This paper focuses on a systematical and indepth analysis of the reactive power and softswitching regions of Dual Active Bridge (DAB) converters with dualphaseshift (DPS) control to achieve high efficiency in a wide operating range. The key features of the DPS operating modes are characterized and verified by analytical calculation and experimental tests. The mathematical expressions of the reactive power are derived and the reductions of the reactive power are illustrated with respect to a wide range of output power and voltage conversion ratios. The ZVS softswitching boundary of the DPS is presented and one more leg with ZVS capability is achieved compared with the CPS control. With the selection of the optimal operating mode, the optimal phaseshift pair is determined by performance indices, which include the minimum peak or rms inductor current. All of the theoretical analysis and optimizations are verified by experimental tests. The experimental results with the DPS demonstrate the efficiency improvement for different load conditions and voltage conversion ratios.
NOMENCLATURE
V_{T1}
magnitude of the transformer primary voltage
v_{T1}
transient value of the transformer primary voltage
V_{T2}
magnitude of the transformer secondary voltage
v_{T2}
transient value of the transformer secondary voltage
I_{S1}
rms current produced by
V_{S1}
I_{L_rms}
rms current flowing through the inductor
L
V_{L_rms}
rms voltage across the inductor
L
Q_{L}
reactive power produced by the inductor
L
I_{peak}
peak current of the inductor
L
I_{peak_min}
minimum value of
I_{peak}
I_{rms_min}
Irms_min minimum value of
I_{L_rms}
I_{peak_min_G}
global minimum value of
I_{peak}
I_{peak_min_L}
local minimum value of
I_{peak}
I. INTRODUCTION
Originally proposed in
[1]
for aerospace power applications, the topology of a dual active bridge (DAB) converter became popular in battery chargers
[2]
, hybrid windphotovoltaic systems
[3]
, solidstate transformers (SSTs)
[4]
, micro grids
[5]
, and hybrid electric vehicles
[6]
. Compared with other isolated dcdc topologies, the DAB converter shows many advantages, such as bidirectional power flow, inherent softswitching capability, power controllability and high efficiency
[7]
.
A DAB DCDC converter typically consists of two full bridges (
B_{1}
and
B_{2}
) that are interconnected through a high frequency transformer
T_{r}
, as shown in
Fig. 1
. The two bridges are composed of the switches of
Q_{11}

Q_{14}
and
Q_{21}

Q_{24}
, respectively. The modulation usually adopted is the conventional phaseshift (
CPS
) technique. The main advantage of the CPS lies in its implementation simplicity because the averaged active power can be directly regulated by the phase shift angle. However, the CPS has the drawbacks of high reactive power and circulating current flowing through the transformer, especially when the voltage of
NV_{T1}
is different from
V_{T2}
, which leads to high conduction losses
[1]
. The DAB converter may also lose the soft switching capability when the voltage conversion ratio deviates from unity
[8]
. However, it is difficult to always fulfill a voltage ratio of 1:1 in practical applications considering the wide operating voltage range of energy storage sources such as batteries or ultracapacitors
[9]
. As a result, the CPS suffers from a low power conversion efficiency due to its high reactive power and hard switching operation
[10]
,
[11]
.
Schematics of dualactive bridge converters.
In order to improve the efficiency of the DAB over a wide operating voltage range, various control algorithms have been proposed. These include a phaseshift plus pulse width modulation (PSPWM) control strategy
[8]
,
[11]

[12]
, triangular modulation (TRM)
[13]
, trapezoidal modulation (TZM)
[14]
and hybrid modulation
[15]
. In addition, the pulseskipping control strategy is also proposed for gridtied converter applications to improve the efficiency for light loads
[16]
. However, the pulseskipping control strategy shows a negative impact on the normal operation of systems
[16]
. The PSPWM is ruled by two manipulated variables, which include the modulation index and the phase shift between the transformer primary and secondary voltages. With PSPWM, the bridge of the DAB converter with dutycycle control varies with the voltage conversion ratio and power flow direction, which increases the implementation complexity
[7]
. Furthermore, the proposed PSPWM with negative values of phase shift shows only half of the attainable maximum output power compared with that of the CPS
[8]
. The TRM and TZM focus on minimizing the current of the switching devices at the turnoff instant to reduce the switching loss. However, they might increase the rms current stress on the transformer and can only be adopted for a limited operating range. Hybrid modulation switches the modulation strategies among the TRM, TZM and CPS with respect to different operation stages. The hybrid modulation has a complicated implementation because various strategies are involved and the operating status of the converter needs to be monitored in real time.
A dualphaseshift (DPS) control is proposed to eliminate the reactive power and then minimize the conduction losses of the DAB converters for electric vehicle applications
[17]
. In
[7]
, various control strategies are compared in terms of maximum output power, efficiency, ZVS range and practical control. The conclusion of this reference is that the “DPS control may be relative optimal method for the largescale practical application from the implementation difficulty and performance.” However, an experimental comparison is conducted in
[18]
to evaluate the performance of both the CPS and the DPS. It shows that the efficiency improvement using the DPS is not as good as expected. The effect of the DPS in in terms of efficiency improvement is also undervalued in other studies
[6]
,
[8]
,
[19]
,
[20]
. The possible reasons may include:
1)
The operating modes of the DPS
: there are four operating modes with respect to the characterization of the phaseshift pairs. The power characteristics of these operating modes are difference. The optimal operating modes must be determined while considering the voltage conversion ratio and load conditions.
2)
Softswitching range
: the performance characteristic of the DAB converter, especially the softswitching range with the DPS, should be presented while considering applications with variable loads.
3)
The quantitive comparison of the reactive power reduction with the DPS
: considering the complexity of the DPS, the analysis of the reactive power in
[17]
only focuses on one special operation condition. However, more general expressions should be given for various operating conditions and the illustration of the reactive power reduction with different operating modes should be provided quantitatively.
4)
The complexity for implementation
: the study in
[6]
demonstrates that the 2D solving problem of the DPS, which is regarded as too complex to be optimized when compared with 1D PWM strategies. However, like PSPWM
[10]
, the efficiency optimization with the DPS is essentially a 1D problem.
In this paper, the reactive power and zero voltage switching (ZVS) softswitching capability of DAB converters with DPS are analyzed. Section II presents a power flow analysis of the DPS and its four operating modes. In section III, the features of the four operating modes are defined to determine the optimal one while considering practical operating conditions. Section IV shows the experimental results, which reveal that the DPS can expand the ZVS operating range and enhance the overall efficiency.
II. POWER FLOW ANALYSIS WITH DPS
DPS manipulates two phase shifts, where
D_{1}
symbolizes the phase shift between the diagonal control signals in the same bridge, for instance, between the gate signals of
Q_{11}
and
Q_{14}
, and
D_{2}
is the phase shift between the primary and the corresponding secondary gate signals, for instance, between the gate signals of
Q_{11}
and
Q_{21}
. All of the switching devices using DPS are operated at a 50% dutycycle, which is consistent with the CPS. Various operating conditions exist in DPS with respect to the power flow direction and buck/boost operation. In the forward mode, the transformer primary voltage
v_{T1}
leads the transformer secondary voltage
v_{T2}
so that power flows from
V_{S1}
to the load. When
v_{T1}
lags
v_{T2}
, the DAB operates in the backward mode, where the power flow is transferred from right to left. The voltage conversion ratio
d
is defined as:
When the DPS operates in the boost condition (
d
> 1 ), the main waveforms with four operating modes are shown in
Fig. 2
, where
β
corresponds to the zero crossing instant of the inductor current
i_{L}
, and
δ
_{1}
~
δ
_{3}
represent the switching angles. The meaning of
v_{T1}
,
v_{T2}
and
I_{S1}
are defined in
Fig. 1
, and their definitions are also explained in the nomenclature. The blue line
i
_{B}
_{1}
indicates the transient current to bridge
B_{1}
, which corresponds to the positive part of the transformer primary voltage
v_{T1}
. The red line
I_{S1}
represents the current produced by voltage source
V_{S1}
. Considering that the variation of the input voltage is small, the current in capacitor
C_{1}
can be neglected. Thus, the relationship between
i_{B1}
and
I_{S1}
can be expressed as:
Operating modes and typical waveforms of the DAB converter with DPS in the boost operation condition. (a) DPS_I: (D_{2}>D_{1}) ˄ (D_{2}+D_{1}≥1). (b) DPS_II: (D_{2}>D_{1}) ˄ (D_{2}+D_{1}<1). (c) DPS_III: (D_{2}≤D_{1}) ˄ (D_{2}+D_{1}<1). (d) DPS_IV: (D_{2}≤D_{1}) ˄ (D_{2}+D_{1}≥1)
To analyze the optimal operating mode,
I_{S1}
is kept constant in
Fig. 2
, which represents the same output power. The reactive power of each operating mode, which is represented by the dark shaded area in
Fig. 2
, for both the input and output sides, is examined and compared. The peak current is marked with a square to symbolize the power transfer features of each mode. With the dynamics of
i_{L}
, shown in
Fig. 2
, the analytical expressions of the current
i_{L}
at the switching angles
δ
_{1}
,
δ
_{2}
,
δ
_{3}
and
π
for each operating mode of the DPS can be derived and are shown in
Table I
. Due to the boost operation, the inductor current at the initial condition,
i_{L}
(0), is larger than zero for DPS_III and DPS_IV. The average output power
P_{o}
, the inductor rms current
I_{L_rms}
, and the inductor peak current
I_{peak}
, for the four operating modes are derived accordingly and shown in
Table II
. All of the quantities shown in
Table I
and
Table II
are normalized by the following base values:
where,
f_{s}
is the switching frequency, and the variables
V_{S1}
,
f_{s}
and
L_{s}
only affect the magnitude of
P_{o}
. The phaseshift pair of
D_{1}
and
D_{2}
solely determines the operating modes and the amount of output power.
EXPRESSIONS OF CURRENT AT THE SWITCHING ANGLES WITH DPS (PU)
EXPRESSIONS OF CURRENT AT THE SWITCHING ANGLES WITH DPS (PU)
EXPRESSIONS OF AVERAGE OUTPUT POWER, INDUCTOR RMS CURRENT AND PEAK CURRENT (PU)
EXPRESSIONS OF AVERAGE OUTPUT POWER, INDUCTOR RMS CURRENT AND PEAK CURRENT (PU)
III. IMPLEMENTATION OF THE DPS CONTROL
 A. Optimal Operating Mode
The optimal operating mode of the DPS should be determined with regard to the voltage conversion ratio and the output power range. Four distinct operating modes exist and their main features must be grasped. In this section, these major features are defined and summarized as follows.
1)
The Ratio of the Reactive Current
: The percentage of reactive current at both the output and input sides are considered. For DPS_III and DPS_IV in the boost operation, the initial inductor current meets
i_{L}
(0)≥0 according to
Table I
. Thus, the reactive power at the input side is zero for the boost operation because the phase of the inductor current
i_{L}
is always the same as the transformer primary voltage
v_{T1}
, as shown in
Fig. 2
(c) and
Fig. 2
(d). Without the reactive current, the conducting current is largely reduced.
2)
The Overlap of v_{T1} and v_{T2}
: With the DPS, both the transformer primary voltage
v_{T1}
and the secondary voltage
v_{T2}
show three levels, including positive, zero, and negative. The period that
v_{T1}
and
v_{T2}
have the same polarity such as positive, is defined as the overlap of
v_{T1}
and
v_{T2}
. It is desirable to constrain the change rate of the inductor current,
i_{L}
, and to reduce the current peak due to voltage cancellation.
3)
The Circulating Current
: The circulating current exists when both
v_{T1}
and
v_{T2}
are zerolevel. Two devices with the same position in a bridge (upside or downside) are conducting for this period. There is no energy transferred between the input, the output and the leakage inductance in the circulating period. However, this increases the rms current without any change in the delivered power. In particular, for DPS_I and DPS_IV, the rms current will be significantly increased because the circulating current is the inductor peak current.
4)
The Duration of
v_{T1}
and
v_{T2}
: With the DPS, the duration of
v_{T1}
and
v_{T2}
with positive voltages are same for all of the operating modes and expressed as (1
D_{1}
). However, the range is different for each operating mode according to the corresponding combination of phaseshift pairs. For DPS_IV, the duration of
v_{T1} and v_{T2}
is the shortest. Thus, both its rms and peak current are high.
Table III
illustrates a comparison of the four operating modes with the DPS in terms of the defined features. Both DPS_II and DPS_III are good candidates for the optimal operating mode according to this tradeoff. However, considering that the circulating current can be tuned to zero by the selection of the phaseshift pairs for DPS_III and it is difficult to reduce the reactive power a lot with DPS_II, DPS_III is selected as the optimal operating mode. This tradeoff result, which is based on the aforementioned features, will be verified by analytical calculations and experimental tests in the following sections.
COMPARISON OF THE OPERATING MODES WITH REGARD TO THE DEFINED FEATURES
COMPARISON OF THE OPERATING MODES WITH REGARD TO THE DEFINED FEATURES
 B. Determination of the PhaseShift Pairs
With the selection of the optimal operating mode while considering the output power range, the optimal phaseshift pair should be determined based on performance indices. In this paper, the inductor rms current
I_{L_rms}
and the inductor peak current
I_{peak}
are chosen as the performance indices because
I_{peak}
is linked with the switching losses and
I_{L_rms}
largely determines the conducting losses and transformer losses. The mathematical expressions for the four operating modes of the DPS are shown in
Table II
. The constraint condition in the optimization process is the average output power
P_{o}
. The expressions shown in
Table II
indicate that the performance indices vary with the phaseshift pair and voltage ratio. Considering that the voltage ratio is a given parameter and not a controllable variable, only the phaseshift pairs can be tuned to optimize these performance indices with the constraint of the output power requirement.
Taking the operation of the DPS_III as example to illustrate the process of determining the optimal phaseshift pairs, the inner phaseshift variable
D_{1}
can be expressed as (4), which is a function of the transferred power flow.
The output power with the DPS is symmetrical with
D_{2}
=0.5, and the performance indices of both the peak current
I_{peak}
and the rms current
I_{L_rms}
are lower in the range of
D_{2}
≤0.5 when compared with the other range. Thus, the range of the outer phaseshift variable is set to vary between 0 and 0.5.
The trajectory of the phaseshift pair can be obtained to achieve either the minimum peak current
I_{peak_min}
or the minimum rms current
I_{rms_min}
. Two kinds of minimum points exist in the optimization process: one is the global minimum point for the whole range and the other is the local minimum point with respect to the range of the phaseshift pairs for each operating mode. Taking the minimum peak current point as an example, with the optimal point of the phaseshift pair, the output power plane and the peak current plane should be met at the global minimum peak current
I_{peak_min_G}
. Thus, the gradients of the output power and the performance index of the inductor peak current should be parallel in
D_{1}
and
D_{2}
coordination. The corresponding expression is shown as:
The expression for the optimal phaseshift pair to achieve the global minimum peak current (
D_{1_Ipeak_min_G}
,
D_{2_Ipeak_min_G}
) can be obtained as:
As shown in this expression, the determination of the optimal phaseshift pair with the DPS is a 1D optimization problem, which is similar to the PSPWM shown in
[10]
.
The local minimum peak current
I_{peak_min_L}
can also be determined by the following numerical equation:
Similarly, the minimum rms current
I_{rms_min}
can be determined by the analytical calculation and numerical equation (8). The phaseshift trajectory for the minimum rms current is obtained from lookup tables because it is extremely complex to calculate online.
Fig. 3
shows the optimal trajectory of the phaseshift pair for the performance indices of the minimum peak current and the minimum rms current with d=2. The red dashed line indicates the phaseshift pairs corresponding to the minimum rms current, and the blue solid line shows the phaseshift pairs corresponding to the minimum peak current. In order to distinguish the global and local optimal phaseshift points, the local optimal phaseshift points
I_{peak_min_L}
and
I_{rms_min_L}
are marked with square and star symbols, respectively.
Fig. 3
indicates that the phaseshift trajectories corresponding to the minimum peak current and the minimum rms current are different.
The optimal trajectory of the phaseshift pair for the minimum peak current (I_{peak_min}) and the minimum rms current (I_{rms_min}) with DPS_III and the meaning of different types of lines and marks representing I_{peak_min_G} (solid blue line), I_{peak_min_L} (solid blue line with square marks), I_{rms_min_G} (dashed red line) and I_{rms_min_L} (dashed red line with star marks) respectively.
IV. CHARACTERISTIC ANALYSIS WITH DPS
 A. SoftSwitching Range of DPS
In order to realize ZVS softswitching operation, the inductor current zero crossing instant should be arranged within the time interval with the voltages
v_{T1}
and
v_{T2}
having the opposite polarities
[8]
,
[10]
,
[21]
,
[22]
. Thus, the inductor current
i_{L}
at different switching angles must fulfill the following inequalities, which are shown in
TABLE IV
. The resultant boundaries of the softswitching region for each operating mode are also derived.
SOFTSWITCHING RESTRICTIONS AND BOUNDARIES WITH DPS
SOFTSWITCHING RESTRICTIONS AND BOUNDARIES WITH DPS
Following the derived expressions in
Table IV
, the ZVS conditions for each phase leg can be illustrated in
Fig. 4
, which shows the corresponding boundaries of the four phase legs versus the operating mode of the DPS and the voltage conversion ratios. The 4bit binary numbers represent the availability of ZVS for each phase leg, from left to right, in the DAB topology, which is shown in
Fig. 1
. When compared with the CPS (
D_{1}
=0), the range with ZVS for the four phase legs has been extended by using the DPS. With the two phaseshift variables,
D_{1}
and
D_{2}
, the DPS is expected to increase the number of phase legs with the ZVS capability. For instance, as shown in
Fig. 5
(c), with the CPS, the ZVS condition is “0011” when
D_{2}
is less than the boundary of “(d1)/(2d)” for the boost operation, while the ZVS conditions can be regulated to “0111” by properly selecting the phaseshift pairs using the DPS.
ZVS softswitching boundaries for four phase legs with respect to the operating modes of DPS and voltage conversion ratios.
Softswitching regions of DAB converter as a function of d and I_{o} [p.u.] with R as parameter. A) Softswitching region using CPS; B)  Softswitching region using the DPS; C)  Hardswitching region using the DPS.
Fig. 5
shows the characteristics of the voltage conversion ratio of the DAB converter versus the output current. The
R
parameter, shown with the dashdot line, represents the normalized load, and the normalized output current
I_{o}
[p.u.] can be expressed as (9) for DPS_II.
The boundaries of the softswitching region with the DPS_II control are illustrated in
Fig. 5
, where the continuous red line represents the boundary for the ZVS softswitching capability with DPS_II. They are obtained by evaluating (9) with “
D_{2}
=
D_{1}
=(
d
1)/(
d
+1)” if
d
>1 or with “
D_{2}
=
D_{1}
=(1
d
)/(
d
+1)” if
d
<1 . The softswitching region with the CPS control is also illustrated with the continuous black line. The different softswitching regions in the twodimensional
d

I_{o}
plane are marked with “A”, “B”, and “C”. The meaning of these marks are given in the captions of
Fig. 5
. When compared with one pattern of the PSPWM, which adopts a positive phaseshift angle, the DPS has a wider range when the voltage conversion ratio is far from unity (
d
>2). However, the DPS cannot extend the region under softswitching into the whole operation range, as shown in
[8]
, by using another pattern of PSPWM, which adopts a negative phaseshift angle. In addition, a ZVS region at zero loads is also achieved by using the DPS.
 B. Reactive Power Minimization
In this paper, the reactive power is defined as in
[8]
,
[23]
and
TABLE V
shows the reactive power expressions for the different operating modes of the DPS.
REACTIVE POWER FOR DIFFERENT OPERATING MODES OF DPS
REACTIVE POWER FOR DIFFERENT OPERATING MODES OF DPS
The reactive power with the CPS and various operating modes of the DPS with regard to the phaseshift angle
D_{2}
and various voltage conversion ratios
d
are illustrated in
Fig. 6
for the condition of a lowpower (
P_{o}
[p.u.] = 0.1). The reactive power with the CPS is also presented as a benchmark. The different types of lines are defined as follows:
CPS
(green line),
DPS_I
(magenta line),
DPS_II
(black line),
DPS_III
(red line) and
DPS_IV
(blue line).
Comparison of reactive power with CPS and various operating modes of DPS with regard to the phaseshift angle D_{2} and various voltage conversion ratios d under the condition of lowpower (P_{o} [p.u.] = 0.1).
As shown in
Fig. 6
, for lowpower applications, the DPS can reduce the reactive power in a wide range of voltage conversion ratios. Specifically, all of the operating modes of the DPS can reduce the reactive power in the case of “
d
=0.5”. Three modes of the DPS show improvement in the case of “
d
=1.8”, and two modes show improvement in the other cases. The effective range of the outer phaseshift angle
D_{2}
in reactive power reduction also changes with the voltage conversion ratio
d
. As shown in
Fig. 6
, the effective ranges of
D_{2}
in terms of reactive power minimization can be specified as (0, 0.8), (0.02, 0.1), (0.02, 0.2) and (0.02, 0.5) corresponding to the following values of
d
: 0.5, 0.8, 1.5, and 2. The operating modes of both DPS_II and DPS_III show improvement for all the considered cases. However, when considering the practical range of
D_{2}
in the control implementation, DPS_III is selected as the optimal operating mode for lowpower applications.
 C. Comparison of the Performance Indices
All four of the operating modes with the DPS are considered in the comparison of the performance indices, which include the inductor peak current and rms current. The phaseshift pairs are determined with the methods discussed above. The main parameters for the comparison are shown as follows:
L_{s}
=1.73uH,
f_{s}
=100 kHz,
P_{o}
=25~250W, and the input voltage
V_{in}
is 20V for boost operation and 40V for buck operation.
Fig. 7
illustrates the comparison results of the performance indices. The optimization target of the minimum inductor peak current and the minimum rms current are considered for all of the operating modes with the DPS. The benchmark is the peak and rms current with the CPS. Based on a comparison of the performance indices, which have been optimized for each operating mode, some conclusions can be made and summarized as follows.
Performance comparison of DAB converter with optimization target of the minimum inductor peak current (top) and the minimum rms current (bottom) considering all operating modes with DPS for the boost operation (d=1.5, 2); the meaning of different types of lines and marks representing CPS (solid black line with xmarks), DPS_I (dashed cyan line with star marks), DPS_II (dashed blue line), DPS_III (dashed black line with square marks) and DPS_IV (dashed magenta line) respectively.
1)
DPS with CPS
: Theoretically, any performance aspect with the DPS should be better than that with the CPS control because an extra phase shift angle has been provided as another degree of freedom. However, as shown in
Fig. 7
(c), the rms current with DPS_I is higher than the benchmark for the whole range of
P_{o}
. In addition, the performance of the rms current with DPS_IV also deteriorates for a majority of the operating range.
2)
Operating Mode of DPS
: For the majority of the operating range, DPS_III shows the best performance irrespective of the optimization target. This result is also consistent with the analysis of the power transfer features, which is shown in Section 3A. DPS_IV shows the minimum rms current for a small zone of the operating range. However, both the peak current and the rms peak of DPS_IV increased sharply with the output power due to the short duration of the effective power transfer interval. For DPS_I, the performance, especially the rms current, is worse than that of the CPS control. DPS_II, always shows a slightly better performance than the CPS and it can be used for highpower applications.
3)
Optimized Target
: With the minimum peak current as the optimization target, the improvement with DPS is clear and the effective range is also wide, which shows the advantages of the DPS in minimizing switching loss.
4)
Voltage Conversion Ratio
: The effect of the DPS is clear when the voltage conversion ratio
d
is far away from unity. The average reduction of the peak current with DPS_III is 17.6% when
d
=1.5.
5)
Output Power Range
: the effect of the DPS is clear for lightload operation. The reduction of the peak current with DPS_III is 9.7% when
P_{o}
=150W, while the corresponding reduction with the same mode is 51.9% when
P_{o}
=25W.
V. EXPERIMENTAL RESULTS
A DAB converter is designed and constructed to verify the analysis and optimization with the DPS. The specifications of the prototype are summarized in
Table VI
. The ferrite core model is RM143F3, and Litz wires are used for the windings so as to minimize the losses resulting from skin and proximity effects. The digital control algorithm is implemented with a TMS320F2808 DSP. In the test, the phaseshift pair is determined by achieving the minimum inductor peak current, and a twoinput table was adopted as the phaseshift pair reference. Power MOSFETs (PSMN5R560YS and STB13NM60N) are adopted as devices for the primary and secondary Hbridges of the DAB converter, respectively.
PARAMETERS OF THE DAB CONVERTER PROTOTYPE
PARAMETERS OF THE DAB CONVERTER PROTOTYPE
 A. Experimental Waveforms of the Operating Modes
TABLE VII
summarizes the measured results and compares the CPS with the different operating modes of the DPS, which are under the same test conditions in regards to the output power, input voltage, and load resistance. In this test, the boost operation with
d
=1.8 is tested for the DAB prototype. The peak and rms values of the inductor current are measured and shown in
TABLE VII
, which corresponds to the CPS and the different operating modes of the DPS. The inductor peak and rms currents with DPS_III are dramatically reduced and the efficiency is 14% higher than that of the CPS control. These results support the theoretical analysis, which is described in Section 3A. The experimental tests also indicate the importance of determining the optimal operating mode for the DPS since DPS_I shows a lower efficiency than the CPS.
EXPERIMENTAL COMPARISON OF DIFFERENT OPERATING MODES
EXPERIMENTAL COMPARISON OF DIFFERENT OPERATING MODES
Fig. 8
also shows steadystate experimental waveforms of the primary voltage
v_{T1}
, secondary voltage
v_{T2}
and inductor current
i_{L}
under the CPS and the various operating modes of the DPS for the same output power, 50W. In
Fig. 8
, the measured peakpeak value of
i_{L}
using DPS_III is reduced from 44.8A to 27.2A, which results in lower switching losses. The rms value of
i_{L}
is also reduced from 10.9A to 7.83A, which corresponds to reductions of the conduction losses and transformer losses.
Experimental waveform of v_{T1}, v_{T2}, and i_{L} using the CPS and different operating modes of DPS to deliver the same output power of 50W with d=1.8. (a) CPS. (b) DPS_II. (c) DPS_III. (d) DPS_IV.
Fig. 9
shows the experimental waveforms of
v_{T1}
,
v_{T2}
, and
i_{L}
using the CPS and DPS_III to deliver the same output power of 200W. The measured efficiency is improved from 88.9% with the CPS to 90.2% with DPS_III.
Experimental waveform of v_{T1}, v_{T2}, and i_{L} using the CPS and DPS_III to deliver the same output power of 200W with d=1.8. (a) CPS. (b) DPS_III.
Fig. 10
shows the ZVS condition of the primary side leg switch,
Q_{14}
, for “
P_{o}
=100W” and “
d
=1.8”. It is easy to find that the ZVS condition is achieved for the
Q_{13}
,
Q_{14}
leg of the primary side, which shows that the DPS will help to increase the number of legs with ZVS performance, as shown in
Fig. 10
(c).
Experimental waveform of ZVS condition for Q_{13}, Q_{14} leg of the primary side. (a) CPS. (b) DPS_III.
 B. RMS Current and Efficiency Comparison
Fig. 11
shows the experimentally measured DAB converter rms current and the summation of the current at the switching angles, versus the delivered power, for two values of
d
: 1.4 and 1.8. It covers a wide output power span, from 10% to 100% of the maximum output power
P_{omax}
. The performance of the CPS is used as a benchmark for the comparison. It can be observed in these figures that DPS_III has apparent advantages over the CPS especially in the cases of a higher voltage conversion ratio and a low power.
Measured DAB converter rms current (top) and summation of the current at the switching angles (bottom) versus the delivered power for different voltage conversion ratio and two control strategies: CPS (dashed black line with circle marks) and DPA_III (solid magenta line with diamond marks).
Based on the parameters of the prototype shown in
Table VI
, the estimated power loss distribution of the prototype with
P_{o}
=50W using the two control strategies of CPS and DPS_III is calculated and shown in
Fig. 12
. DPS_III shows distinguishable advantages in terms of the loss reductions in every aspect, including the lowvoltage side MOSFET conduction
P_{low_con}
and switching losses
P_{low_sw}
, the highvoltage side MOSFET conduction
P_{high_cond}
and switching losses
P_{high_sw}
, the losses of transformer
P_{mag_tr}
, the losses of inductor
P_{mag_L}
and other losses including the parasitic resistor losses. It can be found that the conduction losses make up the dominant part of the loss distribution. From the analysis and experiments, DPS_III effectively minimizes the conducting current by reducing the reactive power. As a result, the losses of
P_{low_con}
,
P_{high_cond}
,
P_{mag_tr}
, and inductor
P_{mag_L}
are reduced. The realization of one leg with ZVS softswitching in the lowvoltage side also contributes to the reduction of
P_{low_sw}
, which represents the most significant part in the power loss minimization.
Comparison of loss breakdown distribution with CPS and DPS_III.
Fig. 13 shows experimental efficiency curves using the CPS and DPS_III versus the output power with two different voltage conversion ratios of
d
=1.4 and
d
=1.8. Using the CPS, the efficiency drops remarkably when the delivered power is reduced for both conversion ratios, as shown in Fig. 13. This is mainly due to the increase of reactive power and circulating current using the CPS. However, the efficiency using the DPS remains at a relatively high value even for very lowpower conditions, showing up to 15% higher than that measured with the CPS for the lowest output power.
VI. CONCLUSIONS
The conventional phaseshift (CPS) control for the DAB suffers from low efficiency under the conditions of light loads and wide voltage conversion ratios. This results from the loss of ZVS and the induced significant reactive power when the voltage ratio deviates from unity. Based on the DualPhaseShift (DPS) control, this study provides an indepth analysis and optimization method to enhance the conversion efficiency by minimizing the reactive power and by extending the ZVS softswitching region. The key features of the four operating modes with the DPS are characterized to determine the optimal mode for improving conversion efficiency. The mathematical expressions of the reactive power for each mode are obtained and the performance in terms of reactive power reduction is illustrated with respect to a wide output power range and voltage conversion ratio. The ZVS softswitching boundary of the DPS is also obtained and compared with that of the CPS control. With the determined optimal operating mode, the peak and rms values of the inductor current are mathematically derived and adopted as the performance indices to find the optimal phaseshift pairs.
A prototype of a DAB converter was built to verify the theoretical analysis with the DPS. The experimental results reveal that the DPS has the capability of extending the ZVS softswitching range and minimizing the reactive power for a wide operating range. The control implementation of the DPS demonstrates the efficiency improvement for every aspect of the load conditions and the voltage conversion ratios. In the case of low power, which is 10% of the rated capacity, a 15% efficiency improvement is observed when compared with the CPS control.
Acknowledgements
This research was supported by University Research Development Fund (RDF1224), Jiangsu Province University Natural Science and Research Program (13KJB470013), and the National Nature Science Foundation of China (5140070155).
BIO
Huiqing Wen received his B.S. and M.S. degrees in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2002 and 2006, respectively. He received his Ph.D. degree in Electrical Engineering from the Chinese Academy of Science, Beijing, China, in 2009. From 2009 to 2010, he was an Electrical Engineer working with the GE (China) Research and Development Center Company, Ltd., Shanghai, China. From 2010 to 2011, he was an Engineer at the China Coal Research Institute, Beijing, China. From 2011 to 2012, he was a Postdoctoral Fellow at the Masdar Institute of Science and Technology, Abu Dhabi, United Arab Emirates. He is presently a Lecturer at Xi’an JiaotongLiverpool University, Suzhou, China. His current research interests include bidirectional DCDC converters, power electronics in flexible ac transmission (FACTS) applications, electrical vehicles (EVs), and high power threelevel electrical driving systems.
Bin Su was born in Wenzhou, China, in 1981. He received his Ph.D. degree in Electrical Engineering from Zhejiang University, Hangzhou, China, in 2010. He has authored or coauthored nine published technical papers. His current research interests include topologies, modeling and control in power electronics.
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