Loss Evaluation of a Series-Parallel
Compensation DC-DC Converter
for a Small Fuel Cell System
Koji Orikawa, Jun-ichi Itoh
Nagaoka University of Technology
Department of Electronics and Information Engineering
E-mail: itoh@vos.nagaokaut.ac.jp
Abstract — This paper proposes a novel DC-DC converter for
hybrid power supplies using both fuel cell and battery. The
output voltage is controlled by a series converter that regulates
only the differential voltage between the fuel cell voltage and theoutput voltage. Although the load condition is changed, thevariation of the fuel cell current is suppressed by a battery
through operation of the parallel converter. The experimental
results confirmed that the proposed circuit could achieve
maximum efficiency point of 98.8% in the small differential
voltage region. In addition, the loss analysis clarified the relations
among the ripple current of the inductors, the inductor voltage
and the inductors losses. As a result, it is confirmed that the
proposed circuit achieves the minimum loss of the copper loss
and the iron loss in the inductors when the differential voltage issmall.
I.

INTRODUCTION

Recently, most mobile electronic devices use batteries as a
power source. The mobile electronic devices are developingwith increasingly high performance and functionality,
accompanied by higher power consumption and the demand
for longer operation times. Fuel cell systems have being
developed as a new power supply for mobile devices toachieve these demands. A direct methanol fuel cell (DMFC)
has possibility to achieve high power density as a power
supply for mobile devices. However the fuel cell system hassome problems as follows.
(1)Output voltage fluctuation according to the load condition
The fuel cell has large internal impedance.
(2)Low dynamic response
The fuel cell does not allow the regeneration from the load
and needs long starting time.
(3)Short lifetime
The output power of a fuel cell should be constant, because
quick power fluctuations of a fuel cell reduce its life time.
The DC-DC converters are required in the fuel cell system
in order to control the output voltage. The efficiency of DCDC converters become an important issue in terms of toprovide longer operation times for these devices. Many circuit
topologies of DC-DC converters for fuel cell applications havebeen studied in order to obtain high efficiency [1-5]. A
resonant type converter, which use zero voltage switching or
zero current switching, is one of the most effective circuit
topologies to obtain high efficiency [1-2]. In Ref. [3], cascade

converter topologies, which compensate differential voltage
between the fuel cell voltage and the output voltage, is a goodsolution to obtain high efficiency. However, one of the
problems of these converters is that the fluctuation of theoutput current is the same as the fluctuation of the fuel cell
current due to the series connection. As a result, the series
converter reduces the life time of the fuel cell although theoutput voltage can be controlled.
In order to compensate the dynamic response, a battery oran electric double layer capacitor (EDLC) is used in a fuel cellsystem. A hybrid power supply using both the fuel cell andbattery also requires high efficiency, downsizing, and quick
response to the load fluctuations. Hybrid power supplies using
both the batteries and fuel cells are being actively studied [69]. One of the popular circuit configurations consists of two
boost choppers for the fuel cell and battery, and a buckchopper for output voltage regulation. When the loadcondition causes a change in the terminal voltage of the fuelcell, the operation of the buck chopper regulates the output
voltage effectively. The buck mode operation is also used tosave the power consumption of the load circuit. The battery
supports the control response of the fuel cell through the boost
chopper. However, this system can not achieve high efficiency
because the power is converted twice between the fuel cell andthe output, resulting in an increased of power loss.
In this paper a novel DC-DC converter is proposed for a
hybrid system using both the fuel cell and battery. The
proposed system consists of a series converter and a parallel
converter to control the input current and the output voltage
respectively. In the proposed circuit, the series converter
generates a positive and negative voltage to achieve boost andbuck operation individually. As a result, high efficiency is
obtained, because the power rating of the DC-DC converter
can be drastically reduced [10]. On the other hand, the parallel
converter with a battery compensates the quick response
according to the load fluctuations. A control strategy is also
proposed to achieve both the quick response of the load andslow power fluctuation of the fuel cell. Finally, theexperimental results are presented to demonstrate theadvantages of the proposed converter in comparison with aconventional circuit. In addition, analysis and measurement of
power loss in each part of the proposed circuit is implemented
to clarify the reason for high efficiency. Overall, the validityof the series-parallel compensation method is confirmed.

II. CONCEPT OF PROPOSED CIRCUIT

Vconv

A. Series compensation
Fig. 1(a) presents a block diagram of a conventional buckboost chopper. These converters convert all the input power,
which is not dominated by the relations between the input andoutput voltage. For example, in a conventional buck-boost
chopper, which consists of a energy storage reactor and asingle switching device, when the input voltage Vin is close to
the output voltage Vout, the duty ratio D of a single stage buckboost chopper is obtained by (1), using switch on time ton, and
off time toff.
D=

t on
Vout
=
= 0.5
t on + t off Vin + Vout

Converter
Vin

Converter(a) Conventional topology.

Vout Vin

Vsb

Vout

(b) Series compensation topology.

(1)

In this case, switching devices should be operated
regardless of the relations between the input voltage and theoutput voltage. Besides, the energy for the output should becharge by an intermediate reactor or capacitor. As a result, theefficiency will be decreased.
Fig. 1(b) shows a block diagram of the series compensation
converter, which is connected in series to the power supply.
The series converter outputs only the differential voltage
between the fuel cell voltage and the output voltage. Therefore,
when the fuel cell voltage is close to the output voltage, theoutput power of the series converter becomes smaller. The
small output power means a small loss even if the efficiency is
not so high. In particular, when the fuel cell voltage agrees
with the output voltage, the output power is directly provided
by the fuel cell without switching operation; therefore, highefficiency is obtained by the series compensation circuit,although fluctuation of the output current directly becomes afluctuation of the fuel cell current due to the series connection,
which will decrease the lifetime of the fuel cell. A voltage
ripple of the fuel cell occurs due to the internal impedance inthe fuel cell.
B. Series-parallel compensation
Fig. 1(c) shows a block diagram of the proposed seriesparallel compensation converter. In the proposed circuit, theparallel converter is connected in parallel to the fuel cell.
When the output power is constant, the parallel converter does
not operate, and the series compensation method can obtainhigh efficiency. The output voltage Vout is obtained by (2),using series converter output voltage Vconv and the fuel cellvoltage Vfc.
Vout = V fc ± Vconv(2)
When the load condition is changed, the parallel converter
will compensate the quick variation of the fuel cell current.
The fluctuation of the output power is compensated by thebattery through the operation of that parallel converter. In
addition, when the battery voltage is decreased or overcharged,
either the battery will be charged from the fuel cell or thebattery supplies the power to the load through the operation ofthat parallel converter.

(c) Proposed circuit.
Fig. 1. Block diagrams of proposed converter in comparison
with a conventional circuit.

Series converter
Boost chopper
Step down chopper
S2
Lfc
Lout
ILout

Iout

S1
Vfc
Ifc

Isb

Parallelconverter Vsb

S3

Cout

S4

Icomp

Vout

P
Fig. 2. Configuration of proposed circuit.

III. PROPOSED CIRCUIT
A. Circuit configuration
Fig. 2 shows the circuit configuration of the proposed
circuit based on Fig. 1(c). The series converter uses a boost
converter and a step-down converter. The series converter
generates a positive and negative voltage according to theboost mode and the buck mode, respectively. The output ofthe parallel converter is connected to the negative terminal of
the fuel cell. The proposed circuit requires only two reactors,
where the conventional circuit needs to use three reactors. To
suppress the ripple current of the fuel cell, an inductor isconnected in series to the fuel cell. Further, the reactor is used
as a boost reactor too when the boost mode is selected.
Fig. 3(a) shows a block diagram of the proposed circuit forseries compensation mode. In this case, the series converter
works as a H-bridge converter. Fig. 3(b) and (c) presents a
block diagram of the proposed circuit for series-parallel
compensation mode. When the load condition is changed, only
the parallel converter will operate. The series converter
compensates the differential voltage between the fuel cellvoltage and the output voltage, and the parallel converter
compensates the quick variation of the fuel cell current. The

battery voltage must be higher than the fuel cell voltage toprevent a rush current from the fuel cell to the battery.

Vconv
Ifc

B. Design of the proposed circuit
In the proposed circuit, the ripple current of the inductors
becomes maximum value when the differential voltage
between the fuel cell voltage and the output voltage is at
maximum. The value of the ripple current of the inductor do
influence on the lifetime of the fuel cell. The ripple current of
the inductor Δifc is obtained by (3), using switch on time ton.
Δi fc =

V fc
L fc

t on =V fc
L fc f sw

Dboost =V fc

Vout − V fc

L fc f sw

Vsb

Vfc

V fc

Vout − V fc

Δi fc f sw

Vsb

=

4
7.2 − 4
= 23.3μH
0.5 × 100 ×10 3 11

Vsb

Vout

(a) Series compensation mode.

(3)

where Lfc is an inductor of the fuel cell side, and Dboost is theduty ratio in boost mode.
Table I shows the specifications for the proposed circuit. In
case of Table I, the ripple current of the inductor becomes the
maximum value when the fuel cell voltage is 4 V in boost
mode. The value of the ripple current of the inductor is limited
to 30% of the output current, and then the ripple current is 0.5
A since the output current is 1.67 A at the output power 12 W.
In this condition, from (3), the inductance of the fuel cell side
is calculated by (4).
L fc =

H- bridge
converter(b) Boost mode (Load change).

(c) Step down mode (Load change).
Fig. 3. Block diagram of proposed circuit.
TABLE ISPECIFICATIONS FOR PROPOSED CIRCUIT
Fuel cell voltage Vfc
4 to 10 (V)Output power Pout
12 (W)
Output voltage Vout
7.2 (V)
Battery voltage Vsb
11 (V)
Switching frequency fsw
100 (kHz)
Inductor current ripple
30% of output current (A)(4)

IV. CONTROL STRATEGY
Fig. 4 shows control diagrams of the proposed circuit. The
proposed control method has two loops; the inner loop is forcontrolling the fuel cell current and the parallel converter
current. As for the outer loop, it is for the output voltage
control.
Operation between the series and parallel converter isconstrained by the load condition in order to reduce theconverter loss. In boost mode, the series converter works as aboost converter. That is, the switch S2 maintains at on state.
The difference voltage is then controlled by PWM modulationof S1. In this case, the battery supplies the power to the load,
because the differential voltage is positive. In buck mode, theseries converter operates as a buck converter; switch S1
maintains at off state. The differential voltage is thencontrolled by PWM of S2. In this case, the battery is charged
from the fuel cell, since the differential voltage is negative.
Boost and buck modes are selected by the control signal of theseries converter according to the relations between the fuelcell voltage and the output voltage. The switches S3 and S4 arefor the parallel converter. The parallel converter works only
when the load is fluctuated. The parallel converter will bestarted when the load fluctuation is detected by the window
comparator and is stopped after the time spends longer than
the time constant of the LPF and HPF.
The current command is divided into the fuel cell current
command and the compensation current command. Low passfilters (LPF) and high pass filters (HPF) are used to divide thecurrent command. The LPF is used to separate thefundamental current fluctuation, for the slow response of thefuel cell. The HPF is used to separate the transient current

Fig. 4. Control diagrams for the proposed circuit.

fluctuation for the fast response of the battery. The HPF
functions simultaneously with the LPF filter, as shown in Fig.
4. The time constants of the LPF and HPF are set to the samevalue.
The frequency responses of the LPF and HPF do not
influence the output current response, as explained by thefollowing. The relations between each current can be
expressed by (5), using the fuel cell current Ifc and the parallel
converter current Icomp.
(5)
I Lout = I fc + I comp
The fuel cell current command Ifc* and the parallel converter
current command Icomp* are obtained by (6) and (7)*I fc =

1*
I Lout1 + sT(6)

*

I comp =sT*
I Lout1 + sT(7)

TABLE II
EXPERIMENTAL CONDITIONS
Fuel cell voltage Vfc
4 to 10 (V)Output voltage Vout
7.2 (V)
Battery voltage Vsb
11 (V)
Switching frequency fsw
100 (kHz)
Input inductor Lfc
30 (μH)
Output inductor Lout
30 (μH)
Output capacitor Cout801 (μF)
AVR response
0.1 (kHz)ACR response
1 (kHz)
LPF time constant T
2.2 (ms)
Load change
2 to 20 (W)where T is the time constant of the filter and ILout* is the output

where G1(s) and G2(s) are the transfer functions of the fuel cell
current control and the parallel converter current control,
respectively.
In addition, the output current is expressed by (9) when bothcurrent regulator designs for the fuel cell and parallel
converter are the same.
*(9)
I Lout = G (s )I Lout
where G(s) is the transfer function of the output current
control. That is, the time constant of the LPF or HPF does notappear in the transfer function of the output current control. In
addition, the operation of the parallel converter is started byvariation of the parallel converter current command Icomp*.
Then, operation of the parallel converter is stopped by a timer
which is used to prevent a decrement of efficiency in the
proposed circuit.

Efficiency [%]current command. Therefore, the output current is obtained by
(8).
*
*
(8)
I Lout = G1 (s )I fc + G2 (s )I compV. EXPERIMENTAL RESULTS
The proposed circuit was tested under the experimental
conditions shown in Table II. The response of the current
regulator was designed as much higher than that of the LPF. It
should be noted that the time constant was set to a shorter timein this experimental condition in order to confirm theeffectiveness of the parallel converter. In order to reduce anegative influence on the lifetime of the fuel cell, the time
constant should be set to a few seconds.
Fig. 5 shows the efficiency of the proposed circuit toconfirm the effectiveness of the series compensation. The
experimental results confirmed that the proposed circuit could
achieve 98.8% at the maximum efficiency point in the small
differential voltage region. The output voltage is kept constantby the PI regulator. It should be noted that the output voltage
waveform has no low frequency component and thefluctuation is in a steady state load.
Fig. 6(a) and (b) show comparisons of the fuel cell current
and the output voltage with and without parallel compensation
when the load condition is changed. In Fig. 6(a), the voltage
drops over 14% at the point of the load change when the
output power is increased by the load, where only series
compensation applied. In addition, the fuel cell current ischanged at high speed. In contrast, Fig. 6(b) shows that thevariation of the fuel cell current is suppressed by the parallel
compensation. The output voltage drops within 7% is achieved.

Fig. 5. Efficiency of the proposed circuit.

(a) Series compensation only.

VI. LOSS ANALYSISIn order to evaluate the power loss of the proposed circuit,the loss measurement and analysis for each part haveexamined. In the proposed circuit, the copper loss and the ironloss of the inductors depends on the ripple current of inductors
and the inductor voltage, respectively. It should be noted thattheoretical calculation of the inductors loss for a fundamental(b) Series compensation with series-parallel compensation.
Fig. 6. Voltage waveforms and current waveforms forincreasing power condition.

where RLDC is a DC component resistance of the inductor, RLAC
is a AC component resistance of the inductor, Iout is an output
current, ILAC is RMS value of the ripple current of the inductor.
The current waveform of the inductor can be approximatedto a triangular shape when the resistance component of theinductor is negligible. Therefore, RMS value of the ripple
current of the inductor ILAC is obtained by (11) from Ref. [11]1(

V fc − Vout)

2 3 L fc + Lout f sw

V fc − Vout

(12)

Vsb

Fig. 7 shows RMS value of the ripple current. In the small
differential voltage region, the ripple current of the inductors
are reduced, as shown in Fig. 7. Finally, the copper loss of theinductors is obtained by (13)(V − V )12(L + L ) f
2

2
LDC OUT

Pind _ copper = R

I+ RLAC

fc

out

fc

out

2

2

D

2

2Vdis _ rms
NAe f sw

0
-5.0

-10.0
0.0

(13)

10.0

Time [ s]

20.0

30.0

20.0

30.0

(a) Vfc=4V.

10.0
5.0
0
-5.0
-10.0
0.0

10.0

Time [ s](b) Vfc=7V.
Fig. 8. Voltage waveforms of the input inductor Lfc.

sw

B. Iron loss of the inductors
Iron loss occurs in the core of the inductor [12]. Fig. 8
shows the voltage waveforms of the input inductor. The
voltage waveform of the inductor is changed according to thedifferential voltage. Fig. 9 shows the RMS value of the input
inductor voltage and output inductor voltage respectively. In
the proposed circuit, the inductor voltage becomes smallerwhen decreasing the differential voltage between the fuel cellvoltage and the output voltage, as shown Fig. 9. That is, in thesmall differential voltage region, the iron loss becomes small
because the RMS value of the inductor voltage is reduced.
Secondly, the relations between the inductor voltage and theiron loss are clarified. Note that it is difficult to calculate theiron loss of the inductor used in DC-DC converters because
DC current flows through the inductor. In this paper, only theeddy-current loss and the hysteresis loss which are caused by
the voltage of the switching frequency component areevaluated. In the proposed circuit, a flux change of the core of
the inductors is expressed by (14)
Bm =

5.0

(11)

D

where D is the duty ratio of the series converter. Then, theduty ratio D is given by (12)
D =1−

10.0

(14)

where Bm is the magnetic flux density, Vdis_rms is the distortion
RMS value of the inductor voltage, N is the number of wireturns, Ae is the effective cross section of the core.
The material of the core is PC40 which is a kind of ferrite.
Iron loss of the inductor consists of the eddy-current loss andDistortion RMS valueof inductor voltage
Vdis_rms [V]

I LAC =

Fig. 7. RMS value of ripple current of the inductors.

Voltage [V]A. Copper loss of the inductors
Copper loss occurs in the winding resistance of theinductors. The copper loss of the inductors is expressed by(10)
2
2
Pind _ copper = RLDC I OUT+ RLAC I LAC(10)

RMS value ofripple current [A]frequency component is indicated because it is difficult to
calculate the PWM loss of the inductor. In addition, the loss
analysis for the switching loss and the conduction loss of the
MOSFETs are presented in this section.

Fig. 9. Distortion RMS value of inductor voltage.

the hysteresis loss is expressed by (15) from Ref. [13]Pind _ iron = 4.50 × 10 −4 × Bm2.5 × f sw1.55 × Vc

(15)

where Vc is the effective volume of the core.
C. Loss analysis of the experimental result
Fig. 10 shows the calculation results of the sum of thecopper loss and the iron loss of the inductors respectively. Fig.
10 confirms that the copper loss and the iron loss of theinductors become small in the small differential voltage region.
In addition, the iron loss is drastically changed according to
the fuel cell voltage.
Fig. 11 shows the result of the loss analysis including theswitch loss. The switching loss and the conduction loss of the
MOSFETs are obtained as follows; the switching loss iscalculated by the measured current and voltage. The
conduction loss is calculated by the measured current using
on-resistance which is obtained from the data sheet of theInductor loss [W]switching device.
The analysis results confirmed that the copper loss and theiron loss of the inductors are reduced when the fuel cellvoltage is close to the output voltage. From the loss analysis,
the major loss in the proposed circuit is comprises by the lossof the inductors, the switching loss of the MOSFETs and theloss in the body diode, which is used as the free wheeling
diode (FWD) of the series converter. It should be noted that inorder to reduce the FWD loss during the dead-time period, thelow voltage forward drop diode is connected in parallel to the
FWD.

Fig. 10. Iron loss and copper loss of the inductors.

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Power loss [W]VII. CONCLUSION
A series-parallel compensation type DC-DC converter has
proposed to achieve high efficiency, downsizing and longer
lifetime of a fuel cell-battery hybrid system. When the output
power is almost constant, the series converter provides only
the differential voltage between the fuel cell voltage and theoutput voltage, while the parallel converter suppresses thevariation of the fuel cell current. In addition, the control
strategy combined a LPF and a HPF to suppress the quick load
fluctuation has proposed. The share rate between the fuel celland battery is controlled by time constant of the LPF and HPF.
The design of the proposed circuit was also clarified by using
the ripple of the inductors.
The experimental results confirmed that the proposed circuit
could achieve a maximum efficiency of 98.8% in the small
differential voltage region. The loss analysis clarified therelations among the ripple current of the inductors, theinductor voltage and inductors loss. Moreover, the copper loss
and the iron loss of the inductors became small in the small
differential voltage region are as well been confirmed. In
addition, the proposed converter suppressed the variation of
the fuel cell current and achieved an output voltage drop of
within 7% for the effect of load change.
Overall, the experimental results confirmed the validity ofthe series-parallel compensation method.

Fig. 11. Loss analysis of the experimental result.
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