Design methodology of fuel cell electric vehicle power...

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Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1270 Design Methodology of Fuel Cell Electric Vehicle Power System Xiaofeng Liu, Demba Diallo, Senior Member, IEEE, Claude Marchand, Member, IEEE, Laboratoire de Genie Electrique de Paris, CNRS UMR8507; SUPELEC; Univ Paris-Sud 11; UPMC Univ Paris 06; 11 rue Joliot-Curie, Plateau de Moulon, F-91192 Gif-sur-Yvette Cedex Tel: (+33)-1-69851664, fax: (+33)-1-69418318 [email protected] AbstrllCl-This paper develops a methodology to optimize the sizing of the power components in a fuel ceD electric vehicle from the driving cycle and the specified acceleration performance. The fuel cell and the energy storage system associated (battery orland ultra capacitor) design parameters are the numbers of series and parallel branches respectively NSi and Npi. They are set so as to minimize an objective function which includes mass, cost and a penalty function. The solution must fulfill the performance requirements and respect the constraints on each power component. The methodology is based on a judicious combination of Matlab-Simulink® and a dedicated software tool Pro@Design® weD suited to treat inverse problems. An application in a fuel ceillbattery power train illustrates the feasibility of the proposed methodology. I. INTRODUCTION To address the energy and environmental impact with the increasing road transport population worldwide, many automo- tive industries are investing in development of fuel cell electric vehicles (FCEV) at present time due to their low exhaust emissions and high energy efficiency in comparison with the internal combustion engine vehicle. In 2002 the first and only commercial fuel cell car Honda FCX was certified by the u.s Environmental Protection Agency (EPA) [1]. There are some recent prototypes like General Motors Sequel and Peugeot 207 EPURE. However the FCEVs are not widely available to the public market yet, because there remain some obstacles to overcome: reduction of the vehicle cost, increase of the transient performance, and reduction of the size and weight of power components. Thus the design procedure is to select, size, build the structure and develop an efficient control of the power flow. The targets of the design are the minimization of cost and weight and the maximization of perfonnance and reliability. Fuel cells (FC) are electrochemical devices that don't allow the bidirectional energy flow, thus it is impossible to recover the braking energy in a pure FCEY. Hybridization with an energy storage system (ESS) is indispensable. On the other hand, the fuel cell downsizing via hybridization allows reduc- ing the power train cost and volume over the pure FCEV in which the fuel cell system is made large enough to meet the maximum power requirement. The ESS is usually a battery module, an ultra capacitor (UC) module, or a combination of both. Batteries have a high energy density, and ultra capacitors 978-1-4244-1736-0/08/$25.00 ©2008 IEEE have a high power density and nearly unlimited number of charge and discharge cycles. A fair comparison study of fuel cell power train with different ESSs is given by [2] in regards to power train cost, fuel economy and acceleration time. The authors show that the fuel cell-battery and the fuel cell-battery- ultra capacitor vehicle are the more interesting choices and are close competitors. One of the ways to minimize the weight and cost of vehicle power train is by using optimal design. The authors of [3] compare a design optimization method of 6 different ESSs for an Internal Combustion Engine hybrid vehicle in terms of efficiency, weight, volume and cost. In a FCEV power train, the sizing of the electric motor and inverter depends on the maximum vehicle power demand. Therefore, their sizes and costs are fixed [4]. However, the weight and cost of the power train can be considerably reduced by using an adapted sizing of power components (fuel cell and ESS). The present study aims at developing a methodology to help the designers to optimise the sizing of the power components in a FCEY. The procedure based on the mechanical power cycle required by the vehicle motion computes for a selected configuration of the DC bus, a set of vectors containing the minimum energy to store in the battery for a given power of the FC and the UC. Using this set of vectors, an optimisation algorithm extracts the dimensions of the FC and the ESSs by simultaneously minimising the mass and cost, under the various technological constraints related to each component. The rest of the paper is organized as follow: the power train system description is given in the second section; the third section addresses the proposed methodology and the optimal design parameters obtained according to this design procedure are also given in this section; in the fourth section, some simulation results validate the consistency of the design; Finally, we conclude in the last section. II. POWER TRAIN SYSTEM DESCRIPTION Fig. I shows the general configuration of the DC bus in a FCEY. The power train consists of a fuel-cell stack, a battery pack, an ultra capacitor pack, three static DC-DC converters (one unidirectional and two bidirectional), an inverter and an electric machine.

Transcript of Design methodology of fuel cell electric vehicle power...

Page 1: Design methodology of fuel cell electric vehicle power systemdownload.xuebalib.com/3chzUSHNrn5K.pdf · In 2002 the first and only commercial fuel cell car Honda FCX was certified

Proceedings of the 2008 International Conference on Electrical Machines Paper ID 1270

Design Methodology of Fuel Cell Electric Vehicle Power System

Xiaofeng Liu, Demba Diallo, Senior Member, IEEE, Claude Marchand, Member, IEEE, Laboratoire de Genie Electrique de Paris,

CNRS UMR8507; SUPELEC; Univ Paris-Sud 11; UPMC Univ Paris 06; 11 rue Joliot-Curie, Plateau de Moulon, F-91192 Gif-sur-Yvette Cedex

Tel: (+33)-1-69851664, fax: (+33)-1-69418318 [email protected]

AbstrllCl-This paper develops a methodology to optimize the sizing of the power components in a fuel ceD electric vehicle from the driving cycle and the specified acceleration performance. The fuel cell and the energy storage system associated (battery orland ultra capacitor) design parameters are the numbers of series and parallel branches respectively NSi and Npi. They are set so as to minimize an objective function which includes mass, cost and a penalty function. The solution must fulfill the performance requirements and respect the constraints on each power component. The methodology is based on a judicious combination of Matlab-Simulink® and a dedicated software tool Pro@Design® weD suited to treat inverse problems. An application in a fuel ceillbattery power train illustrates the feasibility of the proposed methodology.

I. INTRODUCTION

To address the energy and environmental impact with the increasing road transport population worldwide, many automo­tive industries are investing in development of fuel cell electric vehicles (FCEV) at present time due to their low exhaust emissions and high energy efficiency in comparison with the internal combustion engine vehicle. In 2002 the first and only commercial fuel cell car Honda FCX was certified by the u.s Environmental Protection Agency (EPA) [1]. There are some recent prototypes like General Motors Sequel and Peugeot 207 EPURE. However the FCEVs are not widely available to the public market yet, because there remain some obstacles to overcome: reduction of the vehicle cost, increase of the transient performance, and reduction of the size and weight of power components. Thus the design procedure is to select, size, build the structure and develop an efficient control of the power flow. The targets of the design are the minimization of cost and weight and the maximization of perfonnance and reliability.

Fuel cells (FC) are electrochemical devices that don't allow the bidirectional energy flow, thus it is impossible to recover the braking energy in a pure FCEY. Hybridization with an energy storage system (ESS) is indispensable. On the other hand, the fuel cell downsizing via hybridization allows reduc­ing the power train cost and volume over the pure FCEV in which the fuel cell system is made large enough to meet the maximum power requirement. The ESS is usually a battery module, an ultra capacitor (UC) module, or a combination of both. Batteries have a high energy density, and ultra capacitors

978-1-4244-1736-0/08/$25.00 ©2008 IEEE

have a high power density and nearly unlimited number of charge and discharge cycles. A fair comparison study of fuel cell power train with different ESSs is given by [2] in regards to power train cost, fuel economy and acceleration time. The authors show that the fuel cell-battery and the fuel cell-battery­ultra capacitor vehicle are the more interesting choices and are close competitors.

One of the ways to minimize the weight and cost of vehicle power train is by using optimal design. The authors of [3] compare a design optimization method of 6 different ESSs for an Internal Combustion Engine hybrid vehicle in terms of efficiency, weight, volume and cost. In a FCEV power train, the sizing of the electric motor and inverter depends on the maximum vehicle power demand. Therefore, their sizes and costs are fixed [4]. However, the weight and cost of the power train can be considerably reduced by using an adapted sizing of power components (fuel cell and ESS). The present study aims at developing a methodology to help the designers to optimise the sizing of the power components in a FCEY. The procedure based on the mechanical power cycle required by the vehicle motion computes for a selected configuration of the DC bus, a set of vectors containing the minimum energy to store in the battery for a given power of the FC and the UC. Using this set of vectors, an optimisation algorithm extracts the dimensions of the FC and the ESSs by simultaneously minimising the mass and cost, under the various technological constraints related to each component.

The rest of the paper is organized as follow: the power train system description is given in the second section; the third section addresses the proposed methodology and the optimal design parameters obtained according to this design procedure are also given in this section; in the fourth section, some simulation results validate the consistency of the design; Finally, we conclude in the last section.

II. POWER TRAIN SYSTEM DESCRIPTION

Fig. I shows the general configuration of the DC bus in a FCEY. The power train consists of a fuel-cell stack, a battery pack, an ultra capacitor pack, three static DC-DC converters (one unidirectional and two bidirectional), an inverter and an electric machine.

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Proceedings of the 2008 International Conference on Electrical Machines

Fuel Cell

Battery

Electric f--r--,----~ motor

& f-+-,-+-,--~--i Inverter

, ~--~: , , , , , '--__ ..J;

,--------------_____ ~I

Fig. I. Power train configuration

In the FCEV powetrain, when the vehicle power require­ment is high, it's assured by the power sources such as:

(1)

where Pre, PIe, Pbat and Pue are respectively the vehicle power requirement, the maximum power provided by the fuel cell, the battery power and the ultra capacitor power. The losses in the inverter, the electric motor and the transmission are not considered in this study.

As a first application, we assume in the following that the electric power train is only composed of a pack of battery as ESS combined with the fuel cells. The configurations of fuel cell stack and battery pack are shown in Fig. 2 and 3 respectively.

'-~_.....II -L-____ ~ _____________ _L ___ _

'---------------~------------.-I Npp

Fig. 2. Configuration of the fuel cell stack

1 1 1 1 1 1

9-====1 ========R:=.:.=------==-==--[2:::7--1

_ Npb

Fig. 3. Configuration of the battery pack

2

Npp, NPb represent the number of parallel branches to form the fuel cell stack and the battery pack, respectively. N sp, N Sb represent the number of units connected in series in each fuel cell branch and battery branch, respectively.

The total cost of the fuel cell stack and battery pack is given as:

c - N N cunit + N N cunit (2) total - sp· pp. Ie Sb· Pb· bat

where C'j-:it and C;::tit are the cost of each fuel cell unit and battery unit, respectively.

The total mass of the fuel cell stack and battery pack is given as:

M - N N M unit + N N M unit (3) total - sp· pp. Ie Sb· Pb· bat

where M'/-:it and Mi:a~it are the mass of each fuel cell unit and battery unit, respectively.

It is assumed that the values of cunit cunit Munit and . Ie ' bat' Ie Mi:a~·t are fixed for a given technology of fuel cell and battery in this paper. The unit cost, weight and other specifications of the sample fuel cell unit and battery unit used are presented in Table I and II.

From (2) and (3), one can see that the total cost and mass depend on the numbers of fuel cell and battery units, therefore an optimal sizing of fuel cell and battery can reduce considerably the total cost and the total mass of power system.

TABLE I FUEL CELL UNIT SPECIFICATIONS [4]

Fuel cell type Manufacturer Weight Volume

Polymer Electrolyte Membrane (PEM) Relion

Open circuit voltage Cost

TABLE II

16.28 g 0.0142 I

IV 1.23$

BATTERY UNIT SPECIFICATIONS [5] [6]

Battery type Manufacturer Nominal Cell voltage Rated capacity Specific power Specific energy Weight Cost

Plastic Case Prismatic (NI-MH) Panasonic EV energy

1.2 V 6.5 Ah

1300 W/kg 7.8 Wh/kg

228 g 15.16 $

III. POWER SYSTEM DESIGN PROCEDURE

In a FCEV, the fuel cell is considered as the primary power source, so the simple maximum power can be used to size the fuel cell stack; however, the battery is an electrical energy storage unit, it must be sized so that to store sufficient energy (Wh) and provide adequate peak power (W) for the vehicle to have a specified acceleration performance and the capability to meet appropriate driving cycles [7].

The proposed method is used to determine x = [N sp, Npp,N sb,Npb] based on a given driving cycle and a specified

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Proceedings of the 2008 International Conference on Electrical Machines

acceleration; the Extra Urban Drive Cycle (EUDC), as shown in Fig. 4, is taken as an example in this study, but the method is also suitable for the other driving cycles. The acceleration performance required is to propel the vehicle at 50 km/h in 5 s. During this acceleration, both the fuel cell and battery supply the power to the vehicle.

I I

50 100 150 200 250 300 350 400 Time (8)

Fig. 4. Extra Urban Drive Cycle

The optimization procedure is represented in Fig. 5; it can be split in two steps.

Step J

Step 2

Varying Pfc

from Pt" to Pfr'

&::: correspond to

Pfc

Design parameters Ns". NP .. Nsb• and Np.

Matlflb-SimuJlnk®

Pro@)Jesign®

Performance evaluation with the solution Mflliflb-SimuJiItk®

Fig. 5. Design procedure

A. Predictable evolution of power system in Matlab®

The aim of this step for each selected fuel cell maximum power:

• to find the required minimum energy to be stored in the battery for the driving cycle characteristic;

• to find the battery peak power necessary to obtain the acceleration performance

3

The data obtained will be used as the input for the next step. Firstly, the vehicle is considered like a moving mass sub­

jected to the tractive effort provided by the propulsion unit and the vehicle resistance opposing its movement [8] [9] [10], the power demanded by vehicle motion along the longitudinal direction is expressed by (4):

1 2 . dv Pre=f·m.g+"2.p.Cx·8.v +m·g·smo:+m· dt (4)

where m is the vehicle mass in kilograms; 9 is the acceler­ation due to gravity (9.81m/s2 ); Cx is the aerodynamic drag coefficient of vehicle; 8 is the frontal area of the vehicle; p is the air density (1.3kg/m3 ); 0: is the grade angle, it is supposed that 0: is zero in this paper; and v is the vehicle speed in metre per second.

The selected vehicle for the design is a segment MI type (Peugeot 307, Citroen C4, and Honda Civic). Its main characteristics are listed in Table III.

TABLE III BASIC VEHICLE SPECIFICATIONS

m : total weight f : coefficient of rolling resistance S : frontal area ex : Aerodynamic coefficient Wheel radius

1300 Kg 0.0133

2.61 m 2

0.32 0.32m

The required power demand profile corresponding to EUDC is obtained using (4) with Matlab-Simulink®. By varying the value of Pfc from a minimum value ~in to a maximum value ~ax , we search the corresponding values of era~n and pf:tk, which represent the minimum energy stored in the battery and the adequate peak power, respectively.

The areas 81, 82 and 83 in Fig. 6 are the three candidates and the final value is obtained from (5) on the assumption that the battery is fully charged (soc = 0.8) before each power assistance:

Fig. 6. Power requirement profile for test driving cycle EUDC

n min ""'8 ebat = ~ k

k=l

(5)

Fig. 7 shows the required demand to achieve the specified acceleration performance, and for a given maximum fuel cell power, the battery has to provide an adequate peak power to fulfill the maximum power demand.

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oo,-----~----~----~----~----~--__,

Fig. 7. Power requirement for the specified acceleration and the adequate battery peak power

Fig. 8 shows the predictable evolution of the mInImum storage energy for different fuel cell powers. As the fuel cell power level is increased, the battery minimum storage energy requirement decreases. The minimum fuel cell power is set to satisfy for example the embedded auxiliaries' power requirement or the vehicle power at cruise speed.

'" ~6oo 1 {5OO ... 400

~ 15300

'200 !5 ~ 100

~~--~O~.5----~---'~.5----~2--~:2.~5~~3~~"3.5 Fuel cell stack power (W) x 104

Fig. 8. Energy requirement for different fuel cell stack power levels

Fig. 9 shows the predictable evolution of the adequate peak power for different fuel cell powers. As the fuel cell power level is increased, the adequate peak power decreases.

4.5

2

1.50'O-----:O:'c:.5c-----:------:-'c'.5O:-----:2c-----::'2.c:-5 ----:3~---73.5 Fuel cell power (W) x 104

Fig. 9. Adequate peak power for different fuel cell stack power levels

4

B. Optimization with constraints in Pro@design®

The object of this step is to find the optimal design x = [Nsp, Npp,Nsb,NpbJ by minimizing an objective function with a specific software tool Pro@design®. The algorithm integrated in the software is a deterministic one using the gradient technique.

Firstly, an objective function T(x) based on the total mass and cost is defined as:

T(x) = aM . Mtotal(X) + ac . Ctotal(X) + F(x) (6)

where aM and ac are normalised designer factors, selected by the designer to combine the different criteria; and F(x) is a penalty function.

The penalty function takes into account the system con­straints. For example, the (7) and (8) express the battery pack storage energy requirement and peak power.

(7)

N N p,max > p,peak (8) Sb' Pb' bat_cell - bat

where ebaCceli is the nominal energy of battery unit, which can be computed from Table II; D..s, the available working range, is the difference between the upper and the lower limits of the battery State Of Charge (SOC); Pb';;;fxcell is the maximum power of battery cell. -

The constraint on the fuel cell is given in (9)

(9)

where pn~~ell is the maximum fuel cell unit power, as shown in Fig. 10.

__ Voltage curve

0.8

~ ..

- - - Power curve

~-:"1"17.3W~- - .... .,;' ",

, ... 15

;,; ~ -,06 > §

0.4

0.2

-=:.. 0~~~5--~'O~--'~5c--~~~--:2~5c--~3~0--~3~5----4·~

Unit Current (A)

Fig. 10. Power-current and Voltage-current characteristics of the fuel cell unit

In addition, the maximum ratings (battery cell current and fuel cell current) are also considered in the penalty function. For example, the current working range for the battery unit is between Ib:!;n cell (-40 A) and Ib:!fxcell (80A), and the fuel cell unit current limits are shown in FIg. 10, the working range is between Ij,/.::cell (2 A) and 17'c~~ell (35A).

Table IV shows the results obtained with the proposed design procedure. The robustness of the minimum has been evaluated by a random selection of the initial conditions of the optimisation algorithm. The final cost is nearly 8690US$ (or 5615€) and the final mass is nearly 128 kg based on data obtained from Table II and I. It corresponds to different

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configurations (the values of N Si and Npi) and corresponding DC voltage for the same cost and mass. Therefore, the final configuration depends on the application and the appropriate voltage of the DC bus. In addition, the values of the design parameters must be integer values, so the selection of the low integer value would lead to the reduction of the total cost and mass, but to the performance degradation in some extreme operating conditions. On the other hand, the selection of the upper integer value would lead to the increase of powertrain performance to the detriment of augmentation of the total cost and mass.

TABLE IV DESIGN PARAMETERS,CORRESPONDING VBUS, COST AND MASS

Nsp Npp NSb Npb Vbus (V) Cost (~ or €) Mass (kg) 215.9 5.61 128.1 3.71 250 8694.6 or 5614.9 128.1 259.7 4.66 153.7 3.09 300 8688.6 or 5611.0 128.0 303.5 3.99 179.3 2.65 350 8692.7 or 5613.6 128.1 355.6 3.41 205.0 2.32 400 8701.6 or 5619.4 128.2

IV. MODELS AND SIMULATION RESULTS

The optimal parameters N Si and N Pi obtained are loaded in the global simulation environment (including the electric motor, the static converters, the control strategy etc) to evaluate the consistency of the design.

A. Fuel cell unit model

The fuel cell unit model focus on the electrical output characteristic (voltage-current curve) as shown in Fig. 10, so the output voltage ofa single cell can be defined as (10) [11]:

VI;!! = ENernst - V aet - Vohmie - Vcon (10)

where ENernst is the thermodynamic potential, V act , Vohmie

E. Control strategy

A simple control strategy is implemented in the system, but it is not an optimal one compared to the control strategy proposed in [15], which minimizes fuel consumption and maintains the battery soc. The rules of control strategy are described as follow:

• if the power is negative, the battery can recover 65% the regenerative braking energy;

• if the power demand is positive and inferior to the maximum power of fuel cell stack, the fuel cell stack supplies all the required;

• if the power demand is positive and superior to the maxi­mum power of fuel cell stack, the fuel cell stack provides its maximum power, and the battery pack provides the difference.

In addition, the fuel cell stack provides a minimum permanent power (4 kW) for the utilization of the auxiliaries system even If the power demand is negative.

The models of each component of the power train and the control strategy are associated, and simulated in the Matlab Simulink® environment. The power requirement, the fuel cell stack power, the battery pack power during EUDC and during the specified acceleration, the voltage of the DC bus, the currents in the battery cell and the fuel cell during EUDC are simulated and presented as follow.

The power of fuel cell stack and the battery pack during the EUDC cycle and the specified acceleration are shown in Fig. II and 12.

and Veon represent the activation voltage drop, the ohmic ~ voltage drop, and the concentration voltage drop, respectively. J B. Battery cell model

The battery cell is modelled as an internal electromotive force Ebat, which is a function of state of charge (SOC), in series with an internal resistance Rbat[8]. The output voltage can be defined as (11):

(11)

where Ebat(soc) is determined by the discharge characteristic [12].

C. Static converter

The fuel cell system is connected to the DC bus through a Boost converter, and the battery pack is a Buck/Boost one. The dynamic models and the regulators RST are used in this paper, which are described in [13].

D. Electric motor and transmission

The electric motor is modelled using a speed torque map for a 58 kW permanent magnet motor [14]. The transmission is simply considered as an ideal gear ration in this paper.

5

-~L-~~~~~IOO~~~'~~~~~~2~~~~~~~3~~~~~ Tim. (s)

Fig. 11. Power requirement, fuel cell stack and battery powers during EUDC

Fig. 13 shows the dc bus voltage during the EUDC cycle; it is shown that the error of dc bus voltage is acceptable (less than 5% of the reference bus voltage).

Fig. 14 reveals that the currents flowing in and out of the fuel cell and the battery are within the specified characteristics. Nevertheless, one can notice that for the battery, the actual current is far from the limits. This is because the battery has been sized for a specific accleration performance and therefore behaves more like a storage unit.

V. CONCLUSION

This work illustrates a design methodology of the primary source of energy (fuel cell) and the ESS based on the driving

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x 10" 6 --.~--~~---~--~---~~---

Fig. 12. Power requirement, fuel cell stack and battery powers during the specified acceleration

315

310

~ 305

f ~~--~--~~----,-L----r--~~r-~---­~ 295

lelTorl < 5% of vRt! 290

285

2800~--=5":-0 -----c,0'-c0----c",5'-c0-----=:200'::- 250 300 350 400 Time (s)

Fig. 13. DC bus voltage during EUDC

cycle of a FCEV and a specified acceleration performance. This methodology relies on the appropriate combination of Matlab-Simulink® and Pro@Design®. The first one simu­lates the whole system to extract the total mechanical power required to propel the vehicle and to evaluate the design parameters consistency while the second one is devoted to the optimization of design parameters through an objective function. This approach is flexible and can be extended to the design of the electric motor by the combination with an appropriate software.

REFERENCES

[I] c.c. Chan, "The State of the Art of Electric, Hybrid, and Fuel Cell Vehicles, " Proceedings of the IEEE, Vol. 95, N° 4, pp 704-718, April 2007.

[2] J. Bauman, M. Kazerani "A Comparative Study of Fuel Cell-Battery, Fuel Cell-Ultracapacitor, And Fuel Cell-Battery­Ultracapacitor Vehicles, "IEEE Transactions on Vehicular Tech­nology, Vol. 57, Issue 2, pp 760-769, March 2008

[3] T. Hoftnan, D. Hoekstra, R.M. Van Druten, M. Steinbuch, "Optimal design of energy storage systems for hybrid vehicle drivetrains;' IEEE Conference on Vehicle Power and Propulsion, 7-9 September. 2005

[4] Y. Wu, H. Gao, "Optimization of Fuel Cell and Supercapacitor for Fuel-Cell Electric Vehicles," IEEE Transactions on Vehicular Technology, Vol. 55, Issue 6,pp 1748-1755, November 2006.

[5] http://www.toyotapriusbattery.coml [6] K.J. Kelly, M. Mihalic, M. Zolot "Battery usage and thermal

performance of the Toyota Prius and HondaInsight during

6

50 100 150 200 250 Time (s)

300 350 400

~100r---.----.----r-------------.----r---'

~ E ~ 50 a ~ ::l

~

_____ _ Batteryunituppercurrentlimit ______ _

g m _50~_-_-~" __ -_-__ L-~_t_re_~_u_ui_tw_w_u_._urre __ ut_lw_i_t __ -~ __ -_-~-_-_-__ ~

o 50 100 150 200 250 Time (5)

300 350 400

Fig. 14. Fuel cell unit and battery unit current during EUDC with the limits

chassis dynamometer testing," The Seventeenth Annual Battery Conference on Applications and Advance, pp 247-252, 2002.

[7] A.F Burke,"Batteries and Ultracapacitors for Electric, Hybrid, and Fuel Cell Vehicles," Proceedings of the IEEE, Vol. 95, Issue 4, pp 806-820, April 2007.

[8] X. Liu, H. Hannoun, D. Diallo, C. Marchand "Development of a software tool dedicated to EV or HEV structure analysis: Comparison of two electric power trains for a parallel HEV," CInternational Conference on Ecologic Vehicles Renewable Energies, Monaco, March 2007.

[9] M. Ehsani, K.M. Rahman, H.A. Toliyat "Propulsion system design of electric and hybride vehicule application," IEEE Trans. Ind. Electon, Vol. 44, pp 19-27, February 1997.

[10] H. Hannoun, D. Diallo, C. Marchand, "Energy management strategy for a parallel hybrid electric vehicle using fuzzy logic;' International Symposium on Power Electronics, Electri­cal Drives, Automation and Motion, SPEEDAM 2006, pp 229-234,2006.

[II] I.M. Correa, F.A. Farret, L.N. Canha, M.G. Simoes, "An electrochemical-based fuel-cell model suitable for electrical en­gineering automation approach," IEEE Transactions on Indus­trial Electronics, Vol. 51, Issue 5, pp 1103-1112, October 2004.

[12] A.K. Naim, A.S. Mutasim, lS. Niels, "Emissions and fuel economy trade-off for hybrid vehicles using fuzzy logic;' Math­ematics and computers in simulation, Vol. 66, , pp 155-172, 2004.

[13] S. Caux, J. Lachaize, M. Fadel, P. Shott, L. Nicod, "Modelling and control of a Fuel Cell System and Storage Elements in transport applications;' Journal of Process Control, Vol. 15, Issue 4, pp 481-491, 2005.

[14] Advisor software, Advanced Vehicle Simulator, National Re­newable Energy Laboratory (NREL), U.S Department of Energy, http://www.nrel.gov/.

[15] M.J. Kim, H. Peng, "Power management and design optimiza­tion of fuel ceillbattery hybrid vehicles;' Journal of Power Sources, Vol. 165, Issue 2, pp 819-832, March 2007.

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