- Email: [email protected]

33 (2008) 2871 – 2879

Available at www.sciencedirect.com

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

Energy cost analysis of a solar-hydrogen hybrid energy system for stand-alone applications Je´re´my Lagorsea,, Marcelo G. Simo˜esb, Abdellatif Miraouia, Philippe Costergc a

GESC, UTBM, Rue Thierry Mieg, 90000 Belfort, France Power Electronics Laboratory, Department of Engineering, CSM, Golden, CO 80401, USA c Total, 2 place de la Coupole, La De´fense 6, 92078 Paris La De´fense Cedex, France b

art i cle info

ab st rac t

Article history:

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

Received 2 January 2008

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

Received in revised form

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

21 March 2008

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

Accepted 21 March 2008

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

Available online 20 May 2008

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

Keywords: Fuel cells Photovoltaic power systems Solar energy

1.

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

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.

reserved.

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.

Corresponding author.

E-mail address: [email protected] (J. Lagorse). 0360-3199/$ - see front matter & 2008 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.ijhydene.2008.03.054

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Load Power (W)

100 H2

PEM FC

80 60 40 20 0 0

Electrical Converter

Load

2

4

6

8

10 12 14 Time (hours)

16

18

20

22

24

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

Daily average insulation on 1 m2 (Wh)

PV BAT

H2

Electrolyzer

PEM FC

Electrical Converter

6000 5000 4000 3000 2000 1000 0

Load

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Fig. 3 – Daily average insolation on the Odeillo site.

PV

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.

H2

Electrolyzer

PEM FC

Electrical Converter

2.1.2.

Load

PV BAT 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.

2.

7000

System sizing

2.1.

Sizing hypothesis

2.1.1.

Consumption estimation

The 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

Solar power availability

Obviously, the solar power is linked to the weather conditions, 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 efficiency 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 choice

In 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

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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 temperature are available: alkaline and PEM. PEM is a new technology and is twice as expensive as alkaline technology (30 h=W against 15 h=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 sizing

The 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.

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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 ¼

Econsumed on 1 year 438 2:75 m2 ¼ Eproduced on 1 year with 1 m2 160

(1)

This surface represents a 275 W peak PV panel.

2.2.

First sizing

2.2.1.

First configuration

2.2.2. First, 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 according 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

Second configuration

As 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.

80 Stored Energy (kWh)

H2 Volume (m3)

150

100

50

60 40 20 0

12

0

1000 2000 3000 4000 5000 6000 7000 8000 9000 Time (hours)

Fig. 4 – Volume of consumed hydrogen per year against battery capacity for a fixed photovoltaic power.

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.

0 0

2

4 6 8 Battery Capacity (kWh)

10

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Table 1 – First sizing results Device

1st configuration

2nd configuration

3rd configuration (determined by optimization)

2:75 m2 2.4 kWh 60 W

Optimization needed

80 m3 (normal)

13 m2 – 120 W –

60 m3 (normal) –

60 m3 (normal) 1.3 kW

Optimization needed

PV Battery capacity FC H2 consumption H2 storage volume Electrolizer power

But, taking into account the FC efficiency, around 40%, it becomes EH2 ¼

MAXðEstored Þ MINðEstored Þ 8020 ¼ 200 kWh ¼ ZFC 0:4

(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 PV Þ and the part consumed from the energy storage system ðPartfrom storage Þ. 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). ! Partdirectly from PV Partfrom storage þ Eproduced ¼ Econsumed 1 ZH2 storage 0:3 0:7 þ 2048 kWh (4) Eproduced ¼ 438 1 0:16 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 configuration

The 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

Optimization needed 60 W Optimization needed Optimization needed

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 presented. 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 model

The insolation data (expressed in W=m2 ) is required to compute the produced PV power using only a constant coefficient depending on PV surface ðSPV Þ and efficiency ðZPV Þ [9]. PPV ¼ Insolation ZPV SPV

3.1.2.

(5)

Battery model

The battery input power can be positive or negative depending 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: Z SOCBAT ¼ ðPBAT CHARGING ZBAT PBAT

DISCHARGING Þ dt

(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

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

power (see Eq. (8)). PELEC ¼ PPV PLOAD

3.1.3.

(8)

Electrolizer model

The 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). Z SOCELEC ¼ ðPELECTROLIZER ZELECTROLIZER Þ dt Z PFC dt (9) ZFC

3.1.4.

FC model

This model permits to calculate hydrogen consumption according to the delivered power. Indeed FC efficiency ðZFC Þ, 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 ðZglobal Þ. 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 ¼

Pnet 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 ðVðjÞ Þ and the theoretical voltage ðEfictive Þ if the system would transform the entire chemical energy (contained in hydrogen) in electrical energy. Ztotal ¼

VðjÞ ZF Efictive

(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 concentration overpotential. It can also be expressed as in Eq. (14) with the detailed expression of the overpotentials (DV’s). j VðjÞ ¼ E0 Aac ln rj m expðn jÞ (14) b 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 ðPMAX Þ 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 ðPUnitary Þ 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 ¼

VðjÞ j PMAX

(15)

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Table 2 – Ballard Mark V fuel cell parameters Parameter

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.

Value

Unit

b

2:89 102 0.04

mA=cm2

r

2:114 104

m

1:4 105

Aac

n

8 10

V A=cm2 V

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.

700 Voltage

600

Power

1

500

0.8

400

0.6

300

0.4

200

0.2

100

0 0

0.2

0.4 0.6 0.8 1 Current density (A/cm2)

1.2

0 1.4

3.3.

Fig. 7 – Fuel cell voltage and power evolutions against current density.

Global efficiency (%)

Total efficiency

1

0.6 0.4 0.2 0 0.2

0.4 0.6 0.8 Unitary Gross Power

Cost optimization

A cost optimization is realizable based on the third and the first configuration but not for the second one. Indeed, the

0.8

0

Simulation results and discussions

cm =mA

Gross Power (mW)

Cell Voltage (V)

3.2.

2

3

1.4 1.2

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60 50 40 30 20 10 0

1

0

0.2

0.4 0.6 0.8 Unitary Gross Power

1

Fig. 8 – Fuel cell efficiencies against unitary gross power. (a) Total efficiency against unitary gross power and (b) global efficiency against unitary gross power.

3 Gross Power 1 Start FC 2 Power

+ +

-KAdd ++

5 H2 Power

Multiply Unitary Gross Power Efficiency 0-->1

Divide

1 s Integrator

1/10

1 H2 Energy in Wh

Tenth of Hour

Saturation Add1

-CPaux

-K4 Net Power 6 Auxiliary Power Fig. 9 – Simulink FC model.

Wh->m3

2 H2 Quantity in m3 at 15°C 15 C and 1atm

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Table 3 – Costs of the elements 600

PV Bat

500

Device Poly-crystalline PV

Power (W)

400

Lead-acid battery Alkaline electrolizer PEM fuel cell Hydrogen

300 200

Value

Unit

Lifetime

5

h=Wpeak

20 years

90 15 8 0.39

h=kWh h=W h=W

5 years 20 years 5000 h –

h=m3 (normal)

100 0 -100 0

4

8

12 16 Time (hours)

20

24

2700

500 Ebat Pbat Pelec

2600 2500

300

Energy (Wh)

Power (W)

400

2400 200 2300 100

2200

0

2100

-100

2000 0

4

8

12 16 Time (Hours)

20

24

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.

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 combinations 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.

300 PV Bat FC

250

Power (W)

200 150

4.

Comparison of configurations

4.1.

Configurations costs

100 50 0 -50 -100 0

4

8

12

16

20

24

Time (hours) Fig. 11 – Powers evolution during 24 h when FC works. 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.

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 0:12 h=kWh, without taking into account the price of distribution extension in case of isolated site. PkWh ¼

Csystem R 20 years 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.

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Total Cost (€)

12000 10000 8000 6000 4000 7000

2 4

2)

6000

5000 4000 Battery 3000 Capacit y (Wh)

2000

6 1000

e fac

(m

ur Vs

P

Fig. 12 – Cost optimization of the first configuration. Table 4 – Configuration cost during 20 years working

Configuration 1 Configuration 2 Configuration 3

Cost ðhÞ

kWh price ðh=kWhÞ

Global configuration efficiency (%)

4544 43,300 5646

0.519 4:943 0.645

About 50 22:4 About 50

The global configuration efficiency ðZGlobal Configuration Þ is the ratio between the energy consumed by the load ðEConsumed Þ and the energy produced by the PV ðEfrom PV Þ plus the energy consumed under hydrogen form ðEfrom H2 Þ as expressed in Eq. (18) (Efrom H2 applies 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 configuration efficiency can be higher than the FC efficiency. ZGlobal

4.2.

Configuration

¼

EConsumed Efrom PV þ Efrom

(18) H2

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 0:03 h=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 0:5 h=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 dimensioning 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 affordable. 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 fullyautonomous system, the configuration featuring both hydrogen 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

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