Emulation of a PEM Fuel Cell Stack from its Generic and Polynomial
Model using Simulink
LUIS CAMACHO, SECUNDINO MARRERO, CARLOS QUINATOA, CARLOS PACHECO
Department of Electrical Engineering,
University Technical of Cotopaxi,
Barrio El Ejido, Sector San Felipe,
Latacunga,
ECUADOR
Abstract: - This paper will discuss the simulation of a PEMFC fuel cell stack based on its generic
characteristics. To achieve the set objective, a fuel cell model capable of replicating its electrical characteristics
was developed, showcasing the polynomial approximation-based proposed models and the generic model. The
validation of these suggested models involved conducting simulations utilizing converters and comparing the
outcomes with those produced by the Simulink fuel cell stack block. The fuel cell instance underwent testing to
reproduce the electrical behavior of the cell, devoid of the specific data associated with the fuel cell stack.
Key-Words: - Simulation, Cell, Fuel, Model, Stack, Electrical, Generic, Polynomial, Simulink.
Received: August 29, 2023. Revised: May 2, 2024. Accepted: June 9, 2024. Published: July 26, 2024.
1 Introduction
The growing need for traditional energy sources is
imperative for the economic progress of a nation,
consequently resulting in the rise of unconventional
energy sources utilization like thermal, tidal, wind,
solar energy, and fuel cells. These sources are
crucial in fulfilling these requirements. Fuel cells,
through the utilization of hydrogen and oxygen
without combustion, represent a sustainable and
eco-friendly energy source, [1].
For the increase in the use of renewable energies,
fuel cells represent a prominent option as they
produce both heat and energy simultaneously in
small installations that are compatible with other
sources such as natural gas and photovoltaic
systems, [2]. The fuel cell is a device based on
electrochemical processes that convert chemical
energy into electrical energy. This power source can
be utilized in stationary or mobile applications,
utilizing hydrogen as its fuel source. It is
distinguished by its eco-friendly characteristics,
generating water and heat as by-products, [3].
Electricity generation using these devices can be
divided into five types: Proton Exchange Membrane
Fuel Cells (PEMFC), alkaline fuel cells (AFC),
phosphoric acid fuel cells (PAFC), molten carbonate
fuel cells (MCFC), and solid oxide fuel cells
(SOFC). Their practical application requires
pressure stabilizers and the use of controllers for
active and reactive power delivery to solve
problems related to sudden load changes. For this
purpose, converters, filters, and controllers are used,
[4]. The implementation of PEMFC-type fuel cells
is currently hindered by technical and operational
challenges that affect their efficiency and stability.
These challenges include the need to develop
accurate models considering coupling with dynamic
changes, as well as reducing the slow response to
changes in electrical load. Additionally, appropriate
converter design and consideration of its response to
different types of loads are required to
comprehensively address these challenges.
Optimization of performance demands improvement
in the efficiency and adaptability of the cells.
Undoubtedly, this contributes to the successful
application of sustainable energy systems required
today for transitioning towards cleaner energy
sources.
The fuel cell demonstrates the capacity to
effectively transform the chemical energy of
hydrogen into direct current (DC) while avoiding
the generation of pollutants. This feature is
harnessed in various stationary, portable, and
transportation applications. Hydrogen is acquired
from an external tank to facilitate its operation. The
oxidation of this gas occurs at the anode, whereas
the reduction of oxygen from the air takes place at
the cathode. This process leads to the production of
electricity, water, and heat, [5]. These devices
demonstrate a remarkable capacity for adaptation,
[6], therefore, they can also be included in a
distributed electricity generation network. By
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producing energy through a chemical process
without the need for direct combustion, they allow
for the reduction of carbon dioxide emissions, which
are present in the combustion of traditional energy
sources. This undoubtedly contributes to greater
environmental respect. This is how these latest
generation devices such as PEMFC cells achieve
efficiencies higher than 50 %, allowing the
transformation of chemical energy into electricity,
in contrast to the way of operation in conventional
batteries, [7]. This allows its ability to mitigate
power generation variability, which can be achieved
with low inertia power electronic converters to
achieve system stability, [8]. This energy source
finds a variety of applications, due to the energy
efficiency of this technology, especially in PEMFC
cells, [9]. In recent decades, our irresponsible
lifestyle has led to significant environmental harm,
as seen in issues like the depletion of the ozone
layer and the phenomenon of global warming,
PEMFCs are now recognized as a sustainable
alternative, producing water vapor as a by-product,
[10]. The interest in power generation through fuel
cells, especially those of the PEMFC type, used in
small-scale applications, is due to their ability to
operate autonomously or connected to the grid,
being valuable for generation in remote locations,
[11].
Although PEMFC fuel cell power generation
devices were initially deployed in aerospace and
military applications because of their efficiency ,
low noise level and environmental friendliness, [12],
today have a field of increased employment due to
their economic competitiveness and the feasibility
of being combined with photovoltaic generation in
hybrid systems. They are also found in various
applications for the propulsion of automobiles and
submarines, [13]. In this situation, the cells have
attracted the attention of business investments due
to the demand for environmentally friendly power
generation as an option to combustion engines for
power generation, [14].
Global energy consumption as a general trend is
growing every year, and to meet this demand, there
has been an increased reliance on renewable sources
such as solar and wind energy, which are abundant
in certain environments, [15]. However, this
technology also faces challenges that restrict its
commercial viability, [16]. To perform emulation, a
fuel cell model is essential, since the response of the
emulator is based on this specific model. In general,
fuel cell models tend to be complex or require
several tests to obtain the essential parameters for
the model to work. The simplicity of the model and
ease of obtaining the necessary data for its
application are crucial prerequisites, especially in
cases where the fuel cell or the appropriate
equipment is not available for extensive testing to
determine all the fuel cell parameters. For this
reason, the present work proposes the study of
PEMFC type emulator, by adapting converters to
evaluate the behavior of the generic and polynomial
model with loads from the data provided by the
manufacturer.
2 PEM Type Fuel Cell Model
In the literature, there are several fuel cell models
designed to observe how fuel cells behave under
specific operating conditions. However, most of
these models focus on describing the chemical
reactions that take place inside the cell, which
makes them complex and specific, making their
direct application with electrical components
difficult. For this rationale, we move forward with
the assessment of various models to select the most
suitable one for simulating the behavior of a cell
with a simplified structure, as illustrated in Figure 1,
which is composed of a membrane and electrode
assembly (MEA), which includes an anode and a
cathode separated by a PEM. This serves as an
electrolyte, aiding in the conduction of protons from
the anode to the cathode. In this particular situation,
there is a need for a model with the ability to
replicate the electrical performance of either a single
fuel cell or a group of fuel cells. This model should
be developed using the standard data typically
included in the specification sheets supplied by the
manufacturers of such devices. It is important to
note that the majority of manufacturers furnish
detailed information regarding these fuel cells,
which can be outlined as below:
I-V curve.
I-P curve.
Rated power.
Operating temperature.
Nominal hydrogen pressure.
Hydrogen composition.
Fig. 1: Graphic of the PEM fuel cell
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2.1 Generic PEM Fuel Cell Model
[17], the document introduces a proposal for a
universal model of a fuel cell that combines
simplicity with comprehensive detail. This model
comprises an equivalent circuit consisting of
multiple fuel cells functioning under consistent
pressure and temperature environments. In order to
replicate the system, it is essential to calibrate the
voltage levels within the cell at current intensities of
0 A and 1 A, utilizing data derived from the
polarization curve supplied by the manufacturer.
This data illustrates the fluctuations impacting the
open circuit voltage (), the exchange current,
and the Tafel slope.
These values can be modified according to
equations (1) - (3).
(1)
In the context of nominal operating conditions,
denotes the constant voltage, while refers to
the Nernst voltage, reflecting the thermodynamic
voltage of the fuel cell and influenced by factors
such as temperature and partial pressure, which are
contingent upon the composition of reactants and
products within the cell.
The calculation of the exchange current
involves the utilization of equation (2).
(2)
Additionally, denotes the quantity of mobile
electrons, corresponds to the Faraday constant
which is 96485 , stands for the universal
gas constant valued at 8.3145 ), ()
represents the partial pressure of hydrogen within
the cell in atmospheres (), () indicates the
partial pressure of oxygen within the cell in
atmospheres, symbolizes the Boltzmann constant,
having a magnitude of ,
signifies the Planck constant with a value of 6.626
, , indicates the operational temperature
in Kelvin (), and y represents the alteration in
Gibbs free energy.
(3)
In equation (3), denotes the operational
temperature in Kelvin, while represents the charge
transfer coefficient, which is subject to variation
based on the electrode and catalyst type.
The circuit depicted in Figure 2 bears
resemblance to the simplified model illustrated in
Figure 1. Nevertheless, for the comprehensive
model, it is imperative to revise the parameters
(), and.
Fig. 2: Equivalent circuit of the stack upon which
the detailed model used by Simulink is based
In block of Figure 2, the conversion efficiency
of hydrogen () and oxygen () is calculated
the following expressions:
(4)
(5)
signifies the absolute pressure at which the
fuel is provided, while denotes the air supply
pressure. represents the fuel flow rate in
liters per minute , indicates the
air flow rate in liters per minute , and
denotes the percentage of hydrogen.
The cell structure shown in Figure 2 represents
the equivalent circuit of the stack that would
establish the detailed model proposed by [17],
where the fuel (%), Y is the percentage of oxygen in
the oxidant (%), and the value of 60000 comes from
the conversion of the flow rate in liters per minute
used by the model into ().
Block B calculates the Nernst voltage and the
partial pressure of hydrogen, oxygen, and water,
through the equations as follows:
(6)
(7)
(8)
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(9)
In equation (8), represents the partial
pressure of water vapor within the stack, while
signifies the proportion of water vapor in the
oxidant (%). The revised values for the open circuit
voltage () and the exchange current () can be
determined based on the partial pressures of the
gases and the Nernst current.
Block C is tasked with computing the updated
values for the Tafel slope. The parameters α, ∆G,
and are derived from the polarization curve
during standard operating conditions. To determine
the maximum voltage values () and (),
equations (10) and (11) are used respectively.
(10)
(11)
Where η nom represents the nominal efficiency
of the stack (%), with the nominal heating value;
()(gas)) is a constant equal to
; is the nominal voltage,
is the nominal current, is the
nominal air flow rate (); is the
nominal absolute pressure of air supply in Pascales
(Pa) y is the nominal operating temperature.
From these conversion rates, the nominal partial
pressures of the gases and the Nernst voltage can be
calculated.
By considering the values of,, and ,
along with the assumption of the stack operating at
constant conversion rates or under nominal
conditions, it is possible to ascertain the parameters
α, ∆G, and . In cases where fuel or air are
unavailable at the input terminals of the cell, the fuel
cell stack module is engineered to function at a
constant gas conversion rate (referred to as nominal
conversion rate). This involves modifying the gas
intake in order to provide a slightly excess amount
than required across all loads.
The peak maximum voltage ( and its
corresponding voltage variation () are employed
to illustrate the influence of oxygen depletion
(resulting from the delay in the air compressor) on
the cell voltage () produced by the cell, as
determined by equation (12):
(12)
Where represents the nominal oxygen
usage, and is the constant associated with the
voltage undershoot, which is determined in equation
(13):
(13)
2.2 Fuel Cell Emulator
In the academic literature, numerous fuel cell
emulation systems have been documented. These
systems typically rely on DC-DC converters, as
outlined in study, which utilizes a Buck converter,
and in where emulation for an electric vehicle is
carried out. The control of these emulators is
commonly overseen by FPGAs, necessitating the
customization of the fuel cell model to suit the
specific device under consideration. When
employing a DC-DC converter, the intricacy of the
emulation system escalates, as it involves not only
modeling the fuel cell but also designing the
converter and taking into account its electrical
response. In this context, our focus will be directed
towards analyzing in depth the emulation system put
forth in the academic literature.
2.2.1 FPGA-based Fuel Cell Emulation
Various systems have been documented in the
literature to replicate the functionality of the fuel
cell, [18], proposing a simulation system that
leverages an FPGA as its foundation. The authors
delineate in their research the architecture of a fuel
cell model in VHDL, aiming to integrate it into an
FPGA. This approach utilizes bipolar transistors and
passive elements to depict the power condition of
the fuel cell.
Figure 3 illustrates the overall diagram of the
emulator, emphasizing the flow of digitized current
input to the controller, which in turn produces the
digitized output voltage. In order to accomplish this,
a 10-bit resolution analog-to-digital converter is
utilized with a full-scale voltage range of 2V in the
generation of the current waveform, converting it
into a bit stream that reflects the visualized current
signal, [18].
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Fig. 3: Block diagram of the FPGA-based emulator
Following this, the voltage that has been
digitized is transformed into analog form by
utilizing a digital-to-analog converter possessing a
1V full-scale voltage range and 13 bits, while
adjusting the gain of the conversion process with the
help of an operational amplifier. Furthermore, both
and transistors are employed as emitter
followers to ensure a voltage gain of unity and to
prevent any direct current offset by linking an
transistor with a BJT, as depicted in Figure 4,
[18].
Fig. 4: Gain stage for FPGA-based emulation
system
The model utilized in this study is segmented
into two components: a dynamic segment and a
steady-state segment. The steady-state portion
illustrates the I-V characteristic curve of the fuel cell
system over the complete temperature spectrum. An
average value is computed based on a group of
standard features at 30°C, which is subsequently
fine-tuned utilizing a specific equation.
Equation (14) is employed to ascertain the
voltage value (VFC) across the cell.
(14)
IFC denotes the electric current flowing through
the fuel cell, while VFC indicates the electric
potential difference across the cell. A collection of
isothermal I-V curves has been produced for every
particular temperature.
Equation (15) can be utilized to articulate the
output voltage of the steady-state model.
(15)
The output voltage at a temperature , under a
specific current of the fuel cell is denoted by
. The output of the steadystate isothermal
model for the same current but at a reference
temperature of 30°C is represented by
30°C). The output in the correction subsystem,
denoted by , reflects a temperature different
from the nominal temperature of 30°C through
equation 16.
(16)
The FPGA emulation system's dynamic
component is linked in parallel with the stable
section. The model's output corresponds to the
dynamic part's input, generating a specific current.
This current is combined with the external current to
create the steady-state current signal, utilized as the
stable section's input. Utilizing frequency response
analysis (FRA), the dynamic model is defined. The
impedance transfer function is assessed within the
appropriate frequency range of 0 to 200 kHz. To
strike a balance between model complexity and
accuracy, three poles and three zeros are chosen.
The dynamic component is realized through the
utilization of a digital filter that replicates the
transfer function within the z-domain, as specified
in equation (17), derived through the application of
the Euler transform to the estimated transfer
function.
+
(17)
2.3 Polynomial Approximation Model
The fuel cell model using polynomial approximation
is derived from the fuel cell stack block in
Simulink/Matlab. This block is essential for
obtaining the individual points of the I-V curve of
the stack intended to be modeled through this
approach. Knowledge of certain fuel cell data is
required to use this block, which necessitates
information on the following parameters:
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Voltage at 0 A.
Voltage at 1 A.
Current at Nominal Operating Point (PON).
Voltage at PON.
Current at Maximum Operating Point (POM).
Voltage at POM.
Number of cells.
Nominal stack efficiency.
Operating temperature.
Nominal air flow rate.
Nominal hydrogen pressure .
Nominal air pressure.
Nominal hydrogen composition .
Nominal air composition.
The mentioned information can be extracted
from the manufacturer’s technical documentation.
Some of these details are presented explicitly, while
data such as voltage at different current values, the
current at the turn on state PON, the voltage at PON,
the current at the POM, and the voltage at POM are
derived from the typically provided I-V and I-P
curves by the manufacturer. To find the PON, it is
essential to consider both the I-V and I-P curves,
where the PON will be identified as the point of
intersection between both curves. Once this point is
located, the voltage and current values on the I-V
curve at that point are examined, being these values
() and the current (), respectively. To
determine the POM, the maximum power level
() on the I-P curve must be located, and the
corresponding current at that point is observed; this
value will be the current ( ). Then, the voltage
associated with () on the I-V curve is verified,
and this is the voltage (). This graph with the
aforementioned points can be observed in Figure 5.
Fig. 5: Processing of voltage at 0 and 1 A, current
and voltage at PON and current and voltage at POM
Once all the essential data has been gathered, the
simulation of the fuel cell stack can be executed in
Simulink/Matlab.
3 Development of the Fuel Cell
Emulation System
To ensure proper operation and attainment of the
required characteristics for a fuel cell in a specific
application, it is essential to have a deep
understanding of its performance under operating
conditions. Fuel cells can exhibit high sensitivity to
various factors such as changes in reactant pressure,
temperature fluctuations, humidity levels, reactant
concentration and purity, as well as variations in
applied load. Therefore, accurate prediction of the
fuel cell's response to these stimuli is of utmost
importance. While there are numerous studies on
fuel cell emulation in the literature, most require
conducting tests and characterizing the actual cell to
replicate its performance. Consequently, this study
has developed a straightforward approach to
emulate the cell, eliminating the need to rely on it or
decipher a complex model. To analyze the
performance of the fuel cell and evaluate the
polynomial model, simulations were conducted
using the gathered information to verify the
response of the proposed model.
3.1 Simulation of a Fuel Cell with the Fuel
Block Cell Stack
In order to establish a complete connection with the
fuel cell stack block in Simulink/MATLAB, which
is based on the detailed model in section 2.1 and
considering that at that time a specific type of fuel
cell stack was not available to extract the necessary
parameters, it was decided to use the fuel cell stacks
defined by [17]. Therefore, the simulation scheme
obtained can be observed in Figure 6, which
includes three sets of PEM fuel cell stacks with
capacities of 1.26 kW, 6 kW and 50 kW. In this
situation, the 6 kW fuel cell stack was used, whose
parameters are detailed in Table 1.
Fig. 6: Simulation diagram in Simulink
To carry out the simulation, other subsystems are
necessary to observe the behavior of the cell.
Consequently, a gas supply system and a boost
converter with an RL load adjusted to a constant
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voltage of 100V were implemented, as shown in
Figure 7 and Figure 8.
The proposed block in Simulink is already
equipped with outputs that enable the observation of
various cell parameters, such as efficiency, gas
consumption, flow rate, composition, Tafel curve
slope, exchange current, Nernst voltage and open
circuit voltage.
Table 1. Parameters of the 6 kw fuel cell stack
Fuel Cell Stack Parameters
Battery power rating
5998.5 W
Maximum battery power
8325 W
Fuel cell resistance
0.07833
Single cell Nerst voltage ( )
1.1288 V
Nominal use of
99.56 %
Nominal utilization ()
59.3 %
Nominal fuel consumption
60.38
SLPM
Nominal air consumption
143.7
SLPM
Exchange current (io)
0.29197
Exchange ratio (α)
0.60645
Fuel composition
99.95 %
Oxidant composition
21 %
Ratio of nominal fuel flow to utilization
H2 nominal
50.06 LPM
Maximum fuel flow ratio at nominal
utilization )
84.5
LPM
Maximum air flow ratio at nominal
utilization of ()
506.4 LPM
System temperature (T)
338 K
Fuel feed pressure ()
1.5 bar
Air supply pressure ()
1 bar
3.1.1 Generic Fuel Cell Simulation Results
During the simulation, the behavior of the fuel cell
stack while operating under the power demand
imposed by the Boost converter was monitored.
Examination was conducted on the voltage and
current levels at both the fuel cell output and the RL
load of the converter.
Within Figure 7, the gas flow rate provided was
also observed, alongside the consumption of
hydrogen and oxygen by the fuel cell. It was
observed that the fuel flow rate stabilized at 50 lpm
and remained consistent for a duration of 10 seconds
before initiating a linear increase.
Fig. 7: Graph of the fuel flow rate of the stack
This phenomenon is explained by observing that
by providing more fuel than the stack consumes
(Figure 8), waste occurs, resulting in lower
efficiency.
Fig. 8: Graph of the reactant consumption of the
stack
Fig. 9: Graph of the stack efficiency
The rise in the flow rate led to a reduction in the
stack efficiency as depicted in Figure 9.
Furthermore, the behavior shown in Figure 9 of
the stack efficiency leading to a decrease in voltage
and an increase in current is reflected in Figure 10
and Figure 11.
Then, around 3.5 seconds, the flow rate at the
cell inlet becomes constant again, and the other
parameters stabilize.
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Fig. 10: Graph of stack voltage
Fig. 11: Graph of stack current
3.2 Simulation of 20 W Fuel Cell Stack
The objective of this simulation was to assess the
performance of a fuel cell and derive its I-V
characteristic using a polynomial estimation. A 20
W system was chosen, and its specifics are outlined
in Table 2. These specifics, in conjunction with the
current, voltage, and power characteristics, equip us
with the essential parameters for the simulation, all
sourced from the specification document provided
by fuel cell store, the vendor of this unit. Key
parameters needed for the simulation encompass the
voltage and current at the designated PON and
POM, which were established as described in
section (2.3) of the polynomial estimation model for
a power output of 20 W.
Table 2. Parameters of the 20 Kw fuel cell stack
Parameter
Value
Number of cells
10
Power
20 W
Performance
6 V @ 3.4 V
Reactives
Hydrogen and Air
Operating temperature
Pressure of the
0.45 – 0.55 Bar
Purity of
≥ 99.995
Flow ratio at maximum
output
0.25 Lpm
Efficiency
40 % full power
The data obtained from Table 2, along with the
graphical depiction of the I-V curve, provide all the
necessary components for developing a thorough
portrayal of the fuel cell stack and conducting the
simulation. The detailed data is outlined in Table 3.
Table 3. Data required for the 20 W fuel cell stack
simulation
Parameter
Value
Voltage a 0 A
9.6 V
Voltage a 1 A
7.35 V
Current in PON
2.5 A
Voltage in PON
6.1 V
Current in POM
4 A
Voltage in POM
5 V
Number of cells
10
Nominal stack efficiency
40 %
Operating temperature
Nominal airflow ratio
0.25 Lpm
Nominal pressure
0.50 bar
Nominal air pressure
2.5 bar
Nominal composition of the
99.995 %
Nominal air composition
Oxygen 21 %
Humidity 0.5 %
Once the essential data had been gathered for
configuring the fuel cell stack block in
Simulink/Matlab, which represents the fuel cell
stack, it was linked to a DC-DC converter
responsible for maintaining a consistent voltage of
9.6 V on the load side. This enabled the execution of
a current scan to encompass all the polarization
regions of the 20 W fuel cell stack, as depicted in
Figure 12. In contrast to the initial simulation
(Figure 6), the utilization of a flow selection block
was omitted on this occasion. The rationale behind
this decision lies in the primary objective of merely
observing the stack's performance under optimal
circumstances. In the absence of a block facilitating
fuel and/or air input to the stack, it is presumed that
the stack functions at a consistent gas conversion
rate. This implies that the gas provision is regulated
in alignment with the current to guarantee a slightly
excessive supply to the stack, irrespective of the
load.
Fig. 12: 20 W Fuel cell stack simulation diagram
During the simulation development, voltage and
current measurements were taken and these data
were recorded and subsequently used to construct a
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graphical representation of the relationship between
voltage and current. This allowed us to generate the
characteristic curve of the fuel cell, as seen in Figure
13.
Understanding this curve is crucial for
comprehending the behavior and performance of the
cell under various operating conditions, as described
in the simulation results section for a specific stack.
Fig. 13: I-V and I-P plots of the 20 W fuel cell are
presented
3.2.1 Simulation Results of a Specific Stack
In the simulation of the 20W stack, the Boost
converter was adjusted to provide a constant output
of 11.5 V to the load resistive, aiming to
characterize the stack and obtain its I-V curve, as
illustrated in Figure 14. Here, it is demonstrated
how the voltage at load resistive remains around
11.5 V with very little variation.
Fig. 14: Load voltage graph
Figure 15 provides a detailed visual
representation of how the voltage in the cells
evolves over time. It is clearly observed that the
initial voltage, recorded at 10.5 V, coincides with
the maximum level reached under open circuit
conditions, where the current is zero, marking the
starting point before the load connection is
established. Upon activation of the load, there is a
rapid decrease in voltage, dropping to 5.5 V, and
this steep decline indicates the transition of the fuel
cell to a state where it begins to supply current to
the external load. As the load demands more
current, the voltage continues to gradually decrease,
reaching a value of 5.3 V. The gradual decrease in
voltage is indicative of the impact caused by the
rising current requirements, leading to a progressive
reduction in the voltage of the fuel cell.
Fig. 15: Fuel cell stack voltage plot
Figure 16 illustrates the dynamics of the current
in the stack, which starts at zero when the load is
disconnected and increases abruptly to 3.2 A as
soon as the converter starts operating. It then
gradually increases as the load adjusts the output
voltage to keep it constant.
Fig. 16: Fuel cell stack current plot
Figure 17 provides a detailed graphical
representation of the current-voltage (I-V) curve
corresponding to the 20 W fuel cell. This curve is
essential for understanding the electrical behavior
under different operating conditions. By analyzing
this curve, three distinct polarization regions can be
clearly identified, each associated with different loss
mechanisms. The first polarization region is related
to activation loss, where a significant voltage drop is
observed as the current increases. This loss is
associated with the energy required to initiate and
sustain electrochemical reactions in the fuel cell.
The second polarization region is linked to ohmic
loss, characterized by a constant and linear decrease
in voltage as the current increases. Finally, the third
region is associated with mass transfer loss, where
the voltage continues to decrease as the current
increases, but at a slower rate than in the previous
regions.
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.9
Luis Camacho, Secundino Marrero,
Carlos Quinatoa, Carlos Pacheco
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Volume 23, 2024
Fig. 17: 20 W fuel cell I-V curve
Additionally, the cell efficiency, estimated at
approximately 37.5%, is visualized in Figure 18.
Fig. 18: 20 W fuel cell stack efficiency chart
This efficiency value is crucial for assessing the
overall performance of the stack and provides
valuable information for future improvements in
fuel cell system design and optimization, [19].
4 Conclusion
In this work, a fuel cell emulator has been
developed, serving as a valuable tool for fuel cell
evaluation. This emulator allows for testing without
the need for large laboratory investments when
evaluating cell behavior in specific applications,
thereby avoiding risks of damage when subjecting it
to extreme operating points. Experimental results
indicate that the emulator satisfactorily reproduces
the cell’s electrical behavior in response to load and
temperature variations. To simulate the fuel cell
model using polynomial approximation, the
necessary parameters can be obtained through tests
applied to the cell stack to be emulated. The generic
fuel cell model combines electrical and
electrochemical characteristics, being usable from
general data of the fuel cell stack.
According to the model developed in this work,
it is concluded that it is possible to generate the
cell’s electrical behavior without having all its data,
and simulation results suggest that the models
proposed in this work are suitable, as the responses
obtained are very similar to those achieved using the
Simulink fuel cell stack block. However, when the
fuel cell or the appropriate instruments for testing
are not available, nor are all the specific details of
the cell in question, the direct application of the
mentioned models becomes unfeasible. In such
circumstances, the lack of access to the cell and
necessary data hinders the effective implementation
of the previously described models.
Acknowledgement:
The student author, Luis Camacho, would like to
acknowledge and thank the research professors
Secundino Marrero and Carlos Quinatoa for their
advice, guidance, and knowledge throughout his
studies. Also to Professor Carlos Pacheco for his
guidance. Thank you very much.
Declaration of Generative AI and AI-assisted
Technologies in the Writing Process
During the preparation of this work the authors used
typeset.io in order to improve the wording. After
using this tool/service, the authors reviewed and
edited the content as needed and takes full
responsibility for the content of the publication.
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- Luis Camacho is responsible for identifying
research topics, collecting system data, design and
implemen- tation, simulation, original drafting and
revisions.
- Secundino Marrero and Carlos Quinatoa are dedi-
cated to improving the research topics and scope,
working on the methodology, providing technical
advice, refining the simulation scenarios, review-
ing the results, formatting and editing the final
draft, as well as reviewing the revised article to
ensure that it meets the publisher’s requirements.
- Carlos Pacheco is responsible for revising the text
and improving the translation of the article.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors state that they have no financial interests
or personal relationships that could affect the work
done in this study.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on CIRCUITS and SYSTEMS
DOI: 10.37394/23201.2024.23.9
Luis Camacho, Secundino Marrero,
Carlos Quinatoa, Carlos Pacheco
E-ISSN: 2224-266X
103
Volume 23, 2024
