DTU Modeling and Advanced Control of Dual Active Bridge DCDC Converters A Review
DTU Modeling and Advanced Control of Dual Active Bridge DCDC Converters A Review
DTU Modeling and Advanced Control of Dual Active Bridge DCDC Converters A Review
Shao, Shuai; Chen, Linglin; Shan, Zhenyu ; Gao, Fei; Chen, Hui; Sha, Deshang ; Dragicevic, Tomislav
Published in:
IEEE Transactions on Power Electronics
Publication date:
2021
Document Version
Peer reviewed version
Citation (APA):
Shao, S., Chen, L., Shan, Z., Gao, F., Chen, H., Sha, D., & Dragicevic, T. (2021). Modeling and Advanced
Control of Dual Active Bridge DC-DC Converters. IEEE Transactions on Power Electronics, 37(2), 1524 - 1547.
https://doi.org/10.1109/TPEL.2021.3108157
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DC Smart Grid
Abstract—The article classifies, describes and critically com-
pares different modeling techniques and control methods for SST
dual active bridge (DAB) dc-dc converters and provides explicit
guidance about DAB controller design to practicing engineers
and researchers. Firstly, available modeling methods for DAB
including reduced order model, generalized average model and
Home
discrete-time model are classified and quantitatively compared
Appliance
using simulation results. Based on this comparison, recommen- Home
dations for suitable DAB modeling method are given. Then Appliance
we comprehensively review the available control methods in-
cluding feedback-only control, linearization control, feedforward DC PicoGRID
plus feedback, disturbance-observer-based control, feedforward
current control, model predictive current control, sliding mode DC PicoGRID
control and moving discretized control set model predictive
control. Frequency responses of the closed-loop control-to-output DC NanoGRID
and output impedance are selected as the metrics of the ability in
voltage tracking and the load disturbance rejection performance.[1] Yunjie Gu, “Distributed Peer-to-Peer Control for Renewable Power Generation DC Microgrid”, Zhejiang University,
The frequency response plots of closed-loop control-to-output Fig.20151: Diagram of a hierarchical micro grid with SST as the
PhD thesis,
transfer function and output impedance of each control method [2] D. Boroyevich, I. Cvetković, D. Dong, R. Burgos, F. Wang and F. Lee, "Future electronic power distribution systems a
energy
2019/8/3
contemplative
router [2], [3]. 5
view," 2010 12th International Conference on Optimization of Electrical and Electronic Equipment, Basov,
are theoretically derived or swept using simulation software 2010, pp.
PLECS and MATLAB. Based on these plots, remarks on each
control method are drawn. Some practical control issues for DAB conventional AC systems [1]. They also provide more natural
including dead time effect, phase drift and dc magnetic flux
bias are also reviewed. This paper is accompanied by PLECS interface with many types of renewable energy systems (RESs)
simulation files of the reviewed control methods. and energy storage system (ESSs) and better compliance with
consumer electronics [1]. These facts lead to increased appli-
Index Terms—Dual active bridge (DAB), DC-DC, reduced
order model, generalized average model and discrete-time model, cations of DC microgrid-type power architectures in remote
feedback control, feedforward control, model predictive control. households, data/telecom centers, renewable energy systems,
electric vehicle charging stations, ships, aircrafts and others.
In DC microgrids, isolated bidirectional DC/DC (IBDC)
I. I NTRODUCTION power converters play an important role. IBDCs can serve as
the interface of ESSs such as batteries and super capacitors to
DC microgrids have higher efficiency, better current carry- allow energy exchange between ESSs and the DC microgrid.
ing capacity and faster dynamic response when compared to They can also be stacked together to operate in the so-called
solid-state transformer (SST) architecture, that can manage
This work was supported in part by the National Key Research and the power flow between DC microgrid and the upstream
Development Program of China under Grant 2018YFB0904100 and in part distribution network, as illustrated in Fig. 1.
by the National Natural Science Foundation of China under Grant 52007168.
(Corresponding author: Linglin Chen, Hui Chen)
Various IBDC topologies have been proposed, including
Shuai Shao is with the College of Electrical Engineering and the Hangzhou bidirectional resonant converters, dual flyback, dual-Cuk, dual-
Global Scientific and Technological Innovation Center, Zhejiang University, push-pull, and dual active bridge (DAB) [4]. For the ESSs and
Hangzhou 310027, China (e-mail:shaos@zju.edu.cn).
Linglin Chen and Fei Gao are with the Department of Electrical En-
micro-grids applications, the DAB (Fig. 2) originally proposed
gineering, Shanghai Jiao Tong University, Shanghai 200240, China (e- by de Doncker et al. [5] [6] is one of the most promising
mail:linglin.tim.chen@qq.com; fei.gao@sjtu.edu.cn). typologies for the following reasons [7]:
Zhenyu Shan is with the School of Automation Science and Electrical Engi-
neering, Beihang University, Beijing, China (e-mail: zhenyus@buaa.edu.cn). • Auto-adjust bidirectional power flow, ideal for SSTs and
Hui Chen is with the School of Information and Electrical Engineer- ESSs in micro-grids that often requires fast changes in
ing, Zhejiang University City College, Hangzhou 310015, China (e-mail: power flow direction.
chenh@zucc.edu.cn).
Deshang Sha is with the Advanced Power Conversion Center, School of • Wide voltage conversion gain range, which is essential
Automation, Beijing Institute of Technology, Beijing 100081, China (e-mail: to interface ESSs such as batteries or super-capacitors,
shadeshang@bit.edu.cn). whose voltage can vary significantly under different states
Tomislav Dragičević is with the Department of Electrical Engineering,
Technical University of Denmark (DTU), Kongens Lyngby 2800 Kgs, Den- of charge.
mark (e-mail: tomdr@elektro.dtu.dk). • Zero voltage switching (ZVS) capability, able to achieve
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Phase shift ϕ available control methods for DAB including feedback control,
ib1 Phase shift ϕ ib2 linearization control, feedforward plus feedback, disturbance-
g1 g2 g3 g4 iL + v vL - observer-based control, feedforward current control, model
iL + L -
g1
iL
g2 g3 g4 L predictive current control, sliding mode control and mov-
a L L
v1 a iL L c v v ing discretized control set model predictive control (MDCS-
V1 vab vvcd
c V22 v ab
ab vcd MPC). The closed-loop control-to-output Gro (s) and output
b b vab cd
dd Nvcd
vcd
impedance Zo (s) are selected as the metrics of the ability
g1 g g 2g N:1
N:1 gg3 gg 4
1 2 3 4 Nvcd
vcd in voltage tracking and the load disturbance rejection perfor-
mance. The frequency response plots of Gro (s) and Zo (s) of
(a)
(a)
(a) (b)
(b)(b)
each control method are theoretically derived or swept using
simulation software. Based on these plots, remarks on each
Fig. 2: Topology of a DAB converter (a) and its equivalent control method are drawn. Section IV reviews some practical
circuit (b). control issues including dead time effect, phase drift and dc
magnetic flux bias. Finally, Section V draws the conclusion.
high efficiency with proper control. Compared to the existing reviews about modeling and
control [4], [7], [22], [23], this paper provides a more sys-
tematic overview of all known modeling and advanced con-
g1 , g 2 trol techniques for DAB. We are the first to quantitatively
t compare the available modeling methods and to recommend
the most suitable models for controller design. Moreover, we
g3 , g 4
also comprehensively describe the implementation of several
t
vab advanced control methods and systematically evaluate these
vcd methods in frequency domain. We believe that such an ap-
ϕTs proach provides valuable contribution to the field as it gives
iL
t practicing engineers and researchers a clear guidance on how
t1 Ts/2 Ts
to: 1) Choose an appropriate modeling technique, 2) Choose
which control method is the most suitable for their application
Fig. 3: Key waveforms of a DAB using SPS modulation. , and 3) Understand how to formally analyze the performance
of DAB converter in practice and implement its associated
Various applications employing DABs have been proposed. controller.
SSTs based on DABs in power grids have been introduced
to interconnect different scale micro-grids [8] or to connect II. M ODELING OF A DAB
different -ilevels
A
of dc grids [9], [10]. Power electronic traction Modeling is the representation of a physical phenomena by
transformer
iB (PETT) using DABsiLcan reduce the weight, add mathematical means [24]. DAB modeling is more challenging
additionalifunctionalities and improve the energy efficiency compared to modeling of conventional dc-dc converters as one
comparediAto on-board line frequency transformer [11], [12]. of the state variables, the inductor current iL , is purely ac with
DAB is alsoaThpromising solutionTh for on-boardTsbattery charg- an average value 0, as shown in Fig. 3. This section summa-
S1
ers in plug-in electric vehicles S2
(PEVs), especially when the rizes modeling methods for a DAB converter, and compares
vehicle-to-grid (V2G) function is required [13], [14]. With the large and small signal models obtained from these methods
(gallium nitride) GaN devices, a 1MHz 1.2kW/400V DAB using simulation results to give guidance for DAB controller
prototype is reported to achieve 97.5% peak efficiency [15]. design. The modeling methods are introduced based on a DAB
With 1700V (silicon carbide) SiC devices, a 1500V/200kW using the single phase shift (SPS) modulation (Fig. 3), but
DAB prototype is reported to achieve 99.6% peak effi- these methods can be extended to a DAB using dual phase
ciency [16], [17]. Other applications including ESS interface shift (DPS) or triple phase shift (TPS) modulation [7].
converters [18], airborne wind turbines [19], uninterrupted
power supplies (UPS) [20], and power load emulators [21] A. Reduced order model
have also been reported. One way to model DAB is simply ignoring the dynamics
In all these applications, it is essential to model the DAB
of iL , which is called reduced order model [25]–[27]. The
converter and design its controller with specified steady-
average values of input and output currents over one switching
state and dynamic performance. The aim of this paper is to
cycle (or half a cycle) are used to describe the characteristics
classify, describe and critically compare different modeling
of the current. Then a DAB is simplified to a first order system,
techniques and control methods for DAB converters and
as shown in Fig. 4, where hib1 i and hib2 i are the switching
provide explicit guidance about DAB controller design to
cycle average of the currents ib1 and ib2 (Fig. 2).
practicing engineers and researchers. Section II categorizes The output power Po of a DAB modulated using SPS can
the available modeling techniques for the DAB including be expressed as [6]
reduced order model, generalized average model and discrete-
time model. These models are quantitatively compared based N v1 v2 φ(1 − 2|φ|)
Po = (1)
on simulation results. Section III comprehensively describes fs L
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v1 v2 Ls1 Ls2
C1 C2 RL
-
RC1 iL Req L RC2
Fig. 4: Large signal diagram of the DAB reduced order c
model [25]–[27]. C1 a C2
V1 vab vcd V2
b d
1/RL N:1
i2
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Mag(dB)
N Transformer turns ratio 2:1
fs Switching frequency 20kHz 40 Reduced order
L Inductance L0 = 70µH
Imp reduced order
Req Equivalent resistance Req0 = 0.25Ω
Generalized avg
Gv
C2 DC Capacitor 2 C20 = 1mF 20
Discrete time
R Load resistor 4Ω
SIMPLIS simu
Td Dead time 200ns
0
a: The nominal value is the value used in the DAB circuit. The circuit 0
parameters used in the control can be different from this nominal value.
Phase(deg)
-45
Phase shift ϕ
ib1 ib2 ILoad
-90 Reduced order
Imp reduced order
Generalized avg
Req L
Gv
iL -135 Discrete time
a c
v1 C2 v2 SIMPLIS simu
vab vcd RL
b d -180
N:1 100 101 102 103 104
Frequency (Hz)
Fig. 12: Comparison of bode plot of small signal models Gvφ
Fig. 10: The DAB circuit for model comparison.
(from φ to v2 ).
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is a first-order system, and the inductor L does not affect the DAB converter
DAB dynamic response. This interesting phenomenon may be
DC +
Response
explained as follows. The bipolar square voltages vab and vcd
of a DAB only have switching frequency fs and its harmonics, v1 +- v2 RL
and their dc components are 0, as shown in Figs. 2 and 3. The DC
low frequency component (below fs /2) of inductor current iL , -
for instance the envelope in Fig. 46, cannot be transferred to dc G1-G8
side because of the orthogonality relations of the trigonometric
V * Control and
functions: 2 +
+ Modulation
t+T
Z s v2*
sin(n · 2πfs t + φ1 ) · sin(ωL t + φ2 )dt = 0 (2nπfs 6= ωL ) Perturbation
t Fig. 14: The closed-loop transfer function evaluation circuit.
(11)
where ωL is the low frequency component of iL . As result, DAB converter
the perturbation of iL caused by disturbance such as change
of input voltage or phase shift ratio cannot be propagated Zo +
Perturbation
to output side, and the inductor L does not affect the DAB
Response
Idc iac
dynamic response. To further validate above analysis, Fig. 13 +
shows simulation results of the DAB output voltage v2 with V2 v2
-
DAB circuit and the reduced order model (Fig. 4), where the
DAB is controlled using the feedback-only control and the
control parameters are listed in Table III. Under step change -
of the input voltage, load and output reference, the reduced
Fig. 15: The output impedance evaluation circuit.
order model predicts the DAB dynamic performance well.
V2* : 160V response plots based on the derived transfer function are
→170V provided. Gro (s) and Zo (s) plots of the feedforward current
control, predictive current control and mode predictive control
are swept using simulation in Figs. 14 and 15.
Load: 6.4kW In the reference to output (Gro (s)) evaluation circuit
→25W Fig. 14, the reference signal consists of a DC component V2∗
Vi: 400V and an AC component v2∗ . V2∗ sets the equilibrium point while
→450V
v2∗ provides small signal perturbation (sine wave at certain
frequency). The output voltage v2 of the DAB converter is
Load: 25W
measured at each frequency of the reference perturbation v2∗ .
→6.4kW
Gro (s) can be obtained by calculating the magnitude and
phase difference between v2∗ and v2 at each frequency:
v2 (f )
Fig. 13: Simulation results of the DAB output voltage v2 with Gro (f ) = (12)
v2∗ (f )
DAB circuit and the reduced order model.
In the output impedance (Zo (s)) evaluation circuit Fig. 15,
the DAB converter is simplified as a voltage source V2
and an output impedance Zo . Idc represents the steady-state
III. C ONTROL OF A DAB
load current which sets the equilibrium point, and iac stands
This section mainly reviews the available output voltage for the injected small current which provides small signal
control methods including conventional feedback control, lin- perturbation. The output voltage v2 of the DAB converter
earization control, feedforward plus feedback control, distur- is measured at each frequency of the injected current iac .
bance observed based control, feedforward current control, The output impedance can be obtained by calculating the
predictive current control, sliding mode control and model magnitude and phase difference between v2 and iac at each
predictive control. frequency:
To effectively evaluate and compare these output voltage
v2 (f )
control methods, the closed-loop control-to-output transfer Zo (f ) = (13)
function Gro (s) and the output impedance Zo (s) are selected iac (f )
as the metrics of the ability in voltage tracking and load current The evaluation circuit in Figs. 14 and 15 can be eas-
disturbance rejection. The transfer functions Gro (s) and Zo (s) ily implemented using PLECS Multitone Analysis tool or
of the feedback control, linearization control, feedforward SIMetrix/SIMPLIS. Based on the frequency response plots,
plus feedback control are derived theoretically, and frequency remarks for each control method are drawn.
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Gro Mag(dB)
designates algorithms or circuits that takes only the sampling 0
of the voltages and/or currents as inputs to generate the phase
shift duties or active state duties of the DAB to track the -10
output reference. By this definition, the so called “control”
in the literature [39]–[42], are classified as the optimization of -20
0
Gro Phase(deg)
advanced modulations rather than control methods discussed
here. V2 = 160V, Po = 6.4kW
-200 V2 = 160V, Po = 25W
A. Feedback control on the output voltage V2 = 200V,Po = 6.4kW
Feedback control with a proportional-integral (PI) compen- -400
sator is the simplest method to regulate the output voltage. 101 102 103 104
As shown in Fig. 16, the phase shift ratio φ between the Frequency (Hz)
primary and secondary bridges is modified dependent on the (a)
error in the output voltage [43], [44]. The PI compensator
Zo Mag(dB)
(Gc1 (s) = kp + ki /s) is used to minimize the steady state -20
error.
-40
ZL(s) -60
1/RL0
i2
Zo Phase(deg)
-100
0.25 v2
V2* Gc1(s) Gϕi (s) 1/sC20
-0.25 ib2 ic -200 V2 = 160V
v2
V2 = 200V
Fig. 16: Block diagram of feedback-only control. -300
101 102 103 104
Frequency (Hz)
i2 (b)
0.25 v2
V2* Gc1(s) Gϕi (s) 1/sC20 Fig. 18: Bode plot of the feedback only control: (a) Gro (s)
-0.25 ib2 ic under different load conditions, (b) Zo (s).
v2
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DAB Converter
Gro Mag(dB)
0
1/RL0
i2 -10
ib*2 0.25 v2
V2* Gc2(s) Eq.(18) Eq.(16) 1/sC20 -20
-0.25 ib2 ic
v2 -30
0
Gro Phase(deg)
Fig. 19: Block diagram of the linearization control with
resistive load [45]. V2 = 160V, L = L 0
-200
V2 = 200V, L = L0
ZL(s) V = 160V, L = 0.8L0
2
-400
1/RL0 101 102 103 104
i2
Frequency (Hz)
v2
V * Gc2(s) 1/sC20 (a)
2 ib2 ic 0
v2
Zo Mag(dB)
-20
Fig. 20: Equivalent block diagram of the linearization control
with resistive load. -40
-60
Zo Phase(deg)
-100
shown in Fig. 19, where Eq. (18) is inserted into the control
loop. Since Eq. (18) is the solution of Eq. (17), the non- V2 = 160V, L = L 0
linearity of the control loop can be compensated. When the -200
V = 200V, L = L 0
2
circuit parameters used in the control is exactly the same as V2 = 160V, L = 0.8L 0
that of the actual converter, then ib2 = i∗b2 and Fig. 19 can be -300
simplified as Fig. 20. The reference to output transfer function 101 102 103 104
is: Frequency (Hz)
Gc2 ZL e−1.5Ts s (b)
Gro (s) = (19)
1 + Gc2 ZL e−1.5Ts s Fig. 21: Bode plot of the linearization control: (a) Gro (s), (b)
where ZL (s) is shown in (15). By replacing the resistor RL Zo (s).
with a current source (similar to that in Fig. 17), the output
impedance can be calculated as:
1 1) Output current feedforward (OCFF): The relationship of
Zo (s) = − (20) phase shift ratio φ and output power can be as a feedforward
sC2 + Gc2 e−1.5Ts s
term to minimize error between the actual and desired behav-
The PI parameters are designed to achieve 1.2kHz crossover ior. Based on (1), the desired output power can be expressed
frequency with 45◦ phase margin under full load (RL = 4Ω) as:
and we obtain kp2 = 7.3155, ki2 = 1.425×104 . Fig. 21 shows
N v1 v2 Φ∗ (1 − 2|Φ∗ |)
the bode plot of the linearization control based on (19) and Po∗ = (21)
(20). Theoretically, Gro (s) and Zo (s) of the linearization con- fs L
trol will not be affected by output voltage or load conditions. Therefore the desired phase shift Φ∗ can be calculated as:
However, when the circuit parameters in (18) are different r
from the actual ones, for instance L = 0.8L0 , the bandwidth 1 1 fs Li2
− − i2 ≥ 0
of the DAB becomes narrower. Note L is the inductance ∗
Φ = 4 16
r 2N v1 (22)
used in the control, whereas L0 is the inductance used in −1 + 1 fs Li2
+ i2 < 0
the actual DAB circuit (nominal value). Actually, according to 4 16 2N v1
Fig. 18, the closed-loop bandwidth and output impedance of
the feedback-only control almost does not vary with different
output voltage or load conditions, and the linearization may v1 DAB Converter
be not required. i2 Eq. (22) 1/RL0
* i2
C. Feedforward plus feedback control on output voltage
0.25 v2
V2* Gc3(s) Gϕi(s) i 1/sC20
-0.25 b2 ic
Combined feedforward plus feedback control can improve v2
performance over simple feedback control as the disturbance
can be measured and counterbalanced before it affects the Fig. 22: Block diagram of the output current OCFF control.
process output.
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G ro Mag(dB)
Gi(s) 1/RL0 0
* i2
0.25 v2
-10
V2* Gc3(s) Gϕi (s) 1/sC20
-0.25 ib2 ic
v2
-20
Fig. 23: Equivalent block diagram of the OCFF control. 0
G ro Phase(deg)
L = L0
L= 1.1L0
-200
Fig. 22 shows the control diagram, which is termed as L= 1.3L0
output current feedforward (OCFF) control in this paper. Feedback-only
Alternatively Φ∗ can be generated using a lookup table [32]. -400
101 102 103 104
To derive the transfer functions of Gro (s) and Zo (s), it is
Frequency (Hz)
necessary to linearize (22) using small signal analysis. Assume
the input voltage remains constant, local linearization of (22) (a)
yields: -20
Zo Mag(dB)
1
fs LI2 − 2
fs L 1 -40 L = L0
− I2 ≥ 0
dΦ ∗
( ) L = 1.1L0
4N V1 16 2N V1 1 -60
Gi (s) = = −2 L = 1.3L0
di2
fs L ( 1 + fs LI2 ) -80
I2 < 0
Feedback-only
4N V1 16 2N V1 -100
(23)
Zo Phase(deg)
where I2 is the equilibrium value calculated as: 0
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Gro Mag(dB)
0
1.1L0 , the magnitude of Zo (s) increases; when L = 1.3L0 , the
magnitude of Zo (s) becomes the same as that of the feedback -20 P = 6.4kW
o
Gro Phase(deg)
to achieve good load disturbance rejection. The practical
performance of the OCFF control may not be as good as
designed. Similar methods are also found in [46], [47]. -200
2) Virtual Direct Power Control: Another feedforward con-
trol termed as Virtual Direct Power Control (VDPC) has
-400
been proposed in [48]. The advantage of the VDPC is that 101 102 103 104
it eliminates the necessity of using the information of the Freq(Hz)
inductance L by using the unified power to calculate Φ∗ .
(a)
50
DAB Converter
Zo Mag(dB)
v1 ib 2 v2 V2* 0
1/RL0
i2
V2* 0.25 v2 -50
Gc4(s) Eq.(38) Gϕi(s) i 1/sC20
U *
v -0.25 b2 ic
v2 -100
0
Zo Phase(deg)
Fig. 25: Block diagram of the VDPC control [48].
-200 Po = 6.4kW
In this method, a virtual power reference p∗ is defined Po = 640W
-400
∗
p = |Uv∗ |i∗2 , (33) Po = 25.6W
-600
where |Uv∗ | is named as the virtual desired output voltage, 101 102 103 104
which is output value of the PI compensator in Fig. 25. Freq(Hz)
Assuming a resistive load, the desired output current i∗2 can (b)
be described as:
Fig. 26: Bode plot of the VDPC control: (a) Gro (s), (b) Zo (s).
i∗2 i2
= (34)
V2∗ v2
Load: V2*:
Substituting i∗2 from (34) into (33) yields
6.4kW→25W 160V→170V
|Uv∗ | V2∗
p∗ = i2 (35)
v2
On the other hand, the unified power is expressed as:
Ppu = Po /Pbase = V1 v2 φ(1 − 2|φ|) (36)
where the unity base is
Pbase = 1/(fs L) (37)
Let Ppu = p∗ , we can calculate
s
1 1 V2∗ Uv∗ i2
4 − 16 − 4v 2 v i2 ≥ 0
2 1
φ= s (38)
1 1 V2∗ |Uv∗ |i2 Fig. 27: Time domain simulation results of the VDPC,
− 4 + 16 + 4v 2 v
i2 < 0 feedback-only and MDCS-MPC [48].
2 1
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different load conditions. Under the condition Po = 25W , the where v̂˜2 and f˜t are the estimated values of v̂2 and ft
control bandwidth drops significantly (Fig. 26(a)). As a result, respectively.
the output impedance increase significantly (Fig. 26(b)). The Define the estimation error e1 = v̂2 − v̂˜2 and e2 = ft − f˜t ,
narrow bandwidth and high output impedance indicate poor then the following equations can be derived considering (40),
performance on voltage tracking and load current disturbance (41) and (42):
rejection. The above observation is further validated using the
time domain simulation results in Fig. 27. When the load steps ė1 = e2 − β1 e1
(43)
to light at 0.05s, the dynamic performance becomes poor. ė2 = f˙t − β2 e1
By choosing β1 and β2 positive, then e1 and e2 converge
D. Disturbance-Observer-Based Control to zero exponentially, i.e., the estimated states will converge
In the above feedforward control methods, OCFF control to the actual states [50].
can significantly reduce the output impedance and improve the Choose β1 = 2ζωn and β2 = ωn2 . Rearrange the disturbance
load disturbance rejection capability. However, its performance observer (41) and (42) as follows:
deteriorates quickly in the presence of parameter uncertainty.
The VDPC tries to solve the parameter sensitivity problem Ẋ = AX + BU (44)
by using the PI output to estimate the phase shift, but its
where
loop gain is too low under light load conditions. Besides,
v̂˜2
an additional current sensor is required in these feedforward −2ζωn 1
X= A=
control methods. f˜t −ωn2 0
Disturbances and uncertainties exist in all power converter
bo 2ζωn
φ̂
control systems [49]. These disturbances and uncertainties B= U=
0 ωn2 v̂2
include input voltage and load variation, model uncertainty,
and circuit parameter variations due to temperature or ag- From (44), the transfer functions from φ and v2 to f˜t can
ing effects [50]. Disturbance-observer-based control (DOBC) be derived as follows:
employs an observer to estimate the total disturbances and
uncertainties, and corresponding compensation is then gen- f˜t −ωn2 bo
Gf µ (s) = = (45)
erated by making use of the estimate [49]. Therefore the φ̂ s2 + 2ζωn s + ωn2
DOBC can achieve superior control performance. The input to f˜t ωn2 s
the disturbance observer is the output voltage v2 and control Gf v (s) = = 2 (46)
v̂2 s + 2ζωn s + ωn2
signal (phase shift ratio φ), no additional current sensor is
required [50], [51].
DOBC for the DAB converter has been introduced in [50]–
iˆo 1/RL0
[52]. The derivation procedures of the disturbance observer
from [50] are briefly repeated here to illustrate its basic 0.25 v2
V2* Gc5(s) 1/bo Gϕi(s) 1/(sC20)
principles. -0.25 ib2 ic
According to Fig. 4, we can obtain the following small v2 ft
Gfμ(s) Gfv(s)
signal equation
dv̂2 N V1 (1 − 4Φ) v̂2
= φ̂ − (39)
dt fs LC2 RL C2
Rearrange (39), we can get Fig. 28: Block diagram of the disturbance observer based
dv̂2 control [50].
= ft v̂2 , φ̂ + b0 φ̂ (40)
dt Fig. 28 shows the block diagram of the DOBC. The esti-
mated disturbance f˜t is subtracted to compensate the actual
where ft v̂2 , φ̂ = av̂2 + (b − b0 )φ̂ is the total disturbance
which includes external disturbances, circuit parameter varia- disturbance in the control system. Loop gain of the control
tions, and model uncertainties, with system can be calculated as:
1 N V1 (1 − 4Φ) N V10 (1 − 4Φ0 ) Gc5 (s)Gφi ZL e−1.5Ts s b−1
o
a=− ,b = , b0 = Go (s) = (47)
RL C2 fs LC2 fs L0 C20 1 + (Gf v Gφi ZL + Gf µ )e−1.5Ts s b−1
o
where V10 , L0 and C20 are the nominal values of the input
The PI parameters of Gc5 (s) are designed to achieve 1.2kHz
voltage, inductance, and output capacitance respectively.
crossover frequency with 45◦ phase margin under full load
The disturbance observer for the DAB can be designed as
(RL = 4Ω). When L = L0 , C2 = C20 , we obtain kp5 =
follows
7.53 × 103 , ki5 = 1.37 × 107 . These control parameters are
dv̂˜2
large because of the gain 1/bo in the control loop in Fig. 28,
= f˜t + β1 v̂2 − v̂˜2 + b0 φ̂ (41)
dt where bo = 3 × 105 in this design. After multiplying this
df˜t
gain, the PI parameters of DOBC are of the same order of
= β2 v̂2 − v̂˜2 (42)
dt magnitude of that of other control methods.
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Gro Mag(dB) 0 g1 g2 g3 g4
N:1
-10 v1 v2
-20 g1 g2 g3 g4
0
Gro Phase(deg)
iL
L = L0 v1
-200 g1
L = 0.75L0 Eq. (51)
i2 *
L = 1.3L0 iLr
-400 + S Q g3
V2* Gc6(s) +
101 102 103 104 iLr iLr
-1 g4
Frequency (Hz) R Q
v2
(a) g2
Current mode modulator
-20
Zo Mag(dB)
-40 L = L0 Fig. 30: Block diagram of the current mode control with
-60 L = 0.75L0 feedforward of load current [53].
L = 1.3L0
-80
Feedback-only
-100
φTh
vab
v cd
Zo Phase(deg)
0 ∆ iLr
+iLr
-200 +iLr*
iL
0
-400
- iLr*
101 102 103 104 - iLr
Frequency (Hz)
(b) Fig. 31: Key waveforms of the current mode control in [53].
Fig. 29: Bode plot of the DOBC control: (a) Gro (s), (b) Zo (s).
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Gro Mag(dB)
algorithm is compensated by the PI feedback controller. Since 0
the transformer current is directly manipulated, the transient
dc-offset current on the DAB transformer can be inherently -10
eliminated.
-20
The open-loop bode plot of FFCC control (Fig. 30) can
be swept using PLECS multitone analysis tool. Based on the
0
swept open-loop bode plot, the PI compensator for the FFCC
Gro Phase(deg)
control are designed to achieve 1.2kHz crossover frequency
with 45◦ phase margin, and the resultant PI parameters are: -200 FFCC L = L 0
kp6 = 4.35, ki6 = 3.17 × 104 .
FFCC L = 1.3L 0
The bode plots of Gro (s) and Zo (s) of the FFCC are
Feedback-only
swept using the evaluation circuits Figs. 14 and 15 in the -400
software PLECS. The swept Gro (s) and Zo (s) are shown 101 102 103 104
in Fig. 32, where L0 is the actual inductance in DAB and Frequency (Hz)
L is the inductance value used in the FFCC control. With (a)
the feedforward term and current mode control, the output
impedance of the FFCC is the smallest compared to Feedback -20
Zo Mag(dB)
only control and OCFF control. Besides, in the presence of -40
FFCC L = L0
the parameter variation, the performance of the FFCC control -60 FFCC L = 1.3L0
degrades less significantly compared to the OCFF control OCFF
-80
(Fig. 24). Even when L = 1.3L0 , the output impedance of Feedback-only
FFCC control is still much smaller than the feedback-only -100
control.
Zo Phase(deg)
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DAB Converter advantage of a system with sliding mode control (SMC) is that
v1 v2 ir0 1/RL0 it has guaranteed stability and robustness against parameter
i2 uncertainties [62].
*
0.25 v2
The SMC has been applied to the DAB converter in [63]
V2 Gc7(s) Eq.(52) Gϕi(s) i 1/sC20
ir1 -0.25 b2 ic based on generalized average model and in [64] based on the
v2
reduced order model. According to Section II, the reduced
Fig. 34: Block diagram of the predictive current control [56], order model presents better accuracy compared to the gener-
[57] alized average model, therefore the SMC is introduced with
. the reduced order model.
In general, assume the dynamic equation of a system is:
dx
= f + gu (53)
G ro Mag(dB)
0
t
Predictive current L = 1.1L
0
-10 FFCC L = 1.1L
where x is the state variable, f and g are function of x, u is
0
MDCS-MPC
the discontinuous control action expressed as:
-20 Feedback-only
+
U if S(x, t) > 0
u= (54)
U − if S(x, t) < 0
0
where U + and U − are either scalar values or scalar functions
G ro Phase(deg)
100 dS(x, t)
Zo Phase(deg)
=0 (56)
0 dt
The steady state error that occurs with the SMC (54) can be
-100
minimized by comprising an integral term of the state variable
-200 into the sliding surface [65]. This approach is called integral
-300 SMC. However, the integral SMC becomes less effective when
101 102 103 104 equivalent control action is implemented [66]. Therefore, S. C.
Frequency (Hz) Tan et al. proposed an additional double integral term of the
(b) state variables for construction of the sliding surface when the
equivalent SMC is utilized [67].
Fig. 35: Frequency response plot comparison of the predic- In the DAB converter, state variables are chosen to be [68]:
tive current control, FFCC, MDCS-MPC and feedback only Z t Z t
T
control: (a) Gro (s), (b) Zo (s). x = [x1 , x2 , x3 ] = [verr , verr dt, x2 dt]T (57)
0 0
where verr = V2∗ − v2 .
F. Sliding mode control According to Fig. 4 and (2), the state equation of the DAB
can be written as:
Small-signal models and analysis have been widely used in
dv2 v2 v1
the power electronics for stability assessment. However, they =− + φ(1 − 2 |φ|) (58)
dt C2 RL C2 fs L
fail to predict the stability of some converters in presence
of large transient. Worse still, the small-signal model fails According to the double integration approach [67], the
to reveal any stability information of the converter over the sliding surface is constructed as:
entire operating region [59]. In the works [60], [61], it is 3
X
shown that even though stable operation is concluded from the S(x, t) = αi xi (59)
small-signal analysis, the system can be unstable. The main i=1
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DAB Converter
G ro Mag(dB)
0
v2 1/RL0
i2
-10
*
iSM 0.25 v2
V2 Eq.(61) Eq.(60) Eq.(2) i 1/sC20
-0.25 b2 ic -20
v2
G ro Phase(deg)
L = L0 , RL=RL0
1/RL0 -200
i2 L = L0 , no RL feedforward
v2 L = 0.8L0 , RL=RL0
V2* kp8
ib2 ic
1/sC20 -400
101 102 103 104
v2 ki8/s
1/RLc Freq(Hz)
(a)
0
Fig. 37: Equivalent block diagram of the SMC with resistive
Zo Mag(dB)
load. -20
-40
According to the invariance condition (56), the equivalent
control law can be derived as: -60
r
-100
Zo Phase(deg)
1 1 fs LiSM
− − iSM ≥ 0
φ= 4 16 2v1 (60)
r L = L0 , RL=RL0
−1 + 1 fs LiSM -200
+ iSM < 0 L = L0 , no RL feedforward
4 16 2v1 L = 0.8L0 , RL=RL0
iSM used in (60) can be expressed as [68]: -300
101 102 103 104
α3 t
Z
v2 α2 Freq(Hz)
iSM = + C2 verr + C2 verr dt (61)
RLc α1 α1 0
(b)
where RLc is the load resistance value used in the control.
Different from (18), iSM in (60) is a virtual current gener- Fig. 38: Frequency response plot of the SMC: (a) Gro (s), (b)
ated by (61). Based on (60) and (61), the SMC control diagram Zo (s).
is shown in Fig. 36. Essentially, Eq. (61) is PI compensator
plus a feedforward term. Besides, Eq. (60) is the solution of
phase shift ratio φ is divided into the discretized elements to
Eq. (18), similar to the linearization control. Therefore, the
fit digital control.
SMC block diagram Fig. 36 can be equivalent to Fig. 37,
According to (1) and Fig. 5, the DAB output voltage is
where kp8 = C2 α2 /α1 , ki8 = C2 α3 /α1 ,
regulated by the phase shift φ, which is continuous in nature.
Based on Fig. 37, the PI parameters of the SMC is designed
To adapt digital control, φ needs to be discretized. Consider a
to achieve 1.2kHz crossover frequency with 45◦ phase margin:
commercial micro-controller with a peripheral clock fc (Fig.
kp8 = 7.3155, ki8 = 1.425 × 104 , which is the same as that of
39), the finest phase shift value ∆f is:
the linearization control. Similar to the linearization control,
the transfer functions of Gro (s) and Zo (s) can be derived fc
∆f = , (62)
according to Fig. 37. Fig. 38 shows bode plots of Gro (s) and fs
Zo (s) of the SMC control. The feedforward term RLc actually where fs is the DAB switching frequency.
does not affect Gro (s) or Zo (s), and the bode plots of the The range of the DAB phase shift ratio is:
SMC are exact the same as that of the linearization control.
When the inductance value L used in the control is different φ ∈ [−0.25, 0.25] (63)
from the actual one (L0 ) in the circuit, the control bandwidth
The above φ can be further discretized into µm (= 1/∆f + 1)
becomes narrower and the output impedance increases.
elements as described in array:
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This cost function is executed during the time instant [k, k +1]
and v2 [k + 2] is the predicted output voltage at time instance
k + 2 and can be calculated based on Fig. 4 [69]: CMP
ib2 [k + 1] + ib2 [k] − 2i2 [k]
v2 [k + 2] = + v2 [k] (66)
C2 fs
where ib2 [k + 1], ib2 [k] can be calculated using φ[k] (already 0 t
known) and φ[k + 1] (predicted) based on the reduced order 1/fs
model (2). The error caused by power losses can be compen-
CMP
sated using Icomp [28]:
Icomp [k] = ib2− r [k − 1] − ib2 [k − 1] (67)
where ib2 is indicated in Fig. 10 and is calculated using 0
the reduced order model (2) (without power losses); ib2− r is t
calculated using the the measured load current Iload , where gx
the information of power losses is included: t
gy
C2 t
ib2− r [k − 1] = (v2 [k] − v2 [k − 1]) + Iload [k − 1] (68)
Ts
Fig. 40 shows how to choose φ in the next switching cycle. 1/fc
In the control interval k to k + 1, when φ[k + 1] equals to
a − ∆f , a and a + ∆f , the output voltage v2 is predicted as Fig. 39: Demonstration of the finest phase shift value in PWM
(1) (2) (3) modules [69].
v2 [k +2], v2 [k +2] and v2 [k +2] respectively based on (2)
and (66). As shown in Fig. 40, when φ[k + 1] = a + ∆f , the
(3)
predicted output voltage v2 [k + 2] is the closest to V2∗ . This aTs (a+Δf)Ts aTs (a-Δf)Ts
results in the smallest cost function defined in (65). Therefore, vab
the value a + ∆f is applied to φ at time instance k + 1. In the
next control interval, the same process is repeated. However,
vcd
the moving discretized control set has changed and become v2(3)[k+3]
{a, a + ∆f , a + 2∆f }, centered at the previous working point v2(3)[k+2] v2(2)[k+3]
φ[k +1] = a+∆f . In this control interval, φ[k +2] = a results V2*
in smallest cost function. v2(2)[k+2] v2(1)[k+3]
v2
In the above example, µ = 3 points are assessed in each v2(1)[k+2]
switching cycle, larger value of µ can increase the transition
dynamics, but it aggravates the computational burden to the
real-time digital controller. Therefore, an adaptive step for φ
is adopted instead of the finest search step ∆f . Define the
adaptive step ∆adp as (70). The adaptive step ∆adp changes
Evaluate Evaluate Evaluate
with the deviation of the output voltage to the reference. When {a-Δf, a, a+Δf} {a, a+Δf, a+2Δf} {a-Δf, a, a+Δf}
v2 is far from the reference, ∆adp grows large. In contrast, for period for period for period
when v2 equals to the reference, ∆adp becomes ∆f . Such k+1 to k+2 k+2 to k+3 k+3 to k+4
that, the control accuracy remains. k k+1 k+2 k+3
|V2 ∗ − v2 [k]| , |V2 ∗ − v2 [k]| < Vm
Fig. 40: Operating principle of MDCS-MPC and µ is set to
V∆ = (69)
Vm , |V2 ∗ − v2 [k]| > Vm be 3 for illustration [69].
∆adp = ∆f (1 + λV∆ 2 ), (70)
where Vm is the saturated voltage and λ is a coefficient deter- The first term G1 is responsible for regulation of the output
mined according to the requirement of transition performance. voltage v2 to reference value V2∗ while the second term G2
To provide damping and enhance the resistance to analogue takes charge of voltage deviation reduction. When v2 is far
to digital sampling noise in practice, the cost function can be from the reference value, G1 plays a dominant role in the
modified as follows: cost function. However, when v2 reaches close to V2∗ , G2
starts to take effect. G2 puts constraint on variation of v2 .
ct = α1 G1 + α2 G2 , (71) This essentially prevents v2 from dithering due to analogue to
where digital sampling noise. G2 also alleviates the oscillation during
load transitions. More terms can be added to the cost function
G1 = (V2 ∗ − v2 [k + 2])2
(72) to achieve multiple control objectives [71].
G2 = (v2 [k + 2] − v2 [k])2 The development of the analytical small signal model of
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DAB converters with MDCS-MPC is infeasible. The small • The linerization control can transform the control loop
signal evaluation circuit in Figs. 14 and 15 are employed to into linear system and can counterbalance the influence of
obtain the frequency response plot of Gro (s) and Zo (s). The terminal voltage and load variation theoretically, however,
control parameters for MDCS-MPC is set as: α1 = 1, α2 = its performance deteriorates when circuit parameters used
0.5, µ = 11, λ = 1, Vm = 10V . Fig. 35 shows the swept in the control are different from the actual circuit param-
results for Gro (s) and Zo (s). In light of the observation of eters. Besides, the linearization is actually not required
plots in Fig. 35, it can be concluded that the MDCS-MPC since the closed-loop bandwidth and output impedance
presents smaller output impedance compared to predictive of the feedback-only control almost does not vary with
current and feedback only approaches across the frequency different output voltage or load conditions.
range under test. As shown in Fig. 27, the MDCS-MPC has • OCFF control can significantly reduce the output
lower voltage overshoot under step change on load and output impedance and present perfect load current disturbance
reference, compared to feedback-only or VDPC.The MDCS- rejection capability, however, its performance deteriorates
MPC also features a transfer function Gro (s) which always quickly when there are parameter uncertainties. As shown
stays below 0dB. The MDCS-MPS is also employed to control in Fig. 24, when L = 1.3L0 , the output impedance of the
the DAB with TPS modulation [28]. OCFF control becomes the same as that of the feedback
only control.
H. Comparison of output voltage control methods • The VDPC tries to solve parameter sensitivity problem
The above control methods are compared in this section. of the OCFF control by using the PI output to estimate
The control parameters are summarized in Table III. These the phase shift. The biggest problem of the VDPC is
parameters are chosen such that the open-loop of each method the loop gain varies significantly under different load
achieves 1.2kHz crossover frequency with 45◦ phase margin. conditions. Under light load conditions, the bandwidth
Based on the theoretical transfer function or the bode plot, is too narrow and output impedance is too high, leading
these PI parameters can be calculated. to poor performance on voltage tracking and load current
disturbance rejection.
TABLE III: Control parameters. • The DOBC employs an observer to estimate the total dis-
turbances and uncertainties, and corresponding compen-
Control Methods Control Parameters
sation is generated by making use of the estimate. As a
Feedback only, Fig. 16 kp1 = 0.0193, ki1 = 37.6
result, the DOBC shows much smaller output impedance
Linerization, Fig. 19 [45] kp2 = 7.3155, ki2 = 1.425 × 104 compared with feedback-only control. The performance
OCFF, Fig. 22 kp3 = 0.0193, ki3 = 37.6 of the DOBC is not sensitive to the parameter variation.
VDPC, Fig. 25 [48] kp4 = 38.524, ki4 = 1.068 × 105 Besides, only one transducer is required.
DOBC, Fig. 28 [50] kp5 = 7.53 × 103 , ki5 = 1.37 × 107 • FFCC is essentially a peak current mode control method
with feedforward compensation. The DAB with the FFCC
FFCC, Fig. 30 [53] kp6 = 4.35, ki6 = 3.17 × 104
control has small output impedance since the changes on
Predictive current, Fig. 34 [56] kp7 = 24.8, ki7 = 1.45 × 105
output current or voltage can lead to immediate change
SMC, Fig. 36 [68] kp8 = 7.3155, ki8 = 1.425 × 104 at the inductor current. In the presence of the parameter
α1 = 1, α2 = 0.5, µ = 11, tolerance, the performance of FFCC control degrades less
MDCS-MPC [69]
λ = 1, Vm = 10V significantly compared to the OCFF control. However, the
FFCC control is susceptible to noise, especially when the
Table IV compares these control methods in terms of DAB loses ZVS-on.
implementation complexity, dynamic performance, robustness • The predictive current control can also improve the dy-
against parameter variation and implementation cost. The im- namic performance. Under the same control bandwidth,
plementation cost include costs of voltage/current sensors and the output impedance of the predictive current control is
microprocessor computational power for method to be func- lower than that of the feedback only control. This method
tioning. The required microprocessor computational power may not be feasible for high frequency applications,
is related to the control method complexity. The high cost since ac sampling and computation are required for each
methods are those with high implementation complexity and switching cycle.
3 sensors. The low cost methods are those with low complexity • MDCS-MPC has similar ability in load disturbance re-
and 1 sensors. The FFCC and MDCS-MPC have higher jection with the OCFF control. In the meantime, MDCS-
implementation cost compared to other control methods. The MPC provides salient output voltage tracking perfor-
detailed remarks are given as below. Note that these remarks mance. However, MDCS-MPC demands relatively heavy
are only based on theoretical analysis and simulations, and are computation power which is a common issue as with
not validated using experimental results. Practical performance other model predictive control. The control parameters
of these control methods can be different from that listed in such as weighting factors and the number of points
Table IV. calculated in one control cycle have a significant impact
• The feedback only control approach shows mediocre on the control performance. Inappropriate control param-
dynamic performance, however, it is easy to implement eters will cause system instability. Compared with the
and requires only one transducer. feedback-only control, the parameters are mainly selected
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IV. S OME PRACTICAL CONTROL ISSUES Fig. 41: Equivalent circuit of a DAB (modulated using SPS)
during primary side H-bridge dead time.
This section surveys some practical control issues including
dead time effect, phase drift and dc offset during dynamic
transition. Dead
1) Dead time effect: During the dead time period of a leg, time
the power devices turn off and the leg voltages (va , vb in hard
Current polarity
Fig. 41) only depend on the current direction. If the dead transition
swap
time is too long, the voltage may change polarity during
this period [72]–[76]. Consider a DAB modulated using SPS,
during the dead time of the primary side H-bridge, all the
power devices are “OFF” as shown in Fig. 41, vab may change iL
polarity if the dead time is too long, leading to undesirable
voltage spikes, as shown in Fig. 42 [32] [76]. This phe-
vab
nomenon will bring electromagnetic interference (EMI) [72]
and should be avoided by choosing a proper dead time. vcd
The upper limit for the dead time to prevent the voltage
Fig. 42: Experimental waveforms: voltage change polarity
spikes can be estimated assuming linear transformer behavior
during the dead time [76].
and ZVS-on transition. For a DAB modulated using SPS, the
maximum dead time for the primary side device is [77]:
Isw · L
tdead. max = (73) (a). When t < Th , vab = V1 − iL Req , as shown in Fig. 43 (b),
V1 + N V2 where Req is the equivalent resistances of the primary side;
where Isw is the inductor current at the switching instance. while Th < t < Ts , vab = −V1 − iL Req . These voltage drops
0
2) Phase drift: The actual phase shift can be different from cause the equivalent phase of vab and vcd shift to the left and
the theoretical one given in (1). There are a few reasons for right respectively. In the case of Fig. 43, the given phase shift
the phase drift. The first reason is the voltage drop on power is φ < 0, but the phase between the fundamental components
0
devices and other components. Consider a DAB transfers of vab and vcd φ(1) > 0 and the power is transferred from left
positive power using SPS modulation as shown in Fig. 43 to right.
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ϕ With DC bias
vab = V1-ReqiL ϕ iL iL With DC bias
vcd
W/O W/O DC bias
DC bias t
t
iL Ts a iL iL L L 0 0
V1 a a iL c c
Req vab V1V1 V2 V2
Th vabvab im im vcd vcd
b b b d d im im With With DC bias
DC bias
ϕ<0 ϕ(1)>0 N:1N:1
W/O W/O DC bias
DC bias t t
vab = -V1-ReqiL 0 0
(a) (b)
(a) (b)
Fig. 43: Phase drift caused by voltage drop on components (a)
waveforms, (b) equivalent circuit when 0 < t < Th . Fig. 45: Inductor current (iL ) and magnetizing current (im )
with and without steady state DC bias [78].
The second reason is the dead time. As explained in Fig. 41, 100
during the dead time, the H-bridge output voltage depends on
the current direction and its actual phase may vary from the iL
50
given φ [72], [75], [76]. I L
iL(A)
Another important reason for phase drift is the switching
0
delay during the ZVS transition [77]. A large inductor current Φ Φ
will shorten the ZVS transition period, and the phase drift I m
im -50
is severest when the switching currents on the primary and
secondary sides deviate considerably from each other as shown 0
in Fig. 44. (a)
(a)
t to
100
(1
x)iL(Tth) I L e L / Req
V1 = 100V, V2 = 250V V1 = 130V, V2 = 250V
iL
50 vab
I L
iL(A)
Th 2Th
0 DTh xTh
Φ Φ vab
im I m vcd vcd
iL -50
0 0.2 0.4 0.6
Time (ms)
(a) (b) (b)
I max
(a) iL
Fig. 46: (a)DC offset during the load transient, (b) decay of
V1 = 130V, V2 (1 x)T
= 250V
h dc offset over a time constant L/Req [79]. I max
vab
Th 2Th transient DC bias (Fig. 46) is caused by the temporary volt-
second imbalance on inductor due to the update of phase shift
DTh xTh
vab ratio. The steady state DC bias will increase the conduction
vcd vcd losses of the transformer and power devices and lead to loss
iL of ZVS, whereas the transient DC bias may saturate magnetic
cores of the transformer and inductor, leading to the failure of
the converter in the end [78].
I max The simplest way to suppress the steady state DC magnetic
(b) flux bias is to include “dc-blocking capacitors” in series
iL
Fig. 44: Phase drift caused by switching current difference on with the transformer winding, this will however increase the
the primary and secondary sides [77]. I max system volume and cost, especially in high voltage high power
applications. This DC bias can also be eliminated by active
3) DC magnetic flux bias: In practice, a DC magnetic flux controlling the inductor current. One of the prerequisites of
bias will arise both in steady state and transient process for a this control is to accurately measure the steady state dc bias,
DAB converter. As shown in Fig. 45, the steady state DC bias the following measurement methods have been proposed:
is caused by unmatched parameters of the circuit, like small • Digital sampling and averaging. Sample the inductor
discrepancy of the gate-drive signal, different turn on/off delay current several times each switching cycle and average
and unequal on-state resistance of the power devices; while the the sampled values [81];
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m -50
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0 0.2 0.4 0.6
Transactions on Power Electronics
Time (ms)
IEEE TRANSACTIONS ON POWER ELECTRONICS 20
(a) (b)
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IEEE TRANSACTIONS ON POWER ELECTRONICS 21
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0885-8993 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS 23
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[75] B. Zhao, Q. Song, W. Liu, and Y. Sun, “Dead-time effect of the Shuai Shao (M’17) received the B.S. degree from
high-frequency isolated bidirectional full-bridge dc-dc converter: Com- Zhejiang University, China, in 2010, and the Ph.D.
prehensive theoretical analysis and experimental verification,” IEEE degree in electrical and electronic engineering from
Transactions on Power Electronics, vol. 29, no. 4, pp. 1667–1680, April the University of Nottingham, U.K., in 2015.
2014. In 2015, he joined the College of Electrical En-
[76] J. Riedel, D. G. Holmes, B. P. McGrath, and C. Teixeira, “Zvs soft gineering, Zhejiang University, as a lecturer. In Jan.
switching boundaries for dual active bridge dc-dc converters using 2020, he was promoted as an associate professor. His
frequency domain analysis,” IEEE Transactions on Power Electronics, research interests include solid-state transformers,
vol. 32, no. 4, pp. 3166–3179, April 2017. bidirectional dc-dc converters, and fault detection
[77] J. Hiltunen, V. Väisänen, R. Juntunen, and P. Silventoinen, “Variable- in power converters. He has published more than
frequency phase shift modulation of a dual active bridge converter,” 40 peer-reviewed journal and conference papers. He
IEEE Transactions on Power Electronics, vol. 30, no. 12, pp. 7138– served as a Guest Associate Editor for IEEE Journal of Emerging and Selected
7148, Dec 2015. Topics in Power Electronics and CES Transactions on Electrical Machines and
[78] B. Zhang, S. Shao, L. Chen, X. Wu, and J. Zhang, “Steady state and Systems.
transient dc magnetic flux bias suppression methods for a dual active
bridge converter,” IEEE Journal of Emerging and Selected Topics in
Power Electronics, pp. 1–1, 2019.
[79] K. Takagi and H. Fujita, “Dynamic control and performance of a dual-
active-bridge dc–dc converter,” IEEE Transactions on Power Electronics, Linglin Chen received the M.Sc. degree in electrical
pp. 1–1, 2017. engineering from Zhejiang University, Hangzhou,
[80] X. Li and Y. F. Li, “An optimized phase-shift modulation for fast China, in 2016 and the Ph.D degree in electrical
transient response in a dual-active-bridge converter,” IEEE Transactions and electronics engineering from the University of
on Power Electronics, vol. 29, no. 6, pp. 2661–2665, June 2014. Nottingham, Nottingham, U.K., in 2020. From 2018
[81] S. Dutta and S. Bhattacharya, “A method to measure the dc bias in to 2019, he was a Visiting Scholar with the De-
high frequency isolation transformer of the dual active bridge dc to dc partment of Energy Technology, Aalborg Univer-
converter and its removal using current injection and pwm switching,” in sity, Aalborg, Denmark. From 2019 to 2020, he
2014 IEEE Energy Conversion Congress and Exposition (ECCE), Sep. was a Visiting Scholar with the Key Laboratory of
2014, pp. 1134–1139. Control of Power Transmission and Transformation,
[82] G. Ortiz, L. Fässler, J. W. Kolar, and O. Apeldoorn, “Flux balancing Shanghai Jiao Tong University, Shanghai, China. He
of isolation transformers and application of “the magnetic ear” for joined Digital Power Huawei Techonologies in 2020, and he is currently
closed-loop volt–second compensation,” IEEE Transactions on Power with Hisillicon of the same company. His interests include HJT TOPon
Electronics, vol. 29, no. 8, pp. 4078–4090, Aug 2014. PV materials, SiC&GaN device&gate driver, PV optimizer&string inverter,
[83] S. P. Engel, N. Soltau, H. Stagge, and R. W. D. Doncker, “Dynamic telecom&server rectifier, USB&PD charger, OBC etc.
and balanced control of three-phase high-power dual-active bridge dc-
dc converters in dc-grid applications,” IEEE Transactions on Power
Electronics, vol. 28, no. 4, pp. 1880–1889, April 2013.
[84] B. Zhao, Q. Song, W. Liu, and Y. Zhao, “Transient dc bias and current
impact effects of high-frequency-isolated bidirectional dc-dc converter Zhenyu Shan (M’14) received the B.Eng. and
in practice,” IEEE Transactions on Power Electronics, vol. 31, no. 4, M.Eng. degrees in control engineering from Beijing
pp. 3203–3216, April 2016. Jiaotong University, Beijing, China in 2007 and
[85] S. T. Lin, X. Li, C. Sun, and Y. Tang, “Fast transient control for 2009, respectively, and the Ph.D. degree in electrical
power adjustment in a dual-active-bridge converter,” Electronics Letters, engineering from Hong Kong Polytechnic University
vol. 53, no. 16, pp. 1130–1132, 2017. in 2013. He was a visiting student at University of
[86] Y. Tang, X. Li, S. Zhou, C. Sun, and G. Chen, “Comprehensive study Illinois at Urbana-Champaign, U.S. from March to
of fast load modulation with volt-second balance in a dual-active-bridge June in 2013.
converter,” IET Power Electronics, vol. 12, no. 6, pp. 1357–1367, 2019. He was a Postdoctoral Research Fellow at Univer-
[87] C. Sun, X. Li, and S. Zhou, “Transient current control for a step load sity of British Columbia, Vancouver, Canada during
change in a dual-active-bridge converter,” Electronics Letters, vol. 54, November 2013 to June 2016. He was selected into
no. 22, pp. 1290–1292, 2018. Beijing Sea Poly Overseas Young Talent Program at North China University
[88] B. Cui, H. Shi, Q. Sun, X. Tang, L. Hong, and B. Zhao, “A novel of Technology, Beijing, China from 2017 to 2019. He is currently an Assistant
analysis, design, and optimal methodology of high-frequency oscil- Professor and Associate Head of the Department of Electrical Engineering,
lation for dual active bridge converters with wbg switching devices Beihang University, Beijing, China. Dr. Shan is a Professional Committee
and nanocrystalline transformer cores,” IEEE Transactions on Power Member of China Power Supply Society, and serves as a Reviewer for various
Electronics, vol. 36, no. 7, pp. 7665–7678, 2021. IEEE transactions and other international journals on electrical and electronic
[89] Y. Xiao, Z. Zhang, M. A. E. Andersen, and K. Sun, “Impact on zvs engineering. His research interests include modeling and nonlinear control of
operation by splitting inductance to both sides of transformer for 1- power electronic circuits.
0885-8993 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on September 02,2021 at 05:51:33 UTC from IEEE Xplore. Restrictions apply.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2021.3108157, IEEE
Transactions on Power Electronics
IEEE TRANSACTIONS ON POWER ELECTRONICS 24
0885-8993 (c) 2021 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on September 02,2021 at 05:51:33 UTC from IEEE Xplore. Restrictions apply.