Modeling and Simulation of Fuel Cell Electric Vehicles

Mazen Abdel-Salam, Adel Ahmed and Ahmed Elnozahy Electrical Engineering Department

Assiut University

Assiut, Egypt

Mazen2000as@yahoo.com

Ahmad Eid Electrical Engineering Department

Aswan University

Aswan 81542, Egypt

ahmadeid@ieee.org

Abstract - The objective of this paper is to develop a model

for a fuel cell hydrogen vehicle driven by a brushless DC motor.

A two leg directly coupled interleaved boost converter is used to

power the motor from the fuel cell through a three-phase

inverter. The studied system of the fuel-cell vehicle is designed

and simulated using the commercial PSIM9 software. Due the

presence of power converters, different harmonic components

exist in the system, especially in the input voltage/current to the

motor. The ripple contents of current and voltage at the fuel cell

output and the motor input are estimated. An active power filter

is designed in order to reduce the current and voltage harmonics

of brushless DC motor. The instantaneous active and reactive

current components id-iq control method is used in this study to

lessen the harmonic contents at the input of the Brushless DC

motor to the standard values.

Index Terms – Fuel cell, BLDC motor, Interleaved boost

converter, Active power filter and Hybrid vehicles.

I. INTRODUCTION

Fossil fuels including coal, oil, and gas, which are heavily

used as energy sources, can cause air pollution and greenhouse

gas problems. A recent study [1] showed that about 18% of

CO2 (carbon dioxide), being a greenhouse gas, is emitted by

motor vehicles. The development of fuel cell vehicles is very

important to environment and even economical, especially for

a soaring oil price at present. The fuel cell system is widely

regarded as one of the most promising energy sources.

Fuel cell vehicles can be powered directly by hydrogen or other liquid fuels such as gasoline, ethanol or methanol with

an onboard chemical processor. Most analysts agree that

hydrogen is the preferred fuel in terms of reducing vehicle

complexity, but one common perception is that the cost of a

hydrogen infrastructure would be excessive. According to this

conventional wisdom, the automobile industry must therefore

develop complex onboard fuel processors (reformers) to

convert methanol, ethanol or gasoline to hydrogen [2].

Among the various topologies of DC–DC converters,

interleaved boost converter (IBC) or (two leg IBC), has been

proposed as a suitable interface for fuel cells to convert low voltage high current input into a high voltage low current

output. The advantages of interleaved boost converter

compared to the classical boost converter are low input current

ripple, high efficiency, faster transient response, reduced

electromagnetic emission and improved reliability [3].

The application of active power filters (APFs) for mitigating

harmonic currents and compensating for reactive power of the

nonlinear load was proposed. The theory and development of

APFs have become very popular and have attracted much

attention. The APF appears to be a viable solution for

controlling harmonics-associated problems. In operation, the

APF injects equal but opposite distortion as well as absorbing

or generating reactive power, thereby controlling the

harmonics and compensating for reactive power of the

connected load [4].

This paper develops a model for a fuel cell hydrogen vehicle

driven by a Brushless DC Motor (BLDCM). A two leg

directly coupled Interleaved Boost Converter (IBC) is used to

power the motor from the fuel cell through a three-phase

inverter. The studied system of the Fuel-Cell Vehicle (FCV) is designed and simulated using the commercial PSIM9

software. The ripple contents of current and voltage at the fuel

cell output and the motor input are estimated. An APF is

designed in order to reduce the current and voltage harmonics

of BLDC motor. The instantaneous active and reactive current

components id-iq control method is used in this study to lessen

the harmonic contents at the input of the BLDCM to the

standard values.

II. MODELING OF FUEL CELL VEHICLE COMPONENTS

The FCV system consists of a fuel cell connected to a

BLDC motor through an IBC and a 3-phase inverter as shown

in Fig. 1. The IBC is controlled using PI controller to provide

a higher DC voltage Vb from the available fuel cell output

voltage Vfc. The input control signals of the IBC controller is

the IBC output voltage Vb and the output current of the fuel

cell Ifc. A three-phase inverter is controlled to provide the

required input voltage for the BLDC motor which, in turn,

runs following a certain speed profile. To reduce the harmonic

contents of the voltage applied to the BLDC motor, an APF is

connected at the motor terminals as shown in Fig. 1. The APF

is controlled using the id-iq control method which provides efficient way to get rid of the harmonics resulted from the

converters and inverters in the vehicle system. Such control of

the APF is achieved through the motor current (Im ), filter

current (If) and the DC voltage (Vdc ) as shown in Fig. 1. Each

component of the FCV will be explained in the following

subsections.

A. Fuel Cell Model

A proton exchange membrane (PEM) fuel cell consists

mainly of two electrodes (cathode and anode) and an

electrolyte in between. Oxygen (from cathode side) and

Hydrogen (from anode side) are needed for completion of the

reaction. The electrodes are usually made flat and the

electrolyte is a thin layer to increase the contact area. The

structure of the electrode is porous so that both the electrolyte

from one side and the gas from the other can penetrate it. This

is to give the maximum possible contact between the

electrode, the electrolyte and the gas. When an external load is

connected to the fuel cell terminals voltage drops take place to

express activation, ohmic and concentration losses [1].

Fuel cell IBC 3- Phase

inverter BLDC

Motor

APF

Sa, Sb and Sc

Control signals

PI Controller

Ifc Vb

212Vdc 150Vac

51Vdc

Vfc Vb Im

If

If ImAPF control circuit

Vdc

Fig. 1 Proposed FCV system.

1) Activation Voltage Drop: Activation voltage drop

(∆Vact ) is due to the slowness of the reactions taking place in

the cell, which can be minimized by maximizing the catalyst

contact area for reactions. ∆Vact is expressed as [5]:

∆Vact = A ln(ifc +in

io) (1)

Where,

A is constant expressed in V.

in is the internal current density related to internal current

losses expressed in mAcm−2 (the importance of the internal current density is much less in case of higher temperature

operation with no effect on the fuel cell efficiency).

ifc is the output current density given in mAcm−2.

io is the exchange current density related to activation

losses expressed in mAcm−2.

The activation voltage drop of eqn. (1) after removing in is

rearranged to

∆Vact = A ln(ifc

io) = A ln(ifc ) − A ln(io) (2)

∆Vact can be modeled as a resistance 𝑅𝑎𝑐𝑡 as shown in Fig. 2

[1]. 2) Resistive Voltage Drop: Resistive voltage drop

(∆Vohm ) is caused by current flow through the resistance of

the whole electrical circuit including the membrane and

various interconnections, with the biggest contributor being

the membrane [1]. Effective water management to keep it

hydrated reduces its ohmic loss. ∆Vohm is expressed as [1]:

∆Vohm = (ifc + in)r (3)

Where,

r is the area-specific resistance related to resistive losses

expressed in Ωcm−2.

∆Vohm can be modeled as a resistance 𝑅𝑜ℎ𝑚𝑖𝑐 as shown in

Fig. 2 [1].

3) Mass Transport or Concentration Voltage Drop:

Mass transport or concentration voltage drop ( ∆Vconc ) is

caused by gas concentration, which changes at the surface of

the electrodes. ∆Vconc is expressed as [1]:

∆Vconc = mexp(nifc ) (4) Where,

m is constant expressed in V.

n is constant expressed in cm2mA−1.

∆Vconc can be modeled as a resistance 𝑅𝑐𝑜𝑛𝑐 as shown in Fig.

2 [1].

Equation (4) is an empirical one [5] which, gives a good fit to

fuel cell concentration voltage drop with carefully chosen of

constants m and n. Then, the fuel cell terminal voltage (Vcell )

is expressed as [5]:

Vcell = E − ∆Vact − ∆Vohm − ∆Vconc (5) Where,

E is the cell open-circuit voltage at standard pressure and

temperature expressed in V.

E =−∆hf

2F (6)

Where, F is Faraday constant, the charge on one mole of

electrons, 96,485 Coulombs. ∆hf is the change of enthalpy of

formation per mole (= −241.83kj/mol) for water in a steam

form and called lower heating value , and ∆hf = −285.84kj/mol for water in a liquid form and called higher heating

value. According to the above output voltage equations 1-4, an

equivalent circuit [1] is depicted for the fuel cell, as shown in

Fig. 2.

Rohmic

Ract

RconcC

+

-Vcell

+- E

Ifc

Fig. 2 Equivalent circuit of PEM fuel cell.

In the above circuit, C is the equivalent capacitor due to the

double-layer charging effect.

The relation between the fuel cell stack voltage and current

density is [1]:

Vstack = N E − A ln ifc +in

io − ifc + in r − mexp nifc (7)

Where, N denotes number of cells in stack. The later is given

as [1]. Because the second half of eqn. (2) is a constant, one

can deal with this by postulating a real, practical, open circuit

voltage Eoc that is given by the equation [5]:

Eoc = E + A ln(io) (8)

Note that Eoc will always be less than E because io , being

small, will generate negative logarithms. If we substitute

equations (2) and (8) into eqn. (7) and removein , we obtain

[5].

Vstack = N Eoc − A ln ifc − (ifc )r − mexp(nifc ) (9)

The parameters of PEM fuel cell (PEMFC) of eqn. (9) are

given in Table I [5]. There is a difficulty to simulate the fuel

cell according to eqn. (9) because it includes LOG and EXP

Functions. Therefore, a curve fitting command in a software

program in MATLAB package was used to fit the cell I-V

characteristic as expressed by eqn. (9). Fig. 3 shows good

fitting of (I-V) characteristic expressed by equation (10), and

the different voltage drops of fuel cell, which are described by

eqns. (1), (3) and (4).

Vfc = AIfc2 + BIfc + C (10)

Where A = 7 ∗ 10−4 , B = −0.0129 and C = 1.0398

Table I

A Single PEMFC Model Parameters.

Constant Ballard Mark V PEMFC at 70C

E (V)

r (kΩcm−2)

A (V)

m (V)

n (cm2mA−1)

1.031

2.45×10−4

0.03

2.11×10−5

8×10−3

Fig. 3 Fuel Cell (I-V) characteristic according to eqns. (9) and (10).

B. Proposed Fuel Cell Modelling using PSIM

The fuel cell is simulated using the PSIM9 package, as

shown in Fig. 4, where the fuel cell voltage (Vfc ) depends on

fuel cell current (Ifc ).

Math. K C/P

A

V+-

Ifc

Vfc

To IBC

(1) (2) (3)

(4)

(5)

Fig. 4 Fuel cell model.

The proposed fuel cell model consists of:

Block (1) math function block: represents the fuel

cell voltage equation (10).

Block (2) gain block: represents the number of fuel

cell (N).

Block (3) control-power interface block: passes a

control circuit value to the power circuit. It is used as a buffer between the control and the power circuit.

Block (4) current controlled voltage source.

Block (5) current sensor.

C. Two Leg Interleaved Boost Converter

To minimize the ripples, an IBC has been proposed as an

interface for fuel cells to reduce the source current ripples. The

IBC before modification is as shown in Fig. 5, where the fuel

cell current and voltage waveforms contain high ripples, as

shown in Figs. 6 and 7 respectively.

L2

S1

Vfc

S2Load

Control circuit

Vo

I1L1 D1

D2

C

G1G2

Fig. 5 Two leg interleaved boost converter.

Fig. 6 Fuel cell current with time-scale expanded (before insertion of Lf

andCf).

Fig. 7 Fuel cell voltage with time-scale expanded (before insertion of Lf

andCf).

To improve the performance of IBC, the inductor (𝐿𝑓) and the

capacitor (𝐶𝑓) are inserted as shown in Fig. 8. A pronounced

reduction of current and voltage ripples is observed as shown

in Figs. 9 and 10 respectively. The parameters of simulation

for this system are defined in Appendix I.

0 100 200 300 400 500 600 700 800 900 10000.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Fuel Cell Current (mAcm-2)

Fu

el C

ell V

olt

ag

e (

V)

Fuel Cell (I-V) characteristic

Equation (9) Curve

Equation (10) Curve

Ohmic voltagedrop (linear)

Mass transport or concentrationvoltage drop

Activation voltage drop

L2

S1

Vfc

S2Load

Control circuit

Vo

I1L1 D1

D2

C

G1 G2

Lf

Cf

Fig. 8 Modified IBC.

The approximate value of current and voltage ripples in Figs.

6 and 7 before insertion of Lf and Cf are 5A and 0.07V (the

difference between maximum and minimum ripple values)

respectively, while, after insertion of Lf and Cf the values drop

to 0.004A and 0.044Vas shown in Fig. 9 and 10. The output

voltage (Vb) from the IBC after being boosted is shown in Fig.

11, where the fuel cell voltage (Vfc ) is boosted from 51V to 212V, approximately.

III. HARMONICS MITIGATION OF BLDCM Due to the power electronics circuitry, the input supply voltage to the motor contains various harmonics components

[6]. According to the system configuration shown in Fig. 1 the

input voltage (Vo ) to the load (BLDCM with controller) is

boosted to 212V approximately. The line voltage, phase

current and associated harmonics of the BLDCM are plotted

with FFT analysis as shown in Figs. 12 and 13.

To reduce harmonics at the AC load terminal bus, an APF is

shunt connected at the load terminals as shown in Fig. 1.

Fig. 9 Fuel cell current with time-scale expanded (after insertion of Lf andCf).

Fig. 10 Fuel cell voltage with time-scale expanded (after insertion of Lf

andCf).

Fig. 11 IBC output Voltage.

Fig. 12 Current and voltage waveform before using the APF.

Fig. 13 FFT analysis of current and voltage waveform before using the APF.

The APF cancels out the harmonic currents and leaves the

fundamental current component to be provided by the power system [7]. The APF in general consists of a power circuit,

smoothing inductors (Lf1 , Lf2), smoothing high-frequency filter

capacitorsCf, a DC capacitor, Cdc (Fig. 14) and a control circuit

(Fig. 15). The power circuit for a three-phase six-pulse

inverter is shown in Fig. 14. The DC capacitor located in the

DC bus of the voltage-source inverter serves as an energy

storage element. The filter capacitance is used to mitigate the

high-frequency ripple components and thus reducing the

switching stress on the APF switches [8]. The APF with parameters listed in Table II is connected in shunt at point of

common coupling (PCC) as shown in Fig. 14 and controlled

using the instantaneous active and reactive current component

id − iq method as shown in Figs. 15 and 16 [9].

A. APF Control Method

The instantaneous active and reactive current component

theory (p–q theory) is widely used in APF control circuitry to calculate the desired compensation current [10-14] as shown

in Fig. 15.

0 0.05 0.1 0.15 0.2

Time (s)

0

-50

50

100

150

200

250

Vb

0

-10

-20

10

20

Ia

0.15 0.16 0.17 0.18 0.19 0.2

Time (s)

0

-100

-200

-300

100

200

300

Vo

0

5

10

15

20

Ia

0 500 1000 1500 2000 2500

Frequency (Hz)

0

50

100

150

200

Vo

Fig 14 APF schematic diagram.

B. DC Voltage Regulation and Harmonic Current

Generation System

As illustrated in Fig. 16, Imd and Imq are the measured

active and reactive motor current components which are

obtained from abc to dqo transformation block as shown in

Fig. 15 [9]. A dc bus PI controller regulates the dc bus voltage

Vdc to its reference valueVdcr , and compensates for the inverter

losses. The dc bus controller generates a fundamental

harmonic direct current Idh to provide the real power transfer

required to regulate dc bus voltage and compensate the

inverter losses. The reactive power flow is controlled by the

fundamental harmonic quadrature current of positive

sequenceIqh . However, considering that the primary end of the

APF is simply to eliminate current harmonics caused by

nonlinear loads, the current Iqh is set to zero as shown in Fig.

16. The harmonic reference currents Idr and Iqr are

transformed to Ifar , Ifbr , and Ifcr through dqo to abc

transformation block (Fig. 15). By comparing the harmonic

reference currents with actual filter currentsIfa , Ifb , and Ifc , the

gate pulses can be obtained through gate pulse generation system (Fig. 17). Adjusting the PI controller parameters and

comparing the error signal by triangular wave source through

the comparator are sought to generate the gate pulses (𝑄1𝑄6)

as shown in Fig. 17.

IBCFuel

cellIBC

3-phase

inverterBLDC

motor

Smoothing

filter

abc

qd

abc

qd

VdcCdc

Gate pulse

generation

DC voltagr

regulator

Harmonic

current

generation

ImdImq

K

Integrator

Speed

sensor

Vdcr

Vdc

Ifar, Ifbr, IfcrIfa, Ifb, Ifc

g1-6

3-leg

inverter

Iqh=0

α

2

.

.

.

Ima,Imb,Imc

IdrIqr

Idh

ImdhImqh

Fig. 15 APF controls circuit by using the instantaneous active and reactive

current component id − iqmethod.

Table II

APF and its control circuit parameters

Smoothing filter parameters

Filter inductance, 𝐿𝑓1,𝐿𝑓2

Filter capacitance, 𝐶𝑓

2 , 0.5 mH

0.005uf

Filter DC capacitor, 𝐶𝑑𝑐

Voltage regulator system parameters:

Proportional gain for voltage regulator

Tim constant for voltage regulator

DC reference voltage, 𝑉𝑑𝑐

Gate driver system parameters:

Proportional gain for gate pulses

Tim constant for gate pulses

Switching frequency

Triangular wave peak to peak voltage

Transformation angle (θ) parameters:

Proportional gain (k)

Integral time constant

3mF

0.0071

0.001

300 V

0.01

0.005

5kHz

12V

0.1

0.2

C. Simulation Results

After connecting the APF (Fig. 14) at the PCC with the

control circuit (Fig. 15) to the FCV system (Fig. 1), the phase

current at the load side (ima ), the phase current at the source

side (isa ), and the line voltage (vlo ) are shown in Fig. 18. The

Total Harmonic Distortion (THD) of source current is 7.22%

and 4.01% for current at motor side as shown in Fig. 19

against 50.65% for the THD of motor current before using the APF. Therefore, the APF reduced the THD of BLDC motor

current from 50.56% to 4.01%. Fig. 20 shows the three phase

motor currents (ima , imb and imc ), and the three phase source

currents ( isa , isb and isc ), which are harmonic free and the

injected APF currents(Ifa , Ifb , and Ifc ).

IV. CONCLUSIONS

1- A fuel cell model is proposed where the I-V

characteristic of the fuel cell is curve-fitted and

simulated using PSIM9.

2- A two-leg interleaved boost converter is designed to reduce ripple content in fuel-cell output current and

voltage.

3- An APF filter is designed to mitigate the harmonic

content in the brushless DC motor input current and

voltage.

PI Limiter

LPF Idr

Vdc

Vdcr

Imd

LPF Iqr Imq

Imdh

Imqh

Idh

Iqh=0

Fig.16 DC voltage regulation and harmonic current generation circuit.

PI LimiterIfar

Ifa

Q1

Q4

PI LimiterIfbr

Ifb

Q2

Q5

PI LimiterIfcr

Ifc

Q3

Q6

Co

mp

ara

tor

Co

mp

ara

tor

Co

mp

ara

tor

Triangular wave source

Fig. 17 Gate driver system of APF 3-leg inverter.

Fig. 18 Waveforms of phase current at the load side (ima ), the phase current at

the source side (isa ), and the line voltage (vlo ) by using APF.

Fig. 19 FFT analysis of phase current at the load side (ima ), the phase current

at the source side (isa ), and the line voltage (vlo ) by using APF.

Fig. 20 Three phase motor currents, source currents and APF currents

Appendix I:

The values of the parameters that we used in simulation are

shown in the table below.

Parameter The value

N(no. of FC)

Cf(μF)

Lf (mH)

L1,L2 (IBC self inductance mH)

Lm (IBC mutual inductance mH)

F(switching frequency Khz)

Tl (load torque N.m )

PI controller parameters

PI1 gain

PI1 time constant

PI2 gain

PI2 time constant

50

2000

6.5

2

1

5

10

0.99

0.5

0.09

0.0004

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0

-5

-10

5

10

Ima

0

-20

-40

-60

20

40

60

Isa

0.15 0.16 0.17 0.18 0.19 0.2

Time (s)

0

-100

-200

-300

100

200

300

Vlo

0

-5

-10

5

10

Ima Imb Imc

0

-20

-40

-60

20

40

60

Isa Isb Isc

0.15 0.16 0.17 0.18 0.19 0.2

Time (s)

0

-20

-40

-60

20

40

60

Ifa Ifb Ifc