Dehong Xu ,Member,IEEE ,Chuanhong Zhao ,Student Member,IEEE ,and Haifeng Fan
Abstract—A pulse-width modulation (PWM)plus phase-shift control bidirectional dc–dc converter is proposed.In this converter,PWM control and phase-shift control are combined to reduce cur-rent stress and conduction losses,and to expand ZVS range.The operation principle and analysis of the converter are explained,and ZVS condition is derived.A prototype of PWM plus phase-shift bidirectional dc–dc converter is built to verify the analysis.Index Terms—Bidirectional dc–dc converter,conduction loss,phase-shift,pulse-width modulation.
I.I NTRODUCTION
B
IDIRECTIONAL dc–dc converters will be widely used in applications such as dc uninterrupted power supplies,aerospace power systems,electric vehicles and battery chargers.In order to minimize the size and weight of the converters,switching frequency must be increased.But the increase of switching frequency results in higher switching losses.There are many techniques to solve this problem.Some circuits use resonant,quasiresonant,and/or multi-resonant techniques [1]–[3].However,voltage or current stresses in these converters are higher and require the devices of higher V A rating.Some circuits use passive snubbers or active clamp techniques [4].However,these converters become more complicated.Phase-shift ZVS technique has been used in bidirectional dc–dc converters since it can realize ZVS for all switches without auxiliary switches [5],[6].However,when the amplitude of input voltage is not matched with that of output voltage,the current stresses and RMS currents of the converters become higher.In addition the converters can not achieve ZVS in light-load condition.
Fig.1is a phase-shift (PS)bidirectional dc–dc converter [7].There are two switches on both sides of the isolation trans-former.
Switch
and are controlled complementarily.
Switch
and are also controlled complementarily.Duty cycles of the switches are kept in 0.5.The
inductor is used as the main energy transfer element.Fig.1is simplified as Fig.2(a).Fig.3(a)shows the corresponding waveforms of the simplified circuit when the amplitude of equivalent input
voltage is equal to that of equivalent output voltage
Manuscript received December 10,2002;revised October 6,2003.This paper was presented at the APEC’03Conference,Miami Beach,FL,February 2003.This work was supported by the Delta Power Electronics Science and Education Development Fund and the Foundation for University Key Teacher by Ministry of Education of China.Recommended by Associate Editor Y .-F.Liu.
The authors are with the Department of Electrical Engineering,Zhejiang Uni-versity,Hangzhou 310027,China (e-mail:xdh@cee.zju.edu.cn).Digital Object Identifier
10.1109/TPEL.2004.8285
Fig.1.Phase-shift bidirectional dc–dc
converter.
(a)
(b)
Fig.2.(a)Simplified circuit of PS control.(b)Simplified circuit of PPS
control.
,that
is ,
where is the turn ratio of the isolation transformer.When the amplitude of equivalent input
voltage is not equal to that of equivalent output
voltage ,such
as ,Fig.3(b)shows the corresponding waveforms.The current stresses and RMS
0885-93/04$20.00©2004IEEE
(a)
(b)
(c)
Fig.3.(a)PS control when V =2=NV .(b)PS control when V =2=NV .(c)PPS control when V =2=NV .
currents of the converter become much higher and the reactive power transferred also increases,which leads to higher current stresses of the switch devices and higher conduction losses.The converter can not achieve ZVS in light-load condition.This paper proposes a PWM plus phase-shift (PPS)control bidirectional dc –dc converter.Fig.2(b)shows concept of PPS control bidirectional dc –dc converter.The PWM control of duty cycles acts as an electric transformer between equivalent input
voltage and equivalent output
voltage ,so that both positive and negative amplitudes of equivalent input
voltage
are equal to those of equivalent output
voltage .Fig.3(c)shows the corresponding waveforms of the simplified circuit of PPS control bidirectional dc –dc converter.Compared with PS control,PPS control can reduce the current stresses and RMS currents of the converter.The losses of the converter can also decrease.Later,it will be proved that the converter can achieve ZVS in larger load variation.
II.O PERATION P RINCIPLE OF PPS C ONTROL C ONVERTER To simplify the analysis,the operation of PPS control con-verter is explained with the following assumptions.1)The converter has reached steady state.
2)All switch devices are assumed as ideal switches with parallel body diodes and parasitic capacitors.3)The
inductance is composed of the leakage inductance of the transformer and additional series inductance.4)The values of the
capacitors ,
and are so large that the voltage ripples across them are small.
5)The resonant frequency of capacitor (composed
of
,
and )
and is much lower than the
switching frequency of the converter.
Duty cycles
of
and
are ,and duty cycles
of
and are
1-.In the forward mode,the gate drive signals
of
and is leading to those
of
and so that power flows
from
to .The equivalent circuits and key waveforms in the forward mode are shown in Figs.4and 5,respectively.The switching cycle can be divided into eight stages which are explained as follows.1)Stage
1:Just
before is turned
off.is on.The
current is in positive direction.The capacitor in par-allel
with is charged,while the capacitor in parallel
with is discharged.The voltage
across decreases to zero
at
and ’s body diode starts to
conduct.is turned on with ZVS and then works as a synchronous rectifier.The voltage
across
is clamped
at .The current slopes
of
is
(1)
where are average voltages
of ,
and ,respectively.2)Stage 2
:is turned off at .The capacitor in parallel
with is charged linearly by the
current and the capacitor in parallel
with is discharged.The stage terminates at ,while the voltage
across is zero.3)Stage
3
:’s body diode starts to conduct at .
Then is turned on in zero-voltage condition.The current
Fig.4.Operation stages of the converter in the forward
mode.
decreases linearly and its direction is changed from positive to negative.The slope
of
is
(2)
4)Stage
4:
At is turned off.The capacitor in parallel
with is charged and the capacitor in parallel
with
is discharged linearly.At the end of this stage,the voltage
across decreases to zero.5)Stage
5:The body diode
of is conducting at the beginning of this stage.
Therefore is turned on in zero-voltage condition.The slope
of
is
(3)
6)Stage
6
:
At is turned off.The capacitor in parallel
with is charged and the capacitor in parallel
with
is discharged linearly.At the end of this stage,the voltage
across goes down to zero.7)Stage
7:At the beginning of this stage,the body diode
of is conducting
and is turned on in zero-voltage condition.The slope
of
is
(4)
8)Stage
8:
At is turned off.The capacitor in parallel
with is charged and the capacitor in parallel
with
is discharged linearly until the voltage
across reaches zero.
After ,the next switching cycle starts again.
Fig.5.Steady-state waveforms of the converter in the forward mode.
On the contrary,in the backward mode,the gate drive sig-nals
of
and are leading to those
of
and .The equivalent circuits and key waveforms in the backward mode are shown in Figs.6and 7,respectively.The switching cycle can also be divided into 8stages.The principle of operation of the backward mode (power flows
from
to )is sim-ilar to that of the forward mode,so it will not be explained in this paper.
III.A NALYSIS OF C ONVERTER
A.Low-Frequency Average Model
We
use
to represent one switching
cycle.is the phase shift between two cells,which are connected by the
transformer.is defined to be positive
when is leading
to in phase.The duty cycles
of
and
are ,and duty cycles
of
and are
1-.
PWM control is used to regulate the positive amplitude of equivalent input voltage to be equal to that of equivalent output voltage and at the same time the negative amplitude of equiva-lent input voltage is regulated to be equal to that of equivalent output voltage.Hence the slope of the
current is zero in stage 1and stage 5.In other words,the duty cycles
of
and
are
(5)
Referring to the Appendix A,the power flows
from
to
under PPS
control
(6)
where is operation period.
Referring to the Appendix B,the current stress of
inductor under PPS
control
(7)
where
.
The power flows
from
to
under PS control
[7]
(8)
The current stress of
inductor
under PS control
[7]
(9)
B.Current Stress Comparison
Fig.8shows current stress of
inductor under PS control in the following
conditions:
Vdc,Vdc
–
Vdc,
W,switching
frequency kHz,
inductance H
–H.From Fig.8we can see that the smaller the value of
inductance is,the lower current stress is when output voltage is 24V .In other words,input voltage and output voltage match.On the contrary,when input voltage and output voltage do not match,such as output voltage is 30V ,the smaller the value of
inductance is,the higher current stress is.It is difficult to design the value of
inductance when two aspects above are considered.
Here a method to optimize the value of
inductance is pro-posed.Current
stress is averaged within the range of output voltage.Average current
stress is used to determine the value of
inductance
(10)
The variation of average current stress under PS
control,,as a function of value of
inductance is plotted in Fig.9(a)from which we can find that average current
stress is min-imum when the value of inductance is
4.4H.Fig.9(b)shows average current stress under PPS control versus value of induc-
tance .But we are hardly to find the minimum average cur-rent stress since the smaller value of inductance is,the lower
Fig.6.Operation stages of the converter in the backward mode.
average current stress is.But the smaller value of
inductance is,the smaller the phase-shift angle is,and the more difficult the converter is,is controlled.Here we assume the minimum phase-shift angle is 20.Value of
inductance under PPS con-trol is given in previous
conditions
(11)
Fig.10(a)shows current stress of
inductor under PS control and under PPS control in the following
conditions:
Vdc,Vdc
–
Vdc,
W,switching
frequency kHz,
inductance H
–H.From it we can see that PPS
control can reduce current stress except that the value of the
inductance
is large enough.Pspice simulation results and calculation results derived from (7)under PPS control,Pspice simulation results and calcula-tion results derived from (9)under PS control are compared in Fig.10(b).From it we can see that the Pspice simulation traces and calculation results are in a good agreement,PPS control can reduce current stress.C.ZVS Range Comparison
The ZVS range under PS control is
[7]
(12)
Fig.7.Steady-state waveforms of the converter in the backward
mode.
Fig.8.Current stress versus output voltage and inductance L under PS
control.
Fig.11shows ZVS range under PS control.
Referring to the Appendix C,the ZVS range under PPS control
is
(13)
Fig.9.Average current stress versus value of inductance L .(a)PS control.(b)PPS control.
In other words,the converter under PPS control can maintain ZVS in larger load variation.Hence PPS control can expand ZVS range.
IV .E XPERIMENTAL R ESULTS
Fig.12shows the system block diagram of the proposed con-verter.UC3875generates signal g1and signal g2.Signal g1has leading phase according to the error signal of command power (Po*)and actual power (Po)to signal g2.Signal g1and signal g2connect to UC3525respectively.Signal g1has the same phase
as and signal g2has the same phase
as .The
signal modulates the duty cycles
of
and .By
inverting
and ,we can get other two gate signals.A prototype of PPS control bidirectional dc –dc converter is built to verify the analysis.Experiments are performed in the following
conditions:
Vdc,Vdc
–
Vdc,
H,
F,
F,H (PS
control),H (PPS control),switching
frequency 100
kHz,
–:MOSFET IRF540(IR)(referring to Appendix D).
Fig.13shows experimental waveforms
in Vdc with 100W output power condition.Since input
voltage and output
voltage match in this case,current stress of in-
ductance between PS control and PPS control is the same.
(a)
(b)
Fig.10.(a)Current stress versus output voltage and inductance L under PS control and under PPS control.(b)Current stress versus output voltage.
Fig.14shows experimental waveforms
in Vdc with 100W output power condition.In this case,input
voltage and output
voltage do not match.Therefore,current stress of
inductor with PS control is higher than that of PPS con-trol.Fig.15gives curves of current stress versus output voltage under PS and PPS control respectively.From the experimental waveforms and curves,we can easily see that PPS control can reduce current stress and reduce conduction losses.Fig.16shows experimental waveforms
in Vdc with 30W output power condition.The converter under PS control can not achieve ZVS,while the converter under PPS
control
Fig.11.ZVS range versus output voltage under PS control.
can still hold ZVS.Therefore,PPS control can reduce switching losses.
Fig.17shows the efficiency curves of the converter under PS and PPS control.It can be easily found that PPS control has higher efficiency than PS control,especially in light-load condition.
V .C ONCLUSION
A PWM plus phase-shift control bidirectional dc –dc con-verter is proposed in this paper.From the theoretical analysis and the experiments,it can be found that PPS control has the following features.
1)PPS control reduces current stress,conduction losses and switching losses of devices.
2)The converter under PPS control can achieve ZVS in a larger load variation.
A PPENDIX A
From Fig.5,we can see that average voltage of
inductance in one period is
zero
(A1)
Average voltage of
inductance in one period is also
zero
(A2)
Average voltage of output
inductance in one period is zero
too
(A3)
Average current of
capacitance in one period is
zero
(A4)
According to the law of conservation of energy,the following equation is
obtained:
(A5)
Fig.12.System block diagram of the proposed
converter.
Fig.13.Experimental waveforms in V =24Vdc (100W-output)condition (2us/div).(a)PS control.(b)PPS control.
The output current of the converter in bidirectional operation can be obtained as
following:
(A6)
In bidirectional operation,the power transmitted through the converter can be expressed
by
(A7)
Fig.14.Experimental waveforms in V =30Vdc (100W-output)condition (2us/div).(a)PS control.(b)PPS
control.
Fig.15.Experimental result of current stress versus output voltage.
Fig.16.Experimental waveforms in V =30Vdc (30W-output)condition (2us/div).(a)PS control.(b)PPS
control.
Fig.17.
Efficiency waveforms versus output voltage.
A PPENDIX
B
,
and are the currents of
inductance
at
,
and .
We can derive the following equation from
(1):
(B1)
We can derive the following equation from
(2):
(B2)
We can derive the following equation from
(3):
(B3)
Average current of
inductance
in one period is
zero
(B4)
,
and
can be obtained by combining (B1)–
(B4)
(B5)
Equation (7)can be obtained by combining (A7)and (B5).
A PPENDIX C
In the forward mode,the converter can achieve ZVS on con-dition
of
(C1)
(C2)
(C3)(C4)
The ZVS range under PPS control can be obtained by substi-tuting (B5)into (C1)–
(C4)
(C5)
A PPENDIX D
The design of PPS control bidirectional dc –dc converter is illustrated on the prototype built for the following specifi-cations:input voltage rating:48Vdc,output voltage rating:24Vdc,and it varies from 24Vdc to 30Vdc,maximum output power:100-W,switching frequency:100kHz.
In order that duty cycles of M1and M3are 0.5when input voltage and output voltage are equal to their rating value re-spectively,the turn ratio of the transformer can be derived from (5):1:1.
In order to simplify the prototype,the same type of MOSFET
is choosen.From (7)and (9),the current stress
of
–can
be calculated and it is 7.3A.The voltage stress
of
–is 60Vdc when the converter is operated under PS control and the output voltage is 30Vdc.Therefore,IRF540
whose is 100Vdc
and is 28A can satisfy this situation.
The value of the output
inductance
can be calculated
by
(is the maximum ripple of
the output current,here it is 0.5A)and it is
150H.The value
of ,
and can be calculated
by
is the maximum ripple of the
voltage,here it is 1V)
and
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Dehong Xu (M ’94)was born in Hangzhou,China,
in 1961.He received the B.S.,M.S.,and Ph.D.de-grees from the Department of Electrical Engineering,Zhejiang University,China,in 1983,1986,and 19,respectively.
Since 19,he has been a faculty member at Zhe-jiang University,where he is currently a Professor in the Department of Electrical Engineering.He was a Visiting Professor in the Department of Electrical En-gineering,University of Tokyo,Tokyo,Japan,from May 1995to June 1996,and at the Center of Power
Electronics System,Virginia Polytechnic Institute and State University (Virginia Tech),Blacksburg,from June to December 2000.His research interests include application of advanced control in power electronics,high-frequency conver-sion,and power quality.
Dr.Xu is a Vice Chairman of the Chinese Power Supply Society and the Chinese Power Electronics
Society.
Chuanhong Zhao (S ’03)was born in China in 1977.She received the B.S.and M.S.degrees in electrical engineering from Zhejiang University,Hangzhou,China,in 2000and 2003,respectively,and is currently pursuing the Ph.D.degree in power electronic systems in the Department of Information Technology and Electrical Engineering,Swiss Federal Institute of Technology (ETH),Zurich,Switzerland.
Her research fields of interest include bidirectional converters,control of Matrix converters,and soft
switching
technique.
Haifeng Fan was born in China in 1978.He received the B.S.degree in electrical engineering from the Huazhong University of Science and Technology,Wuhan,China,in 2001and is currently pursuing the M.S.degree in electrical engineering at Zhejiang University,Hangzhou,China.
His research interests include topology of bidirec-tional dc –dc converter and its control.
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