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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5

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Power management strategies for a stand-alonepower system using renewable energy sources andhydrogen storage

Dimitris Ipsakisa,1, Spyros Voutetakisa,*, Panos Seferlisa,2,Fotis Stergiopoulosa, Costas Elmasidesb

aChemical Process Engineering Research Institute (C.P.E.R.I.), CEntre for Research and Technology Hellas (CE.R.T.H.),

P.O. Box 60361, 57001 Thermi-Thessaloniki, GreecebSystems Sunlight SA, 67200, Neo Olvio, Xanthi, Greece

a r t i c l e i n f o

Article history:

Received 22 November 2007

Received in revised form

28 May 2008

Accepted 4 June 2008

Available online 4 September 2008

Keywords:

Renewable energy sources

Stand-alone power system

PEM Electrolyzer

PEM fuel cell

Lead-acid accumulator

Hydrogen production

Power management strategy

* Corresponding author. Tel.: þ30 2310 498 3E-mail address: paris@cperi.certh.gr (S. V

1 Department of Chemical Engineering, Ar2 Department of Mechanical Engineering,

0360-3199/$ – see front matter ª 2008 Interndoi:10.1016/j.ijhydene.2008.06.051

a b s t r a c t

A stand-alone power system based on a photovoltaic array and wind generators that stores

the excessive energy from renewable energy sources (RES) in the form of hydrogen via

water electrolysis for future use in a polymer electrolyte membrane (PEM) fuel cell is

currently in operation at Neo Olvio of Xanthi, Greece. Efficient power management strate-

gies (PMSs) for the system have been developed. The PMSs have been assessed on their

capacity to meet the power load requirements through effective utilization of the electro-

lyzer and fuel cell under variable energy generation from RES (solar and wind). The evalu-

ation of the PMS has been performed through simulated experiments with anticipated

conditions over a typical four-month time period for the region of installation. The key

decision factors for the PMSs are the level of the power provided by the RES and the state

of charge (SOC) of the accumulator. Therefore, the operating policies for the hydrogen

production via water electrolysis and the hydrogen consumption at the fuel cell depend

on the excess or shortage of power from the RES and the level of SOC. A parametric sensi-

tivity analysis investigates the influence of major operating variables for the PMSs such as

the minimum SOC level and the operating characteristics of the electrolyzer and the fuel

cell in the performance of the integrated system.

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

reserved.

1. Introduction

Power systems based on RES offer off-grid energy supply for

various applications, such us electrification of rural and

remote areas with problematic grid connection, powering of

telecommunication stations, energy intensive desalination

17; fax: þ30 2310 498 380.outetakis).istotle University of ThesAristotle University of Thational Association for H

of water and water pumping for irrigation or drinking

purposes. These systems are usually a combination of photo-

voltaic systems (PV-systems), wind generators and diesel

generators [1–4]. Sometimes they are accompanied by micro-

hydro generators that utilize water potential energy to

produce electricity [5–7].

saloniki, P.O. Box 1517, 54124 Thessaloniki, Greece.essaloniki, P.O. Box 484, 54124 Thessaloniki, Greece.ydrogen Energy. Published by Elsevier Ltd. All rights reserved.

Nomenclature

Aelec electrode area, m2

Aw wind generator swept area, m2

cp performance coefficient of the wind generator

F Faraday’s constant, Cb/mol

Ibat charging/discharging current, A

ID diode current for the PV-system, A

Ielec operation current for the PEM electrolyzer, A

IL light current for the PV-system, A

Io diode reverse saturation current for the

PV-system, A

Ipv operation current for the PV-system, A

Ish shunt current for the PV-system, A

i current density for the PEM fuel cell, A/m2

io Tafel parameter for the PEM fuel cell, A/m2

l parameter for the overvoltage due to mass

transportation limitations for the PEM fuel cell,

m2/A

m parameter for the overvoltage due to mass

transportation limitations for the PEM fuel cell, V

n number of mol of hydrogen, mol

nc number of cells for the PEM electrolyzer or the PEM

fuel cell

ne number of electrons

nF Faraday’s efficiency

nH2 hydrogen flow rate, mol/s

P shortage or surplus power, J/s

PAcc power from/to the accumulator, J/s

Pc1 hydrogen pressure before the compression, bar

Pc2 hydrogen pressure after the compression, bar

Pcr critical pressure of hydrogen, bar

Pload power demand of the load, J/s

Pw output power from the wind generator, J/s

Ppv output power from the PV-system, J/s

PRES produced power from the RES, J/s

PT pressure in the storage tanks, bar

PMSs/PMS power management strategies/strategy

R universal gas constant, bar m3/mol K

Rs series resistance for the PV-system, U

Rsh shunt resistance for the PV-system, U

SOC State of Charge of the accumulator

r resistance for the PEM fuel cell, U m2

ri parameters for the ohmic resistance of the

electrolyte of the PEM electrolyzer, i¼ 1,2

si parameters for the overvoltage at the electrodes of

the PEM electrolyzer, i¼ 1,.3

T temperature, �C

Tc1 temperature of the hydrogen before the

compression, K

Tc2 temperature of the hydrogen after the

compression, K

Tcr critical temperature of hydrogen, K

ti parameters for the overvoltage at the electrodes of

the PEM electrolyzer, i¼ 1,.3

Vc1 volume of the hydrogen before the

compression, m3

Vc2 volume of the hydrogen after the compression, m3

Velec operation cell voltage for the PEM electrolyzer, V

Vfc operation cell voltage for the PEM fuel cell, V

Vo open circuit voltage for the PEM fuel cell, V

Vpv operation voltage for the PV-system, V

Vrev,elec reversible voltage for the PEM electrolyzer, V

Vrev,fc theoretical reversible voltage for the PEM fuel

cell, V

VT tank volume, m3

Greek symbols

a curve fitting parameter for the PV-system, V

aT Tafel slope for the PEM fuel cell, V

b blade pitch angle for the wind generator, degree

l tip speed ratio

vwind wind speed, m/s

r air density, kg/m3

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57082

Global warming is considered as one of the most critical

environmental problems that people will face in the next

50 years [8]. The use of RES for the production of electrical

energy can contribute significantly to the reduction of green-

house emissions such as carbon dioxide and nitrogen oxides

and protect the environment from further degradation. More-

over, solar and wind energy is abundant, free, clean and inex-

haustible. Other advantages of PV-systems and wind

generators include the long lifetime and low maintenance

requirements for both systems [9]. The time variations of the

weather conditions, however, require the design of a robust

system in order to compensate for the fluctuations of the

available energy from RES. Traditionally, deep-cycle lead-

acid accumulators have been used as the means of short-

term energy storage. Accumulators though, have a relatively

small lifespan (around 3–6 years) and due to their heavy utili-

zation affect the operation and maintenance costs of the

system. Therefore, utilization of surplus energy from RES in

a water electrolyzer for hydrogen production and subsequent

use in a fuel cell in cases of shortage of energy provides

a viable, efficient and promising alternative storage of energy

[9–16]. Such integrated stand-alone systems have been

recently developed and implemented in various locations

around the world [15,17,18].

The design, analysis and optimization of such systems

require the development of mathematical models for all indi-

vidual components [19–21]. Accurate models predict the daily

profiles of produced energy from PV-systems and wind gener-

ators based on meteorological data [22,23]. Dynamic PEM

electrolyzer and hydrogen storage analysis calculate the

necessary power for hydrogen production and storage pres-

sure in pressurized tanks [24]. Several models predict fuel

cell characteristics with empirical equations [22,25–27] and

rigorous mathematical dynamic models [28]. The proper

sizing of the various subsystems is a major challenge that

depends on weather conditions at the place of installation,

the selected operating policy and of course economic data

(e.g., cost of purchase, maintenance, operation and so forth).

Numerous studies have been published on this subject that

deal with different configurations of stand-alone power

systems [9,16,29–32]. Optimization strategies based on cost

minimization of the integrated system utilizing a short-term

Fig. 1 – Block diagram of the proposed stand-alone power

system.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7083

and a long-term storage system can be proved quite efficient

[29,33–35]. Several power management algorithms that use

models to predict the behavior of stand-alone power systems

have been developed and evaluated based on the achieved

performance [32,36,37]. The experience gained from the oper-

ation of different stand-alone power systems across the world

is a valuable resource for the selection of a proper operating

policy in a similar system [38–45]. The main conclusion is

that PMSs strongly affect the lifetime of the various subsys-

tems and in particular the lifetime of the accumulator, the

electrolyzer and the fuel cell. The key decisions in a PMS are

based on the SOC levels of the accumulator [22,35,37,46]. The

minimum SOC limit, SOCmin, designates the operation of the

fuel cell and the maximum limit, SOCmax, regulates the oper-

ation of the electrolyzer. The operation of the electrolyzer can

be supported either solely by the RES or by the RES and the

accumulator. In some cases, as described in Refs. [22,35,37],

a hysteresis band was used around those limits that would

ensure a smoother operation for the units.

Nevertheless, little is reported about the influence that key

variables like the operation limits of SOC of the accumulator

and the output power of the fuel cell have on the operation

time and operation variables (e.g. hydrogen inventory) of the

stand-alone power system, but caution was mainly given to

the operation of the accumulator as a sensitive subsystem.

For example, low SOCmin limits (increased depth of discharge,

DOD) might lead to increased hydrogen inventory, but at the

expense of more intense usage of the accumulator [46]. The

identification of such key variables could be used in optimiza-

tion studies that would take into account the operation costs

along with the key variables and guide the designer to suitable

decisions on enhancing the performance of the system for an

economical and reliable operation. In the present work, three

PMSs are proposed that ultimately aim to ensure the reliable

satisfaction of the system load requirement and safeguard

the units from undesirable operating conditions. The perfor-

mance of the entire power system under each PMS is then

estimated and assessed under variable conditions. Hence,

the interactions among the various components of the power

system are being fully explored and analyzed. The assessment

criteria include the satisfaction of the specifications of the

subsystems (electrolyzer, fuel cell, and accumulator) and the

maximization of the efficient power utilization. The key deci-

sion parameters in the PMS are the level of the power provided

by the RES and the SOC levels of the accumulator. Therefore,

the operating policies of the hydrogen production via water

electrolysis and the hydrogen consumption in the fuel cell

mainly depend on the excess or shortage of energy from the

RES and the level of SOC for the accumulator. Constraints

associated with the operation of the electrolyzer and the

fuel cell are also taken into consideration. The proposed

logical block diagrams are given in such a way that the imple-

mentation in various simulation programs is quite easy to

handle.

The structure of the paper is as follows: in Section 2 the

mathematical models employed for each subsystem are

briefly described. The major equations are provided and the

key model parameters are defined. Section 3 presents the

proposed PMSs for the integrated system through logical block

diagrams and provides the implementation details. Section

4 reports the simulated results and evaluates the performance

of each PMSs towards certain criteria. A sensitivity analysis of

the system performance with respect to key decision parame-

ters attempts to identify the optimal operating factors for the

PMSs in Section 5.

2. Stand-alone power system: systemdescription and unit modeling

An application utilizing solar and wind energy with hydrogen

production through water electrolysis, storage and utilization

in fuel cell is currently in operation installed at Neo Olvio of

Xanthi, Greece. Fig. 1 shows a layout of the stand-alone power

system. The RES production subsystem comprises a PV-array

with a nominal capacity of 5 kWp and three wind generators

rated at 3 kWp in total. The system is attached to a 1 kW

load. Surplus energy from RES can potentially be used to oper-

ate a PEM electrolyzer, rated at 4.2 kWp. The produced

hydrogen is stored in cylinders under medium pressure with

total volume 6 m3 (equivalent energy is around 190 kW h,

giving about 8 days of autonomy). In case that RES fail to

meet the load specification, a PEM fuel cell rated at 4 kWp

that utilizes the stored hydrogen can be used as an alternative

energy source. The produced water from the fuel cell is

recycled in a closed loop back to the water storage tank for

use in the electrolyzer. Furthermore, in order to account for

short-term produced energy fluctuations and ensure

smoother operation of the system, a lead-acid accumulator

with a total capacity of 3000 A h at 48 V has been installed.

Optionally, a back up unit (diesel generator or grid) can be

used in order to cover the electrical needs during periods of

low RES energy and hydrogen inventory. Furthermore, power

electronic converters are employed for power conditioning

and integration of the various subsystems through a 48 V DC

bus. Thus, in order to assess the performance of the integrated

system, detailed and accurate mathematical models are

employed for the simulation of each subsystem in the inte-

grated system.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57084

2.1. Photovoltaic system

Commonly available PV-systems usually use crystalline or

polycrystalline cells [22,47]. A photovoltaic cell has the ability

to convert photon energy into electrical energy in the form of

direct current (DC). This is possible due to two basic properties

of PV cells:

� Electrons are freed in a semiconductor when photons with

sufficient energy are absorbed within them.

� When dissimilar semiconductors are joined at a common

boundary, a fixed electric field is usually induced across

that boundary.

The model that is widely used is the one-diode model and is

referred in subsystems with a specific number of cells in series.

The relationship between current and voltage is given by [22]:

Ipv ¼ IL � ID � Ish ¼ IL � Io

�exp

�Vpv þ IpvRs

a

�� 1

�� Vpv þ IpvRs

Rsh

(1)

The output power from the PV-array is given by:

Ppv ¼ VpvIpvhconv (2)

where hconv is the efficiency of a DC/DC converter (typically

w90–95%). Variables IL, Io, Rs and a, are obtained by non-linear

algebraic equations that are described and presented else-

where [22,47,48]. Eq. (1) requires the PV manufacturer data

regarding the values of current and voltage at the maximum

power point, the value of current at short circuit current

conditions, the value of voltage at open voltage conditions,

the values of the temperature coefficient at short circuit and

open voltage conditions and finally the number of solar cells.

2.2. Wind generators

A wind turbine converts the kinetic energy of wind into

mechanical energy. Wind generators can be separated accord-

ing to the type of the axis about which the turbine rotates.

Turbines that rotate around a horizontal axis are more

commonly used than those that rotate around a vertical axis.

The model isbased onthe characteristics of thepowerof turbine

at steady state. The produced power is proportional to the cube

of the wind speed and is given by the following equation [49]:

Pw ¼ cpðl;bÞrAw

2v3

windhinv (3)

where hinv is the efficiency of an AC/DC inverter (typically w90–

95%). The calculation of cp is based on the characteristics of the

turbine [49].

2.3. Lead-acid accumulator

A lead-acid accumulator is an electrochemical device that

converts electrical energy into chemical energy during the

charging process and vice versa during the discharging

process [22,50]. As in any electrochemical device, an anodic

and a cathodic electrode are present. The reactions that take

place are the following:

Anode: PbþHSO�4 /PbSO4 þHþ þ 2e� (4)

Cathode: PbO2 þHSO�4 þ 3Hþ þ 2e�/PbSO4 þ 2H2O (5)

Overall reaction (discharge)

Pbþ PbO2 þ 2H2SO4/2PbSO4 þ 2H2O (6)

The employed KiBaM model [50] requires as input information

the experimental data describing the discharging current as

a function of the discharging time. The mathematical model

calculates the charging and discharging current, voltage and

the SOC of the accumulator. The SOC of the accumulator is

the fraction of the current capacity of the accumulator at

each time instant, divided by its nominal capacity:

SOCðtÞ ¼ SOCðt� 1Þð1� sÞ þ IbathbatðDtÞ (7)

where s is the self-discharge rate (w2.5%), hbat is the efficiency

factor (w95%) and t is the time in h. The depth of discharge

(DOD), is defined as the difference between the maximum

and the minimum allowed operation limit of the SOC of the

accumulator.

2.4. Polymer electrolyte membrane electrolyzer

A PEM electrolyzer decomposes water into hydrogen and

oxygen by passing an electrical current (DC) between two elec-

trodes separated by an aqueous electrolyte with good ionic

conductivity. The reactions that take place at the anode and

the cathode of a PEM electrolyzer are as follows:

Anode: H2O/12O2 þ 2Hþ þ 2e� (8)

Cathode: 2Hþ þ 2e�/H2 (9)

In order to properly model the voltage–current characteristics

of the PEM electrolyzer, the overvoltages that occur at the

electrodes and the ohmic resistance must be taken into

consideration. The voltage–current relationship is based on

the following equation [22]:

Velec ¼ Vrev;elec þr1 þ r2T

AelecIelec þ

�s1 þ s2T

þ s3T2�log

�t1 þ t2=Tþ t3=T2

AelecIelec þ 1

�(10)

The reversible voltage is simply the maximum voltage that

can be applied across the electrodes of an electrolyzer. The

above semi-empirical model has been applied for alkaline

electrolyzers, but can be also used for a PEM electrolyzer if

sufficient experimental data exist for the model validation.

The production rate of hydrogen in an electrolyzer is given

by the Faraday’s Law [51]:

nH2¼ nF

ncIelec

neF(11)

The Faraday’s efficiency, nF, is the ratio between the actual

and the theoretical amount of hydrogen produced and is

usually around 80–100%.

The PEM electrolyzer of the stand-alone power system can

operate under variable power mode that must be between

a minimum and a maximum power level.

2.5. Polymer electrolyte membrane fuel cell

The opposite reactions that occur in an electrolyzer take place

in a fuel cell. Hydrogen in the anode is ionized releasing

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7085

electrons and protons. Electrons flow to the cathode through

a circuit producing electric current. Protons diffuse through

a polymer electrolyte membrane and react in the cathode

with oxygen and electrons to form water. The reactions that

take place are:

Anode: H2/2Hþ þ 2e� (12)

Cathode:12O2 þ 2Hþ þ 2e�/H2O (13)

The following equation describes the voltage–current relation-

ship that takes into consideration the activation overvoltage

(Tafel equation), the ohmic overvoltage from the resistances

in the cell as well the mass transport limitations [22,51]:

Vfc ¼ Vo � aT logðiÞ � irþm expðilÞ (14)

Vo ¼ Vrev;FC þ aT logðioÞ (15)

Similar to the electrolyzer operation, the flow rates of

hydrogen and oxygen are given from Eq. (11). The fuel cell of

the proposed stand-alone power system is rated at 4 kWp,

but can be used at various levels of output power depending

on the hydrogen inlet flow rate. The factors that mainly affect

the fuel cell performance are the operating temperature and

the gas pressure in the anode and cathode [22,26,27,47]. In

general, higher temperature and gas pressure generally lead

to better fuel cell performance but at the expense of higher

thermal requirements for the cooling system and increased

energy for the compression of the gases.

2.6. Medium pressure hydrogen storage

Hydrogen can either be stored as a liquid or as a gas. Liquid

hydrogen can be stored in cryogenic tanks and gaseous hydrogen

can be stored in either medium or high pressure cylinders or

near atmospheric pressure in metal hydrides. Storage under

pressure requires the use of an energy demanding gas

compressor. In the case of metal hydrides the use of

a compressor is not required but energy should be supplied

to help the chemical desorption of the hydrogen from the

metal. Metal hydride technology for hydrogen storage is

a fairly new technology with significant recent developments

[52–58]. However, the industrial use of metal hydride tech-

nology is still at an early stage.

The system under investigation stores hydrogen in pres-

surized tanks. Specifically, hydrogen is temporarily stored in

low pressure buffer tanks until the pressure inside these tanks

reaches the limit of 7 bar. Hydrogen is then compressed to the

medium pressure level (approx. 20 bar) of the final storage

tank. The buffer storage serves as a regulatory unit for

hydrogen flow and pressure. The basic equations (Van der

Waals law) that describes the pressure inside the storage

tanks are as follows [22]:

PT ¼nRT

VT � nbs� as

n2

V2T

(16)

as ¼27R2T2

cr

64Pcr(17)

bs ¼RTcr

8Pcr(18)

where as and bs are specific parameters for hydrogen.

The relationship between conditions before the compres-

sion (state 1) and after the compression (state 2) for polytropic

compression is given by the following relation:

Pc2

Pc1¼�

Vc1

Vc2

�k

¼�

Tc2

Tc1

�k=ðk�1Þ

(19)

where k is the polytropic coefficient.

Similarly, the polytropic work (DWpol) for the compression

of hydrogen is related to the pressure difference as:

DWpol ¼k

k� 1nH2

RTc1

"�Pc2

Pc1

�ðk�1Þ=k

�1

#(20)

It is noted that the actual work from the compressor as well

as the electrical energy demand for the operation of the

compressor motor is calculated by Eq. (20) after dividing it

by the respective efficiency coefficients for total compressor

power and for total electrical consumption. The compressor

is not considered as an integrated part of the stand-alone

power system where it would be powered by the various

subsystems (e.g. the RES or the accumulator) but rather

as an auxiliary unit whose electrical needs are met by the

grid.

The values for all the parameters engaged in the mathe-

matical models are given in Appendix.

3. Power management strategies

The main objective for the applied PMSs in the integrated

system is the satisfaction of the load requirements. RES

produce power that is basically used to meet the 1 kW

constant load. Any surplus of power can be potentially stored

in the form of hydrogen through water electrolysis and any

shortage of power can be met by the fuel cell provided that

sufficient inventory of hydrogen is available. The operating

logic would have been quite simple if the RES power was

constant or varying slowly over time. However, the large vari-

ability of power generation, mainly due to the stochastic

behavior of the RES, increases the complexity of the manage-

ment of the system [46]. Furthermore, the operation of the

electrolyzer and the fuel cell should satisfy certain specifica-

tions regarding the duration and power level of operation

every time the units are ignited. Frequent start-up and

shut-down actions for the electrolyzer and the fuel cell will

eventually degrade their performance and possibly reduce

their lifespan. Therefore, the lead-acid accumulator becomes

an important component of the system that aims at absorbing

the short-term variability of the RES power generation. On the

other hand, the operation cycles that an accumulator

undergoes affect its lifespan and subsequently influence the

operating and maintenance costs of the entire system. In

a nutshell, the PMSs aim at providing operating policies under

variable weather conditions that would ensure the satisfac-

tion of the power requirements and maintain the operating

costs at a reasonable level.

Table 2 – Component characteristics in the stand-alonepower system.

PV-system

Windgenerators

Lead-acidaccumulator

PEMelectrolyzer

PEMfuelcell

Storageunit

5 kWp 3 kWp 144 kW h 4.2 kWp 4 kWp 6 m3/

190 kW h

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57086

Solar radiation intensity, air temperature and wind speed

profiles averaged over hourly time intervals during a typical

four-month time period for Neo Olvio, Xanthi, are shown in

Table 1. The size of the time interval is suitable to represent

the variation in the wind and solar energy adequately. Table 2

provides the operational characteristics of the various compo-

nents in the integrated power system. Based on the input data

(weather profiles) during the given four-month time period,

the net power for the system is calculated as the difference

between the output power from the RES, Pres (i.e. the sum of

the output power from the PV-array and the wind generators)

and the constant power demand, Pload.

P ¼ PRES � Pload (21)

Table 3 summarizes the characteristics of the cumulative net

energy for the integrated system for each month. In 56.4% of

the total time period, an excess of energy is available (positive

values) and in 43.6% of the time a shortage of energy is

obtained (negative values).

3.1. Description of the power management strategies

As observed in the simulation results for the system under the

specific weather conditions (Table 3), the system operates in

energy deficit for a large period of time. Hence, the lead-acid

accumulator or the fuel cell should be capable of providing

the necessary power to meet the load requirement. Therefore,

the operation of the integrated system involves a number of

decisions regarding the management and use of power. The

key indicator that governs the operation of the system is the

SOC of the accumulator. The dynamics of the accumulator

are much faster than those of the electrolyzer and that of

the fuel cell and, therefore, can efficiently cover the energy

fluctuations due to the stochastic nature of the RES. Addition-

ally, frequent changes in the operation of the electrolyzer and

the fuel cell (e.g., start-ups and shut-downs) are not recom-

mended because they reduce the lifespan of the units. Given

the importance of the accumulator in the smooth operation

of the overall system, it is essential to keep the accumulator

SOC at the highest allowable level, SOCmax, while prevent

a SOC drop below a minimum level, SOCmin [46].

In general, when the accumulator SOC reaches SOCmax,

excess energy can be directed to the electrolyzer for hydrogen

production (the electrolyzer can also operate in various power

levels between the minimum and maximum rated power) and

when the accumulator system reaches SOCmin, the fuel cell

may cover the energy shortage. However, operational

constraints of the individual components may impose certain

restrictions on the underlined power management scheme.

The effect of these constraints on the operational

Table 1 – Average values for solar radiation, temperatureand wind speed for each month.

Month 1 Month 2 Month 3 Month 4

G (W/m2) 207.8 275.5 285.7 254.1

T (K) 296.8 303.8 305.7 304.8

vwind (m/s) 1.54 1.44 1.95 1.75

characteristics of the overall system will be explored through

the implementation of three PMSs.

For the integrated systemunder consideration the following

values for the operating parameters are selected (unless stated

otherwise): SOCmin, 84%; SOCmax, 91%; load, 1 kW; fuel cell

output power, 1 kW (operating current, 30.19 A; operating

voltage, 33.18 V); initial accumulator capacity, 2700 A h

(SOC¼ 90%); minimum allowed power level (Pmin,elec) for the

electrolyzer, 1.05 kW; maximum allowed power level (Pmax,elec)

for the electrolyzer, 4.2 kW; initially hydrogen inventory level,

60.5 Nm3 of hydrogen (55% of the maximum capacity of the

pressurized tanks which is equivalent to about 110 kW h).

3.2. Power management strategy 1 (PMS1)

The logical block diagram for PMS1 is shown in Fig. 2. If P� 0,

based on hourly averaged power supply, then the necessary

power to satisfy the load is provided by the lead-acid accumu-

lator or the fuel cell. The source of additional power is deter-

mined based on the SOC of the accumulator. If

SOC� SOCmin then the accumulator provides the necessary

power to the system. If SOC� SOCmin, then the fuel cell

provides the necessary power to meet the total load demand.

In the case that the output power of the fuel cell is higher than

the power deficit, the excess power is utilized by the accumu-

lator. If P> 0 then the surplus power is either used in the elec-

trolyzer for the production of hydrogen or in the charging of

the accumulator. However, since the electrolyzer has

a minimum load level for efficient operation, the excess power

must be higher than Pmin,elec for the initiation of the electro-

lyzer in case that SOC� SOCmax. If SOC� SOCmax and

P� Pmin,elec then the available power is used to charge the

accumulator with some provision to avoid overcharging

(dump load). If P� Pmax,elec then the electrolyzer operates at

its maximum power and the rest of the power, PAcc,charge¼P� Pmax,elec is used for charging the accumulator.

3.3. Power management strategy 2 (PMS2)

The logical block diagram for PMS2 is shown in Fig. 3. If P� 0,

then PMS2 is exactly the same as PMS1. If P> 0, then the

Table 3 – Net energy cumulative over the four-month timeperiod.

Month 1 Month 2 Month 3 Month 4 Overall

Excess of

energy (kW h)

412.3 506.5 599.1 461.2 1979.1

Shortage of

energy (kW h)

�421.8 �349.1 �357.3 �380.4 �1508.6

Fig. 2 – Logical block diagram for PMS1.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7087

surplus power is driven to the electrolyzer for the production

of hydrogen or for charging the accumulator. If SOC� SOCmax,

then the surplus power is utilized in the electrolyzer as long as

Pmin,elec� P� Pmax,elec. If P� Pmin,elec, then the accumulator

provides the power that is required for the electrolyzer to

operate at the lowest allowable level, Pmin,elec. The power

that the accumulator provides to the electrolyzer for its oper-

ation is calculated as follows:

PAcc;discharge ¼ fPmax;elec � P (22)

where f is the ratio of the electrolyzer current operation to its

maximum operation level. For this study, parameter f is

selected equal to 0.25.

If P� Pmax,elec, then the electrolyzer operates at its

maximum power and the rest of the power is used to charge

the accumulator. It is evident that PMS2 utilizes the electro-

lyzer more than PMS1 at the expense of more intense usage

of the accumulator. As in PMS1, in order to avoid the accumu-

lator from overcharging, excess power is dumped if the SOC

level reaches that of 100%.

3.4. Power management strategy 3 (PMS3)

The logical block diagram for PMS3 is shown in Fig. 4. PMS3 is

a unique strategy that was presented among others in

Ref. [37], and differs from the simple logic of PMS1 and PMS2

that are mainly used in stand-alone power systems. In

PMS3, when the SOC reaches its upper limit the accumulator

is disconnected from the RES supply and solely provides the

necessary load demand. RES power is then directed to the

electrolyzer for hydrogen production. This policy aims to

protect the accumulator from overcharging. More specifically,

when SOC� SOCmax and Pmin,elec� PRES� Pmax,elec then the

RES provide the power to the electrolyzer and the accumulator

meets the load demand. If PRES� Pmin,elec then the excess

power is dumped and if PRES� Pmax,elec then the electrolyzer

uses the Pmax,elec power and the remaining power is also

dumped. If SOCmin< SOC< SOCmax then the accumulator is

charged or discharged with respect to the excess or shortage

of power, respectively. Whenever SOC� SOCmin, the fuel cell

solely provides the load demand (its output power is always

Fig. 3 – Logical block diagram for PMS2.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57088

equal to the load demand) and the RES solely charge the

accumulator.

4. PMS performance

The performance of the stand-alone power system under the

three proposed PMSs over a typical four-month time period

has been evaluated. Table 4 shows the percentage of time

that the SOC was below SOCmin, between SOCmin and SOCmax,

and above SOCmax for the three PMSs, respectively. As

observed, in PMS1 the percentage of time that SOC was above

its upper limit was the highest as compared to the other two

PMSs and moreover, the time that SOC was below the lower

limit was the lowest among all PMSs. On the other side,

PMS3, where the accumulator was disconnected and used

for the load whenever SOC> SOCmax, exhibited the highest

percentage of time with the accumulator SOC below its lower

limit. This is characteristic of a heavier utilization of the

accumulator for the power requirements of the integrated

system. For all PMSs, the largest power shortages were

observed during month 1 (large percentage of time that SOC

was below the lower limit) that resulted in intensive use of

the fuel cell. On the contrary, month 3 exhibited the highest

power surplus, exceeding Pmin,elec for long periods of time,

and therefore the electrolyzer was used extensively for

hydrogen production. Regarding the accumulator, the extent

of violation for the limits was not very significant in any of

the PMSs. Therefore, the risk for overcharging or exhausting

the accumulator was totally avoided.

Figs. 5–7 show the total hydrogen production in the electro-

lyzer, consumption in the fuel cell and the hydrogen inventory

in the system, respectively, during the simulated time period

for the three PMSs. As expected, the intermittent energy

supply to the electrolyzer due to the wide fluctuations of the

weather conditions caused the non-continuous operation of

the electrolyzer. Despite the fact that PMS1 exhibited the

longest period that SOC> SOCmax, it was PMS3 that resulted

Fig. 4 – Logical block diagram for PMS3.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7089

in the highest production of hydrogen. However, in PMS1 the

SOC of the accumulator didn’t reach the lower limit as

frequent as in PMS2 and PMS3 and hydrogen consumption

in the fuel cell was less than the other two strategies.

PMS3 resulted in the highest hydrogen production because

the entire RES power was directed to the electrolyzer when-

ever the maximum SOC limit was reached. However, the

largest variability in the SOC for the accumulator caused the

fuel cell to operate more intensively. Therefore, hydrogen

inventory was depleted during the four-month time period

leading to significant deficit in hydrogen. Such a situation

requires additional power from an outside source (e.g., diesel

generator or electrical grid connection). Overall, PMS1 and

PMS2 adequately managed to operate the stand-alone power

system without depleting the initial hydrogen inventory.

Tables 5 and 6 present the mean values and the standard devi-

ation of the population of the values of the hydrogen inven-

tory for each month and for each PMSs.

5. Parametric sensitivity studies

5.1. Effect of the minimum state-of-charge, SOCmin

Lead-acid accumulator manufacturers recommend that a very

low value for SOCmin should be avoided in order to prolong the

life of the accumulator. Furthermore, the use of the fuel cell at

high output power would cause the fuel cell to work less time

in order to cover the required power of the system and would

therefore increase its lifetime at the expense of higher

hydrogen consumption. Fig. 8a–c depict the effect of three

different levels for SOCmin to the hydrogen inventory during

the simulated period for the three PMSs, respectively (output

power of fuel cell is fixed at 1 kW). The reduction in the

minimum SOC limit resulted in higher hydrogen inventory

during the simulation time for all PMSs. Especially, in PMS3

the reduction of the SOCmin at 80% and 76% eliminated the

Table 4 – SOC levels during a typical four-month time period.

Month 1 Month 2 Month 3 Month 4 Overall

SOCmin> SOC PMS1 16% 3.9% 2.9% 8.4% 7.8%

PMS2 18.5% 7.9% 5.1% 12.1% 10.9%

PMS3 19.5% 10.1% 9.4% 15.1% 13.5%

SOCmin< SOC< SOCmax PMS1 72.6% 73.2% 69.1% 73.5% 72.1%

PMS2 72.7% 76.4% 73.7% 76.2% 74.7%

PMS3 75.3% 80.3% 78.9% 78.2% 78.2%

SOC> SOCmax PMS1 11.4% 22.9% 28% 18.1% 20.1%

PMS2 8.8% 15.7% 21.2% 11.7% 14.4%

PMS3 5.2% 9.6% 11.7% 6.7% 8.3%

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57090

risk of hydrogen inventory depletion at the end of the four-

month time period.

5.2. Effect of the fuel cell output power, PFC

In the simulated examples so far, the fuel cell output power was

fixed at 1 kW independent of the RES power level. The effect of

operating the fuel cell at a variable level was investigated. Vari-

able power mode implies that the fuel cell only provides the

power deficit for the load without charging the accumulator.

Since PMS3 is only applicable for constant output power of the

fuel cell to solely meet the load demand, only PMS1 and PMS2

are discussed here. Fig. 9a,b shows the effect of three levels of

output power operation for the fuel cell on hydrogen inventory

for PMS1 and PMS2, respectively (SOCmin¼ 84%). Results

suggest that the operation of the fuel cell at a higher output

power level (2 kW fixed output power) increased hydrogen

consumption and subsequently reduced the hydrogen inven-

tory during the four-month time period. In particular, hydrogen

inventory in PMS2 became negative at some time instances

implying the need for auxiliary power source (e.g., diesel gener-

ator or connection to electrical grid). On the contrary, fuel cell

operation with variable power mode resulted in higher

hydrogen inventory at the end of the four-month time period.

5.3. Discussion on parametric sensitivity studies

Tables 7 and 8 summarize the results from all the simulated

studies. An operation cycle for the accumulator is defined as

the process where a discharging (or charging) mode is

Fig. 5 – Cumulative hydrogen production during a typical

four-month time period.

followed by a charging (or discharging) mode. The efficiency

of the accumulator is defined as the ratio between the dis-

charging energy and the charging energy [37]. Table 7 presents

the percentage of time that each subsystem in the integrated

system was in operation during the four-month time period

for all PMSs. It is clear that the decrease in the SOCmin caused

the accumulator to charge for shorter times and discharge for

longer periods, while the electrolyzer and the fuel cell oper-

ated for shorter overall time. Moreover, the reduction in the

SOCmin had an increasing effect on the number of the total

accumulator cycles. Due to the fact that the required power

for electrolysis and the generated power from the fuel cell

reduced, higher hydrogen inventory levels were present

during the simulated period. Regarding the suitable selection

of the minimum level for the SOC, the key decision relates

to the operation pattern of the accumulator, electrolyzer and

fuel cell. A value of SOCmin that would combine reduced

percentage of cycles for the accumulator and a smooth oper-

ation pattern with less number of start-ups and shut-downs

for the electrolyzer and fuel cell would be the most beneficial.

Such a behavior could be accomplished with the introduction

of a hysteresis band for the operation of the electrolyzer and

the fuel cell at the critical SOC levels [35,59]. Special care,

however, should be given at the hydrogen inventory were

depletion should be avoided.

A comparison among the three PMSs reveals that in PMS3

the accumulator operated for longer periods while the fuel

cell was utilized more than the other two strategies. Moreover,

the electrolyzer in PMS2 operated for a longer time period than

in PMS1 but, hydrogen inventory was higher in PMS1 due to

Fig. 6 – Cumulative hydrogen consumption during a typical

four-month time period.

Fig. 7 – Hydrogen inventory during a typical four-month

time period.

Table 6 – Standard deviation values of the hydrogeninventory for each PMS.

Month 1 Month 2 Month 3 Month 4

PMS1 15.64 5.11 9.61 5.35

PMS2 17.27 3.16 8.2 7.5

PMS3 18.13 2.61 4.37 8.76

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7091

higher hydrogen consumption by the fuel cell in PMS2.

Furthermore, the amount of hydrogen consumed was much

higher in PMS3 than in the other two PMS and this resulted

in the lower hydrogen inventory at the end of the simulated

time period.

As far as the output power of the fuel cell is of concern, it is

noted that an increased output power from the fuel cell results

in more power for the charging of the accumulator. An

increase in the peak output power from the fuel cell (from

1 kW to 2 kW) caused the accumulator to operate for slightly

shorter period (sum of charge and discharge time). Further-

more, the electrolyzer was forced to operate for slightly longer

period while the fuel cell operated for a shorter period.

Hydrogen inventory at the end of the four-month time period

was reduced as the fuel cell operating power level increased

the hydrogen consumption. In some cases (PFC at 2 kW for

the PMS2), hydrogen inventory was totally depleted. The vari-

able power mode operation of the fuel cell resulted in lower

operation time for both the accumulator and the electrolyzer.

However, the fuel cell operated for longer periods of time than

in the cases of fixed output power level but hydrogen inven-

tory was significantly higher throughout the simulated period.

In conclusion, output power level for the fuel cell exceeding

that of the load should be avoided and the operation of the

fuel cell at power level equal that of the load demand would

be the most beneficial for the performance of the overall

system as far as hydrogen inventory is of primary concern.

A comparison among PMS1 and PMS2 reveals that the

accumulator in PMS1 operated for shorter period than in

PMS2, while the electrolyzer and the fuel cell also operated

for shorter period. Furthermore, hydrogen production and

Table 5 – Mean values of the hydrogen inventory (N m3)for each PMS.

Month 1 Month 2 Month 3 Month 4

PMS1 43.05 27.16 48.16 64.31

PMS2 39.89 16.68 31.28 40.43

PMS3 37.65 9.71 14.28 13.12

consumption was higher in PMS2 than in PMS1, but the

hydrogen inventory was less for all the cases of the fuel cell

output power. An interesting observation is that the increase

in the fuel cell output power operating level from 1 kW to

Fig. 8 – Effectof theSOCmin onthe hydrogen inventoryduring

a typical four-month time period (a. PMS1; b. PMS2; c. PMS3).

Fig. 9 – Effect of the fuel cell output power on the hydrogen

inventory during a typical four-month time period (a.

PMS1; b. PMS2).

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57092

2 kW resulted in increased percentage of cycles for the accu-

mulator but when the fuel cell operated in variable power

resulted in decreased cycles. Such a variable mode operation

behavior may prolong the life of the accumulator but in the

Table 7 – Subsystem operational data for the four-month time

% Tcharge % Tdischarge

SOCmin¼ 84% PMS1 40.92 52.07

PMS2 40.07 53.59

PMS3 45.16 54.84

SOCmin¼ 80% PMS1 39.36 54.88

PMS2 38.04 57.38

PMS3 40.65 59.35

SOCmin¼ 76% PMS1 38.79 55.79

PMS2 37.50 58.20

PMS3 39.97 60.03

PFC¼ 1 kW PMS1 40.92 52.07

PMS2 40.07 53.59

PMS3 45.16 54.84

PFC¼ 2 kW PMS1 38.01 54.81

PMS2 35.84 57.25

PMS3 – –

PFC¼ variable PMS1 35.2 51.12

PMS2 32.25 51.69

PMS3 – –

expense of a more frequent use of the fuel cell and a possible

early replacement. Energy requirements for hydrogen

compression are also reported in Tables 7 and 8. As expected,

compression energy is correlated to electrolyzer operation. An

increase in the electrolyzer operation time increases the total

compression operation time and the total energy demand.

Special care should be given to the fact that the compression

of hydrogen provokes the inevitable temperature increase

(Eq. (19)) and thus cooling utilities need to be present to cool

hydrogen before it is stored.

6. Conclusions

Three different PMSs for an integrated power system that

comprises energy generation from RES and hydrogen produc-

tion as an alternative to energy storage have been developed.

The evaluation of the PMSs performance required the devel-

opment of mathematical models for the calculation of the

response of the individual components of the system using

real weather data for the region of installation. The PMSs

used as decision variables the net power from the RES after

satisfying the load and the accumulator SOC. The accumu-

lator maximum and minimum SOC levels determined the

operation of the electrolyzer and the fuel cell, respectively.

Several modes of operation for the electrolyzer and the fuel

cell were investigated (e.g., minimum capacity level, fixed or

variable power level etc.). The simulated results over a typical

four-month time period based on hourly averaged data

revealed the characteristics of the operating performance for

the three proposed strategies. PMS3 performance was consid-

ered unsatisfactory for the system under investigation since

the cycles and time for the accumulator were too high, while

the average hydrogen inventory was quite low. PMS1 resulted

in less operation time for all the subsystems and in higher

average hydrogen inventory than in PMS2. However, the usage

of the accumulator for the electrolyzer operation in cases of

low RES energy surplus in PMS2 is considered an advantage

period.

% Telec % TFC % Tcomp Cycles, %

7.08 5.96 3.01 3.70

10.40 8.43 3.52 4.08

7.66 10.84 3.86 6.48

5.76 3.15 2.47 4.32

7.35 3.42 2.51 4.32

4.91 3.59 2.47 5.90

5.42 2.24 2.41 4.92

6.88 2.41 2.30 5.11

4.47 2.47 2.24 6.84

7.08 5.96 3.01 3.70

10.40 8.43 3.52 4.08

7.66 10.84 3.86 6.48

7.25 3.22 3.12 5.44

11.21 5.01 3.90 6.22

– – – –

6.84 6.91 2.95 2.43

9.76 9.96 3.42 2.43

– – – –

Table 8 – Hydrogen production and consumption and power data for the operation of the subsystems for the four-monthtime period.

ECharge,kW h

EDischarge,kW h

Efficiency,%

EElec,kW h

EFC,kW h

H2

prod.,m3

H2

cons., m3Net

H2, m3H2

deficit,m3

ELoss,kW h

Ecomp,

kW h

SOCmin¼ 84% PMS1 1560.5 1370.9 87.85 456.94 176 92.06 102.08 50.45 0 0 57.41

PMS2 1571 1381.3 87.92 529.82 249 106.74 144.42 22.80 0 0 68.05

PMS3 1691.2 1494.1 88.35 585.56 320 117.97 185.60 �7.16 10.44 7.75 74.57

SOCmin¼ 80% PMS1 1620.9 1430.8 88.27 373.39 93 75.22 53.94 81.76 0 0 47.65

PMS2 1664.2 1469.2 88.29 376.7 101 75.89 58.58 77.79 0 0 48.40

PMS3 1770 1566.9 88.53 370.21 106 74.58 61.48 73.58 0 3.15 48.5

SOCmin¼ 76% PMS1 1634.4 1450.5 88.75 352.55 66 71.03 38.28 93.22 0 0 45.86

PMS2 1675.2 1487.2 88.78 353.46 71 71.21 41.18 90.50 0 0 45.40

PMS3 1775.6 1578.9 88.92 344.1 73 69.32 42.34 87.46 0 2.62 43.03

PFC¼ 1 kW PMS1 1560.5 1370.9 87.85 456.94 176 92.06 102.08 50.45 0 0 57.41

PMS2 1571 1381.3 87.92 529.82 249 106.74 144.42 22.80 0 0 68.05

PMS3 1691.2 1494.1 88.35 585.56 320 117.97 185.60 �7.16 10.44 7.75 74.57

PFC¼ 2 kW PMS1 1625.9 1431.6 88.05 466.16 190 93.91 114.80 39.59 0 0 59.40

PMS2 1659.3 1464.1 88.24 571.31 296 115.10 178.84 �3.27 4.83 0 75.70

PMS3 – – – – – – – – – – –

PFC¼ variable PMS1 1536.3 1349.5 87.84 442.74 159 89.19 90.91 58.76 0 0 56.13

PMS2 1536.9 1351.5 87.94 501.42 216.43 101.02 123.75 37.74 0 0 67.20

PMS3 – – – – – – – – – – –

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7093

as the hydrogen production will increase. Moreover, the inter-

mittent energy supply from the RES would not always guar-

antee the smooth operation of the electrolyzer in PMS1 and

frequent start-ups and shut-downs might occur. PMS1 would

be efficient in places where enough energy from the RES is

available for long periods of time. In contrast, in places such

as the Neo Olvio in Xanthi, such periods are not very frequent

and PMS2 is also considered a viable option. The suitable

selection of the PMS decision variable values (e.g. SOCmin,

SOCmax, operating power for the fuel cell and minimum oper-

ating level of the electrolyzer, hydrogen compression pattern

and so forth) requires the consideration of the operating and

maintenance costs for the various subsystems over a specified

period of time under a detailed optimization strategy.

Acknowledgements

The financial support of the European Fund of Regional

Growth and the Region of Eastern Macedonia and Thrace

with final beneficiary the General Secretariat of research and

technology under project contract (PEP/AMQ 9) in the oper-

ating project Eastern Macedonia and Thrace is gratefully

acknowledged.

Appendix

All parameter values of the system components are given

below (see literature references as well):

PV-system: Imp, 4.25 A; Vmp, 16.5 V; Isc, 4.7 A; Voc, 21.4 V; Ns,

36; mI,sc, 2.06� 10�3 A/K; mV,oc, �0.077 V/K.

Wind generator: D, 2.7 m.

Accumulator: c, 0.151; k, 1.56; qmax, 866.48 A h; Eoc, 1.9 V/cell;

Eod, 2.097 V/cell; Emin, 1.94 V/cell; Emax, 2.35 V/cell; Ro, from

0.5� 10�3 to 1.32� 10�3 U; sac, 2.5%; nac, 95%.

Electrolyzer: r1, 2.3� 10�3 U/m2; r2,�1.107� 10�7 U/�C m2; s1,

1.286� 10�1 V; s2, 2.378� 10�3 V/�C; s3, �2.606� 10�5 V/�C2; t1,

3.559� 10�1 m2/A; t2, �1.302 m2 �C/A; t3, 2.513 103 m2 �C2/A.

Fuel cell: Vo, 0.86 V; aT, 0.0121 V; r, 0.0130 U cm2; m, 0; l, 0.

Storage system: VT, 6 m3; nH2 , 0.0125 mol/s.

r e f e r e n c e s

[1] Isherwood W, Ray Smith J, Aceves SM, Berry G, Clark W,Johnson R, et al. Remote power systems with advancedstorage technologies for Alaskan villages. Energy 2000;25:1005–20.

[2] Bhatti TS, Al-Ademi AAF, Bansal NK. Load–frequency controlof isolated wind-diesel microhydro hybrid power systems(WDMHPS). Energy 1997;22:461–70.

[3] Kane M, Larrain D, Favrat D, Allani Y. Small hybrid solarpower system. Energy 2003;28:1427–43.

[4] Nfah EM, Ngundam JM, Tchinda R. Modelling of solar/diesel/battery hybrid power systems for far-north Cameroon.Renewable Energy 2007;32:832–44.

[5] Zvonko B. Short-term optimization of the new Avcepumping plant and three existing hydro power plants on theSoca river in Slovenia. Electric Power Systems Research2007;77:1410–7.

[6] Forouzbakhsh F, Hosseini SMH, Vakilian M. An approach tothe investment analysis of small and medium hydro-powerplants. Energy Policy 2007;35:1013–24.

[7] Bueno C, Carta JA. Wind powered pumped hydro storagesystems, a means of increasing the penetration of renewableenergy in the Canary Islands. Renewable and SustainableEnergy Reviews 2006;10:312–40.

[8] Mathews J. Seven steps to curb global warming. Energy Policy2007;35:4247–59.

[9] Nelson DB, Nehrir MH, Wang C. Unit sizing and cost analysisof stand-alone hybrid wind/PV/fuel cell power generationsystems. Renewable Energy 2006;31:1641–56.

[10] Ghosh PC, Emonts B, Stolten D. Comparison of hydrogenstorage with diesel-generator system in a PV–WEC hybridsystem. Solar Energy 2003;75:187–98.

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 57094

[11] Contreras A, Carpio J, Molero M, Veziroglu TN. Solar-hydrogenan energy system for sustainable development in Spain.International Journal of Hydrogen Energy 1999;24:1041–52.

[12] Abdallah M, Asfour SS, Veziroglu TN. Solar-hydrogen energysystem for Egypt. International Journal of Hydrogen Energy1999;24:505–17.

[13] Almogren S, Veziroglu TN. Solar-hydrogen energy system forSaudi Arabia. International Journal of Hydrogen Energy 2004;29:1181–90.

[14] Steinfeld A, Kuhn P, Reller A, Palumbo R, Murray J,Tamaura Y. Solar-processed metals as clean energy carriersand water-splitters. International Journal of HydrogenEnergy 1998;23:767–74.

[15] Little M, Thomson M, Infield D. Electrical integration ofrenewable energy into stand-alone power suppliesincorporating hydrogen storage. International Journal ofHydrogen Energy 2007;32:1582–8.

[16] Barra L, Coiante D. Hydrogen-photovoltaic stand-alonepower stations: a sizing method. International Journal ofHydrogen Energy 1993;18:337–44.

[17] Thomson M, Infield D. Laboratory demonstration ofa photovoltaic-powered seawater reverse-osmosis systemwithout batteries. Desalination 2005;183:105–11.

[18] Thomson M, Infield D. A photovoltaic-powered seawaterreverse-osmosis system without batteries. Desalination2003;153:1–8.

[19] Carpetis C. A study of water electrolysis with photovoltaicsolar energy conversion. International Journal of HydrogenEnergy 1982;7:287–310.

[20] Seigel A, Schott T. Optimization of photovoltaic hydrogenproduction. International Journal of Hydrogen Energy 1988;19:659–75.

[21] Bilgen E. Solar hydrogen from photovoltaic-electrolyzersystems. Energy Conversion Management 2001;42:1047–57.

[22] Ulleberg Ø. Stand-alone power systems for the future:optimal design, operation & control of solar-hydrogen energysystems. PhD thesis. Norwegian University of Science andTechnology, Trondheim; 1998.

[23] Kolhe M, Agbossou K, Hamelin J, Bose TK. Analytical model forpredicting the performance of photovoltaic array coupledwith a wind turbine in a stand-alone renewable energy systembased on hydrogen. Renewable Energy 2003;28:727–42.

[24] Gorgun H. Dynamic modelling of a proton exchangemembrane (PEM) electrolyzer. International Journal ofHydrogen Energy 2006;31:29–38.

[25] Busquet S, Hubert CE, Labbe J, Mayer D, Metkeemeijer R. Anew approach to empirical electrical modelling of a fuel cell,an electrolyser or a regenerative fuel cell. Journal of PowerSources 2004;134:41–8.

[26] Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR.Performance modeling of the ballard mark IV solid polymerelectrolyte fuel cell I. Mechanistic model development.Journal of Electrochemical Society 1995;142:1–8.

[27] Amphlett JC, Baumert RM, Mann RF, Peppley BA, Roberge PR.Performance modeling of the ballard mark IV solid polymerelectrolyte fuel cell II. Empirical model development. Journalof Electrochemical Society 1995;142:9–15.

[28] Khan MJ, Iqbal MT. Dynamic modeling and simulation ofa small wind-fuel cell hybrid energy system. RenewableEnergy 2005;30:421–39.

[29] Vosen SR, Keller JO. Hybrid energy storage systems for stand-alone electric power systems: optimization of systemperformance and cost through control strategies.International Journal of Hydrogen Energy 1999;24:1139–56.

[30] Richards BS, Conibeerb GJ. A comparison of hydrogen storagetechnologies for solar-powered stand-alone power supplies:a photovoltaic system sizing approach. International Journalof Hydrogen Energy 2007;32:2712–8.

[31] Yang H, Lu L, Zhou W. A novel optimization sizing model forhybrid solar–wind power generation system. Solar Energy2007;81:76–84.

[32] Zhou K, Ferreira JA, de Haan SWH. Optimal energymanagement strategy and system sizing method for stand-alone photovoltaic-hydrogen systems. International Journalof Hydrogen Energy 2008;32:477–89.

[33] Santrelli M, Cali M, Macagno S. Design and analysis of stand-alone hydrogen energy systems with different renewablesources. International Journal of Hydrogen Energy 2004;29:1571–86.

[34] Kelouwani S, Agbossou K, Chahine R. Model for energyconversion in renewable energy system with hydrogenstorage. Journal of Power Sources 2005;140:392–9.

[35] Ulleberg Ø. The importance of control strategies in PV-hydrogen systems. Solar Energy 2004;76:323–9.

[36] Dufo-Lopez R, Bernal-Agustın JL, Contreras J. Optimization ofcontrol strategies for stand-alone renewable energy systemswith hydrogen storage. Renewable Energy 2007;32:1102–26.

[37] Ghosh PC. Cost optimization of a self-sufficient hydrogenbased energy supply system PhD thesis, ForschungszentrumJulich in der Helmhotltz-Gemeinschaft, Institut furWerkstoffe und Verfahren der Energietechnik Institut 3:Energieverfahrenstechnik (Diss. Aachen, RTWH, 2003).

[38] Meurer C, Barthels H, Brocke WA, Emonts B, Groehn HG.Phobeusdan autonomous supply system with renewableenergy: six years of operational experience and advancedconcepts. Solar Energy 1999;67:131–8.

[39] Gazey R, Salman SK, Aklil-D’Ahalluin DD. A field applicationexperience of integrating hydrogen technology with windpower in a remote island location. Journal of Power Sources2006;157:841–7.

[40] Chaparro AM, Soler J, Escudero MJ, de Ceballos MJ,Wittstadt U, Daza L. Data results and operational experiencewith a solar hydrogen system. Journal of Power Sources 2005;144:165–9.

[41] Lehman PA, Chamberlin CE, Pauletto G, Rocheleau MA.Operating experience with photovoltaic-hydrogen energysystem. International Journal of Hydrogen Energy 1997;22:465–70.

[42] Hollmuller P, Joubert JM, Lachal B, Yvon K. Evaluation ofa 5 kWp photovoltaic hydrogen production and storageinstallation for a residential home in Switzerland.International Journal of Hydrogen Energy 2000;25:97–109.

[43] Galli S, Stefanoni M. Development of a solar-hydrogen cyclein Italy. International Journal of Hydrogen Energy 1997;22:453–8.

[44] Vanhanen JP, Kauranen PS, Lund PD. Operation experiencesof a phosphoric acid fuel cell in a solar hydrogen energysystem. International Journal of Hydrogen Energy 1997;22:707–13.

[45] Lehman PA, Chamberlin CE. Design of a photovoltaic-hydrogen-fuel cell energy system. International Journal ofHydrogen Energy 1991;22:349–52.

[46] Ipsakis D, Stergiopoulos F, Voutetakis S, Elmasides C,Seferlis P, Papadopoulou S. Study of an autonomous powersystem based on solar and wind energy with hydrogen as theintermittent energy source for future use. Conferenceproceedings of the 4th Dubrovnik Conference on SustainableDevelopment of Energy Water and Environmental Systems,Dubrovnik, Croatia; June 4–8 2007.

[47] Deshmukh SS, Boehm RF. Review of modeling details relatedto renewably powered hydrogen systems. Renewable andSustainable Energy Reviews 2007; doi:10.1016/j.rser.2007.06.008.

[48] Band structure and carrier concentration. See also: http://www.ioffe.rssi.ru/SVA/NSM/Semicond/SiGe/bandstr.html(accessed January 2008).

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 4 ( 2 0 0 9 ) 7 0 8 1 – 7 0 9 5 7095

[49] Siegfried H. Grid integration of wind energy conversionsystems. John Wiley & Sons Ltd; 1998.

[50] Manwell JF, McGowan JG. Lead acid battery storage model forhybrid energy systems. Solar Energy 1993;50:399–405.

[51] Larminie J, Dicks A. Fuel cell systems explained. 2nd ed. JohnWiley & Sons Ltd; 2003.

[52] Kikkinides ES, Georgiadis MC, Stubos AK. Dynamic modellingand optimization of hydrogen storage in metal hydride beds.Energy 2006;31:2428–46.

[53] Li Q, Lu XG, Chou KC, Xu KD, Zhang JU, Chen SL. Feasibilitystudy on the controlled hydriding combustion synthesis ofMg–La–Ni ternary hydrogen storage composite. InternationalJournal of Hydrogen Energy 2007;32:1875–84.

[54] Elam CC, Catherine E, Padro G, Sandrock G, Luzzi A,Lindblad P, et al. Realizing the hydrogen future: theInternational Energy Agency’s efforts to advance hydrogenenergy technologies. International Journal of HydrogenEnergy 2003;28:601–7.

[55] Vanhanen JP, Lund PD, Tolonen JS. Electrolyser-metalhydride-fuel cell system for seasonal energy storage.International Journal of Hydrogen Energy 1998;23:267–71.

[56] Bossi C, Del Corno A, Scagliotti M, Valli C. Characterisation ofa 3 kW PEFC power system coupled with a metal hydride H2

storage. Journal of Power Sources 2007;171:122–9.[57] Botzung M, Chaudourne S, Gillia O, Perret C, Latroche M,

Percheron-Guegan A, et al. Simulation and experimentalvalidation of a hydrogen storage tank with metal hydrides.International Journal of Hydrogen Energy 2008;33:98–104.

[58] Sakintuna B, Lamari-Darkrim F, Hirscher M. Metal hydridematerials for solid hydrogen storage: a review. InternationalJournal of Hydrogen Energy 2007;32:1121–40.

[59] Ipsakis D, Voutetakis S, Seferlis P, Stergiopoulos F,Papadopoulou S, Elmasides C. The effect of the hysteresisband on power management strategies in a stand-alonepower system, Energy, in press, doi:10.1016/j.energy.2008.07.012.