
0
is,dc
is,dc
0Ts/2 Ts
(c)
0
DpTs
t1t2
ip
is,dc
is,dc
0
ip
DpTs
DsTs
DφTs
is,dc
is,dc
DsTs
S1S2
S3S4
S4
Q1, Q4Q2, Q3
DφTs
Fig. 3: Switching patterns and waveforms of the selected modulation modes.
(a) TPS-TCM (d<1). (b) TPS-TZM. (c) Dedicated EPS-TZM.
dDp
dt. The typical ac voltages and current waveforms are also
shown in Fig. 2. The inner phase-shift determines the duty
ratio of vAB, which limits the peak value of the transformer
current when the output voltage is still low. Meanwhile, the
resulting triangular transformer current flows into the output
diode rectifier and charges the output capacitor until the output
voltage Vsreaches the input one Vp(a turns ratio Ntr =1is
assumed hereinafter without loss of generality). The dDp
dtis the
key design parameter in this stage. As shown in Fig. 2, a lower
dDp
dtin case 2 results in a lower peak inrush current but a longer
ramp time of the output dc voltage. However, considering the
non-linear slope of Vsespecially when a load is connected, a
generic analytical design of dDp
dtfor different load conditions
is challenging. This usually leads to a conservative choice of
dDp
dtand a long start-up duration.
The second step, known as the closed-loop ramp phase,
starts when Vsis equal or sufficiently close to Vp. The gate
signals of Q1−Q4in the output bridge are also activated, and
the closed-loop voltage control is enabled to regulate Vs. If the
final reference value V∗
sis different from Vp, a ramp slope-rate
dV∗
s
dtis also required to limit the peak current as depicted in
Fig. 2, which is also difficult to calculate analytically.
Therefore, the state-of-the-art soft start-up method requires
a careful fine-tuning of both dDp
dtand dV∗
s
dtin simulations or
even experiments to precisely limit the inrush current. It lacks
generality for different load conditions and additional degree
of freedom to optimize the start-up time.
III. PROP OS ED CL OS ED -LO OP BL ACK STA RT-UP CON TROL
The DAB converter has normally three control variables,
which are the inner phase-shift ratios Dp,Dsfor the input
bridge and the output bridge respectively and the outer phase-
shift ratio Dϕbetween two bridges as depicted in Fig. 3. To
minimize the start-up time, a operation mode is desired to
deliver the maximum output current with a limited transformer
peak current under the low-output-voltage condition.
SPS
EPS-TZM
EPS-TZM*
(Ip,lim = 1.3 pu)
TPS-TZM
TPS-TZM*
(Ip,lim = 1.3 pu)
TPS-TCM
(d < 1)
TPS-TCM
(d > 1)
Start-up trajectory
with Ip,lim = 1.3 pu
˰
˰
˰
Fig. 4: Output current capability of different modulation schemes.
As already mentioned, the SPS modulation is not suitable
for the soft start-up operation due to the large inrush current,
although it can deliver the highest possible output current,
i.e. Vp
8f Lσ
=1 p.u.[1], as depicted in Fig. 4. On the
other hand, the triple phase-shift with the triangular-current
modulation (TPS-TCM) as depicted in Fig. 3(a) can limit the
inrush current, which is similar to the open-loop ramp phase
in the conventional soft start-up method. But the maximum
output current of the TPS-TCM mode is limited when the
voltage ratio d=NtrVs
Vpis very low as shown in Fig. 4. As
an extension of the TPS-TCM mode [8], the triple phase-
shift with the trapezoidal-current modulation (TPS-TZM) as
depicted in Fig. 3(b) can further increase the maximum output
current, but the difference is only remarkable when dis above
0.4 as depicted in Fig. 4. The analytical expression of the
output current for the aforementioned modulation modes can
be found in Table I [8].
To fill in the gap in the range of a very low d, the extended
phase-shift with the trapezoidal current modulation (EPS-
TZM) is proposed for d<1as shown in Fig. 3(c). As another
form of extension from the TPS-TCM mode, the EPS-TZM
fixes Ds=0.5to maximize the output current, and adjusts Dϕ
and Dpto limit the peak current while realizing zero-current
switching (ZCS) for the output bridge. The switches in the
input bridge can realize zero-voltage switching (ZVS). The
transformer current is calculated as
ip(t)=


















ip(0)+
(1−d)Vpt
Lσ
for 0 ≤t≤t1,
ip(t1) − dVp(t−t1)
Lσ
for t1≤t≤t2,
ip(t2) − (1+d)Vp(t−t2)
Lσ
for t2≤t≤Ts
2.
(1)
where t1=DpTs−DϕTsand t2=0.5Ts−DϕTs.Ts=1
fdenotes
the switching period, where fis the switching frequency.
Assigning ip(0)=−ip(T s
2)=0yields
Dp=2Dϕ+0.5d.(2)
The transformer peak current is expressed as
ip−pk =ip(t1)=
(1−d)(2Dϕ+d)Vp
2f Lσ
.(3)

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TABLE I: Expressions of the output current for related modulation modes.
Mode DpDsIs,out Is,out,max Is,out,min
TPS-TCM (d<1)2d Dϕ
1−d
2Dϕ
1−d
4dVpD2
ϕ
f Lσ(1−d)
d(1−d)Vp
4f Lσ0
TPS-TCM (d>1)2d Dϕ
(d−1)
2Dϕ
(d−1)
4VpD2
ϕ
f Lσ(d−1)
(d−1)Vp
4f Lσd20
TPS-TZM d(1−2Dϕ)
1+d
(1−2Dϕ)
1+d
Vp[2d(1−8D2
ϕ)−(1+d2)(1−4Dϕ)2]
4f Lσd(1+d)2
dVp
4f Lσ(1+d+d2)
d(1−d)Vp
4f Lσfor d<1or (d−1)Vp
4f Lσd2for d>1
SPS 0.5 0.5 VpDϕ(1−2Dϕ)
f Lσ
Vp
8f Lσ0
EPS-TZM 2Dϕ+0.5d0.5 Vp[−8D2
ϕ+4(1−d)Dϕ−d2+d]
4f Lσ
(1−d2)Vp
8f Lσ
d(1−d)Vp
4f Lσ
DAB
Vs
Vs
*
PI
Vs
Vp
Mode selection &
Calculate control
parameters
Pulse
generator
Dφ
Dp
Ds
Iload
Iout
Fig. 5: Generic closed-loop control block diagram of the DAB converter.
The output current of the EPS-TZM mode is expressed as
is,out =
Vp[−8D2
ϕ+4(1−d)Dϕ−d2+d]
4f Lσ
.(4)
From (4), the maximum and minimum values of the output
current are derived










is,out,max =
(1−d2)Vp
8f Lσ
at Dϕ=1−d
4,
is,out,min =
d(1−d)Vp
4f Lσ
at Dϕ=0.
(5)
According to (5), is,out,max of the EPS-TZM mode decreases
quadratically with an increasing d. As depicted in Fig.4,
the EPS-TZM mode can deliver a significantly higher output
current than the TPS-TZM mode when d<0.6, which fills in
the gap under the condition of a very low output-voltage.
Thereafter, the maximum allowable pre-charge current with
a limited current stress can be conveniently determined in the
following steps. 1) Identify the nominal current stress ˆ
Ip,nom
at the nominal voltage and power rating. 2) Pre-define the
maximum allowable current stress ˆ
Ip,lim ≥ˆ
Ip,nom for the start-
up procedure depending on the current rating, safe operating
area (SOA) and the cooling capacity of the devices. The
potential maximum transformer peak current of the EPS-TZM
mode can be calculated by (3) with Dϕ=1−d
4. When ip−pk
needs to be limited to a lower value ˆ
Ip,lim, steps 3) and 4) are
conducted. 3) Substitute ˆ
Ip,lim into (3) to obtain the maximum
allowable Dϕ,max of the EPS-TZM mode. 4) Substitute Dϕ,max
into (4) to obtain the maximum allowable pre-charge current
of the EPS-TZM mode. Similar procedure can be applied to
determine the maximum allowable pre-charge/output current
of the TPS-TZM mode.
As an example, the maximum allowable is,out of the EPS-
TZM and TPS-TZM modes for ˆ
Ip,lim =1.3 p.u.are depicted in
Fig. 4 (marked with *). Following the upper boundary of these
two modes constrained by Ip,lim, the DAB converter can start
up from zero to the nominal output voltage with the maximum
allowable output current. This can not only limit the inrush
current but also minimize the start-up time. Moreover, due to
the ZCS nature of the trapezoidal current, a smooth transition
of the transformer current is realized from the EPS-TZM to
the TPS-TZM mode with soft-switching operation in the whole
start-up procedure.
More importantly, the proposed EPS-TZM mode can be
generically implemented in the closed-loop controller together
with other modulation modes such as TPS-TZM and TPS-
TCM as depicted in Fig. 5. A standard voltage PI regulator
is adopted to produce the reference output current. With
the measured voltage ratio, the maximum allowable output
currents of the EPS-TZM, TPS-TCM and TPS-TZM modes
with a limited peak current ˆ
Ip,lim are then calculated and
compared with the reference output current to select the proper
mode as referred to Fig. 4. An anti-windup is required to
limit the output reference current and avoid a saturation of
the integrator. Due to a large voltage error in the beginning of
the black start-up, the reference output current will be instan-
taneously set to the maximum allowable output current of the
EPS-TZM mode. With an increasing d, the modulation mode
is automatically transited to TPS-TZM or TPS-TCM until
the reference output voltage is reached. Benefited from the
closed-loop control implementation, the proposed black start-
up method is inherently adaptive to different load conditions
which avoids complex process of parameter tuning as in the
conventional method.
IV. EXP ER IM EN TAL VALIDATION
Experiments are preformed on a down-scaled DAB con-
verter prototype (as shown in Fig. 6) to compare the black
start-up performance of the conventional and the proposed
methods under different load conditions. Detailed parameters
of the DAB converter are given in Table II. It is worth
mentioning that the potential maximum transformer peak
current during the black start-up procedure is Vp
4f Lσ
=34.5 A
at Vs=0 V with Dp=Ds=0and Dϕ=0.25, which is too
large for the designed prototype. Notice that the peak current
under the nominal voltage and power condition is only about
12 A. Therefore, in the experiments, the maximum transformer
peak current is always limited to 15 A, which is approximately
Fig. 6: DAB converter prototype.
Input dc voltage 80 V
Output dc voltage reference 90 V
Total leakage inductance 29 µH
Transformer turns ratio 1:1
Switching frequency 20 kHz
Output capacitance 2 mF
Proportional gain 1.244
Integral gain 39.081
TABLE II: Experimental parameters.

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10ms/div
tstart = 37.6ms
ip-pk = 15.3A
vAB 60V/div
vCD 60V/div
ip 10A/div
Vs 20V/div
Open-loop ramp Closed-loop ramp
(a)
(b)
10ms/div
tstart = 21.2ms
ip-pk = 15.0A
vAB 60V/div
vCD 60V/div
ip 10A/div
Vs 20V/div
EPS-TZM TPS-TZM
Fig. 7: Measured black start-up waveforms under the no-load condition with
a maximum transformer peak current of 15 A. (a) Conventional method. (b)
Proposed method.
10ms/div
tstart = 41.5ms
ip-pk = 15.0A
vAB 60V/div
vCD 60V/div
ip 10A/div
Vs 20V/div
EPS-TZM TPS-TZM
(a)
(b)
20ms/div
tstart = 93.4ms
ip-pk = 15.2A
vAB 60V/div
vCD 60V/div
ip 10A/div
Vs 20V/div
Open-loop ramp Closed-loop ramp
Fig. 8: Measured black start-up waveforms with a load resistor Rload =13.5Ω
(600 W at Vs=90 V) and a maximum transformer peak current of 15 A. (a)
Conventional method. (b) Proposed method.
25 % higher than the steady-state peak current for a nominal
power of 600 W at Vs=90 V.
Fig. 7 depicts the measured black start-up waveforms un-
der the no-load condition. For the conventional soft start-up
method, the slope ramp-rates of Dpand V∗
sare carefully tuned
to dDp
dt=0.022/ms and dV∗
s
dt=5 V/ms respectively to limit
the maximum peak current to 15 A. This results in a start-
up period of tstart =37.6 ms and a maximum peak current of
15.3 A as shown in Fig. 7(a). When the proposed method is
applied, Vsramps to the nominal voltage of 90 V within only
21.2 ms as shown in Fig. 7(b), which is significantly reduced
by 43.6 % compared to the conventional method. Moreover,
the transformer peak current in the proposed method is not
only limited to 15 A but also maintained close to the maximum
allowable peak current during the whole start-up procedure,
20μs/div
vAB 60V/div
vCD 60V/div
ip 10A/div
Vs 20V/div
ip-pk = 14.9A EPS-TZM
EPS-TZM
ip-pk = 15.0A
20μs/div
S3 ZVS-on
S1 ZVS-on
Q2,Q3 ZCS-off
Q1,Q4 ZCS-off
(a) (b)
20μs/div
EPS-TZM TPS-TZM
ip-pk = 14.3A
(c) (d)
20μs/div
TPS-TZM
S3 ZVS-on
S1 ZVS-on
Q1 ZVS-on
Q4 ZCS-off
ip-pk = 12.1A
Fig. 9: Zoomed-in waveforms of the proposed black start-up control with
Rload =13.5Ωin Fig. 8(b). (a) Initial EPS-TZM waveforms at Vs=0 V.
(b) EPS-TZM mode at Vs=35 V. (c) Mode transition from EPS-TZM to
TPS-TZM at Vs=52 V. (d) TPS-TZM mode at Vs=90 V.
Fig. 10: Measured no-load start-up trajectories (is,out against Vs) of the DAB
converter with the conventional- and the proposed method.
which is distinguished from the conventional method.
Fig. 8 depicts the measured black start-up waveforms when
a load resistor Rload =13.5Ω(Pnom =600 W) is connected.
For the conventional method, the slope ramp-rates are re-tuned
to dDp
dt=0.0125/ms and dV∗
s
dt=0.8 V/ms for the same
maximum peak current, which result in a start-up period of
tstart =93.4 ms as shown in Fig. 8(a). It can be noticed that the
slope-rate of Vsbecomes very low in the end of the open-loop
ramp stage due to a relatively large load current. Therefore,
to minimize the start-up time, the closed-loop ramp stage has
already started when Vs≥64 V, i.e. 0.8Vp. On the other hand,
when the proposed method is applied, the start-up period is
41.5 ms with even a 55.6 % reduction as shown in Fig. 8(b).
Furthermore, Fig. 9 shows zoomed-in waveforms of the
proposed method with Rload =13.5Ω. In Fig. 9(a), the DAB
converter starts up in the EPS-TZM mode with ip−pk =14.9 A
at Vs=0 V. In Fig. 9(b), the DAB converter continues to
operate in the EPS-TZM mode with the maximum allowable
peak current. The ZVS and ZCS are realized for the input-
and output bridge, respectively. In Fig. 9(c), when Vsincreases
to 52 V, a mode transition occurs from the EPS-TZM to the
TPS-TZM mode with a smooth transformer current. The DAB
converter continues to operate in the TPS-TZM mode until
reaching the steady state at Vs=90 V as shown in Fig. 9(d).

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Enabled by the combination of the EPS-TZM and TPS-TZM
modes, the DAB converter realizes ZVS and ZCS operation
during the whole start-up procedure.
Fig. 10 shows a comparison of the measured start-up trajec-
tory, i.e. is,out against Vs, under the no-load condition between
the conventional and the proposed methods. It is validated that
a higher output current is delivered by the proposed method
at almost every value of the output dc voltage.
V. CONCLUSION
This article introduces a novel black start-up control of the
DAB converter, which can be generically implemented into
the closed-loop controller without complex tuning process.
The proposed control is enabled by the EPS-TZM mode
which is able to deliver a high output current with a limited
peak value at a very low voltage ratio. Combining the EPS-
TZM and TPS-TZM mode, the DAB converter can start up
with the maximum allowable output current while maintaining
soft-switching operation during the whole start-up procedure.
Experiments validate the effectiveness of the proposed method,
and demonstrate a significant reduction of the start-up time up
to 55.6 % compared to the state-of-the-art method.
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