Multi-Sine EIS for Early Detection of PEMFC Failure Modes

Abstract

Electrochemical impedance spectroscopy (EIS) is a powerful technique that can be used to detect small changes in electrochemical systems and subsequently identify the source of the change. While promising, analysis is often non-intuitive and time-consuming, where collection times of a single EIS spectrum can reach several minutes. To circumvent the long collection times associated with traditional EIS measurements, a multi-sine EIS technique was proposed in which the simultaneous application of many frequencies can reduce the acquisition time to less than a minute. This shortened acquisition time opens the possibility to use multi-sine EIS as a real-time diagnostic tool for monitoring the state-of-health of commercial fuel cell systems. In this work, a single-cell proton exchange membrane fuel cell (PEMFC) was characterised using multi-sine EIS, by establishing steady-state impedance response under baseline conditions before systematically changing operating conditions and monitoring the dynamic changes of the impedance response. Our initial results demonstrate that full multi-sine EIS spectra, encompassing a frequency range from 50 kHz to 0.5 Hz, can be collected and analysed using simple equivalent circuit models in 50 s. It is shown that this timeframe is sufficiently short to capture the dynamic response of the fuel cell in response to changing operating conditions, thereby validating the use of multi-sine EIS as a diagnostic technique for in-situ monitoring and fault detection during fuel cell operation.

Full text

Multi-Sine EIS for Early Detection of
PEMFC Failure Modes
Patrick Fortin
1
, Michael R. Gerhardt
1
, Øystein Ulleberg
2
, Federico Zenith
3
and
Thomas Holm
2
*
1
New Energy Solutions, SINTEF Industry, Trondheim, Norway,
2
Institute for Energy Technology, Kjeller, Norway,
3
Mathematics
and Cybernetics, SINTEF Digital, Trondheim, Norway
Electrochemical impedance spectroscopy (EIS) is a powerful technique that can be used
to detect small changes in electrochemical systems and subsequently identify the source
of the change. While promising, analysis is often non-intuitive and time-consuming, where
collection times of a single EIS spectrum can reach several minutes. To circumvent the long
collection times associated with traditional EIS measurements, a multi-sine EIS technique
was proposed in which the simultaneous application of many frequencies can reduce the
acquisition time to less than a minute. This shortened acquisition time opens the possibility
to use multi-sine EIS as a real-time diagnostic tool for monitoring the state-of-health of
commercial fuel cell systems. In this work, a single-cell proton exchange membrane fuel
cell (PEMFC) was characterised using multi-sine EIS, by establishing steady-state
impedance response under baseline conditions before systematically changing
operating conditions and monitoring the dynamic changes of the impedance response.
Our initial results demonstrate that full multi-sine EIS spectra, encompassing a frequency
range from 50 kHz to 0.5 Hz, can be collected and analysed using simple equivalent circuit
models in 50 s. It is shown that this timeframe is sufficiently short to capture the dynamic
response of the fuel cell in response to changing operating conditions, thereby validating
the use of multi-sine EIS as a diagnostic technique for in-situ monitoring and fault detection
during fuel cell operation.
Keywords: PEMFC, hydrogen, fuel cells, electrochemical impedance spectroscopy (EIS), diagnostics
INTRODUCTION
Since their introduction and commercialization in the 1990’s, fuel cells have gradually developed into
an option for carbon-neutral drivetrains for transportation applications, as well as for stationary
power applications and for use in combined heat and power systems. Currently, several companies
are making modular stacks of hundreds of kWs (Ballard Product Data Sheet: FCWave, 2021;EKPO
PEMFC stack module NM12 Twin, 2021;Nedstack PemGen MT-FCPI-500, 2021;PowerCell
PowerCellution Marine System 200, 2021). Heavy-duty transportation and maritime applications
have recently been considered the most viable option for the use of fuel cells, and various
demonstration projects are underway around the world (IEA, 2019;Baumann et al., 2021). With
these developments, fuel cell lifetime has become a key limitation to large-scale operation as current
fuel cells designed for heavy-duty transport applications have a nominal lifetime of approximately
20,000 h (MoZEES, 2020). Significant efforts are now underway to extend heavy-duty fuel cell
lifetimes even further, e.g., more than 40,000 h by 2030, to reduce the total cost of ownership of fuel
cell systems as replacement fuel cell units are expensive. Although degradation is less pronounced
Edited by:
Ivan Pivac,
University of Split, FESB, Croatia
Reviewed by:
Stephane Rael,
Université de Lorraine, France
Antonio Martínez Chaparro,
Centro de Investigaciones
Energéticas, Medioambientales y
Tecnológicas, Spain
*Correspondence:
Thomas Holm
thomas.holm@ife.no
Specialty section:
This article was submitted to
Fuel Cells,
a section of the journal
Frontiers in Energy Research
Received: 16 January 2022
Accepted: 09 May 2022
Published: 26 May 2022
Citation:
Fortin P, Gerhardt MR, Ulleberg Ø,
Zenith F and Holm T (2022) Multi-Sine
EIS for Early Detection of PEMFC
Failure Modes.
Front. Energy Res. 10:855985.
doi: 10.3389/fenrg.2022.855985
Frontiers in Energy Research | www.frontiersin.org May 2022 | Volume 10 | Article 8559851
ORIGINAL RESEARCH
published: 26 May 2022
doi: 10.3389/fenrg.2022.855985

during steady operation, the rate of degradation increases
significantly during dynamic operation and operation at high
current densities (Fletcher et al., 2016). In addition, leaving the
fuel cell at open-circuit with delivery of fuel or frequent start-stop
sequences will also lead to accelerated degradation (Reiser et al.,
2005;Baroody & Kjeang, 2021). Fuel cell monitoring is becoming
an important aspect of operation of large-scale fuel cell systems,
in which it is desirable for the monitoring techniques to
determine the state-of-health of the fuel cell, and provide
information about optimized operation strategies to minimize
degradation (Wu et al., 2008;Rodat et al., 2009;Onanena et al.,
2011;Reid et al., 2013;Fletcher et al., 2016).
Degradation can happen at a combination of slow and very
fast time scales, down to less than tens of seconds, for example
due to short-circuit or starvation of the fuel cell stack or
individual cells, and up to minutes and hours in the case of
flooding, drying and poisoning (Wang et al., 2019a). Therefore, it
is desirable that the fuel cell is continuously monitored during
operation so that the operator can have information about the
stack condition before failure or accelerated degradation.
Traditional monitoring of fuel cells consists of measuring the
voltage and current over time, along with operational parameters
such as temperature, pressure, relative humidity, and gas supply
flow rates. While useful, it often lacks information about the
processes and can often only determine that failure or
degradation is happening and not why. Electrochemical
impedance spectroscopy (EIS) has been used to monitor fuel
cells to provide some of this information (Yuan et al., 2007;Wu
et al., 2008;Rezaei Niya & Hoorfar, 2013). For example,
qualitative detection of flooding/drying (Mérida et al., 2006;
Rodat et al., 2009;Kang & Kim, 2010;Debenjak et al., 2013;
Morin et al., 2013;Chevalier et al., 2016;Depernet et al., 2016;
Engebretsen et al., 2018;Shan et al., 2018), mass transport
conditions (Cruz-Manzo et al., 2013;Depernet et al., 2016),
temperature (Tang et al., 2013), starvation (Migliardi & Corbo,
2013;de Beer, 2014), and catalyst poisoning (Wagner & Gülzow,
2004;Deseure, 2008;Brunetto et al., 2009;Asghari et al., 2010;
Migliardi & Corbo, 2013;de Beer, 2014;Reshetenko et al., 2014)
has been demonstrated in the literature and highlights the
potential of the technique as a diagnostic tool (Yuan et al.,
2006a;Yuan et al., 2007;Halvorsen et al., 2020). EIS is done
by applying a sinusoidal current (or voltage) signal to the fuel cell
stack during operation and measuring the sinusoidal potential (or
current) response at the stack or cell level while varying the
frequency of the signal. This technique is non-destructive and
information-dense, but the interpretation of the response is non-
intuitive and puts a high demand on the experimenter. In
addition, the response of non-optimal conditions such as
drying or starvation may look very similar to normal
degradation of the fuel cell, such that it is hard to know the
source of power loss in the fuel cell stack. Therefore, it is desirable
that the fuel cell is continuously monitored to distinguish these
processes at least qualitatively such that the operator can be
informed about how to optimize operation. A full measurement
of an EIS spectra in the typical range of about 0.1 Hz to 10 s of
kHz takes about 15 min (Brunetto et al., 2009). On the other
hand, a solution suggested in the literature is to measure only a
single or a few frequencies such that the data acquisition for each
point take less than 1 s (Lochner et al., 2020;Najafiet al., 2020).
The last approach is feasible and fast, but is not able to provide
information about several fuel cell parameters simultaneously as
they do not capture the entire frequency-range required.
Therefore, as a trade-off, it is desirable that the measurement
and interpretation time is reduced as much as possible while still
having information about all processes, i.e., a full EIS spectra.
Multi-sine EIS, in which several sine waves of different
frequencies are added together simultaneously and applied to
the fuel cell instead of applying individual frequencies in
succession, has been shown to reduce the measurement time
by about 70% while providing the same response (Brunetto et al.,
2009). The reduced acquisition time makes multi-sine EIS an
intriguing option for online monitoring of operational fuel cells.
The implementation of multi-sine EIS monitoring methods in
combination with rapid analysis methods, e.g., equivalent circuit
fitting, distribution of relaxation times (DRT) (Deseure, 2008;
Simon Araya et al., 2019;Dierickx et al., 2020), or other
simplifications of the impedance spectra (Becherif et al., 2018),
and subsequent optimization feedback relays can enable rapid,
automated online state-of-health monitoring and optimization of
fuel cell operating conditions with respect to degradation
phenomena.
Herein, we investigate the feasibility of the multi-sine EIS
technique as a tool to monitor and detect changes in the
operational conditions of a single-cell PEMFC. First, the
multi-sine EIS collection protocol was optimized to minimize
collection time, while ensuring the collection of high-quality data.
The target acquisition time was set to less than 1 min due to the
ability to trace development of the more common degradation
methods (drying, flowing, and poisoning) as this happens on the
scale of minutes (Wang et al., 2019b). Following the initial multi-
sine EIS optimization, the dynamic impedance response under
each of the two simulated stressor conditions, cell drying and
mild cathode starvation, was measured by manipulating the
operating conditions of the fuel cell, namely, relative humidity
(RH) and oxidant gas stoichiometry. We show that the multi-sine
EIS technique is sufficiently rapid and sensitive to achieve early
detection of drying and mild cathode starvation. Due to the speed
of acquisition, this technique ultimately has the potential to be
used for online state-of-health monitoring and optimized fuel cell
performance when coupled with the appropriate diagnostic,
prognostic, and control algorithms.
EXPERIMENTAL
PEMFC Cell for Experiments
A25cm
2
fuel cell hardware with graphitic bipolar plates and a 5-
fold serpentine flow field pattern from balticFuelCells GmbH was
used for all measurements. PRIMEA
®
catalyst coated membranes
(GORE
®
) consisting of a PFSA-based membrane (15 μm thick),
Pt loadings of 0.1 mg cm
−2
at the anode and 0.4 mg cm
−2
at the
cathode; Sigracet 22BB gas diffusion media (SGL Carbon); and
51 μm thick Teflon gasketing (FuelCellStore) were all used as
received. The design of the balticFuelCells hardware separates
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Fortin et al. Multi-Sine EIS for FC Monitoring

sealing and contact pressure, as the Teflon gasketing simply acts
to support the underlying CCM, while the active area
compression is controlled via a pneumatic piston. 3.25 bar
g
of
compressed air is supplied to the pneumatic piston, translating to
a contact pressure of 1 N/mm
2
over the active area of the cell. The
fuel cell hardware was mounted to a Greenlight Innovation G60
fuel cell test station and a BioLogic VMP3 potentiostat equipped
with a 10 A booster was used to perform electrochemical
impedance spectroscopy measurements.
Electrochemical Measurements
Baseline Conditions—The baseline EIS experiments were
performed with pure hydrogen (5.0, Linde Gas AS) supplied
to the anode with a stoichiometry of 2.0, compressed filtered air
(in-house) supplied to the cathode with a stoichiometry of 2.5, a
cell temperature of 80°C, anode and cathode dewpoints of 71.4°C
(i.e., 70% RH), and 0.5 bar
g
backpressure at both the anode and
cathode. All EIS measurements were performed with a DC
current of 25 A and an AC perturbation of 1.25 A. Unless
otherwise stated, EIS spectra were collected between 50 kHz
and 0.5 Hz with 10 points per decade, using a wait time of 0.5
wave periods before each frequency (i.e., 1 s in the case of a
frequency of 0.5 Hz), and measuring a total of 3 wave periods per
frequency (i.e., a 0.5 Hz measurement takes 6 s + the wait time).
These settings allowed for multi-sine EIS spectra to be acquired at
a rate of 44 s per spectrum. Multi-sine EIS measurements were
performed with the EC-Lab software while the Greenlight test
station logged the relevant fuel cell data (e.g., gas composition, gas
stoichiometry, dew point, etc.). In the method used by EC-lab,
multi-sine signal is applied for frequencies below 10 Hz, up to a
maximum of 15 frequencies. In our case, 10 frequencies were
applied in the multi-sine mode, from 8.15 to 0.5 Hz. The
amplitude for each frequency was the 1.25 A, and the phase of
the imposed signal was shifted according to Eq. 1.
ΦkΦ1−2π
k−1
n1
(k−n)
N(1)
Here, Φkis the phase of frequency number k, and Nis the total
number of frequencies (10). The selection of frequencies using
this method, is the same as for the single-sine method, such that
these are equally spaced logarithmically. Other methods have
been suggested to minimize the interference of frequencies that
are within orders of each other, such as the distribution suggested
by Popkirov (Popkirov & Schindler, 1993), however, this was not
applied in the case of this work. The total imposed signal during
multi-sine measurements were then according to Eq. 2.
u(t)A
N
k1
cos2πfkt+Φk(2)
Here, u(t) is the applied signal as a function of time, A is the
amplitude (1.25 A), and fkis the frequency number k. For all
dynamic experiments, only a single operating condition was
changed at a time to isolate the influence of that specific
condition on the features of the Nyquist plots. Multi-sine EIS
spectra were collected continually to capture the dynamic
response of the Nyquist plot features as fuel cell operating
conditions were changed. The experimental parameters used
here are summarised in Table 1.
Relative Humidity—Multi-sine EIS was data was collected
under baseline conditions for 5 min, i.e., dew point (DP)
71.4°C (RH 70%), then the DP was reduced to 63.8°C (RH
50%) for 30 min, further again to 52.9°C (RH 30%) for 30 min,
and finally the DP was increased back to 71.4°C (RH 70%). The
dew points took ~10 min to reach their new set point and the next
20 min ensured that water balance within the membrane
electrode assembly reached an equilibrium before moving to
the next dew point. Both the anode and cathode gas inlets
were kept at the same DP during the measurement.
Gas Stoichiometry at the Cathode—Multi-sine EIS data was
collected under baseline conditions, i.e., cathode stoichiometry of
2.5 for 5 min. The cathode stoichiometry was then reduced to 2.0
for 10 min and increased back to 2.5 for 15 min.
Data Analysis of EIS
A literature review was done to assess the most suitable equivalent
circuit models, and a set of 4 equivalent circuits were identified
(shown in Figure 1A). In general, the circuits have two or three
time constants. In Figure 1A, R is a resistor, C is a capacitor, and
Q is a constant-phase element, i.e., a non-ideal capacitor. The
3CR circuit was determined to be the most representative
equivalent circuit model for the fuel cell setup used in our
measurements. Initial EIS fitting was done using the built-in Z
fit protocol in EC-lab which uses nonlinear least square fitting
and the Simplex algorithm. For the multi-sine data, processing
was automated by building an in-house Python script using the
impedance.py package (Getting started with impedance.py,
2021).
RESULTS
Determination and Interpretation of
Equivalent Circuit
To interpret the obtained EIS spectra, a good equivalent circuit
model is needed. A good equivalent circuit is characterized by
obtaining a good fit of key parameters, while simultaneously not
be a case of overfitting, i.e., using several redundant fitting
elements. Several equivalent circuits have been proposed for
PEMFC measurements and used successfully in the literature.
These can vary depending on the experimental conditions. For
example a low-frequency inductive loop appears at very low
frequencies or at low current densities (Cruz-Manzo & Chen,
2013;Cruz-Manzo et al., 2015;Dierickx et al., 2020;Pan et al.,
2020). These additional Nyquist plot features necessitate
additional equivalent circuit elements to accurately represent
the different physical phenomena taking place within the fuel
cell. To choose an equivalent circuit, four proposed equivalent
circuits based on the literature (Figure 1A) were each fit to the
high-quality, single-sine EIS data measured experimentally. To
identify the most suitable equivalent circuit, the proposed
equivalent circuits were then sorted according to: 1) fit quality,
2) ability to estimate the low-frequency and high-frequency
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Fortin et al. Multi-Sine EIS for FC Monitoring

intercepts, and 3) the avoidance of non-ideal circuit elements,
i.e., the constant phase element (CPE). The avoidance of a CPE is
an important aspect to consider as this element is not a true
capacitor, often leading to increased error in the fitting process
due to its flexibility as well as a more complex interpretation when
estimating the system capacitance. Figure 1B shows the
experimental data collected at 1,000 mA cm
−2
,fitted with the
equivalent circuits depicted in Figure 1A. Note that the QRCR fit
is omitted from Figure 1B as it gave an identical fit to the 2CR
circuit. Note also here that the maximum frequency of 50 kHz is
not visible in the figure, as from about 7 kHz and higher, the
signal goes into the fourth quadrant of the Nyquist plot and is not
fitted because the use of a linear inductor does not provide
additional information about the electrode processes. Based on
the criteria above, the fit quality (sum of square error function
with modulus fit) improved in the order 3CR >QRQR >2CR.
Both the QRQR and 3CR circuits were able to accurately estimate
the high- and low-frequency intercepts, but only the 3CR circuit
accurately predicted the spectrum across the entire frequency
range, i.e., it accounts for the small high-frequency loop (shown
in the inset of Figure 1B). For these reasons, in addition to the
avoidance of CPEs, the 3CR circuit was chosen for all subsequent
equivalent circuit fitting.
Many circuits have been considered in the literature, ranging
from more complex circuits that attempt to describe the full
system (Fardoun et al., 2017;Giner-Sanz et al., 2018;Pivac et al.,
2018) to simpler circuits that are used to interpret changes
quickly and only serve as a quasi-measure of system
parameters (Cruz-Manzo et al., 2013;Depernet et al., 2016;
Engebretsen et al., 2018;Mérida et al., 2006;Yuan et al.,
2006b). Some authors have also tried to estimate the full EIS
spectra from a limited amount of frequencies measured (Becherif
et al., 2018). Here, the 3CR circuit is chosen for both its
robustness of the analysis and its ability to identify, and
separate, key physical parameters. In addition, the 3CR circuit
is simple enough to be generally applicable even though the
experimental conditions are far from the baseline. The following
key elements of the Nyquist plot, and their corresponding
equivalent circuit elements, can be attributed to physical
parameters of an operational fuel cell: 1) the high frequency
intercept, 2) the small high-frequency loop, 3) the medium-
frequency loop, and 4) the low frequency loop. These features
are all highlighted in Figure 2 as sections in the Nyquist plot. The
high frequency intercept of the real impedance axis is attributed
to the total Ohmic resistance, R
Ω
, of the cell, i.e., the sum of all
electrical and ionic resistances. In an operating fuel cell, the
Ohmic resistance is dominated by the ionic resistance of the
membrane and so the high frequency intercept is often used to
approximate the membrane resistance (Springer et al., 1996). The
appearance of a small, high-frequency loop, whose size is
independent of potential, has been previously observed in the
literature and has been attributed to the distributed Ohmic
resistances and contact capacitances that arise within the
nanoporous catalyst layer structure (Fischer et al., 1998;
Paganin et al., 1998;Freire & Gonzalez, 2001;Romero-
Castañón et al., 2003). The medium-frequency loop can be
attributed to the catalyst layer kinetics at the cathode. The
equivalent circuit elements, R2 and C2, that can be extracted
from the appropriate fitting techniques represent the charge-
transfer resistance, R
ct
, and double-layer capacitance, C
dl
, of the
cathode catalyst layer, respectively. Finally, the low-frequency
loop can be attributed to mass transport-related phenomena at
TABLE 1 | Table of experimental parameters used in this work.
Experiment Temperature (°C) Current density
(mA cm
−2
)
Relative humidity
(%)
O
2
gas
stoichiometry
Time at
setpoint (min)
Baseline 80 1,000 70 2.5 n/a
Relative humidity (medium) 80 1,000 50 2.5 30
Relative humidity (low) 80 1,000 30 2.5 30
Gas stoichiometry 80 1,000 70 2.0 10
FIGURE 1 | (A) Selected equivalent circuit candidates identified from the
literature, and (B) a single-sine Nyquist plot recorded at a current density of
1,000 mA cm
−2
and over a frequency range of 50 kHz to 0.5 Hz. The
experimental data is shown as black triangles, with the 2CR, 2QR, and
3CR fits represented by the blue, green, and red lines, respectively.
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Fortin et al. Multi-Sine EIS for FC Monitoring

the cathode. The equivalent circuit element, R3, is therefore
referred to as the mass transport resistance at the cathode,
R
mt
. In general, R
Ω
,R
ct
,C
dl
, and R
mt
are among the most
important parameters used to indicate the state-of-health of a
fuel cell membrane electrode assembly. As such, these parameters
will be the focus of investigation herein.
Multi-Sine EIS Measurements
When approaching EIS data collection with the goal of
reducing measurement time, the most important parameters
to consider are: 1) the minimum frequency, f
min
,2)thenumber
of repeat measurements at each frequency, N
rep
,and3)the
number of periods before each frequency, N
wait
.Thesedata
collection settings were varied systematically to find an
optimal balance between data quality and acquisition speed.
First, a comparison between the single-sine and multi-sine EIS
was done to assess the time saving by using the multi-sine
technique. These results are presented in Figure 3 with varying
number of repeats, N
rep
,N
wait
= 1, and a frequency range of
50 kHz–0.5 Hz. The time saving is significant, where at N
rep
=
15, the multi-sine experiment represents a time saving of 59%
(161 s vs. 395 s). As the number of repetitions is reduced, the
relative time saving is also reduced to 30% at N
rep
=1.Visually,
the multi-sine EIS spectra are noisier at the low frequencies,
but this noise is reduced as the number of repetitions are
increased, and at N
rep
>3, the noise is small and would not be
expected to significantly impact the fitted parameters. The
frequency range was chosen as it ensures resolution of both the
high- and low-frequency intercepts, ensuring accurate
determination of R
Ω
and R
mt
, respectively. While extending
the low frequency limit by an order of magnitude to 50 mHz
allows for the resolution of a low-frequency inductive loop that
may provide insightful information about the hydrogen
peroxide formation at low current densities (Cruz-Manzo
et al., 2015;Cruz-Manzo et al., 2016) or the interface
dissolution resistance in the cathode catalyst layer in a
PEMFC (Pivac et al., 2018), the measurement time was
approximately tripled. Second, N
rep
and N
wait
were varied to
find an optimal balance between data quality and acquisition
speed. Figure 2 highlights selected Nyquist plots in which the
influence of the data collection settings can be seen. Although
the EIS spectra converge in the high and medium frequency
regions of the Nyquist plots, increased noise is observed in the
low-frequency region as the number of repeats, N
rep
,was
reduced. The wait time, N
wait
, exhibited little influence on
the EIS spectra. The optimal data collection settings chosen to
be carried forward in the dynamic fuel cell operation
experiments were a frequency range of 50 kHz–0.5 Hz, N
rep
=3,andN
wait
= 0.5. These settings allow for collection of a full
EIS spectrum in 44 s.
Table 2 shows the fitted parameter values obtained at different
EIS data collection settings. The parameters further investigated
here, R
Ω
,R
ct
,C
dl
, and R
mt
, were all within a standard deviation of
the most time-consuming measurements, N
rep
= 15 and N
wait
=1,
assumed to be the baseline and most accurate measurement in
this case. The largest variation lies in the mass transport
resistance, R
mt
, estimated from the low-frequency loop where
the data collection settings seemingly influence the Nyquist plot
the most. Additionally, the use of a lower minimum frequency
does not improve the fitted parameter value, rather, it can be
argued that the small inductive loop can give some uncertainty in
the determination of the mass-transport resistance.
Detecting Changes in Relative Humidity
The ability of the multi-sine EIS technique to detect dynamic changes
in relative humidity was examined by the continual collection of multi-
sine EIS spectra as the relative humidity of a single-cell PEMFC was
varied. The values of R
Ω
,R
ct
,C
dl
,andR
mt
were subsequently plotted as
a function of time. The relative humidity (RH) was varied in a stepwise
manner, from 70%, down to 50%, and finally down to 30%, to
FIGURE 2 | Measured EIS spectra as a function of experimental settings; (A) varying the repeating wavelengths, N
rep
, and initial waiting time, N
wait
. Important
Nyquist plot featured are identified: i) the high frequency intercept, ii) the small high-frequency loop, iii) the medium-frequency loop, and iv) the low frequency loop. (B)
Measured EIS spectra as a function of minimum frequency, f
min
.
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Fortin et al. Multi-Sine EIS for FC Monitoring

investigate how this influences the EIS spectra and the subsequently
fitted parameters. Figure 4A shows Nyquist plots collected as a
function of RH over time. As RH is decreased, there is a clear shift
in all the Nyquist plot features to higher real impedance values. The
observed increase in ohmic resistance of the cell, R
Ω
,isexpectedasa
lower relative humidity will lead to less water content in the membrane,
which reduces ionic conductivity within proton exchange membranes
(Peckham et al., 2008). A similar effect is observed for the ionomer
present in the catalyst layer, that is; under reduced RH
conditions there will be less water content within the
ionomer and subsequent morphological changes will reduce
the triple phase boundary between the ionomer, catalyst, and
gas-filled pores (Cetinbas et al., 2020). Furthermore, it has been
shown that at low RH values, the oxygen permeability through
the ionomer is significantly reduced (Novitski & Holdcroft,
2015). These changes in catalyst layer ionomer properties are
responsible for the observed increase in charge-transfer
resistance, R
ct
, through decreased electrochemically active
surface area and decreased availability of dissolved oxygen
leading to reduced kinetics. The observed decrease in double-
layer capacitance, C
dl
, can also be explained by reduced surface area
between the ionomer and catalyst; and the observed increase in
mass transport resistance, R
mt
, likely arises from the decreased
permeability of oxygen through the catalyst layer and decreased
availability of oxygen at the ionomer-catalyst interface.
The main highlight of these results is the demonstration of
multi-sine EIS as a technique to capture dynamic changes in
water balance phenomena. The longer timescale (seconds to
minutes) of water transport and equilibration within the fuel
cell membrane electrode assembly allows dynamic changes to be
captured by the multi-sine EIS technique. This result suggests that
multi-sine EIS has the ability to be applied as a diagnostic
technique for fault detection in operational PEMFCs, at least
concerning phenomena that take place over longer timescales.
Detecting Changes in Cathode
Stoichiometry
The ability of the multi-sine EIS technique to detect dynamic
changes in oxygen concentration was examined by the
FIGURE 3 | Comparison of single-sine and multi-sine EIS with an N
rep
of (A) 15, (B) 5, (C) 3, and (D) 1. The total measurement time is indicated in the legends.
TABLE 2 | Fitted EIS parameters for various EIS data collection settings.
f
min
(Hz) N
rep
N
wait
R
Ω
(mΩcm
2
)R
ct
(mΩcm
2
)C
dl
(mF cm
−2
)R
mt
(mΩcm
2
)t
tot
(s)
0.5 15 1 30 ± 3.5% 90 ± 25% 42 ± 37% 174 ± 14% 161
0.5 5 0.5 30 ± 3.4% 93 ± 25% 44 ± 37% 157 ± 15% 64
0.5 3 0.5 30 ± 3.4% 92 ± 25% 44 ± 37% 155 ± 15% 45
0.5 1 0.5 30 ± 3.4% 89 ± 29% 46 ± 41% 164 ± 16% 26
0.5 5 1 30 ± 3.5% 91 ± 30% 44 ± 42% 172 ± 16% 71
0.05 5 1 30 ± 3.7% 93 ± 29% 43 ± 42% 166 ± 17% 183
Frontiers in Energy Research | www.frontiersin.org May 2022 | Volume 10 | Article 8559856
Fortin et al. Multi-Sine EIS for FC Monitoring

continual collection of multi-sine EIS spectra as the cathode
stoichiometry of a single-cell PEMFC was varied. The values of
R
Ω
,R
ct
,C
dl
,andR
mt
were subsequently plotted as a function of
time. A mild change in cathode stoichiometry was performed,
varying the set point from 2.5 to 2 and back again. A
comparison of the Nyquist plots collected immediately
beforeandafterthechangeincathodestoichiometryis
shown in Figure 5B, and there is a clear increase in the
low-frequency loop as cathode stoichiometry is reduced.
This observation is confirmed by the fitted resistance values
plotted as a function of time, Figure 5C,inwhichasignificant
increase is observed for the R
mt
parameter, whereas a more
subtle change was detected in the charge-transfer resistance,
R
ct
, and no changes in ohmic resistance, R
Ω
, or double-layer
capacitance, C
dl
, were observed. The significant increase in the
magnitude of both real and imaginary impedance in the low-
frequency mass transport loop, and fitted R
mt
values, can be
explainedbythereductioninavailableoxygenascathode
stoichiometry is decreased. Similarly, the slight increase in
magnitude of the mid-frequency loop, and fitted R
ct
values, is
related to the reduced oxygen concentration in the catalyst
pore space and gas diffusion media, leading to reduced
kinetics. Because the dielectric constant, triple phase
boundary surface area, and double-layer distance do not
vary as a function of oxygen concentration, no change in
the double-layer capacitance, C
dl
, is expected. Additionally,
the ionic transport properties of the membrane are not
influenced by oxygen concentration, and therefore no
change in Ohmic resistance, R
Ω
,isexpected.
In contrast to the slower changes in water transport and
equilibrium observed when the relative humidity of the fuel
cell is changed, the change in oxygen flow rate occurs
immediately upon changing the cathode stoichiometry set
point. Figure 5A shows every multi-sine EIS Nyquist plot
collected before and after the switch in cathode stoichiometry.
All the spectra collected at their respective cathode stoichiometry
values show an identical response, suggesting that no dynamic
response can be captured with the multi-sine EIS protocol used
here. A comparison of the Nyquist plots collected immediately
before and after the change in cathode stoichiometry is shown in
Figure 5B for simplicity. Although the rapid change in fuel cell
parameters as a result of varying cathode stoichiometry cannot be
captured dynamically by the multi-sine EIS technique, it is
noteworthy that this method is able to capture the change in
operating conditions in the very next Nyquist plot acquired. Even
though this technique will do little to prevent rapid degradation
from severe oxygen starvation that can occur on the order of a few
seconds or less, it can be useful in providing diagnostic
information for control strategies and relay algorithms to
provide optimised operating conditions under mild starvation
conditions, e.g., flooding or poisoning at the cathode
catalyst layer.
FIGURE 4 | EIS spectra and fitted values from changes in relative humidity; (A) Nyquist plot of all measurements, (B) Nyquist plot of selected measurements at the
relative humidity setpoints, (C) fitted resistance values and relative humidity as a function of time, and (D) fitted capacitance value and relative humidity as a function
of time.
Frontiers in Energy Research | www.frontiersin.org May 2022 | Volume 10 | Article 8559857
Fortin et al. Multi-Sine EIS for FC Monitoring

Practical Application of the Technique to
Fuel Cell Stacks
While not part of the experiments in this work, it is important to
consider the applicability of the technique to stack-level systems.
We have demonstrated that multi-sine EIS can capture the
dynamic response of a single-cell fuel cell, and that it has
potential as a method to continually monitor a cell and
acquire diagnostic information during operation.
Experimentally, it is not really more complicated to do the
measurement at the stack level as the current at the stack level
is the same as for the cell level. However, the larger potential and
surface area of large stack systems, may then require the
experimenter to develop specialized hardware for the system
to be studied. In addition, the larger surface area leads to less
detailed information as the response is averaged over a larger
area. In the end, what is required is a ac current signal generator
able to generate sufficiently large signal (5–10% of the steady-state
current), and then, the EIS can be measured both at stack level
and cell level by sampling the potential response at stack and cell
level. Several examples of such systems have been shown in the
literature, either through the DC-DC converter (Wang et al.,
2019a;2019b) or through a separate system of signal generation
(Yuan et al., 2006a). While these examples don’t specifically use
the multi-sine technique, there is no practical difference in
hardware between the two types of implementation. In
addition, the multi-sine technique has attracted commercial
interest and commercialization of such systems for signal
generation and cell level sampling is underway by among
others a Canadian company (Pulsenics, 2022).
The practical application of the multi-sine EIS technique
is feasible, but the multi-sine technique requires a larger total
amplitude than the single-sine technique. This may be a
problem practically, as such an signal has similarities with
ripple current originating in the power converter, which has
been shown to lead to some degradation (Wahdame et al.,
2008;Gerard et al., 2010;Zhan et al., 2019). Further studies
are therefore necessary to verify that both techniques do not
FIGURE 5 | EIS spectra and fitted values from changes in cathode stoichiometry; (A) Nyquist plot of all measurements, (B) Nyquist plot of selected measurements
at the cathode stoichiometry setpoints, (C) fitted resistance values and cathode stoichiometry as a function of time, and (D) fitted capacitance value and cathode
stoichiometry as a function of time.
TABLE 3 | Summary of influence on parameters for the various changes
investigated in this work.
Relative humidity Cathode stoichiometry
R
Ω
Negative No correlation
R
ct
Negative Negative
C
dl
Positive No correlation
R
mt
Negative Negative
Frontiers in Energy Research | www.frontiersin.org May 2022 | Volume 10 | Article 8559858
Fortin et al. Multi-Sine EIS for FC Monitoring

contribute significantly to degradation when run in a
continual manner.
CONCLUSION
We have shown that changes in fuel cell operating conditions,
e.g., relative humidity and cathode stoichiometry, can be
monitored using multi-sine EIS. Table 3 shows the four
equivalent circuit parameters along with their approximate
correlation to each of the operating conditions. The changes in
operating conditions give rise to different EIS responses, making
it possible to qualitatively identify the source of the change, in
corroboration with previous literature results (de Beer, 2014).
While the examples illustrated here, i.e., changes in RH and
cathode stoichiometry, represent only a few examples of possible
non-ideal operation (flooding, drying, starvation, poisoning etc.)
or failure modes encountered during fuel cell operation, they
demonstrate that the different physical phenomena occurring
within the fuel cell have EIS responses that can be differentiated
from one another and provide insight into potential corrective
actions by the control system. The results here demonstrate that
the multi-sine approach is a suitable technique to reduce the
acquisition time of a full EIS spectrum, compared to the
traditional single-sine approach, and can reliably provide
information about several important fuel cell parameters, e.g.,
R
Ω
,R
ct
,C
dl
, and R
mt
. The EIS data acquisition can be used in
conjunction with widely-available and open-source software, e.g.,
PyEIS or impedance.py, to obtain a full EIS spectrum from
50 kHz–0.5 Hz and high-quality fit of the data in as little as
50 s. Although this timeframe is suitable for observing the
response of slower phenomena such as water balance, mild
starvation, or catalyst poisoning, it is too long to rely on for
observing phenomena that can lead to catastrophic failure in only
a few seconds, such as severe starvation. Further optimisation of
the multi-sine EIS technique to reduce acquisition time is
therefore required to provide rapid analysis of the various
processes occurring in the fuel cell.
DATA AVAILABILITY STATEMENT
The raw data supporting the conclusion of this article will be
made available by the authors, without undue reservation.
AUTHOR CONTRIBUTIONS
TH and PF conceived and designed the analysis. PF performed
the experiments and collected the data. The data analysis was
done by TH, PF, and MG. The authors PF and TH prepared the
manuscript. MG, ØU, and FZ reviewed and edited the
manuscript.
FUNDING
The authors gratefully acknowledge support from MoZEES, a
Norwegian Centre for Environment-friendly Energy Research
(FME), co-sponsored by the Research Council of Norway (project
number 257653) and 37 partners from research, industry, and
public sector. The infrastructure used in the project is part of the
Norwegian Fuel Cell and Hydrogen Centre (NFCH) fully funded
by the Research Council of Norway (245678).
ACKNOWLEDGMENTS
The authors also thanks Christoffer Askvik Faugstad for making
the software to automate EIS data fitting.
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Conflict of Interest: The authors declare that the research was conducted in the
absence of any commercial or financial relationships that could be construed as a
potential conflict of interest.
The handling editor IP declared a past co-authorship and collaboration with the
author(s) FZ.
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Frontiers in Energy Research | www.frontiersin.org May 2022 | Volume 10 | Article 85598511
Fortin et al. Multi-Sine EIS for FC Monitoring