A 25 cm² 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 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/mm² 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.

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. Φ k = Φ 1 − 2 π ∑ n = 1 k − 1 ( k − n ) N (1)

Here, Φ k is the phase of frequency number k, and N is 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 ∑ k = 1 N cos ( 2 π f k t + Φ k ) (2)

Here, u(t) is the applied signal as a function of time, A is the amplitude (1.25 A), and f k is 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.

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).

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 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 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.

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) the number of repeat measurements at each frequency, N _rep, and 3) the number of periods before each frequency, N _wait. These data 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, and N _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.

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, and R _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 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, is expected as a 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.

The ability of the multi-sine EIS technique to detect dynamic changes in oxygen concentration was examined by the 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, and R _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 before and after the change in cathode stoichiometry is 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, in which a significant 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 explained by the reduction in available oxygen as cathode 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, is expected.

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.

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 contribute significantly to degradation when run in a continual manner.