EXPERIMENTAL AND THEORETICAL DEVELOPMENT OF A PEM
ELECTROLYZER MODEL APPLIED TO ENERGY STORAGE SYSTEMS
Francisco da Costa Lopes (1,2) and Edson H. Watanabe (2)
(1)
(2)
CEPEL – Electric Power Research Center
Av. Horácio Macedo, 354
Cidade Universitária
21941-911 – Rio de Janeiro – RJ
fcl@cepel.br
Abstract – Electrolyzers have been pointed out as a
promising technology for use in energy storage
applications. Basically, electrolyzers convert electrical
energy to electrochemical energy, which stays
encapsulated in diatomic hydrogen molecule for posterior
use in fuel cells, which convert the electrochemical energy
back to electrical energy. The main advantages of the
electrolysis process are the zero-emission of greenhouse
gases, the use of water as the source of hydrogen, and the
high efficiency in energy conversion. Electrolyzers can be
fed by the grid or by renewable sources such as solar and
wind. In both cases a power converter is necessary to
conditioning the electrical energy in order to deliver a
clean DC current to the electrolyzer. In this context, this
work shows a modeling of a PEM (proton exchange
membrane) electrolyzer intending its use in conjunction
with power converters. The main losses in such
electrolyzer are modeled and it is shown the influence of
the current ripple in the electrolyzer behavior and
efficiency.
Keywords – Current Harmonics, Electrolyzer, Energy
Storage, Fuel Cell, Hydrogen, Renewable Systems.
I. INTRODUCTION
Electrolyzers are devices that dissociate some molecules
by means the injection of a DC controlled current. The
hydrogen electrolyzer dissociates the water molecule,
delivering diatomic hydrogen (H2) and oxygen (O2) as
reaction products [1]. In other words, electrolyzers convert
electrical energy to electrochemical energy and for this
reason they find practical applications in energy storage
systems, where the storage element in this case is the
hydrogen, which has one of the highest energy density per
mass (120 MJ.kg–1). Compared with systems using batteries,
the systems employing hydrogen as storage element are more
appropriate for long-term energy storage because they do not
present the self-discharge effect as occurs with batteries.
Further, batteries may leak, which rarely occur with
hydrogen gas tanks due to the high safety concerns and
consequent high reliability of such systems.
Several studies have been conducted involving
electrolyzers and renewable energy sources [2]-[9] such as
photovoltaic and wind-powered systems. In such systems the
renewable source feeds DC current to the electrolyzer that
storages energy in the hydrogen. Power management and
control is an important issue in such systems. For this reason,
COPPE/UFRJ
Electrical Engineering Department
P.O. Box 68504
21941-972 – Rio de Janeiro – RJ
watanabe@coe.ufrj.br
it is important to have an accurate model of the electrolyzer
that relates current, voltage, electrical power and hydrogen
flow. In this way, this work presents a more accurate
modeling of a proton exchange membrane electrolyzer –
PEM electrolyzer – taking into account some electrical
characteristics that are important in power converter design
and control such as current ripple influence on the
electrolyzer power demand and efficiency.
II. EXPERIMENTAL SETUP
The electrolyzer studied in this work is a one-cell PEM
electrolyzer made by the company h-tec energy systems [10]
and shown in Fig. 1. It is composed by the membrane
electrolyte enveloped by two electrodes (anode and cathode),
and two tubes filled with water, each one connected to one
electrode as shown in Fig. 1 (a). The water flows from
oxygen tube to the anode where the first half of the
electrolysis reaction takes place. Two molecules of water are
then dissociated in four H+ ions and one O2 molecule is
formed. In this process four electrons are released flowing
around an external circuit. These four H+ ions pass through
the membrane and reach the cathode where they combine
with the electrons producing two H2 molecules that bubble
up inside the hydrogen tube. The electrolyzer in operation is
shown in Fig. 1 (b), where it can be seen hydrogen bubbles
emerging from the electrode surface. The known parameters
of h-tec electrolyzer are shown in TABLE I.
Oxygen
tube
Membrane
+
electrodes
Hydrogen
tube
(a) h-tec electrolyzer.
(b) Hydrogen bubbles at the
electrode surface.
Fig. 1. Electrolyzer used in experiments.
TABLE I
Known parameters of the h-tec electrolyzer.
Parameter
A (Membrane Area)
ϕ (Membrane thickness)
Value
12.25 cm2
178 μm
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775
The experimental setup is shown in Fig. 2. It is composed
by the electrolyzer, a bubble counting instrument to measure
the hydrogen flow, a programmable DC current source, an
oscilloscope with data storage, a datalogger for long data
acquisitions, a signal generator for modulate the DC current
with an AC ripple, and a notebook for data acquisition and
processing. All the experimental results along this paper
were obtained using this arrangement. The calculations
shown in this work can be extended for an n-cells
electrolyzer by multiplying the results by n.
where:
•
•
_
Δ g is the change in the molar Gibbs free energy;
Erev is the voltage of the electrolyzer without losses.
And then:
_
Δg ,
Erev = −
2F
that is the reversible potential of an electrolyzer.
(4)
The change in Gibbs free energy is temperature dependent
and is defined by:
_
_
_
Δ g f = Δ h f − TΔ s ,
(5)
where:
_
•
Δ g f is the change in the molar Gibbs free energy of
formation (J.mol-1);
•
•
Δ h f is the change in the molar enthalpy of
formation (J.mol-1);
T is the temperature (K);
•
Δ s is the change in the molar entropy (J.mol-1.K-1).
_
_
_
In turn, the changes in molar enthalpy of formation ( Δ h f )
Fig. 2. Experimental setup.
_
and molar entropy ( Δ s ) are given by:
III. ELECTROCHEMICAL FUNDAMENTALS
The PEM electrolyzer is a device that breaks the water
molecule by means of an electrical current to produces
diatomic hydrogen and oxygen, as shown below:
(1)
H2O ⇒ H2 + ½ O2 , ΔH = 285.84 kJ,
where:
0
is the enthalpy of the reaction at 1 atm and 25 °C.
ΔH 25
0
25
A. Reversible potential
For the hydrogen electrolyzer, two electrons pass through
the external circuit for each water molecule consumed and
each molecule of hydrogen produced. Being – e the charge of
one electron, where e is the elementary charge (1.602 x 10-19
coulombs), and Na the Avogadro’s number (6.022 x 1023), so
the charge transferred through the external circuit for one
mole of hydrogen produced is:
Charge per mole = – 2 eNa = – 2F ,
•
(3)
(7)
_
_
_
2
2
2
of formation of hydrogen, oxygen and water,
respectively;
•
_
_
_
(s ) H , (s ) O
2
2
and (s ) H
2O
are the molar entropy of
hydrogen, oxygen and water, respectively.
However, the molar enthalpy of formation and the molar
entropy of each substance change with reaction temperature
as follows:
_
_
hTr = h 298.15 +
F (= eNa) is the Faraday constant, which is equal to 96485
coulombs and is the charge of “one mole of electrons” [1].
_
_
_
_
1 _
Δ s = (s) H + ( s) O − ( s) H O ,
2
2
2
2
(h f ) H , (h f ) O and (h f ) H O are the molar enthalpy
where:
Δ g = −2FErev ,
(6)
where:
(2)
The change in Gibbs free energy (ΔG) of an
electrochemical reaction is defined as the “energy available
to do external work, neglecting any work done by changes in
pressure and/or volume” [1]. In an electrolyzer, this ‘external
work’ corresponds to the flow of electrons through the
external circuit. If the system has no losses, this external
work will be equal to the electrical work, so the following
equation is established:
_
_
_
1 _
Δ h f = (h f ) H + (h f ) O − (h f ) H O ,
2
2
2
2
_
_
s Tr = s 298.15 +
∫
∫
Tr
298.15
_
c p dT ,
1_
c p dT ,
298.15 T
Tr
(8)
(9)
where:
•
•
_
_
h 298.15 and s 298.15 are the molar enthalpy of
formation and molar entropy at ambient temperature
(298.15 K);
_
c p is the molar heat capacity of each substance (H2O,
H2, O2) at constant pressure.
The values of the molar enthalpy of formation, molar
entropy and molar heat capacity of each substance are
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776
E
0
rev
= 1.449 − 0.0006139 T − 4.592 × 10 T + 1.46 × 10 T .
−7
− 10
2
1.25
(10)
Definition
Adjusted polynomial
1.24
Reversible potential (V)
3
1.23
m3 ,
(13)
s
that is the volumetric hydrogen flow. Changing from m3.s–1
to ml.min–1:
H 2 flow = 1.2462 × 10 −7 × I
H 2 flow = 7.477 × I
1.22
40
35
30
25
20
15
10
5
0
(14)
Experimental flow
Theoretical flow
0
1
1.21
2
3
Current (A)
4
5
Fig. 4. Experimental and theoretical hydrogen flow.
1.2
C. Efficiency
1.19
1.18
ml .
min
Fig. 4 shows the measured and the theoretical hydrogen
flow for 0.75 to 4.5 A DC current range. It is noted that
experimental and theoretical hydrogen flows agree quite well
for most of the range. The maximum percent error found was
7 % at 2.5 A, and the average percent error was 5 %, which
reveals a good agreement between theoretical and
experimental results. The linear relationship expected
between hydrogen flow and current is also observed in the
experimental measurements.
Hydrogen flow (ml/min)
obtained from thermodynamics tables [11][12] and are
shown in the Appendix.
With the help of MathCAD software, the integrals shown
in (8) and (9) are calculated for Tr varying from 273.15 K
(0 °C) to 353.15 K (80 °C) and the molar enthalpy of
formation ( hf ) and molar entropy ( s ) of each substance are
found. By applying these values in (6) and (7) and finally
substituting the results in (5), the change in the molar Gibbs
free energy of formation (Δgf) is obtained for the temperature
range above.
The reversible potential is obtained by substituting the
values of Δgf in (4). By using the MATLAB curve fitting
toolbox it was found that the curve of the reversible potential
is better adjusted by a 3rd order polynomial as shown in (10).
Fig. 3 shows the reversible potential in function of
temperature calculated by the definition and the adjusted
polynomial.
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
Temperature ( °C)
Fig. 3. Relationship between reversible potential and temperature.
The reversible potential is also influenced by pressure of
reactants and products (the voltage increases with the
pressure). However, in this work the effect of pressure on
reversible potential is neglected because the electrolyzer
operates at ambient pressure and its effects is imperceptible.
B. Hydrogen flow
As mentioned before, for each mole of hydrogen
produced, two electrons circulate through the external circuit.
Since the charge of one mole of electrons that pass round the
external circuit is given by (2) then:
Total charge = − 2 F nH ,
2
(11)
where:
n H 2 is the total amount of moles of hydrogen that are
produced.
Taking the absolute value of (11), dividing both terms by
time, and rearranging gives:
H 2 flow =
I
2F
moles ,
s
(12)
where:
I is the DC current injected into the electrolyzer.
Multiplying the expression above by hydrogen mass
(2.02 x 10–3 kg.mole–1) and dividing by hydrogen density
(0.084 kg.m–3) gives:
The enthalpy of formation is the energy that would be
released if the fuel were burnt [1]. For this reason, this entity
is also called ‘calorific value’. When the water involved in
the reaction is in the steam form, this figure is equal to –
241.83 kJ.mole–1 for 1 atm and 25 °C and is called the lower
heating value (LHV), and when the water is in the liquid
form, this figure is equal to –285.84 kJ.mole–1 for 1 atm and
25 °C and is called the higher heating value (HHV) [1]. So if
all the electrical energy injected into the electrolyzer were
transformed into hydrogen, then the reversible potential
would be given by:
_
Erev
Δh ,
=−
2F
= 1.25 V, for the LHV, and
= 1.48 V, for the HHV.
(15)
Thus, it is reasonable to define the electrolyzer efficiency
as a ratio between the voltage shown in (15) and the actual
voltage of the electrolyzer. So, using the HHV, the
electrolyzer efficiency is given by:
Efficiency =
1.48
× 100% .
ETotal
(16)
Fig. 5 shows the experimental efficiency of the h-tec
electrolyzer calculated using (16), where ETotal is the actual
voltage measured at electrolyzer terminals. The graph shows
that the efficiency reduces for higher currents. This is
explained by the fact that the losses increase with higher
currents, as will be show in the next section. However, it is
clear that the electrolyzer is very efficient in converting
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777
electrical energy to electrochemical energy and can be
compared with batteries which efficiency is around 80 %.
The high efficiency of the electrolyzer makes it suitable to be
employed in energy storage systems.
100%
Efficiency
90%
80%
70%
60%
voltage across the resistance ROhm represents the ohmic
overpotential and the voltage across the resistance RAct in
parallel with the capacitance C represents the activation
overpotential. This capacitance C represents the charge
double layer phenomenon that takes place at the electrodeelectrolyte interface and is treated in details in [1] and [16].
The reversible potential is also represented by a constant DC
voltage source (if the temperature is fixed). The second
representation using resistances and capacitance (Fig. 6 (b))
is useful to analyze the dynamic behavior of the electrolyzer.
I
I
50%
0
1
2
3
Current (A)
4
+
5
EOhm
+
_
EAct
+
_
Fig. 5. Experimental efficiency.
IV. OVERPOTENTIALS MODELING
The main overpotentials (or irreversible losses) that affect
the electrolyzer voltage in low currents are the ohmic
overpotential and activation overpotential. So the total
voltage of the electrolyzer is given by the sum of reversible
potential and these overpotentials as follows:
(17)
ETotal = ERev + EOhm + EAct.
Equation (17) suggests that the voltage at the electrolyzer
terminals (ETotal) can be represented by a circuit composed by
three voltage sources as shown in Fig. 6 (a). For a fixed
temperature the reversible potential is constant and can be
represented by a constant DC voltage source. The ohmic
overpotential and activation overpotential are represented as
current-controlled voltage sources. Many authors adopt the
representation shown in Fig. 6 (b) [1][13][14][15], where the
ETotal
Erev
RAct
ETotal
C
Erev
_
_
(b)
(a)
Fig. 6. Equivalent electrical circuit representations of a PEM
electrolyzer.
A. Ohmic Overpotential
The ohmic overpotential is modeled according to (18).
EOhm =
ϕ ,
j
σ
(18)
where:
• ϕ is the thickness of the membrane that is 178 μm;
• σ is the conductivity of the membrane (S.cm-1);
• j is the current density (A.cm-2).
According to Larminie and Dicks [1], the ohmic
overpotential can be found by ‘interrupt current technique’.
Considering a clean and well shaped DC current circulating
through the circuit of the Fig. 6 (b), in steady state the
capacitance C is fully charged and the current flows only
through ROhm and RAct. If the current is suddenly cut off, the
voltage across the resistance ROhm will immediately reduce to
zero while the voltage across RAct will take some time to
decay due to charge double layer capacitance time constant.
Fig. 7 shows an experimental measurement of the voltage at
the electrolyzer terminals where can be clearly noted the
abrupt voltage drop that corresponds to the ohmic
overpotential.
The ohmic overpotential measured for each current value
is shown in Fig. 8. This overpotential behaves fairly linear in
the range between 0 and 1.5 A. Beyond this interval, the
ohmic overpotential becomes nonlinear due to the bubble
voltage effect. The study of this phenomenon is out of the
scope of this work, but more information can be found
in [17].
1.90
1.80
Voltage (V)
D. Irreversibilities
Irreversibility is a more precise term to describe the
‘losses’ in thermodynamic and electrochemical systems.
Many times the ‘lost energy’ can be recovered and thus it is
not an irreversible loss. The term irreversibility is more
precise because describes the energy that cannot be
recovered, that is, an irreversible loss. In electrolyzers the
irreversibilities appear under the form of overpotentials or
overvoltages that are summed to the reversible potential
given by (4). Thus, the main overpotentials of an electrolyzer
are the activation overpotential, ohmic overpotential, and
concentration overpotential.
The activation overpotential is caused by the slowness of
the reactions that take place at the electrodes surface. A
proportion of the voltage generated is lost in driving the
chemical reaction that transfers the electrons to or from the
electrode. This overpotential is highly nonlinear and varies
with the current, predominating in lower currents.
The ohmic overpotential is due to the resistance to flow of
electrons through the electrodes (electronic resistance) and
the resistance to flow of ions through the membrane
electrolyte (protonic resistance). This overpotential is
proportional to current and linear.
The concentration overpotential is the result in change of
the concentration of reactants at the surface of the electrode
as it is consumed. However, this overpotential predominates
at higher currents and can be neglected in this work since the
studied electrolyzer operates with lower currents.
+
ROhm
1.70
Ohmic overpotential
1.60
1.50
1.40
0
2
4
6
8
10
12
14
16
18
20
22
Time (s)
Fig. 7. Voltage variation due to current interrupt (ΔI = 2 A).
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0.12
0.08
0.04
0.00
0
0.5
1
Current (A)
1.5
Fig. 8. Ohmic overpotential obtained by current interrupt method.
The conductivity is calculated using (18) and is plotted in
Fig. 9. It can be seen that the conductivity is almost constant
for that current range. Taking the average value of
conductivity, that is, 0.0165 S.cm-1, the ohmic resistance is
calculated and the following linear equation is established
relating current and ohmic overpotential.
E Ohm
linearized
(19)
= 0.09 × I .
Conductivity (S.cm-1)
0.025
0.020
0.015
0.010
Activation overpotential (V)
Ohmic overpotential (V)
applications, electrolyzers operate in higher temperatures
(sometimes reaching 80 °C) to increase efficiency [4] so (10)
will have to be taken into account to find the right value of
the reversible potential. The activation overpotential for each
current value is shown in Fig. 10.
0.16
0.40
0.35
0.30
0.25
0.20
0
0.5
1
1.5
Current (A)
Fig. 10. Activation overpotential.
The charge transfer coefficient of the cathode (αC) shown
in (20) is considered constant and equal to 0.5 by many
authors [1][19][20]. This assumption is also adopted in this
work. The other parameters shown in (20) (αA, jA,o, jC,o) can
be found using a curve fitting algorithm. The data shown in
Fig. 10 was then fitted using the MATLAB curve fitting
toolbox, as shown in Fig. 11, and the parameters found by
this algorithm are shown in TABLE II.
0.005
0.000
0
0.5
1
Current (A)
1.5
Fig. 9. Membrane conductivity (σ).
B. Activation Overpotential
The activation overpotential (EAct) is modeled according
to the Butler-Volmer equation [1][13][16]. It is used the
hyperbolic sine approximation for the Butler-Volmer
equation [18][19][20] instead of the traditional form using a
logarithm function because the hyperbolic sine function is
easier to model using curve fitting algorithms. The
hyperbolic sine form for EAct is given below:
EAct =
⎛ j
RT
sinh −1 ⎜⎜
2α A F
⎝ 2 jA,o
⎞
⎛
⎟ + RT sinh −1 ⎜ j
⎟ 2α F
⎜2j
C
⎠
⎝ C,o
⎞
⎟,
⎟
⎠
Goodness of fit:
SSE: 0.0001318
R-square: 0.9906
Adjusted R-square: 0.9881
RMSE: 0.003461
(20)
where:
• αA is the charge transfer coefficient at the anode;
• αC is the charge transfer coefficient at the cathode;
• jA,o is the exchange current density at the anode
(A.cm-2);
• jC,o is the exchange current density at the cathode
(A.cm-2).
1) Finding αA, αC, jA,o, jC,o by curve fitting
The experimental values of activation overpotential (EAct)
can be obtained using (17) by subtracting the ohmic
overpotential (EOhm) values obtained by current interrupt
method (Fig. 8) and the reversible potential (ERev) from the
total voltage (ETotal) measured at the electrolyzer terminals.
Since the temperature does not change very much during the
experiments, the reversible potential can be considered
constant and equal to 1.23 V (Erev for 25 °C). In practical
Fig. 11. Activation overpotential curve fitting.
TABLE II
h-tec electrolyzer parameters found by curve fitting
Parameter
αA
αC
jA,o
jC,o
σ
Value
0.42
0.5
3.348 x 10-6
0.04957
0.02
2) Activation overpotential linearization
It is observed that the activation overpotential curve
shown in Fig. 10 is almost linear between 0.5 and 1.5 A.
From this observation, that overpotential can be linearized
around some operating point. By using the parameters shown
in TABLE II, the differentiation of EAct at the operating point
is calculated as shown in (21).
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779
dE Act
dj
=
+
1
1
RT
⋅
⋅
2α A F 2 jA,o ⎛
⎜ j
⎜2j
⎝ A,o
RT
1
1
⋅
⋅
2α C F 2 jC,o ⎛
⎜ j
⎜2j
⎝ C,o
V. EXPERIMENTAL DYNAMIC ANALYSIS
2
⎞
⎟ +1
⎟
⎠
+
2
(21)
⎞
⎟ +1
⎟
⎠
The calculations were made for I = 0.9 A point (j =
0.9/12.25 = 0.073 A.cm-2), once this point is in the middle of
the linear range. In this way, by converting current density
(A.cm-2) to current (A) and finding the linear coefficient, the
linear equation that represents the activation overpotential is
found:
E Act
linearized
(22)
= 0.0514 × I + 0.2798 .
C. Linear Model Validation
The linearized ohmic and activation overpotentials were
calculated using (19) and (22) and were plotted with the
experimental measurements in order to validate the model.
Fig. 12 shows the activation and ohmic overpotentials and
Fig. 13 shows the total voltage at the electrolyzer terminals.
The figures show that, for the current range considered in the
linearization process, the error is very small and, therefore,
the linear model developed is suitable to represent the
electrolyzer for the current range between 0.5 and 1.5 A.
Naturally, the linearization technique can be further applied
to other points if one wants to find a better approximation of
the total voltage at each point.
0.5
Experimental Eact
Linearized Eact
Experimental Eohm
Linearized Eohm
Voltage (V)
0.4
0.3
0.2
A. Laplace Domain Analysis
Laplace Transformation can be applied to circuit variables
of Fig. 6 (b) considering the linear behavior presented by the
electrolyzer between 0.5 and 1.5 A. By applying the Laplace
Transformation to circuit variables of Fig. 6 (b) gives:
⎛ R + RAct ⎞
⎟
sROhm + ⎜⎜ Ohm
RAct C ⎟⎠ .
E rev
⎝
(23)
E Total (s ) =
+ I (s )
1
s
s+
RAct C
that is the expression of the total voltage (ETotal) in the
Laplace Domain.
The second term of (23) represents the impedance formed
by ROhm, RAct and C. It is clear that this term imposes a first
order behavior to the electrolyzer dynamic response.
Equation (23) also suggests that the response time of the
electrolyzer depends on the activation resistance (RAct) and
the double layer capacitance (C) values. Some authors report
values about 10-30 μF.cm–2 for the double layer capacitance
for a PEM fuel cell fed by methanol [14]. If this value were
applied to the studied PEM electrolyzer, its capacitance
would be 122.5-367.5 μF. However, its value varies from
cell to cell and cannot be generalized since it depends on the
membrane humidity, operating temperature, concentration of
catalysts on the electrodes surface, etc. In addition, it is not
so easy to determine the exact value of this capacitance. The
impedance spectroscopy technique is a more suitable method
to find the double layer capacitance value, but the
employment and the study of this technique are out of the
scope of this work. The ohmic resistance ROhm and the
activation resistance RAct can be estimated by (19) and (21),
respectively.
Fig. 14 shows the experimental response of the
electrolyzer voltage to a current step from 0 to 1 A. It is
noted that the response looks quite well with a first order
system response, validating the dynamic circuit model
proposed in Fig. 6 (b) and, consequently, the expression
shown in (23).
1.70
0.1
0
0.5
Current (A)
1
1.5
Fig. 12. Activation and ohmic overpotentials.
Voltage (V)
0
1.65
1.60
1.55
1.50
1.45
1.40
1.35
1.8
1.30
Experimental
Linearized
0
4
6
8
10
12
14
16
18
20
22
24
Time (s)
Fig. 14. Experimental response of the electrolyzer voltage to a
current step.
1.7
Voltage (V)
2
1.6
1.5
0
0.5
Current (A)
1
Fig. 13. Total voltage (ETotal) of the electrolyzer.
1.5
B. Current ripple analysis
In order to analyze the influence of the current ripple (or
current harmonics) on the electrolyzer dynamic behavior, it
was applied a frequency- and amplitude-controlled CA signal
over the DC current of the electrolyzer. The current source
shown in Fig. 2 was programmed to supply 1.25 A DC with
a 1.5 A (peak to peak) CA current superimposed to DC level.
The frequency was changed at each experiment and total
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780
voltage (ETotal) and hydrogen flow were measured for each
frequency. The total voltage and current were plotted in v-i
plots as shown in Fig. 15.
It was observed a notable hysteresis between total voltage
and current of the electrolyzer for frequencies below 40 Hz,
revealing that voltage and current are out of phase for these
frequencies. Fig. 16 shows voltage and current of the 10 Hz
experiment without DC level, where is possible to see that
the voltage lags the current, as a RC circuit. This effect is due
to the charge double layer capacitance as explained
previously. For frequencies higher than 40 Hz, the hysteresis
behavior disappears because the impedance related to the
double layer capacitance is reduced and the v-i curve
becomes a straight line, so in very high frequencies (20-100
kHz), where many power converters operate, the circuit
behaves like a resistive circuit.
power consumed when there is current ripple is higher than
the average power without current ripple.
These observations lead to the conclusion that the AC
current ripple causes energy waste, because it increases the
power consumed by the electrolyzer without increasing the
hydrogen production. The lower the frequency of the current
ripple, the higher is the power loss in the electrolyzer. Up to
the present, there are no evidences if the current harmonics
can harm the membrane or other electrolyzer component.
The study of the consequences of the harmonics on the
membrane integrity is then left for further works.
TABLE III
Relationship between hydrogen flow and current harmonics.
Frequency
10
60
Only DC
Hydrogen flow (ml/min)
4.60
4.76
4.76
4
3,5
Power (W)
3
(b) 20 Hz.
(a) 10 Hz.
Average power consumed
with 10 Hz current ripple
2,5
DC Power
10 Hz Power
2
1,5
1
0,5
1153
1105
1057
961
913
1009
865
817
769
721
673
625
577
529
481
433
385
337
289
241
97
193
145
1
49
0
Time (s)
Fig. 17. Average power level of 10 Hz ripple.
VI. CONCLUSION
(d) 40 Hz.
(c) 30 Hz.
Fig. 15. Electrolyzer voltage and current hysteresis.
Voltage (V) , Current (A)
1
Voltage
Current
-1
Time (s)
Fig. 16. Voltage and current out of phase – 10 Hz.
TABLE III shows hydrogen flow measured in three
situations: (i) current ripple of 10 Hz superimposed to DC
current, (ii) current ripple of 60 Hz superimposed to DC
current, and (iii) DC current without ripple. TABLE III
shows that the hydrogen flow practically does not vary when
the DC current has AC ripple superimposed to it.
Fig. 17 shows the average power consumed by
electrolyzer with a 10 Hz current ripple and without current
ripple (only DC current). It can be seen that the average
The high efficiency in energy conversion, the zeroemission of greenhouse gases, and the use of water as
hydrogen source make the electrolysis process a good choice
for use in energy storage systems employing renewable
sources. Besides, the high energy density by weight of the
hydrogen, and the absence of self-discharging effect makes
this element ideal for long-term energy storage.
Electrolyzers can be fed by the grid or by renewable
sources such as solar and wind. In both cases a power
converter is necessary to conditioning the electrical energy in
order to deliver a clean DC current to the electrolyzer. Thus,
it is important to have a more accurate model of the
electrolyzer that relates its current, voltage, electrical power
demand and hydrogen flow.
This work has presented a modeling of a proton exchange
membrane electrolyzer (PEM electrolyzer). A more rigorous
calculation of the electrolyzer reversible potential relating it
with temperature was presented. In practical applications,
where the temperature reaches 60-80 °C, this relationship
must be taken into account to find the right value for the
reversible potential in order to get a more accurate model.
The main losses in such electrolyzer were modeled and
linearized. It was shown the influence of the current ripple in
the electrolyzer behavior and efficiency. The AC current
ripple causes energy waste, because it increases the power
consumed by the electrolyzer without increasing the
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781
hydrogen production. The lower the frequency of the current
ripple, the higher is the power loss in the electrolyzer. Thus,
this issue must be taken into account in the power converter
design.
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APPENDIX
The values of the molar enthalpy of formation and molar
entropy of each substance (H2O, H2, O2) at ambient
temperature are given in TABLE IV.
TABLE IV
Molar enthalpy of formation and molar entropy at 298.15 K
_
h 298.15 (J.mol-1)
H2O (liquid)
–285.838
H2O (steam)
_
s 298.15
(J.mol-1.K-1)
70.05
–241.827
188.83
H2
0
130.59
O2
0
205.14
_
The molar heat capacity ( c p ) is also obtained from
thermodynamics tables [11][12]. For the liquid water, the
molar heat capacity is given by:
_
-1 -1
(24)
c p = 75.79 J.mole .K .
For the hydrogen, the molar heat capacity at constant
pressure is given by:
_
c p = 56.5 − 2.2 × 10 4 T −0,75 + 1.17 × 10 5 T −1 − 5.6 × 10 5 T −1,5
J.mole-1.K-1.
(25)
And for the oxygen, the molar heat capacity at constant
pressure is given by:
_
c p = 29.154 + 6.477 × 10 −3 T − 0.184 × 10 6 T −2 − 1.017 × 10 −6 T
J.mole-1.K-1.
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(26)
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