Introduction
Ohmic resistance (Rohm) is a key performance driver of fuel cells [1, 2]. The three sources of ohmic voltage loss are (i) resistance to ion migration within the electrolyte, (ii) resistance to electron transport within the cell components (electrodes, gas diffusion layer, flow field/current collectors), and (iii) contact resistances. Although the dominate source of ohmic resistance varies with the type of fuel cell, the total internal resistance of a fuel cell (or fuel cell stack) is an important consideration: small amounts of ohmic resistance (on the order of milliohms) have a significant effect on overall efficiency because of the high current densities at which these electrochemical devices generally operate [2]. As a result, it is desirable to measure the resistance of the cells during their development, manufacture and long-term operation.
This article examines and compares presently available methods for measuring the internal resistance of fuel cells during operation. Because the resistance of the cell is often a complex function of many parameters (e.g., temperature, current density, hydration, etc.) it is desirable to measure the resistance of the cell under operating conditions. Therefore, we focus on methods suitable for on-line, real-time monitoring of functioning cells. The four methods generally used for internal cell resistance measurement are: Current Interrupt (iR), AC Resistance, Electrochemical Impedance Spectroscopy (EIS), and High Frequency Resistance (HFR). A comparison of these methods follows a discussion of the measurement principle, and the pros and cons of each.
The fuel cell can be modeled by the equivalent circuit shown in Figure 1(a). This simple model circuit is commonly applied to electrochemical systems in which contact resistance and other effects are small enough to ignore. For simplicity, assume that the polarization resistance of one electrode (say the cathode) is much larger than that of the other electrode (the anode), so that one can legitimately omit circuit elements associated with one of the electrodes (the anode in this example). Polarization resistance is the reaction equivalent, double-layer capacitance is the interfacial capacitance of the cathode, and the ohmic resistance is the resistive component of the fuel cell to be evaluated. The voltage source element is an ideal DC voltage source (zero internal impedance and constant voltage) with a potential equal to the open circuit voltage of the fuel cell. The voltage source element does not affect AC analysis but allows the model to approximate the DC behavior of the fuel cell. Note that the values of these equivalent circuit components are a function of the cell’s operating current or voltage, making the fuel cell an electrically non-linear device.
Looking at the equivalent circuit in Figure 1(a), the double-layer capacitance will exhibit very low impedance at high frequencies, essentially providing a short at the electrochemical interface. At high frequencies only the bulk ionic and electronic ohmic resistance and contact resistances are observed. Cell resistance measurements take advantage of the capacitance of the electrochemical interface which decouples ohmic effects from the activation polarization contributions under some conditions. As described below, this may be implemented several different ways, but all have some traits in common:
• All methods impose a changing electrical condition on the cell.
• All methods measure current and/or voltage waveforms resulting from that change.
• All methods require an accurate voltage measurement directly at the cell terminals using the four-terminal (Kelvin) method.
Fig. 1: (a)Simplified, idealized equivalant circuit for a H2 PEM fuel cell. (b)Nyquist plot of the imedance of the equivalent circuit shown in (a).
Current Interrupt Method
In this time-domain AC technique, the cell current is very rapidly interrupted and the terminal voltage before and during the interruption measured [3, 4]. The current interrupt technique is probably the most widely used method of ohmic drop and ohmic resistance evaluation of electrochemical systems, including batteries [5], corrosion [6, 7], and fuel cells [8-10].
The principle of the current interrupter method is shown in Figure 2. The cell voltage is a combination of the charged anode and cathode potentials less the cumulative resistive potential drop of the electrolyte, electrical conductors and contact resistances. Thus, in principle, the cell voltage rises nearly instantaneously by the amount of the ohmic potential drop, delta(V) (Volts), upon interruption of the current. The ohmic resistance of the cell Rohm (ohm-cm2) is determined as the quotient of the instantaneous change in voltage and the cell current density i (A cm-2) just prior to the interrupt event, Rohm = delta(V) / i.
Advantages of this method include a single data value which is easily interpreted. Furthermore, there is no requirement for additional equipment because the interrupt is brought about by the load. The primary disadvantage of this method is that it imposes a significant perturbation on the cell, if only for a short duration (i.e., tens of micro-seconds). Users of this method are also cautioned that data is degraded when long cell cables are used due to excessive ‘ringing’ caused by cable inductance; leads should be kept as short as possible to minimize pick up of stray capacitances and inductances [5]. Finally, under some circumstances for electrochemical systems with porous electrodes, the interrupter method may overestimate the ohmic voltage change and therefore overestimate the ohmic resistance of the cell. This latter point is discussed further in reference [11].
AC Resistance Method
This method uses an AC resistance measurement device, such as an external AC milliohm meter, to apply a single, high frequency sine wave (typically ~1 kHz) to the fuel cell under test to measure the total impedance magnitude of the cell and the load in parallel at that frequency. The set-up is shown in Figure 3. The ohmic resistance of the cell can be extracted after correcting for the impedance of the load.
Like the current interrupt technique, this method provides a single data point. Because the AC perturbation is generally small relative to the DC current, the cell is minimally disturbed electrochemically by the measurement and therefore this method is suitable for interrogation of a functioning cell.
However, accurate results from the AC resistance method require exact gain-phase characterization of the impedance of the load at the operating conditions of the fuel cell during the AC measurement. Knowledge of the complex impedance of the load is required because the milliohm meter measures the zero-phase condition of the parallel fuel cell-load combination, which does not necessarily equal the zero-phase impedance of the cell (i.e., referring to Figure 3 in this configuration the load has a complex impedance in parallel with the complex impedance of the cell). To accurately determine the high frequency resistance of the fuel cell one should account for the contribution of the impedance of the load to the impedance measured with the AC milliohm meter. As such, one must determine with external frequency analysis equipment the complex impedance of the load at the DC voltage and DC current of interest at the frequency of the AC resistance measurement. The difficulties of this technique stem from the milliohm meter not being intended to measure energy sources under load.
High Frequency Resistance (HFR) Method
In the HFR method to determine internal cell resistance, a small AC signal is applied to the electronic load to modulate the DC load current, as illustrated in Figure 4. The resulting magnitude and phase of the AC voltage and current response are measured by a frequency response analyzer. A single, high frequency is used, typically on the order of 1 kHz. This method is actually a subset of the EIS method described below wherein a broad range of frequencies are employed. Of interest is the real component of the impedance (Z’ or Re(Z)).
HFR measurement minimally disturbs the cell from its operating condition, both in magnitude and duration, and therefore it is suitable for routine, periodic application during normal fuel cell operation.
The appropriate frequency for an HFR measurement varies with the electrochemical system under study. Selection of the proper frequency is best accomplished by examining the phase difference between the AC current and voltage signals at a range of frequencies. It should ideally be the frequency at which the imaginary component of the impedance is zero (Im(Z) or Z” = 0) and therefore the cell is behaving in a purely resistive manner. In terms of a Nyquist plot, this condition exists when the impedance data cross the real axis (Figure 1(b)) at high frequency. Typical HFR measurement frequencies range from 1 kHz to 10 kHz. In any case, the same frequency must be used for valid data comparison.
Note that the method for choosing the HFR frequency requires that the test system also have EIS capability. This is generally not a problem because a true frequency response analyzer can measure over a wide range of frequencies, so a test system capable of true HFR measurement will also be capable of performing EIS measurements.
Electrochemical Impedance Spectroscopy (EIS) Method
EIS is an extension of the HFR method previously described and differs in two ways. Whereas HFR employs a single frequency and only examines the real component of the impedance, EIS involves imposing the AC perturbation over a broad range of frequencies – typically 10 kHz to 1 Hz or lower – and monitoring the resulting variations in magnitude and phase of the cell voltage and current in order to determine the complex impedance (Z’, Z” or Z-phase relation) of the electrochemical system being studied. This results in a rich data set from which several parameters may be extracted via equivalent circuit modeling. These parameters include non-electrode ohmic resistance, electrode properties such as ohmic resistance and activation polarization resistance, double-layer capacitance, and transport properties [12-16].
The real component of the impedance measured using EIS at the frequency used for an HFR measurement should be identical to the resistance obtained using HFR.
References
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