experimental validation of high-voltage-ratio low-input...

3430 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 61, NO. 8, OCTOBER 2012

Experimental Validation of High-Voltage-RatioLow-Input-Current-Ripple Converters for Hybrid

Fuel Cell Supercapacitor SystemsMohammad Kabalo, Student Member, IEEE, Damien Paire, Benjamin Blunier, David Bouquain,

Marcelo Godoy Simões, and Abdellatif Miraoui, Senior Member, IEEE

Abstract—Electric vehicle technology has been adopting fuelcells (FCs) for hybrid applications over the past few years. There-fore, the development of advanced power electronic systems forthe integration of fuel cells with on-board energy managementis fundamental for achieving high-performance systems. An FCfor vehicular applications is usually a low-voltage current-sourcelike device that produces electricity and heat directly from inputhydrogen and oxygen. Most often, it is required that the FCs bestacked for high-voltage dc-link in order to supply the input powerfor the drivetrain and electric motor drive system. The FC has anonlinear nature, and it must be controlled to operate in the high-efficiency operating range. Hybrid electric vehicles have physicalconstraints such as volume and weight under limited cost and ex-pected lifetime. There is a need for high-voltage input/output ratioof dc-dc boost converters to be connected between the FC to themotor drive dc-link. In addition, it is necessary to have low inputripple at the dc-dc boost converter in order to maximize the FClifetime, and the traditional dc-dc boost converter topologies havepoor performance on these specifications. This paper proposes anew dc-dc converter family of topologies aimed at improving theapplication to electric vehicle power control. This family is definedas floating-interleaving boost converters (FIBCs). The paper willthoroughly show analysis and experimental verification of FIBC’s,and they will be compared with conventional boost converter char-acteristics. The paper supports how performance figures related tothe passive components, i.e., the inductor and capacitor, will havebetter volume and weight, extremely low input current ripple,and improved efficiency and transfer ratio. The analysis presentedin this paper shows how to choose the most suitable topology inorder to achieve the desired specifications. The selected topologyis fully validated experimentally using advanced nonlinear slidingmode control, which has the additional feature of operating evenin faulty conditions.

Index Terms—Boost converter, dc-dc converter, fuel cell (FC)hybrid vehicle, sliding mode control.

Manuscript received December 8, 2011; revised March 28, 2012; acceptedJune 20, 2012. Date of publication July 11, 2012; date of current versionOctober 12, 2012. The review of this paper was coordinated by Dr. Z. Nie.

M. Kabalo, D. Paire, and D. Bouquain are with the Université de Tech-nologie de Belfort-Montbéliard, 90010 Belfort, France (e-mail: [email protected]; [email protected]; [email protected]).

B. Blunier, deceased, was with the Université de Technologie de Belfort-Montbéliard, 90010 Belfort, France.

M. G. Simões is with Colorado School of Mines, Golden, CO 804010-1887USA (e-mail: [email protected]).

A. Miraoui is with Cadi Ayyad University, Marrakech 511-40000, Morocco(e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2012.2208132

I. INTRODUCTION

A FUEL cell (FC) may be one of the promising solutions todecrease carbon dioxide emissions under the assumption

that the hydrogen can be produced from renewable-energysources such as photovoltaic and wind energy or as a subprod-uct of currently wasted energy of large power plants under alow-load situation (e.g., when base power plants are producinghigher power than the demand). In automotive applications,proton exchange membrane FCs appear to be the most suitable,because their working conditions at low temperature allow thesystem to start up faster than those technologies using high-temperature FCs; moreover, the solid state of their electrolyte(no leakage and low corrosion) and their high power densitymake them fit for transport applications. Finally, they alsoprovide very good tank-to-wheel efficiency, compared with in-ternal combustion engines [1], [2]. FCs are low-voltage currentintensive sources. A single cell produces a voltage of approxi-mately 1 V; therefore, several cells must be stacked to achievehigh voltage output. FC stacking reduces its reliability andlifetime as a chain of series-connected cells is as strong as theweakest cell. Due to reliability and lifetime reasons, practicalFC stack output voltage is reduced to approximately 100 V. Onthe other hand, the vehicle powertrain dc bus has a high voltageof a few hundred volts. Therefore, a dc-dc converter is requiredto interface the FC stack with the powertrain dc-bus voltage andto achieve good power management of the input power source[3]–[8]. The FC dc-dc converter is also required for voltageconditioning as the FC output voltage strongly varies with theload. Ideally, the power conditioner must have minimal losses,leading to higher efficiency [9]. Power-conditioning efficiencyvalues can typically be higher than 90% [10].

The most important requirements expected from dc-dc con-verter for FC applications are high voltage ratio and low currentripple [11]. The lower the current ripple, the longer the FClifetime [12], [13]. However, in an FC electric vehicle (FCEV),the high voltage ratio and low current ripple, which are associ-ated with volume, weight, reliability, and efficiency constraints,are very important requirements. A cascade dc-dc convertercomposing of two phase-interleaved boost converters and threelevel series boost converters is proposed in [14]. This solutionsuffers from low efficiency and reliability problem. In [15] and[16], a parallel resonnant converter resonant topology with acapacitor as output filter is proposed. However, in this topology,determination of the leakage inductance and capacitance, as

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KABALO et al.: VALIDATION OF RIPPLE CONVERTER FOR HYBRID FC SUPERCAPACITOR SYSTEM 3431

well as the topology modeling, is very complex. A multiphaseinterleaved boost converter for FC applications is proposedin [17]. The proposed topology has a voltage ratio identicalto that of the classic boost converter, which leads to lowefficiency for applications where high voltage ratio is required.A review of isolated and nonisolated boost dc-dc converterssuitable for FC and photovoltaic grid-connected applications isproposed in [18] and [19]. The limitations of the conventionalboost converters in these applications are analyzed. Further-more, the advantages and disadvantages of these converters arediscussed.

In this paper, new dc-dc converter topologies defined asthe floating-interleaving boost converter (FIBC) family will bepresented. These topologies are compared to conventional boostconverters, and the analysis will support the choice for the besttopology corresponding to specified constraints. The selectedtopology is then experimentally validated using an advancednonlinear sliding-mode controller, which, for technical reasons,will be explained later.

II. SYSTEM SPECIFICATIONS AND

PROPOSED TOPOLOGIES

In high-power FCEV applications, the major drawbacks ofusing conventional boost converters are the difficulty in thedesign of magnetic components and high input current ripple,which may lead to reduce the FC stack lifetime. Reducingthe rating current and voltage applied to passive and powerelectronic components (keeping the same system rated power)is a proposed solution. This makes the magnetic componentconstruction easier, giving further flexibility for the selectionof power electronic components used in the converters. Fig. 1shows the proposed topologies in addition to the conventionalboost converter.

These topologies have a floating output and interleavinginput, which permits reduction in not only current stress butalso voltage stress, unlike conventional interleaved topologies.The benefits of the N -phase FIBC are the following:

1) increasing the overall converter efficiency;2) increasing the input and output ripple frequency without

increasing the switching frequency;3) decreasing the input ripple current;4) enhancing the system reliability by paralleling phases and

not by paralleling multiple devices;5) decreasing current and voltage ratings of power electronic

devices;6) reducing the size and weight of the passive components.

The system specifications are presented in Table I.Table II shows that the current and voltage ratings of the

power electronic devices of FIBCs are smaller than those ofthe boost and interleaving boost converters.

The duty cycle of the proposed topologies is expressed asfollows:

D =VBus − VFC

VBus + VFC. (1)

Fig. 1. Proposed topologies. (a) Conventional boost. (b) Two-phase FIBC.(c) Four-phase FIBC. (d) Six-phase FIBC.

On the other hand, the conventional boost converter dutycycle is given by

D =VBus − VFC

VBus. (2)


TABLE ISYSTEM SPECIFICATIONS

TABLE IICURRENT AND VOLTAGE RATINGS OF POWER ELECTRONIC DEVICES

Fig. 2. Duty cycle comparison.

Fig. 2 shows that, for the same FC rated power, the basicboost duty cycle is higher than the proposed topology dutycycle. The higher the duty cycle, the lower the converterefficiency [20].

III. INPUT CURRENT RIPPLE EVALUATION

The mathematical expressions for input current ripple arederived under six assumptions.

1) The resistances of inductor and capacitor are negligible.2) Stray inductor and capacitor are negligible.3) Switches are ideal.4) Passive components are identical.5) Switches in parallel operate (360/N)◦ out of phase.6) The converters operate in continuous conduction mode

(CCM).

The ratio of the input current ripple to the inductor currentripple is given by

M(D) =ΔiFCΔiL

. (3)

For conventional boost converter

ΔiFC = ΔiL =DVFC

Lfs. (4)

The input current slope of the N -phase FIBC is expressed asfollows:

diFCdt

=

n=N∑n=1

diLn

dt− diLoad

dt. (5)

The ratio of the input current ripple to the inductor currentripple of a two-phase FIBC as a function of duty cycle M2(D)is given by

M2(D) =

{ 1−2D1−D , 0 < D < 0.52D−1D , 0.5 < D < 1.

(6)

The ratio of the input current ripple to the inductor cur-rent ripple of a four-phase FIBC as a function of duty cycleM4(D) is

M4(D) =

⎧⎪⎪⎪⎨⎪⎪⎪⎩

1−4D1−D , 0 < D < 0.253D−4D2−0.5

D(1−D) , 0.25 < D < 0.55D−4D2−1.5

D(1−D) , 0.5 < D < 0.754D−1D , 0.75 < D < 1.

(7)

The ratio of the input current ripple to the inductor currentripple of a six-phase FIBC as a function of duty cycle M6(D)is given by

M6(D) =

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

1−6D1−D , 0 < D < 1/63D−6D2−1/3

D(1−D) , 1/6 < D < 1/39D−6D21D(1−D) , 1/3 < D < 1/27D−6D22D(1−D) , 1/2 < D < 2/39D−6D2−10/3

D(1−D) , 2/3 < D < 5/66D−5D , 5/6 < D < 1.

(8)

The previous analysis permits having the generalized expres-sion of the ratio of the input current ripple to the inductorcurrent ripple of the N -phase FIBC as a function of duty cycleMN (D)

MN (D) =ΔiFCΔiL

=(X −ND)

(D − X−1

N

)D(1 −D)

(9)

where X is the interval between two duty cycle values, resultingin zero current ripple. The variation of the ratio of input currentripple to inductor current ripple as a function of duty cycle isshown in Fig. 3. On the one hand, by studying Fig. 3, it can beobserved that input current ripple cancelation occurs at specificduty cycles, which are multiple duties of 1/N , such as 0.5 ina two-phase FIBC; 0.25, 0.5, and 0.75 in a four-phase FIBC;and 0.16, 0.33, 0.5, 0.66, and 0.83 in a six-phase FIBC. Onthe other hand, it is clear that the input current ripple is alwaysless than the inductor current ripple. The fact that the inputcurrent ripple is always less than the inductor current ripplepermits to increase this latter and, consequently, decrease theinductor value according to (4). However, due to core losses


Fig. 3. Ratio between the input current ripple and the inductor current rippleversus duty cycle.

and the CCM condition, the critical inductor current ripple forthe proposed N -phase FIBC is defined as follows:

ΔiLcritical≤ 4IFC

N(1 +D). (10)

Decreasing both the inductor value and the current flowingthrough it permits to reduce its volume, weight, and cost, aswill be shown in the next section.

The best way to show how the input current ripple (as apercentage of input rated current) decreases with the numberof phases is to determine this first according to the systemspecifications presented in Table I for a given inductor value.For this evaluation, the inductor value will be chosen as 100 μH.On the one hand, Fig. 4 shows that decreasing the input currentripple from a four-phase to a six-phase FIBC is not important.It is not the case from a one-phase or a two-phase to a four-phase FIBC. On the other hand, depending on the rated powerof the system, a six-phase FIBC can have input current ripplebigger than a four-phase FIBC, which is not the case when onecompares a four-phase with a two-phase FIBC for any ratedpower. Consequently, from the input current ripple reductionpoint of view, we can see that the benefits of six-phase converterare not so attractive compared with its increased complexity andcosts.

IV. EVALUATION OF THE INDUCTOR VOLUME

To evaluate the reduction in the inductor volume for theproposed topologies compared with that of the conventionalboost, it is necessary to go through the details of the electro-magnetic used for similar magnetic cores. In this analysis, thematerial of the selected core is ferrite. Fig. 5 shows the top andfrontal views of the inductor magnetic circuit. Some guidelinesof magnetic material comparison and selection for high-power

Fig. 4. Input current ripple as a percentage of the FC rated current accordingto the number of phases.

Fig. 5. Geometry of the inductor core.

high-frequency inductors in dc-dc converter can be found in[21] and [22].

The stored energy in the inductor is proportional to theinductor and peak current value, i.e.,

E =12LI2peak. (11)


On the other hand, the stored energy as a function of theinductor’s dimensions for the proposed geometry is given by

E =12

∫∫∫−→H · −→BdV =

B2g b2

4μo(12)

where−→B and

−→H are the magnetic field density and strength,

respectively, and μo is the magnetic permeability of air. Thevolume of the geometry shown in Fig. 5 is given by

V = (2b+ 2kbb)(b+ 2kbb)(b+ h+

g

2

). (13)

This volume can be expressed as follows [23]:

V =K

(4kBLI2LJΔB

)0.75

K =

(2

k0.75B

)(1 + kb)

(1 +

kBkb

)(1 + 2kb). (14)

ΔB = 0.2 T is the change in flux density J , which is the currentdensity varying between 2 and 5 A/mm2. In our analysis, it ischosen as 3.5 A/mm2. kB is a coefficient greater than 1, whichtakes into account the difference between the effective sectionof the conductors and the required section windings. It is relatedto the shape of the conductors and the presence of differentlevels of isolation. In this analysis, it is chosen as (kB = 1.5).kb is a geometric coefficient, and in our case, it is taken to beequal to 1.

Equation (15), shown below, gives the reduction in total in-ductor stored energy and associated magnetic volume, as com-pared with that in the conventional boost converter. EInductor(1)

and VInductor(1) are the stored energy and the associated vol-ume in the traditional boost, respectively. EInductor(N) andVInductor(N) are the stored energy in the single-phase inductorand the corresponding volume of the N -phase FIBC, respec-tively. E(N) and V (N) are the percentage of inductor storedenergy and volume reduction, respectively, given by

E(N)

100=

(EInductor(1) −N × EInductor(N)

EInductor(1)

)

V (N)

100=

(VInductor(1) −N × VInductor(N)

VInductor(1)

). (15)

From (15), the total stored energy and volume going fromconventional boost to a two-phase FIBC have been reduced by62.6% and 49.3%, respectively. For a four-phase FIBC, theyare reduced by 86% and 83.7% and by 87.2% and 87.35% fora six-phase FIBC. In conclusion, from this point of view, it canbe seen that there is no great benefit to use a six-phase FIBC,compared with a four-phase FIBC.

V. ROOT MEAN SQUARE CAPACITOR CURRENT

EVALUATION

The output filter capacitor ensures dc-bus stabilization andalso filters discontinuous diode current behavior. In the onehand, reducing the root mean square (RMS) value of the capac-itor current leads to avoiding utilization of a bulky capacitor;

on the other hand, it permits the reduction of capacitor heatingby decreasing resistive losses because of the equivalent seriesinternal resistance (ESR). The lower the capacitor temperatureand RMS current, the longer the capacitor lifetime [24].

The boost RMS capacitor current as a function of the dutycycle and the FC rated current is given by

IRMSC= IFC

√D(1 −D), 0 ≤ D ≤ 1. (16)

For a two-phase FIBC, the RMS capacitor currents asa function of the duty cycle and the FC rated current aregiven by

IRMSC1,C2= IFC

√D(1 −D)

(1 +D)2, 0 ≤ D ≤ 1. (17)

For a four-phase FIBC, the RMS capacitor currents asa function of duty cycle and the FC rated current areexpressed as

IRMSC1,C2=

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

IFC

√D−2D2

2(1+D)2 , 0 ≤ D ≤ 0.25

IFC

√4D−4D2−0.5

4(1+D)2 , 0.25 ≤ D ≤ 0.75

IFC

√3D−2D2−12(1+D)2 , 0.75 ≤ D ≤ 1.

(18)

Finally, a six-phase FIBC, the RMS capacitor currentsas a function of duty cycle, and the FC rated current areexpressed as

IRMSC1,C2=

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

IFC

√D(1−3D)3(1+D)2 , 0 ≤ D ≤ 1/6

IFC

√7D−9D2−2/3

9(1+D)2 , 1/6 ≤ D ≤ 1/3

IFC

√9D−9D2−4/3

9(1+D)2 , 1/3 ≤ D ≤ 2/3

IFC

√11D−9D2−8/3

9(1+D)2 , 2/3 ≤ D ≤ 5/6

IFC

√5D−3D2−23(1+D)2 , 5/6 ≤ D ≤ 1.

(19)

The following gives the percentage of the RMS capacitorcurrent reduction:

I(N)

100=

(IRMSC(1) − IRMSC(N)

IRMSC(1)

). (20)

From (20), it can be seen that the RMS capacitor currentfrom a traditional boost to a two-phase FIBC is reduced by30%, by 56% from a two-phase to a four-phase FIBC, and by60% from a four-phase to a six-phase FIBC. This reduction inRMS current will reduce electrical stress in the output capacitorand improve the converter’s reliability and lifetime. The RMScapacitor current analysis shows that the four-phase FIBC is thebest choice among the proposed topologies.

VI. EFFICIENCY ANALYSIS

An N -phase FIBC is analyzed to evaluate losses in everycomponent and compare them with those of a conventional


boost topology. This allows determining the most suitable con-verter among these topologies from the efficiency point of view.This analysis is reported according to the system specificationspresented in Table I.

• Traditional boost converter losses:

1) Inductor losses: These losses include copper losses(Pcop), which are caused by the skin effect andproximity effect, and core losses (Pcore), which arecaused by the hysteresis phenomenon and eddy cur-rents. These losses depend on the core type and thewire type used, i.e.,

Pcop =RL

(I2FC +

Δi2FC12

)

Pcore = 6.5(fs)1.51

(ΔB

2

)1.74

m (21)

where RL is the equivalent series resistance of theinductor, and m is the weight of the magnetic circuitin kilograms.

2) Capacitor losses: They are due to ESR; in this anal-ysis, they are neglected.

3) Switch losses: These losses include the conduction(Psconl) and the switching losses (Pswl)

Psconl =D

(Rs

(I2FC +

Δi2FC12

)+ VsIFC

)

Pswl =I2FCV

2bustfs

2ItestVtest

t = td(on) + tr + td(off) + tf (22)

where Vs are Rs are the voltage drop and the re-sistance in the ON-state of the switch, respectively;and td(on), tr, td(off), and tf are the turn-on delaytime, turn-on rise time, turn-off delay time, and turn-off fall time, respectively. They can be obtained fromthe manufacturer’s data sheet. Itest and Vtest are thecurrent and the voltage, respectively, under which theswitch was tested to determine its data sheet.

4) Diode losses: These losses include the conduction(Pdconl) and reverse recovery (Pdrrl) losses

Pdconl =(1 −D) (Rdλ+ VdIFC)

λ =

(I2FC +

Δi2FC12

)

Pdrrl =V 2busIFCIRMtrrfs

2ItestVtest(23)

where Vd and Rd are the voltage drop and the re-sistance in the ON-state of the diode, respectively.IRM and trr are the reverse recovery current andreverse recovery time, respectively. They can also beobtained from the manufacturer’s data sheet.

• N -phase FIBC: The switch current and voltage duringthe commutation of the proposed N -phase FIBC are

given by

IS =IFC

N2 (1 +D)

(24)

VS =Vbus

(1 +D). (25)

By increasing the number of phases, the ratio(ISV S/ItestVtest) becomes lower, and consequently, theswitching losses become lower.

1) Inductor losses: These losses are the sum of thelosses of each inductor of an N -phase FIBC, andthey are expressed as a function of phases number,i.e.,

PNcop =RL

(4I2FC

N(1 +D)2+

NΔi2L12

)

PNcore =N6.5 (fs)1.51

(ΔB

2

)1.74

m. (26)

2) Switch losses: These losses represent the sum of thelosses of each switch of an N -phase FIBC. They aregiven by

PNsconl =D

(Rsκ+

2IFCVs

1 +D

)

κ =

(4I2FC

N(1 +D)2+

NΔi2L12

)

PNswl =2I2FCV

2bustfs

N(1 +D)4ItestVtest. (27)

3) Diode losses: These losses represent the sum of thelosses of each diode of an N -phase FIBC. They aregiven by

PNdconl =(1 −D)

(Rdκ+

2IFCVd

1 +D

)

PNdrrl =2V 2

busIFCIRMtrrfsN(1 +D)4ItestVtest

. (28)

Fig. 6 shows the proposed converter efficiency as afunction of the FC current.

By analyzing Fig. 6, one can see, on the one hand,that a four-phase FIBC and a six-phase FIBC keep highefficiency for a wide range of load power. However, a tra-ditional boost and a two-phase FIBC efficiency drasticallydecrease when increasing the system power. For the ratedpower of the system in Table I, a four-phase and a six-phase FIBC have nearly the same efficiency. Therefore,from the efficiency analysis point of view, we can see thata four-phase FIBC is the best choice among the proposedconverters. It has to be noted that the previous calculationsare based on an insulated-gate bipolar transistor (IGBT)switch (ref. 38NAB066V1) from Mitsubishi Electric com-pany. For the diode, the antiparallel emitter-to-collectorfree-wheel diode (FWDi) of the previous IGBT has beenused. The inductor series resistance numerical value hasbeen chosen to correspond to the one of the real inductor.


Fig. 6. Efficiency versus input current.

Fig. 7. Implemented four-phase FIBC.

Fig. 8. FCEV architecture.

VII. EXPERIMENTAL VALIDATION OF FOUR-PHASE

FLOATING INTERLEAVING BOOST CONVERTER

The previous evaluations show that the four-phase FIBCis top choice among all the proposed topologies. The imple-mented four-phase FIBC and the FCEV architecture are shownin Figs. 7 and 8, respectively. The high-voltage battery in Fig. 8can be replaced by a supercapacitor connected to the dc bus viabidirectional four-phase FIBC.

To achieve instantaneous power sharing between the phasesand good power management of the input power source, eachconverter phase has its own current controller. A nonlinearsliding-mode controller is used to generate the required controlinput for each switch of the four-phase FIBC [25]–[27].

Fig. 9. Convergence relation for control of four-phase FIBC.

A. Sliding-Mode Controller

Since a sliding-mode controller is based on the large signalmodel of dc-dc converters, its stability is not restricted by thevariations around the operating point, which contributes to anoverall improved controller performance. Therefore, the largesignal model of the four-phase FIBC is defined as follows:

dIL1

dt=

12L1

((D1 + 1)VFC − 2rL1IL1

+ (D1 − 1)VBus)

dIL2

dt=

12L2

((D2 + 1)VFC − 2rL2IL2

+ (D2 − 1)VBus)

dIL3

dt=

12L3

((D3 + 1)VFC − 2rL3IL3

+ (D3 − 1)VBus)

dIL4

dt=

12L4

((D4 + 1)VFC − 2rL4IL4

+ (D4 − 1)VBus)

dVC1

dt=

1C1

((1 −D1)IL1+ (1 −D2)IL2

− ILoad)

dVC2

dt=

1C2

((1 −D3)IL3+ (1 −D4)IL4

− ILoad) . (29)

The sliding surfaces or the control laws are defined by thefollowing expression:

SILi= ILi

−Ki +KILi

∫ t

0

(ILi−Ki) dτ (30)

where i = [1, . . . , 4], ILiis the average value of the inductor

current, Ki is the desired inductors current, and KILiis a

coefficient that defines the dynamic of convergence to zeroof the static error. The convergence dynamic of the slidingsurfaces to zero is defined as follows:

˙SILi= −λILi

SILi(31)

where λILiare positive real numbers and are called the con-

vergence factors. The convergence relation for control of four-phase FIBC is shown in Fig. 9.

According to (31), the larger the convergence factors, thefaster the system reaches its steady state. However, due to limitson the system parameters such as duty cycle, it is not possibleto increase the convergence factors beyond a certain value.


To design the controller, it is necessary to combine (31) with(29) and (30). This will result in equations for control inputs interms of the state variables and the system parameters.

The duty cycle of each phase of the four-phase FIBC as afunction of time is shown by

Di(t) = 1 +2 (rLi

ILi− VFC + Liχ)

VFC + VBus(32)

where χ = (Ki − λILiSILi

−KILi(ILi

−Ki)).Equation (32) shows that the control inputs are irrelevant

with the value of load resistance R. Therefore, this controllerwill not be perturbed by the variations of the load. Becauseeach duty cycle is relevant with its own phase parameters, thiscontroller is able to work in degraded mode. This is a veryimportant feature as the reliability is a major criterion in FCEV.

At the steady state, where the state variables ILi are follow-ing the commanded references Ki, the duty cycle is given by

Di =VBus − VFC

VFC + VBus. (33)

By replacing the control inputs in the large signal model offour-phase FIBC, we get

y + (KILi+ λILi

)y +KILiλILi

∫ t

0

y dτ = 0 (34)

where y = ILi−Ki by deriving (34)

y + (KILi+ λILi

)y +KILiλILi

y = 0. (35)

This equation is irrelevant with the topology parameters,which underlines the robustness of the controller. The coef-ficients in (35) are positive. This means that all roots of thesystem have negative real parts, which ensure its stability.The method for a second-order system can be used to determinethe coefficients KILi

and the convergence factors λILito

get the desired performance.

B. Experimental Setup

The four-phase FIBC test bench and the four-phase FIBCconverter are shown in Fig. 10. Each inductor current has zero-flux Hall effect current sensor for feedback control where theinductor current references Ki are generated by a real-timeboard dSPACE DS 1104. The control system developed in thisstudy has been downloaded using the Matlab-Simulink andControlDesk software. Experimental results have been obtainedby an emulated FC power source. The benefits of interleavingthe input current ripple make the control signals of the mainswitches be shifted 90◦ from each other. In the experimentalevaluation implemented for this project, the control signals areshifted by means of a Field-Programmable Gate Array controlcard.

The specification of the implemented four-phase FIBC aredetailed in Table III.

C. Experimental Results

1) Sliding-Mode Controller Validation: The dynamic re-sponse of the sliding-mode controller for a step variation ofinductor current from 13 to 20 A shown in Fig. 11. It shows that

Fig. 10. Test bench and four-phase FIBC converter. (a) Test bench. (b) Four-phase FIBC converter.

TABLE IIIFOUR-PHASE FIBC SPECIFICATION

the currents perfectly follow the reference signal with a settlingtime of 0.8 ms and with no noticeable ringing or overshoot. Thisindicates that the proposed controller has excellent dynamicperformance.

Fig. 12 shows the steady-state FC current, the converterinput current, and the inductor current for an inductor currentreference of 17.5 A. Similar to its dynamic performance, theproposed sliding controller has very good steady-state responsewith negligible steady-state error around 17.5 A.


Fig. 11. Sliding-mode controller dynamic response for a step variation ofinductor current from 13 to 20 A.

The value of the coefficients KILiand the convergence

factors λILifor this excellent performance of the proposed

sliding-mode controller are given by

λILi= KILi

= 6000. (36)

The steady-state waveforms underline the great benefit of thefour-phase FIBC from the current ripple point of view. One cango from a 22-A current ripple in the inductors to 3 A at theconverter input. By using a second-order low-pass filter, the FCcurrent ripple is nearly zero, as shown in Fig. 12.

The steady-state switch driving signals with 70% steady-stateduty cycle and 90◦ out of phase from each other are shownin Fig. 13.

Fig. 14 shows experimental and analytical four-phase FIBCefficiency curves, which indicate that the implemented con-verter has a maximum efficiency of 95% at a power demandof 2.5 kW and an efficiency of 94.7% at a power demandof 5 kW (operating point). Such efficiency is very good forintensive-current low-voltage power source and much higherthan an equivalent traditional dc-dc boost converter for the sameapplication.

VIII. CONCLUSION

This paper has proposed a new family of converter topologiesfor optimized hybrid integration of FCs and supercapacitors.Three different solutions have been investigated, i.e., two-

Fig. 12. Sliding-mode controller steady-state response for inductor currentreference of 17.5 A.

phase, four-phase, and six-phase FIBCs have been comparedwith the conventional dc-dc boost converter. Analysis hasshown that these proposed FIBC converters have all bettercharacteristics for input current ripple, inductor volume, andcapacitor stress better than classic boost converters. Studieshave been made to evaluate their operation for an increasednumber of phases. As a result, it has been concluded that asix-phase FIBC shows that is an efficiency figure comparablewith a four-phase FIBC for the same rated power and similarcircuit complexity. In addition, there are benefits in decreasinginductor volume and capacitor stress, corroborating that all therelevant design parameters are optimized for a four-phase FIBCwhen compared with other FIBC structures. As a conclusion,a four-phase FIBC has been selected, and nonlinear sliding-mode control has been implemented for the feedback look,


Fig. 13. Steady-state switch driving signals with 70% steady-state duty cycleand 90◦ out of phase from each other.

Fig. 14. Implemented converter efficiency. The four-phase FIBC has anefficiency of 94.7% at a power demand of 5 kW (operating point).

where experimental results showed excellent performance withaugmented characteristics such as improved input current ripplereduction, a decrease in inductor volume, and higher efficiencyunder a full-range transfer function voltage. The proposed so-lution demonstrates much potential and promise for utilizationin modern FCEV applications.

ACKNOWLEDGMENT

The authors dedicate this paper to the memory of theirfriend and coauthor Dr. B. Blunier, Associate Professor with theUniversité de Technologie de Belfort-Montbéliard, who passedaway on February 23, 2012.

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Mohammad Kabalo (S’09) received the B.S. degreefrom the University of Tishreen, Lattakia, Syria, andthe M.S. degree in electrical engineering from theEcole Centrale de Lyon, Ecully, France, in 2005and 2009, respectively. He is currently working to-ward the Ph.D. degree in electrical engineering withthe Research Institute on Transportation, Energyand Society, Université de Technologie de Belfort-Montbéliard, Belfort, France.

His current research interests include power elec-tronics and dc-dc power converters for fuel cell

applications.

Damien Paire was born in France in 1979. Hereceived the M.S. degree in electrical engineeringfrom INSA of Lyon, Villeurbanne, France, in 2002,the Agregation degree from the Ecole Normale Su-perieure de Cachan, Cachan, France, in 2003, and thePh.D. degree from System and Transport Laboratory,Université de Technologie de Belfort-Montbéliard(UTBM), Belfort, France, in 2010.

He was a Lecturer with UTBM from 2004 to 2011and has been an Associate Professor since 2011.His research interests include energy management,

power electronics, and hybrid systems.

Benjamin Blunier (deceased) received the M.Sc.and Ph.D. degrees in electrical engineering from theUniversité de Technologie de Belfort-Montbéliard(UTBM), Belfort, France, in 2004 and 2007, respec-tively. He studied fuel cell system modeling andparticularly their air management and control forhybrid and electric vehicles.

He was an Associate Professor with UTBM untilhis death on February 23, 2012. His research in-terests included fuel cells systems; electric, hybrid,and plug-in hybrid vehicles; and intelligent energy

management in smart grids and microgrids.

David Bouquain received the M.S. degree in electri-cal engineering from the Franche-Comté University,Besancon, France, in 1999 and the Ph.D. degree inelectrical engineering from the Université de Tech-nologie de Belfort-Montbéliard (UTBM), Belfort,France, in 2008.

From 2000 to 2002, he has been an Engineerwith the Laboratory of Electrical Engineering andSystems. He worked on a prototype of hybrid truckfor the French army. Since September 2002, he hasbeen Teacher and Researcher with the UTBM. He

is currently an Associate Professor with System and Transport Laboratory,UTBM, working in the research field of energy management of electric andhybrid vehicles and fuel cell systems.

Marcelo Godoy Simões received the B.S. and M.S.degrees from the University of São Paulo, SãoCarlos, Brazil, the Ph.D. degree from The Universityof Tennessee, Knoxville, in 1985, 1990, and 1995,respectively, and the D. Sc. degree (Liv re-Docência)from the University of São Paulo, São Carlos,Brazil, in 1998.

He is currently an Associate Professor withColorado School of Mines (CSM), Golden, wherehe has been establishing research and educationactivities for the development of intelligent control

for high-power-electronic applications in renewable and distributed energysystems, where he currently serves as Director of the Center for the AdvancedControl of Energy and Power Systems. He has been involved in activities relatedto control and management of smart grid applications since joining CSM.

Abdellatif Miraoui (SM’09) was born in Moroccoin 1962. He received the M.Sc. degree from HauteAlsace University, Mulhouse, France, in 1988 andthe Ph.D. and Habilitation degrees from the Univer-sity of Franche-Comté, Besancon, France, in 1992and 1999, respectively.

He is currently the President of Cadi AyyadUniversity, Marrakech, Morocco. Since 2000, hehas been a Full Professor of electrical engineering(electrical machines and energy) with the Univer-sité de Technologie de Belfort-Montbéliard, Belfort,

France, where he was the Vice President of Research Affairs from 2008 to2011, the Director of the Electrical Engineering Department from 2001 to 2009,and the Head of the “Energy Conversion and Command” Research Team (38researchers in 2007). He is a Doctor Honoris Causa of the Technical Universityof Cluj-Napoca, Cluj-Napoca, Romania. He was an Editor of the InternationalJournal on Electrical Engineering Transportation. He is the author of morethan 80 journal and 150 international conference proceeding papers. He is alsothe author of four textbooks about fuel cells. His special research interestsinclude fuel cell energy, energy management in transportation, and the designand optimization of electrical propulsions/tractions.

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