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International Journal of Hydrogen Energy 31 (2006) 29–38

www.elsevier.com/locate/ijhydene

Dynamic modelling of a proton exchange membrane(PEM) electrolyzer

Haluk Görgün∗

Yildiz Technical University, Electrical-Electronics Faculty, Istanbul 80750, Turkey

Available online 26 May 2005

Abstract

This paper describes a dynamic model for PEM electrolyzer based on conservation of mole balance at the anode and

the cathode. A further feature of the model is it includes water phenomena, electro-osmotic drag and diffusion, through the

membrane. The model considers PEM electrolyzer to be composed of four ancillaries: anode, cathode, membrane and voltage

ancillary. Additionally, hydrogen storage dynamics is presented. The developed model is suitable for determining control

strategy that will ensure efficient and reliable operation of the electrolyzer. Moreover, the dynamic model can be integrated

with renewable energy systems models to design, analyze and optimize sustainable energy systems. The study illustrates the

dynamic interactions within a PEM electrolyzer and shows the necessity of the proposed approach of separate ancillaries.

2005 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

1. Introduction

Electrolyzers are unique devices to produce pure hydro-

gen and oxygen. They could be widely distributed and rated

to meet the hydrogen and oxygen requirements of different

users such as units for individuals, renewable energy sys-

tems, fuelling stations and industrial applications. Among

the other types of electrolyzers PEM electrolyzers are very

simple and compact. Besides they ensure high purity and

efficiency at high current density levels. In PEM electrolyz-

ers, the bonds between the hydrogen and oxygen in the H2O

are broken by electromotive force and the catalytic action

of the platinum when dc voltage is supplied. The membrane

separates the H2 from the O2. The hydrogen protons, H +,migrates through the membrane and recombines at the cath-

ode with the returning electrons, e−, and form hydrogen,

H2. PEM electrolyzers offer the potential for low cost in

mass production, if inexpensive membranes are developed.

Last but not least, the other notable advantage of PEM elec-

trolyzers is that the PEM electrolyzer can be used as a fuel

∗ Tel.: +90212 25970 70 (2781); fax: +90212 2594967.

E-mail address: [email protected].

0360-3199/$30.00 2005 International Association for Hydrogen Energy. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijhydene.2005.04.001

cell to produce electricity from hydrogen and oxygen withsmall modifications.

In addition to the cell stack an electrolyzer must have a

dc power supply, a water pump, water–gas separators as il-

lustrated in Fig. 1. Although electrolyzers produce both H2

and O2 by splitting water electrochemically only few appli-

cations uses both products. Most of the time electrolyzer is

considered as a hydrogen generator. Electrolyzers are cat-

egorized as anode feed system or cathode feed system de-

pending on where the water enters the unit. When the elec-

trolyzer is used for just hydrogen generator, cathode feed

system could be a good option because the separator which

separates oxygen and water is eliminated at the anode andoxygen is ventilated with water. The penalty in this case is

that mass transfer limitations occurs and only low current

densities can be achieved. In this study, anode feed elec-

trolyzer modelling is studied since most of the commercial

electrolyzers and military units are anode feed electrolyzers.

However, it should be mentioned that modelling of cath-

ode feed electrolyzer can be accomplished with couple of

changes in water transport phenomena.

Applications of electrolyzers include: O2 for life sup-

port, fuel cells, sustainable energy systems, providing H2 for

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30 H. Görgün / International Journal of Hydrogen Energy 31 (2006) 29 – 38

DC Power

Supply

A C

+ - H2

O2

PEM Electrolyzer

Seperator

Seperator

H2O in

H2 Bottle

Water Pump

Fig. 1. PEM electrolyzer.

corrosion control, gas chromatograph sensors, metal form-

ing and welding. Electrolyzers are currently being studied

by several researchers from industry, academia and mili-tary and research results are being published at an increas-

ing rate. There are several studies to model electrolyzers

and renewable energy systems. Among them, Onda [1] has

developed a two dimensional mathematical model to ana-

lyze PEM electrolyzer. Ulleberg [2] has shown a model for

alkaline electrolyzers based on thermodynamics and heat

transfer theory. More recently on renewable energy systems,

Kélouwani et al. [3] have demonstrated stand alone renew-

able energy system with hydrogen storage. Khan et al. [4]

have presented modelling of a small wind–fuel cell hybrid

energy system. In an earlier study, Busquet et al. [5] have

established an empirical approach to model a electrolyzer or

a regenerative fuel cell. In general, electrolyzer, renewable

energy or regenerative fuel cell studies have been formulated

electrolyzers with just Faraday’s Law. There is a need for an

electrolyzer model which explains its dynamics in detail and

is suitable for dynamic simulation together with renewable

energy systems. This paper gives a detailed control oriented

model for a PEM electrolyzer based on mole balance in the

anode and the cathode subsystems. The model is capable of

characterizing PEM electrolyzer and essential for determin-

ing control strategy that will ensure efficient and reliable

operation of the electrolyzer. Besides, the PEM electrolyzer

dynamic model can be employed in the optimization of sus-

tainable energy systems. This paper is organized as follows:model details are presented in Section 2. Simulation studies

demonstrated in Section 3. Finally, conclusions are given in

Section 4.

2. Modelling

To clearly quantify the dynamic interactions, the PEM

electrolyzer is considered to have four ancillaries: anode,

cathode, membrane and voltage ancillary. Each ancillaries

dynamics and interaction between them are contemplated.

Voltage ancillary calculates electrolyzer applied voltage

level by using Nernst Equation, ohmic polarization and

activation polarization. Membrane ancillary computes

water content, electro-osmotic drag, water diffusion andconductivity of the membrane. The anode ancillary dy-

namically calculates oxygen and water flows and partial

pressures. Similarly, hydrogen and water partial pressures

and their flows are obtained in the cathode subsystem.

Storage ancillary shows storage dynamics of the generated

hydrogen in a bottle by taking account the initial hydro-

gen level in it and compressibility of the hydrogen. The

Simulink Model of the electrolyzer is shown in Fig. 2 and

in the following subsections, the model is explained in

detail.

2.1. Anode ancillary

Electrochemically, all electron transfer reactions are con-

sidered oxidation and reduction. The substance gaining elec-

trons is oxidizing the substance that is losing electrons. The

anode electrode is the electrode where the oxidation occurs

in electrolyzers by definition. In this side of the electrolyzer

the states are oxygen, and water molar hold-ups. The dy-

namics in the model are:

N O2 = F O2ai − F O2ao + O2g ,

N H2Oa = F H2Oai

− F H2Oao − F H2Oeod

− F H2Od , (1)

where, F O2ai , F O2ao , F H2Oai , F H2Oao (mol/s) are cathode

inlet and outlet molar flows of oxygen and water, respec-

tively. One should note that F O2ai is zero because only in-

put is the water, this term is written to show the general

complete mole balance dynamics. F H2Oeod and F H2Od are

electro-osmatic drag and diffusion flows. O2g is the rate of

oxygen generated at the anode.

The partial pressures of the oxygen and water at the anode

are

pO2 =

N O2RT el

V a

and pH2Oa =

N H2OaRT el

V a

, (2)



H. Görgün / International Journal of Hydrogen Energy 31 (2006) 29 – 38 31

Storage Ancillary

Voltage Ancillary

Membrane Ancillary

Bottle Pressure

H2 Flow pb

Cathode Ancillary

FH20n

Faef

Tel

pelec

Ourrent

Cathode Ancillary

FH20n

Water in

Faref

Tel

pelec

Current

Curd

Current Density

Current

Cu

1/A5

t

t

1

L

Clock

101325

Electrolyzer pressure

TSTACK

1 Fef

Faraday Efficiency

C

P02

Fia Fia

Ph2

Fic Fic

VelVel

Fic

Fia

Tst

FH2

FH20mFH20m

lamn

lamn

Pb

landern

i

Tic

H2

px

Fig. 2. PEM electrolyzer simulink diagram.

where V a (m3) is the anode volume, and the total anode

pressure, P a , is

P a = pO2 + pH2Oa . (3)

Oxygen mole fraction at the anode outlet is as follows:

yO2 =

pO2

P a, (4)

and the flows are computed as

F ao = F O2ao + F H2Oao ,

F O2ao = yO2F ao ,

F H2Oao = (1 − yO2 )F ao , (5)

where the anode total out-flow, F co, is obtained by

F ao = kao (P a − P a0), (6)

where kco is the cathode outlet flow coefficient. Finally, the

rate of oxygen generated is

O2g =nI

4F

F

, (7)

where n is the number of the electrolyzer cells, I is the

electrolyzer current, F is the Faraday constant and F is

Faraday efficiency which is given as [6,7],

F =i − iLoss

i, (8)

where iLoss is internal current and hydrogen loss that could

be result of oxygen travel from anode to cathode or hydrogen

travel from cathode to anode in general iLoss is less than

1% of the operating current density.

2.2. Cathode ancillary

Cathode is the electrode where the reduction takes place

in electrolyzers by definition. The states of the cathode side

of the electrolyzer are hydrogen and water molar hold-ups,

N H2 and N H2Oc, respectively,

N H2 = F H2ci − F H2 co + H2g ,

N H2Oc = F H2Oci

− F H2Oco + F H2Oeod

+ F H2Od , (9)

where F H2ci and F H2Oci (mol/s) are cathode electrode hy-

drogen and water inlet molar flows and they are equal to

zero since there is no in flows. F H2co are F H2Oco (mol/s)

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are cathode outlet molar flows of hydrogen and wa-

ter, respectively, F H2Oeod (mol/s) and F H2Od

(mol/s) are

electro-osmotic drag and diffusion from anode electrode

through the membrane, and H2g is the rate of hydrogen

generated.

The partial pressures of hydrogen and water in the cathode

are obtained from the ideal gas law as in the anode,

pH2Oc =

N H2OcRT el

V cand pH2

=N H2 RT el

V c, (10)

where V c(m3) is the cathode volume, and the total cathode

pressure is

P c = pH2 + pH2Oc . (11)

Similar to the anode, hydrogen and water molar flows at the

cathode are computed from cathode out total flow and mole

fractions.

yH2 =pH2

P c(12)

and the flows are

F co = F H2co + F H2Oco,

F H2co = yH2F co,

F H2Oco = (1 − yH2

)F co, (13)

where the cathode subsystem out-flow, F co, is

F co = kco(P c − P 0), (14)

0 200 400 600 800 1000 1200 14000

1

2

3

4

5

6

7

8

9

10

i (mA/cm2)

V o l t ( V o l t s )

Fig. 3. Electrolyzer polarization.

where kco is flow coefficient and P 0 is the cathode out

pressure. The rate of hydrogen reacted is calculated as

H2g =nI

2F F . (15)

2.3. Membrane ancillary

Membrane ancillary is of importance to understand the

water transport phenomena in electrolyzers. There are two

main water flows occurring through the membrane: Electro-

osmatic drag and diffusion. Both of them are function of the

water content of the membrane.

When the H + protons moves through the membrane, wa-

ter molecules accompany them. This phenomenon is well-

known as electro-osmotic drag and this water transportation

is expressed by

F H2Oeod =

nd

i

F M H2OAn, (16)

where M H2O is molecular weight of water, A is the area of

the cell and nd is the electro-osmotic drag coefficient which

is given as

nd = 0.00292m + 0.05m − 3.4 × 10−19, (17)

where m is the arithmetic mean of both ’s for the anode

and the cathode which are calculated by their own water

activities by (18). Membrane water content, is given as

in [8]

= 0.43 + 17.81aa − 39.85a2a + 36a

3a , 0 < aa1,

= 14 + 1.4(aa − 1), 1 < aa3. (18)




The water diffusion coefficient is computed as

Dw = D exp

2416

1

303 −

1

T f c

, (19)

where

D = 10−10, < 2;

D = 10−10(1 + 2(m − 2)), 2m3;

D = 10−10(3 − 1.67(m − 3)), 3m4.5;

D = 1.25 × 10−10, m4.5. (20)

Water diffusion through the membrane is given from Fick’s

first law of diffusion as follows:

F H2Od = Dw

(Cwc − Cwa )

t mM H2OAn, (21)

where t m is the thickness of the membrane and Cwc and Cwa

are water concentration for the cathode and anode surfaceof the membrane, respectively, and they are expressed as

Cwa =m,dry

M m,drya , Cwc =

m,dry

M m,dryc. (22)

2.4. Voltage ancillary

Electrolyzers operates in either current mode or voltage

mode. When they are run in voltage mode, voltage is applied

to the electrolyzer and depending on the operating conditions

the electrolyzer draws the current from the source and after

a couple of transient cycles it has its steady state value. This

mode is suitable for when photovoltaic source is used for anelectrolyzer. However, most of the commercially available

electrolyzers run in current mode and operating voltage of

an electrolyzer is given as

V el = E + V act + V ohm, (23)

where E is open circuit voltage, V act is activation polariza-

tion, V ohm is ohmic polarization. Open circuit voltage, E , is

defined as Nernst Equation [9]

E = E0 +RT el

2F

ln

pH2 p

1/2O2

aH2O

, (24)

where E0 is the standard potential, R is the universal gas

constant, T el is the cell temperature and aH2O is water ac-

tivity between anode and electrolyte for simplicity it is as-

sumed here to be 1. Standard voltage E0 is

E0 =Gf

2F , (25)

where Gf is Gibbs free energy of formation. The activa-

tion polarization is obtained by

V act =RT el

2F ln

i

i0 , (26)

0 500 1000 15000

0.2

0.4

0.6

0.8

1

i (mA/cm2)

E f f i c i e n c y

Fig. 4. Electrolyzer efficiency.

where is charge transfer coefficient, i is the current density

and i0 is the exchange current density.

The ohmic polarization is calculated by

V ohm = iRohm, (27)

where the membrane resistance, Rohm, is

Rohm =t m

m, (28)

where m is the conductivity of the membrane which is

calculated from water content of the membrane, m, and the

electrolyzer temperature, T el, as follows [10]:

m = (0.00514m − 0.00326) exp

1268

1

303 −

1

T el

.

(29)

2.5. Storage ancillary

Produced H2 by electrolyzer is stored in H2 bottle. Con-stant H2 flow fills up the bottle until its pressure reaches

up the electrolyzer cathode pressure. The dynamics of the

storage is obtained as follows:

P b−P bi = zN H2 RT b

M H2V b

, (30)

where P bi is the initial H2 pressure in the bottle, z is the

compressibility factor of the hydrogen. The compressibility

factor is a function of temperature and pressure, it is equal

to 1 when the pressure is below 2000psi at room temper-

ature but it is higher than 1 when the pressure is above




FH2Oa0

FO2a0x

x

+−

+

++

−

+

−

Fao

Fia

1

2

1

Peleo

0.95

yo2

Psata

Pa

pH2Oa

×

×

××

÷

pO2

pO2

1s

1s

3

5

6

4

1

Tel

FH2Om

Water in

faref

CurrentNO2

O2g

R

n*u[1]/(4*F)

Fig. 7. PEM electrolyzer anode ancillary simulink diagram.

FH2Oco

FH2Cox

x

+−

+

++

−

+

−

+

−

Fco

Fic

1

2

1

P elec

0.45

yh2

P satc

(u[1]/u[2])

Pc

pH2OcNH2Oc

×

×

××

÷

pH2

ph2

f(u)

1s

3

5

4

1

Tel

faref

CurrentNH2

H2g

R

n*u[1]/(2*F)

u[2]*u[1]

1/Vc

3

FH2

2

1s

FH2Om

Fig. 8. PEM electrolyzer cathode ancillary simulink diagram.




lama

larnc

aen lama

aca lamc

Gain

5

3

2

Fic

Fia

u[1]*romd/Mmd

u[1]*romd/Mmd

u[1]*(u[2]-u[3])tm

u[1]*expt(2416*((1/303)-(1/u[2])))

CVa

CVC

am

am

4

2

Tst

lamm

lamm

lamm Diamm Dlam

FH2Od

DW

nd0029*u[1]∧

2+0.05*u[1]-3.4e-19

1

i (u[1]*u[2])F FH20eod

FH2Om+

+

1

FH20m

u[1]*MH2O*A*n

Fig. 9. PEM electrolyzer membrane ancillary simulink diagram.

2000psi [11]: At higher pressure values it affects the bottle

pressure dynamics remarkably. T b and V b are the bottle

temperature and volume, respectively. It is assumed that the

bottle temperature is constant through the storing process

since the process is slow.

3. Simulation results

This section presents simulation results for a PEM elec-

trolyzer. For the simulations we implement the model de-rived in Section 2 in Matlab-Simulink. Simulation studies

are pursued assuming PEM electrolyzer stack consists of

n=3 cells, with Am=50cm2 active area each, and with t m=

0.0051cm thickness. Electrolyzer operating temperature and

pressure are chosen as T =300 K and P =101325 Pa. Figs. 3

and 4 shows polarization and efficiency of the stack, respec-

tively. Fig. 5 illustrates hydrogen bottle pressure changes.

The bottle pressure can be set one value so that when it

is reached, current flow is stopped. In Fig. 6, current tran-

sients are introduced and responding hydrogen partial pres-

sure are presented. At t = 300 s operating current is stepped

up from 20 to 50A, and at t = 500 s the current is stepped

down from 50 to 10A, and again it is increased to 70A

at t = 300 s. These figures exhibit that the model can cap-

ture the transient dynamic behavior of the PEM electrolyzer

(Figs. 7–11).

4. Conclusion

A dynamic PEM electrolyzer model has been developed

by exploiting conservation of mole balance. Special atten-

tion has been given to the modelling of subsystems to clearlyquantify the dynamic interactions of a PEM electrolyzer. The

integrated model is implemented by using Matlab-Simulink.

Simulation studies demonstrated that the model can capture

the transient dynamic behavior of the PEM electrolyzer. This

model is essential for determining control strategy that will

ensure efficient and reliable operation of the electrolyzer.

Furthermore, the PEM electrolyzer dynamic model can be

integrated with renewable energy systems models to de-

sign, analyze and optimize sustainable energy systems. The

extension of this study will be to fully validate the model

with PEM electrolyzers in Connecticut Global Fuel Cell

Center.

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0.3

+

−

×

×

×

×

÷

÷

+

+

+

Va2

Elf

1

Vel

1.482

i

io

Tfc

Vohm

lam

Tfc

i

dam

Vohm

RmohmRmohm

n

number of stack2

Ε

v32

10

5

4

i

lamdam

Limiting Current1

3

1

2 0.00001

0.00001

Tfc

pO2

pH2

pH2

pO2

Stack Tem p

OCV

Fig. 10. PEM electrolyzer voltage ancillary simulink diagram.

1+

−

1

S

-c-

Bottle intial pressure-c-

-c-

1

300

Room Temp

Ideal Gas Constant

Bottle Volume

Compresibility Factor

MH2

H2 Flow

H2 Molecular Mass

R

×

×

×

×

÷

÷

pb

Fig. 11. PEM electrolyzer storage ancillary simulink diagram.

Acknowledgements

The author would like to acknowledge Dr. Frano Barbir

and Mr. Trent Molter of Connecticut Global Fuel Cell Center

for very useful discussions and suggestions that contributed

this paper.

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[2] Ulleberg ]. Modeling of advanced alkaline electrolyzers:

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[3] Kélouwani S, Agbossou K, Chahine R. Model for energy

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[4] Khan MJ, Iqbal MT. Dynamic modeling and simulation of a

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[5] Busquet S, Hubert CE, Labbé J, Mayer D, Metkemeijer R. A

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[6] Barbir F. Pem electrolysis for production of hydrogen from

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