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Pardis Khayyer, Afshin Izadian and Parviz Famouri

West Virginia UniversityMorgantown, WV 26506 USA

Abstract-Fuel cell electric vehicles are mostly relying onoperation of their fuel cell and battery system. Single powersource systems use battery units as backup; however, inheavy loads or instances with low State Of Charge (SOC)levels, there is a need for other mechanisms to providereliable energy for the system. This paper investigates thenatural enhanced reliability of operation in an advancedsystem configuration with two downsized fuel cells. The twofuel cell configuration brings high fuel efficiency byeconomic load sharing between two fuel cells. The reliability

of this system configuration is investigated and comparedwith conventional designs of hybrid fuel cell vehicles.

Keywords: Hybrid Fuel Cell Vehicle, Reliability, Double FuelCell.

I. INTRODUCTIONRecent advancements in fuel cell technology have made

them suitable candidates for portable applications andspecifically in vehicles. Electric vehicles take the mostadvantage of fuel cells in different configurations. They

bring the advantage of longer driving range compare tobattery-powered vehicles and increase the performance ofthe system by providing fuel-economy configurations.

Electric vehicles use fuel cells either as the only source ofenergy or they are connected to a backup source of powersuch as battery or ultracapacitors to configure non-hybridor hybrid fuel cell electric vehicles respectively.Traditional designs of hybrid electric cars utilize a singlefuel cell and battery backup. The new configuration oftwo fuel cell power sources in hybrid fuel cell vehicleswas proposed in [1]. Fuel cells were downsized to providethe same amount of power and offered the advantage of ahighly fuel economic design. Highly efficient drivingconditions in urban applications were obtained. Figure 1shows the double downsized fuel cell vehicle topology.

Figure 1, Double downsized fuel cell vehicle topology

One of the major obstacles in commercialization of fuelcell vehicles is their low reliability of operation [2] whichresults in a huge reduction in the overall systemreliabilities. [2] and [3] have conducted research on

overall reliability of fuel cell vehicles. Reliability analysisof a single PEM (Proton Exchange Membrane) fuel cellsystem is studied in [4] and [5]. [6] has focused on thereliability analysis of a single Direct Methanol Fuel Cell.

Reliability of a single source fuel cell system highlydepends on the operation of the source. Reliability of afuel cell power source follows the Weibull distributionthat decreases over time. This means that an aged fuelsystem is less reliable. In addition, backup sources such as

battery units in electric vehicles are designed for transientoperations and cannot provide energy for long time to actas a reliable source. This paper investigates the reliabilityof operation of a two fuel cell source without consideringthe contribution of the battery unit since it is designed fora short period of operation.

In the following sections, reliability enhancement of adouble fuel cell power source is compared with thereliability of traditional designs. The reliability isintroduced and used for various system configurations.

II. RELIABILITYReliability by definition is the probability that an itemwill perform its function adequately for the desired periodof time when operated according to specified conditions[7]. Reliability is defined mathematically as

=

t

dxxftR )()( , (1)

wheref (x)is the failure probability density function and tis the time period. F(t), the cumulative probabilitydistribution function which is also called the failure

probability, is defined as

=t

dxxftF )()( , (2)

In reliability analysis, it is assumed that the system havethe chance to operate without failure during a specific

period of time. A fuel cell is a two state device whicheither operates or fails during its operation. Configurationof components in the system can categorize a network intofour distinctive cases of series, parallel, k-out-of-m unitnetwork and standby redundant system. These systems aredefined for the convenience of readers.

M. Iskander et al. (eds.), Technological Developments in Education and Automation,

DOI 10.1007/978-90-481-3656-8_89, Springer Science+Business Media B.V. 2010

Reliability Investigation of a Hybrid Fuel Cell Electric

Vehicle Powered by Downsized Fuel Cells

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A. Series NetworkIf the devices/subsystems of a network are connected in

series, it is called a series network. In such network,failure of any of the components leads to failure of thewhole system. In the series network, overall reliability ofthis network consisting of k components is calculated by

{ } { } { } { })(1...)(1)(1)(1)( 321 tFtFtFtFtR ks = , (3)

where )(tRi is the ith unit/component reliability

and )(tFi is the ith component failure probability for

ki ,....2,1= and is defined as,

{ } )()(1 tRtF ii . (4)

B. Parallel NetworkIf the devices/subsystems of a network are connected in

parallel, the network is called a parallel network. Thistype of system only fails when all itscomponents/subsystems fail to operate; therefore, this

configuration is used to increase reliability of the overallsystem. The reliability of the overall system is calculated

by

=

=k

iip tFtR

1

)(1)( . (5)

C. k-out-of-m Unit NetworkThis type of network contains munits and operates if k

parallel units operate. The reliability is defined as

[ ] [ ] ikim

ki imk tRtRmtR

=

= )(1)()()( , (6)

where )(tR is the unit reliability, mis the total number ofsystem units and kis the number of units required for thefunction of the system.

D. Standby Redundant SystemIn a standby redundant system, kunits are on standby

while one unit functions. The system reliability in thiscase is calculated by

1

0

)(

0

)!().()( 0 =

= iedtttRk

i

dttit

s

t

, (7)

where is the hazard rate or instantaneous failure rateand is defined as the rate of change of the failedcomponents quantity divided by number of survivedcomponents at time t [7].

III. WEIBULL DISTRIBUTIONDifferent distributions such as Weibull, Normal,

Exponential Uniform, Extreme value, etc. have

applications in reliability engineering analysis. Weibulldistribution is commonly used for reliability analysisrelated to PEM fuel cell systems [5]. The hazard rate forthe Weibull distribution is defined as,

BAtt =)( . (8)

More details are defined as1

0)(

=

ttt , (9)

where is defined as the shape parameter, is the

characteristic life or scale parameter and 0t is the location

parameter. The probability density function of Weibulldistribution is expressed as,

=

t

ett

tf

1

0)( (10)

.

The reliability function is expressed as

=

0

)(

tt

etR . (11)

Weibull distribution becomes an exponential casewhen 1= (the failure rate is independent of age). In thenext section the system reliability analysis for the

proposed configuration of multiple fuel cells in hybridfuel cell vehicle is presented.

IV. RELIABILITY ANALYSIS FOR DOUBLE FUEL CELLSYSTEM

In this section, reliability analysis of one fuel cell isformulated and is used for analysis of a parallel network.The probability of a single fuel cell is considered 1 atthe start of operation and is decreased as time increases. In(11), equals 1 [8] which results in a constant failure rate

of

1

= , and 0t is zero for a brand new fuel cell unit [9].

Figure 2 shows the reliability of individual fuel cellsand the resultant parallel network of double power sourcesfor different failure rate values. This figure illustrates acase where failure rate of fuel cell #1 is more than failurerate of fuel cell 2; therefore, the reliability of fuel cell #1decays faster. This figure also shows an improvement inthe overall reliability of the system which is greater thaneach of fuel cells individually. This demonstrates higherreliability of the multiple fuel cell configuration proposedin this research.

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Figure 2, Each fuel cell and the parallel system reliability curves for

21 >

Figure 3 shows the reliability evaluation of fuel cellswith the same failure rate values. In this case, both fuelcell reliability curves decay with the same rate; however,

the overall reliability of the parallel system is higher thanthe individual cells.

Figure 3, Each fuel cell and the parallel system reliability curves for

21 =

Simulations indicate that by using the multiple fuelcell configuration not only higher efficiency is gained forthe system in urban driving cycles, but also a morereliable system is achieved by implementing the newtopology.

V. CONCLUSIONIn this paper the reliability analysis for the newconfiguration of a double fuel cell vehicle was discussed.The configuration of double fuel cells in hybrid fuel cellvehicles brings the advantage of high efficiency and fueleconomic operation while enhancing the reliability ofoperation in power sources. Results demonstrated thathigher reliability was obtained in the system bydownsizing the fuel cell power source.

REFERENCES

[1] P. Khayyer and P. Famouri, Application of Two Fuel Cells inHybrid Fuel Cell Vehicles, Powertrains, Fuels and LubricantsMeeting, October 2008, Chicago, IL, USA

[2] M. Marchesoni and S. Savio, Reliability Analysis of a Fuel CellElectric Car. 2005 European Conference on Power Electronicsand Applications, 11-14 Sept. 2005. 10 pp.

[3] L. Wu and H. Li, H, The Reliability Work in Fuel Cell VehiclesRoad Test, IEEE International Conference on VehicularElectronics and Safety, 2006. ICVES 2006. 13-15 Dec. 2006. pp.481 484.

[4] V. Mangoni, M. Pagano and G. Velotto, Fuel Cell ReliabilityModel based on Uncertain Data, International Conference onClean Electrical Power, 2007. ICCEP '07. 21-23 May 2007. pp.730 735.

[5] S. A. Feitelberg,, J. Stathopoulos and Z. Qi, Reliability of PlugPower GenSysTM Fuel Cell Systems, Journal of Power Sources,vol. 147, Issues 1-2, 9 September 2005, pp. 203-207.

[6] G. Aydinli, N.S. Sisworahardjo and M.S. Alam, Reliability andSensitivity Analysis of Low Power Portable Direct Methanol FuelCell, The International Conference on "Computer as aTool"EUROCON, 2007. 9-12 Sept. 2007, pp. 1457 1462.

[7] B. S. Dhillon, Reliability Engineering in Systems Design andOperation, Publisher: Van Nostrand Reinhold Company Inc.,1983.

[8] K. strm, E. Fontell and S. Virtanen, Reliability analysis andinitial requirements for FC systems and stacks, Journal of PowerSources, Volume 171, Issue 1, 19 September 2007, Pages 46-54

[9] Relex Web Page:http://www.relex.com/resources/art/art_weibull3.asp

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