Energy cost analysis of a solar-hydrogen hybrid energy system for ...

ARTICLE IN PRESS

Available at www.sciencedirect.com

journal homepage: www.elsevier.com/locate/he

I N T E R N A T I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 9

0360-3199/$ - see frodoi:10.1016/j.ijhyde

�Corresponding auE-mail address:

Energy cost analysis of a solar-hydrogen hybrid energysystem for stand-alone applications

Jeremy Lagorsea,�, Marcelo G. Simoesb, Abdellatif Miraouia, Philippe Costergc

aGESC, UTBM, Rue Thierry Mieg, 90000 Belfort, FrancebPower Electronics Laboratory, Department of Engineering, CSM, Golden, CO 80401, USAcTotal, 2 place de la Coupole, La Defense 6, 92078 Paris La Defense Cedex, France

a r t i c l e i n f o

Article history:

Received 2 January 2008

Received in revised form

21 March 2008

Accepted 21 March 2008

Available online 20 May 2008

Keywords:

Fuel cells

Photovoltaic power systems

Solar energy

nt matter & 2008 Internane.2008.03.054

[email protected] (

a b s t r a c t

Three configurations of fuel cell and photovoltaic hybrid systems were evaluated in this

paper based on economic constraints. In order to estimate the energy cost of each

configuration, sources were sized with an analytical approach. An energy based modelling

has been developed with Matlab/Simulink to observe evolution of the system during the

period of one year. The simulation results were used for optimizing the configuration costs

in order to obtain the most cost effective system. An appropriate system sizing based on

the proposed optimization solution, showed that a system composed with a photovoltaic

generator, a fuel cell, an electrolizer and a battery can deliver energy in a stand-alone

installation with an acceptable cost.

& 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights

reserved.

1. Introduction

In order to produce electricity for a domestic stand-alone

system, the classical solution associating photovoltaic (PV)

cells and batteries presents limits when required to feed a

system throughout one year cycle. Indeed, the battery and the

solar generator have to be over-sized to respond to the critical

periods when the solar insolation delivers a very small

amount of energy. Currently, most of the systems avoid

over-sizing by adding a diesel generator which supplies the

load during critical periods [1]. A possible solution consists in

adding a proton exchange membrane fuel cell (PEM FC) [2].

This kind of fuel cell (FC) has the advantage to produce

electricity without greenhouse emissions when the fuel is

hydrogen. However, when the fuel is methane, for example,

CO2 emissions are produced. Therefore, we consider only

hydrogen as fuel in this study. Fig. 1(a)–(c) show the three

configurations considered in this paper.

tional Association for HyJ. Lagorse).

The configuration in Fig. 1(a) consists of a PV generator, a

battery and a FC fed by hydrogen (H2) from an external source

to supply the system during critical periods (i.e. winter in

north hemisphere). A second configuration is shown in Fig.

1(b) that does not use batteries to store energy but only an

electrolizer supplied by PV producing H2 from water by

electrolysis. The water is collected from the rain; and the H2

produced is then stored in a tank and feeds the FC [3,4]. The

last configuration shown in Fig. 1(c) mixes the storage system

of the two previous configurations using both a battery and an

electrolizer to store the energy [5].

In this paper, a methodology to design each configuration

analytically is proposed. The simulation modelling approach

is presented in the next section. The results are discussed and

an optimization based on a cost function is introduced. For

final sizing of each system the energy cost (kWh cost) is

evaluated to discuss and to compare the economic feasibility

of each of those systems.

drogen Energy. Published by Elsevier Ltd. All rights reserved.

ARTICLE IN PRESS

0 2 4 6 8 10 12 14 16 18 20 22 240

20

40

60

80

100

Time (hours)

Loa

d Po

wer

(W

)

Fig. 2 – Load profile on a 24 h period.

H2

PEMFC

BAT

ElectricalConverter

Load

PV

H2

PEMFC

ElectricalConverter

PV

Electrolyzer

Load

H2

PEMFC

ElectricalConverter

PV

Electrolyzer

BAT

Load

Fig. 1 – Configurations layouts. (a) Configuration 1: PV,

battery, FC is fed by an external hydrogen tank; (b)

configuration 2: PV, FC, electrolizer and hydrogen tank and

(c) configuration 3: PV, battery, FC, electrolizer and hydrogen

tank.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0

1000

2000

3000

4000

5000

6000

7000

Dai

ly a

vera

ge in

sula

tion

on 1

m2 (

Wh)

Fig. 3 – Daily average insolation on the Odeillo site.

I N T E R N AT I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 92872

2. System sizing

2.1. Sizing hypothesis

2.1.1. Consumption estimationThe first step to size the sources and the other devices is to

evaluate the load profile. The chosen profile is presented in

Fig. 2; the load average power is 50 W which represents an

annual energy consumption of 438 kWh. This consumption

evolution is based on a domestic consumption in countries of

North Africa, like for instance Morocco. Two consumption

peaks are represented in the morning and in the evening. The

night consumption corresponds to devices in sleep mode.

2.1.2. Solar power availabilityObviously, the solar power is linked to the weather condi-

tions, and hence is unpredictable, especially on the insolation

received on a specified area. Based on a real case near

‘‘Perpignan’’ (French Pyrenees), the solar radiation data come

from the year 1999, which appears as a typical year. Indeed,

the radiation data among the seasons belong to the average

values of the site. On this site, the total annual solar energy

received on 1 m2 is about 1.6 MWh. Assuming that a PV

generator with polycrystalline technology presents an effi-

ciency of 10%, 160 kWh are annually obtained using 1 m2 PV

array. The solar radiation data are sampled every 6 min, Fig. 3

shows the variation of daily average insolation over the year

[6]. Because of Sun–Earth geometry, the variations decrease

near the equatorial regions, and increase towards the polar

regions [7].

2.1.3. Technology choiceIn order to obtain a precise energy cost, the technologies of

each device have to be understood. For the FC, a PEM (proton

exchange membrane) cell is considered. This kind of FC

operates with hydrogen as fuel under normal temperature

conditions (from 30 to 200 1C and can work with a pressure of

1 atm. Moreover, this technology becomes commercialized

with stack electrical efficiency about 40%.

The chosen battery is a regular lead-acid battery.

This technology has a good efficiency, low cost and low

ARTICLE IN PRESS

I N T E R N A T I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 9 2873

self-discharge (less than 5% per month). The main drawback

for this battery is its weight, but in a stationary system, that is

not important.

The polycrystalline PV cells are currently the best choice in

terms of quality and price. They present an efficiency lower

than the monocrystalline technology (respectively, about

10–13% compared to 15–22%) but they are cheaper. That is

why this technology is commonly used in most of PV

systems.

The last element considered is the electrolizer. At this

moment, two technologies working under normal tempera-

ture are available: alkaline and PEM. PEM is a new technology

and is twice as expensive as alkaline technology (30h=W

against 15h=W [8]). Furthermore, alkaline technology has

been used for a long time in industry and its lifetime reaches

about 20 years.

2.1.4. Element sizingThe last step of the sizing is to find the power or capacity of

each device. It depends on the considered configuration.

Several solutions are available and an optimization is needed.

The following section details a first approach, without using

optimization but only the analytical relations.

2.2. First sizing

2.2.1. First configurationFirst, for the configuration number 1 as in Fig. 1(a), the FC

power is fixed. FC net power can be equal to the load average

power (50 W). The load surplus is generated by another device

(PV if available or battery). Considering that the FC auxiliary

systems need about 20% of the net power (for cooling and air

pressurization), it is necessary to use a 60 W FC gross power.

Then, the hydrogen consumption and the battery capacity

have to be fixed. These two variables are linked but there is no

analytical relation between them. Thanks to an estimation

given by a simulation model which is detailed in the next

section, the evolution of hydrogen volume consumed accord-

ing to battery capacity can be observed. The simulation model

is run with several battery capacities and the corresponding

hydrogen consumption is plotted in Fig. 4. With a low battery

capacity, the hydrogen consumption is high because the FC is

0 2 4 6 8 10 120

50

100

150

Battery Capacity (kWh)

H2

Vol

ume

(m3 )

Fig. 4 – Volume of consumed hydrogen per year against

battery capacity for a fixed photovoltaic power.

often activated. On the contrary when the battery capacity is

bigger, the FC is less activated and so, few hydrogen is

consumed. Over a certain battery capacity, the hydrogen

consumption remains quite constant. This is because the PV

power is constant and so, even if the battery is larger, it will

not be fully charged and the autonomy is not improved. Then,

to decrease the hydrogen consumption, the PV and the

battery has to be enlarged. This problem of optimization is

presented in Section 3.3.

Fig. 4 shows that the hydrogen consumption does not

change much when the battery capacity is over 2 kWh. Below

this limit, the capacity decrease involves a sharp hydrogen

consumption increase. So a battery of 2.4 kWh is chosen,

which represents 2 days of autonomy for the system. With

such battery capacity, the yearly hydrogen consumption is

less than 70 m3 (normal) (normal cubic meter with normal

conditions: pressure of 1013.25 hPa and temperature of 0 1C).

Using hydrogen compressed at 200 bar, a 350 L tank is

sufficient to stock the hydrogen during one year.

Finally, the PV surface can be easily calculated assuming

that solar generator delivers the whole energy consumed.

SPV ¼Econsumed on 1 year

Eproduced on 1 year with 1 m2

¼438160� 2:75 m2 (1)

This surface represents a 275 W peak PV panel.

2.2.2. Second configurationAs in the first configuration, FC power has to be determined

first. In this configuration shown in Fig. 1(b), the FC must be

able to supply the load all by itself. So, the FC net power is

100 W (load maximum power) and considering auxiliary

systems consuming 20% of this power, the gross power is

120 W.

Then, it is necessary to estimate the hydrogen tank

capacity. In an initial approach, it is considered that the

hydrogen energy storage system (electrolizer, compressor,

tank and FC) has 100% efficiency. Based on this assumption

and through simulation results, the evolution of stored

energy during a year (8760 h) can be observed in Fig. 5.

The stored energy ranges between 0 and about 80 kWh, so

on this initial approach, the tank has to store this difference

of energy. It is a seasonal storage system: energy produced

during summer period is consumed during winter periods.

0 1000 2000 3000 4000 5000 6000 7000 8000 90000

20

40

60

80

Time (hours)

Stor

ed E

nerg

y (k

Wh)

Fig. 5 – Amount of stored energy during one year. It is

assumed that a certain energy quantity is present at the

beginning of the year coming from the previous year.

ARTICLE IN PRESS

Table 1 – First sizing results

Device 1st configuration 2nd configuration 3rd configuration (determined by optimization)

PV 2:75 m2 13 m2 Optimization needed

Battery capacity 2.4 kWh – Optimization needed

FC 60 W 120 W 60 W

H2 consumption 80 m3 (normal) – Optimization needed

H2 storage volume 60 m3 (normal) 60 m3 (normal) Optimization needed

Electrolizer power – 1.3 kW Optimization needed

I N T E R N AT I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 92874

But, taking into account the FC efficiency, around 40%, it

becomes

EH2 ¼MAXðEstoredÞ �MINðEstoredÞ

ZFC¼

80200:4¼ 200 kWh (2)

Considering the hydrogen higher heating value (142 MJ/kg

or 39.4 kWh/kg), the amount of energy to store on chemical

form represents a volume of about 60 m3 (normal). Such an

amount of hydrogen must be reduced using a compressor and

an electrolizer working under pressure. A pressure of 200 bar

would enable to store the hydrogen in a 300 L tank. It should

be noticed that this quantity of hydrogen is not the quantity

consumed, but the quantity to be stored. That is why this

value is less than the one presented in the first configuration.

To size the PV power, it is necessary to evaluate the part of

energy directly consumed from PV ðPart directly from PVÞ and

the part consumed from the energy storage system

ðPartfrom storageÞ. An estimation, confirmed later with the

simulation model, considers that 30% of energy consumed

comes directly from the PV with an efficiency of 100%

neglecting the electrical conversion components efficiency.

The remaining 70% comes from the hydrogen storage. The

hydrogen storage efficiency can be estimated using the

following relation:

ZH2 storage ¼ Zelectrolizer � ZFC ¼ 0:4� 0:4 ¼ 16% (3)

The compression efficiency is neglected in comparison to

others efficiencies. Indeed, the compression efficiency is

about 95% [11]. The quantity of energy to produce in one

year can be expressed by Eq. (4).

Eproduced ¼ Econsumed �Partdirectly from PV

1þ

Partfrom storage

ZH2 storage

!

Eproduced ¼ 438�0:31þ

0:70:16

� �� 2048 kWh (4)

To produce such an energy amount, a PV array of 12:8 m2 is

required, which represents about 1.3 kWh.

The last element to define is the electrolizer. In this

approach, the electrolizer power is equal to the PV maximum

power to convert all the surplus of PV power in hydrogen.

Hence the electrolizer power is about 1.3 kW.

2.2.3. Third configurationThe third configuration showed in Fig. 1(c), based on the two

previous configurations, consists of several elements: PV, FC,

electrolizer and battery. It is impossible to size each element

analytically because the characteristics of the different

devices are linked together. For example, the battery capacity

should increase if the electrolizer power or PV power

decreases. Therefore, this sizing comes from a computer

optimization based on the simulation model further pre-

sented. Only FC power is sized like in the first configuration:

its net power is equal to the load average power.

2.3. First sizing overview

Table 1 presents the results of the first sizing method for the

three configurations, to compare them easily.

3. System cost optimization

3.1. Simulation model

The goal of this model is to observe the system on the energy

point of view. Three models have been developed using

Matlab/Simulink, one for each configuration. As the model of

the third configuration is the most complete one, combining

other two configurations, only this model is described in the

paper (Fig. 6).

3.1.1. PV modelThe insolation data (expressed in W=m2) is required to

compute the produced PV power using only a con-

stant coefficient depending on PV surface ðSPVÞ and efficiency

ðZPVÞ [9].

PPV ¼ Insolation� ZPV � SPV (5)

3.1.2. Battery modelThe battery input power can be positive or negative depend-

ing on the charge or discharge mode of operation. The battery

power is obtained from Eq. (6).

PBAT ¼ PPV þ PFC � PLOAD (6)

The state of charge (SOC) is deduced from the battery power

and efficiency:

SOCBAT ¼

ZðPBAT CHARGING � ZBAT

� PBAT DISCHARGINGÞdt (7)

When the battery SOC is lower than a threshold value the FC

is activated. On the contrary, when SOC is higher to a

threshold value, FC is stopped and the electrolizer starts up:

the battery power given in Eq. (6) becomes the electrolizer

ARTICLE IN PRESS

Fig. 6 – Third configuration model: storage with hydrogen and lead acid-battery, photovoltaic source and load are also

present.

I N T E R N A T I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 9 2875

power (see Eq. (8)).

PELEC ¼ PPV � PLOAD (8)

3.1.3. Electrolizer modelThe electrolizer is simply considered as a constant gain

corresponding to the electrolizer efficiency and an integrator

to determine the amount of produced hydrogen. The amount

of hydrogen consumed by the FC is also determined. The

difference between both gives the amount of available stored

hydrogen, following Eq. (9).

SOCELEC ¼

ZðPELECTROLIZER � ZELECTROLIZERÞdt

�

ZPFC

ZFC

� �dt (9)

3.1.4. FC modelThis model permits to calculate hydrogen consumption

according to the delivered power. Indeed FC efficiency ðZFCÞ,

appearing in Eq. (9), is not constant. The difficulty is to

consider that the FC efficiency only depends on the power

delivered. The ratio of energy consumed in hydrogen form

and the electrical energy produced is called global efficiency

ðZglobalÞ. As shown in Eq. (10), it can be expressed as function

of other efficiencies.

Zglobal ¼ Ztotal � Zmatter � Zsystem (10)

where Zsystem takes into account the auxiliary consumptions.

Eq. (11) defines it as the ratio between the net and the gross

power:

Zsystem ¼Pnet

Pgross(11)

Efficiency Zmatter takes into account the hydrogen losses. In

fact, all the fuel is not consumed and the efficiency depends

on the FC hydrogen supply mode. The case considered here is

the closed mode where the matter efficiency is estimated

between 2% and 5% due to frequents purges of hydrogen

circuit.

Efficiency Ztotal is the ratio between the real voltage ðVðjÞÞ and

the theoretical voltage ðEfictiveÞ if the system would transform

the entire chemical energy (contained in hydrogen) in

electrical energy.

Ztotal ¼VðjÞ

Efictive� ZF (12)

Efficiency ZF is called faradic efficiency and is assumed to be

100%. Eq. (13) links FC voltage V with the current density j

[10,11].

VðjÞ ¼ E0 � DVact � DVohm � DVconc (13)

In Eq. (13), E0 represents the open cell voltage, DVact

represents the activation overpotential, DVohm represents

the ohmic overpotential and DVconc represents the concentra-

tion overpotential. It can also be expressed as in Eq. (14) with

the detailed expression of the overpotentials (DV’s).

VðjÞ ¼ E0 � Aac lnjb

� �� rj�m expðn� jÞ (14)

In this empirical equation, Aac represents the Tafel slope, b

the activation coefficient, r the ohmic resistance coefficient, m

and n are the concentration coefficients. Considering a

Ballard Mark V FC where the parameters are given in

Table 2, the gross power and voltage FC against current

density is plotted (Fig. 7) [12].

A maximal power working point ðPMAXÞ of 622 wm=cm2

exists for a current density of 1012 mA=cm2. An operational

point over this value is not of any interest, because it would

increase losses for a lower power. Considering unitary gross

power ðPUnitaryÞ defined in Eq. (15), a correspondence between

voltage and gross power is obtained. Then the total efficiency

and the gross power can also be linked (Fig. 8).

PUnitary ¼VðjÞ � j

PMAX(15)

ARTICLE IN PRESS

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

Unitary Gross Power

Tota

l eff

icie

ncy

Fig. 8 – Fuel cell efficiencies against unitary gross power. (a)

efficiency against unitary gross power.

Start FCStart FCAddAdd

SaturationSaturationPowerPower

2

1

++MultiplyMultiply

Gross PowerGross Power

EfficiencyEfficiency

-C--C-

PauxPaux

Add1Add1

Net PowerNet Power

Auxiliary PowerAuxiliary Power

Unitary Gross PowerUnitary Gross Power0-->10-->1

-K--K-

3

4

6

Fig. 9 – Simulin

Table 2 – Ballard Mark V fuel cell parameters

Parameter Value Unit

Aac 2:89� 10�2 V

b 0.04 mA=cm2

r 2:114� 10�4 A=cm2

m 1:4� 10�5 V

n 8� 10�3 cm2=mA

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.2

0.4

0.6

0.8

1

1.2

1.4

Cel

l Vol

tage

(V

)

0

100

200

300

400

500

600

700

Current density (A/cm2)

Gro

ss P

ower

(m

W)

Voltage

Power

Fig. 7 – Fuel cell voltage and power evolutions against

current density.

I N T E R N AT I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 92876

Finally, based on Eqs. (11) and (15), it is possible to obtain a

relation between global efficiency and the unitary gross

power.

The FC model developed with Simulink is shown Fig. 9. The

signal ‘‘Start FC’’ controls the FC start and stop.

3.2. Simulation results and discussions

When the FC does not work because the battery SOC is high

enough (see Fig. 10(a)) and the solar power is too weak, the

load is supplied by the battery. When the solar power rises

during the day, load is directly supplied by PV and battery is in

charging mode. When the battery SOC reaches its nominal

value, battery charging is stopped and electrolizer is activated

(see Fig. 10(b)).

When the FC is working (see Fig. 11), it supplies the load up

to 50 W. Over this value, either PV supplies the additional load

or the battery supplies it when solar radiation does not exist.

During the day, the PV charges the battery and when battery

reaches its nominal SOC, the FC is stopped.

Many other energy management techniques could be

implemented but a simple energy approach has been

preferred to support the economic stand-point.

3.3. Cost optimization

A cost optimization is realizable based on the third and the

first configuration but not for the second one. Indeed, the

0 0.2 0.4 0.6 0.8 10

10

20

30

40

50

60

Unitary Gross Power

Glo

bal e

ffic

ienc

y (%

)

Total efficiency against unitary gross power and (b) global

DivideDivide IntegratorIntegrator Tenth of HourTenth of Hour

-K--K-

Wh->m3Wh->m3H2 Quantity in m3H2 Quantity in m3at 15at 15°C and 1atmC and 1atm

H2 EnergyH2 Energyin Whin Wh

1

2

5

H2 PowerH2 Power

1/101/101s

++

k FC model.

ARTICLE IN PRESS

0 4 8 12 16 20 24-100

0

100

200

300

400

500

600

Time (hours)

Pow

er (

W)

PVBat

4 8 12 16 20-100

0

100

200

300

400

500

Pow

er (

W)

0 242000

2100

2200

2300

2400

2500

2600

2700

Time (Hours)

Ene

rgy

(Wh)

EbatPbatPelec

Fig. 10 – Powers and energies evolutions during 24 h when

FC does not work. (a) PV and BAT powers and (b) battery

and electrolizer powers and stored energy in the battery.

0 4 8 12 16 20 24-100

-50

0

50

100

150

200

250

300

Time (hours)

Pow

er (

W)

PVBatFC

Fig. 11 – Powers evolution during 24 h when FC works.

Table 3 – Costs of the elements

Device Value Unit Lifetime

Poly-crystalline PV 5 h=Wpeak 20 years

Lead-acid battery 90 h=kWh 5 years

Alkaline electrolizer 15 h=W 20 years

PEM fuel cell 8 h=W 5000 h

Hydrogen 0.39 h=m3 (normal) –

I N T E R N A T I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 9 2877

second configuration is fully determined with the first sizing

presented in Section 2.2.2 and, consequently, it does not need

an optimization.

The function to optimize is the system cost. The system

cost function is defined as a sum of PV cost, battery cost,

hydrogen cost and FC cost.

Csystem ¼ CPV þ CBAT þ CH2 þ CFC (16)

The PV cost is proportional to the PV power (or PV surface)

and the battery cost is proportional to the battery capacity.

This hypothesis is verified for low-power systems. Table 3

details the unitary cost of the elements [8].

The hydrogen cost applies only for the first configuration

and this cost takes into account the production from a large

plant by electrolysis and the transportation. The details of the

hydrogen cost are available in [13].

Based on those unitary costs, the system total cost is

defined, but the amount of consumed hydrogen remains to be

determined. This information comes directly from the

simulation. The simulation model is run for several combina-

tions of PV power and battery capacity and the hydrogen

consumption and the FC working rate is obtained. After that,

these results are used to calculate the total cost of the system,

assuming the system lifetime is 20 years (equal to the PV

lifetime). Fig. 12 shows the optimal combination of PV power

and battery capacity.

In the configuration 1, the minimum system cost is

obtained for the following combination of PV power and

battery capacity:

PPV ¼ 540 W; CapBAT ¼ 2 kWh

This leads to a cost of 4544h for 20 years of operation.

4. Comparison of configurations

4.1. Configurations costs

With the optimization of configurations 1 and 3, the costs are

estimated and presented in Table 4. The kWh price based on a

20 years lifetime is also presented (see Eq. (17)). The kWh

price can be compared to the average price proposed by EDF

(Electricity of France, French company producing electricity)

which is about 0:12h=kWh, without taking into account the

price of distribution extension in case of isolated site.

PkWh ¼Csystem

20 yearsR

Pload(17)

The second configuration is 10 times more costly than the

other systems because it uses only the hydrogen storage

system. Indeed, the efficiency of the hydrogen storage system

is very low and therefore the PV has to be larger to produce

more energy. Furthermore, the FC has also to be more

powerful to supply the maximum load power. Consequently,

based on the current cost of FCs and the efficiency of a

hydrogen storage system, a configuration relying only on a

hydrogen storage system is much more expensive than a

solution implying a battery.

ARTICLE IN PRESS

10002000

30004000

50006000

7000

2

4

6

4000

6000

8000

10000

12000

PV surface (m

2 )

Battery Capacity (Wh)

Tota

l Cos

t (€

)

Fig. 12 – Cost optimization of the first configuration.

Table 4 – Configuration cost during 20 years working

Cost ðhÞ kWh priceðh=kWhÞ

Globalconfigurationefficiency (%)

Configuration 1 4544 0.519 About 50

Configuration 2 43,300 4:943 22:4

Configuration 3 5646 0.645 About 50

I N T E R N AT I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 92878

The global configuration efficiency ðZGlobal ConfigurationÞ is the

ratio between the energy consumed by the load ðEConsumedÞ

and the energy produced by the PV ðEfrom PVÞ plus the energy

consumed under hydrogen form ðEfrom H2Þ as expressed in

Eq. (18) (Efrom H2applies only for the first configuration). The

global configuration efficiency allows to estimate the waste of

energy between the production and the consumption. This

waste is due to the FC efficiency and the battery efficiency.

Consequently, it should be remarked that the global config-

uration efficiency can be higher than the FC efficiency.

ZGlobal Configuration ¼EConsumed

Efrom PV þ Efrom H2

(18)

4.2. Best configuration choice

Regarding the cost, the configuration 2 is not currently

feasible. However, according to the DOE, the target cost for

FC in 2015 is about 0:03h=W [14,15]. Furthermore, the

improvements for FC should also concern the electrolizer. In

this way, the cost of the second configuration could be less

than 0:5h=kWh and so, the configuration 2 remains a

promising solution for the future.

The two other configurations are feasible in term of cost;

the cost is about 5 times higher than the tariffs of EDF.

However, configuration 3 proposes a completely stand-alone

solution, producing hydrogen on site. On the other hand it is

more expensive and configuration 1 could be preferred.

Configuration 1 is a real alternative to the classical system

coupling PV, battery and diesel generator.

5. Conclusion

This paper developed the economic study of three different

systems associating photovoltaic sources and fuel cells. Three

major ways to gather two sources have been covered: battery

storage, hydrogen storage and the use of both. A dimension-

ing procedure for the systems has been presented. In order to

check the validity of this procedure, a simulation model has

been made for each configuration. The simulation, based on a

realistic photovoltaic production over one year, has allowed to

observe the energy flow. The models and results of the

dimensioning have been used to find the optimal sizing of the

configurations. An optimal sizing of each configuration

allowed to fairly compare the three possibilities of mixing

the two sources of energy. It was concluded that the solution

relying on the only use of hydrogen storage is currently not

feasible. However, this solution could be preferred in near

future when electrolizers and fuel cells become more afford-

able. The two other configurations are similar on the cost

point of view. The choice among them mainly relies on the

use of the system. If the system’s site can be reached to bring

hydrogen, the configuration relying on battery storage and

fuel cell supplied by an external tank is the best. For a fully-

autonomous system, the configuration featuring both hydro-

gen and battery storage is preferred.

Acknowledgment

The authors thank Total to have originated this project and

for their interest on this work.

R E F E R E N C E S

[1] Anne L, Michel V. Energie solaire photovoltaique. Paris:Dunod; 2006.

ARTICLE IN PRESS

I N T E R N A T I O N A L J O U R N A L O F H Y D R O G E N E N E R G Y 3 3 ( 2 0 0 8 ) 2 8 7 1 – 2 8 7 9 2879

[2] Kroposki B, Levene J, Harrison K, Sen PK, Novachek F.Electrolysis: opportunities for electric power utilities in ahydrogen economy. 38th North American power symposium;2006. p. 567–76.

[3] Nelson DB, Nehrir MH, Wang C. Unit sizing of stand-alonehybrid wind/PV/fuel cell power generation systems. IEEEPower Eng Soc General Meeting 2005;3:2116–22.

[4] Padro CEG, Lau F. Advances in hydrogen energy. New York:Plenum Publishing; 2000.

[5] Iannone F, Leva S, Zaninelli D. Hybrid photovoltaic and hybridphotovoltaic-fuel cell system: economic and environmentalanalysis. IEEE Power Eng Soc General Meeting 2005;2:1503–9.

[6] CNRS, Weather data hhttp://www.imp.cnrs.fr/meteo/index.shtmli.

[7] Tiwari GN. Solar energy: fundamentals, design, modellingand applications. Alpha Science; 2002.

[8] Busquet S. Etude d’un systeme autonome de productiond’energie couplant un champ photovoltaıque, un electro-lyseur et une pile a combustible: realisation d’un banc d’essai etmodelisation. Dept. Energetique, Ecole des Mines de Paris, 2003.

[9] Chedid R, Akiki H, Rahman S. A decision support techniquefor the design of hybrid solar-wind power systems. IEEETrans Energy Conversion 1998;13(1):76–83.

[10] Larminie J, Dicks A. Fuel cell systems explained. New York:Wiley; 2000.

[11] Blunier B, Miraoui A. Piles a combustible, Principe, modelisa-tion et applications. Technosup; 2007 [in French].

[12] Laurencelle F, Chahine R, Hamelin J. Characterization of aBallard MK5-E proton exchange membrane fuel cell stack.Fuel Cells 2001(1):66–71.

[13] hwww.afh2.orgi, Etude technico-economique prospective surle cout de l’hydrogene. Memento de l’Hydrogene, Fiche 10,2006, available online: hhttp://www.afh2.orgi.

[14] DOE hydrogen, fuel cells and infrastructure technologiesprogram, multi-year research, development and demonstra-tion plan. U.S. Department of Energy, May 2007, availableonline: hwww1.eere.energy.gov/hydrogenandfuelcells/mypp/i.

[15] Blunier B, Miraoui A. Air management in PEM fuel cell: state-of-the-art and prospectives. IEEE-PES-MSC, ACEMP’07, Elec-tromotion, 2007, p. 245–53.