Determining cell impedance is critical for the further development and optimization of fuel cells and batteries. Decreasing impedance reduces the internal losses and therefore increases cell efficiency. For the sake of simplification, lets assume that the impedance is affected by two major elements:
- Membrane resistance
- Electrochemical resistance
Membrane resistance (R1) is a resistance that is determined by the material and the physical conditions (humidity, temperature, contamination). Electrochemical resistance (R2) is primarily determined by the operating point or current.
The following figure shows a simple, but nevertheless typical, equivalent circuit of a fuel cell. In this figure, R1 represents the membrane resistance and R2 represents the polarisation resistance. Capacitor C1 represents the double-layer capacitance.
Resistor R1 is connected in series to the paralleled components R2 and C1.
There are two basic ways for determining the impedance of a fuel cell or battery:
- Current Interrupt (determination of step response)
- Impedance spectroscopy
The Current Interrupt or step response, respectively, is obtained by varying the current stepwise, recording the voltage and then determining the change in voltage from the voltage recordings. In impedance spectroscopy, the fuel cell is activated by means of a signal having various frequencies.
The CI method is a very simple method that can be implemented using simple means. For example, an electronic load (TrueData-LOAD) is used and the operating current is changed stepwise.
When the current applied to the network comprising [R1+R2||C1] is changed stepwise, the voltage across resistor R1 will immediately change showing a small step, while the voltage across R2 will change gradually in the course of time.
When the current is changed e.g. by 5 A and the voltage step change is 50 mV, the membrane resistance is as follows:
R1 = 50 mV / 5 A = 10 mΩ. This method is appropriate for membrane resistances larger than 5 mΩ.
In universities and R&D, small size active cell surfaces are often used, measuring e.g. 2.5 x 2.5 cm, which results in a surface resistance of 31.25 mΩ/cm² for a membrane resistance of 5 mΩ.Problems are to be expected when these materials are used for larger surfaces, e.g. measuring 100 cm² or 200 cm². The electrical resistance is calculated as
R = roh x l / A
With the surface A is increased, resistance R will become smaller.
|Cell size||Area||Membrane Resistance|
|0 mΩ/cm²||50 mΩ/cm²||100 mΩ/cm²|
|2.5 cm x 2.5 cm||6.25 cm²||4.80 mΩ||8.00 mΩ||16.00 mΩ|
|5.0 cm x 5.0 cm||25.00 cm²||1.20 mΩ||2.00 mΩ||4.00 mΩ|
|10.0 cm x 10.0 cm||100.00 cm²||0.30 mΩ||0.50 mΩ||1.00 mΩ|
|10.0 cm x 25.0 cm||250.00 cm²||0.120 mΩ||0.20 mΩ||0.40 mΩ|
For a surface of 100 cm² and a membrane resistance of 30 mΩ/cm², a total membrane resistance of 0.3 mΩ is obtained. What is actually measured, is the total membrane resistance (mΩ).
The membrane resistance (mΩ/cm²) is a calculated number. In the Current Interrupt method, the voltage step - caused by the low resistance - is ranging from some microvolts (µV) to some millivolts (mV) only. For this reason, some sources of error become important which usually can be neglected in case of large resistances.
- Sampling rate and extrapolation
- Interfering capacitances of the cable and switching transistors
The error caused by the sampling rate and subsequent extrapolation is illustrated in the following figure. The voltage changes stepwise and is sampled by 10 kHz (100 µs). Subsequently, the voltage is extrapolated to the time of 0 seconds (0 µs) to be able to determine the voltage drop occurring across R1.
After the step, the voltage changes exponentially. From the values of 100 µs and 200 µs, extrapolation is done backwards to the time of 0 µs. The error resulting from this is clearly seen in the diagram.The extrapolated voltage drop is typically larger than the actual change in voltage. In the example, a difference of 228 mV instead of 50 mV is measured. So the calculated resistance would be 4.5 times higher than the actual value.
The lower the measured voltage, the more important noise will become. Noise voltages or interference of some millivolts (mV) are quite normal. Extrapolation is very susceptible to noise, as shown in the following figure.
Even by averaging across several measurements, the error can not be reduced as noise is often not zero-mean.
Each measuring setup has a measuring error. Particularly for large currents, cables of large cross-sections exhibiting a relatively high cable capacitance have to be used. Cable capacitance is typically ranging from 0.3 to 1.0 nF per meter (nF/m). Furthermore, the transistors used for switching have switching capacitances.
The wanted signal is superimposed by the impact of cable and switching capacitances.
These interfering capacitances prevent the voltage step from being clearly identified. It is very difficult or even impossible to calculate resistor R1.
One would think that there will be problems in impedance spectroscopy also at low impedances. However, impedance spectroscopy has a significant advantage over Current Interrupt method, since the amplitude of an AC voltage is measured instead of a voltage signal decaying in time domain. No signal is extrapolated, but the quotient from AC voltage and AC current is calculated.
Impedances below 1 mΩ can be determined at high accuracy.
In recent years, Current Interrupt method was a simple method for determining the impedance or membrane resistance, respectively, of fuel cells and batteries. It was implemented in test stations, particularly in the Evaluator C50 series, for investigating small cells.
See also FuelCon patent DE10226339 “Testing and monitoring of fuel cells, involves applying suddenly-changing load and assessing measured effects on voltage and current output” . Because of the fact, that the impedances are becoming smaller, the Current Interrupt method has been completely replaced by the impedance spectroscopy. Within the next few years, impedance spectroscopy will continue to play an important role for investigating fuel cells having larger active surfaces.