Fuel-cell testing: polarisation curve, EIS and ohmic-resistance measurement
1 Theory
Thermodynamics and losses
The reversible voltage of the hydrogen/oxygen fuel cell is 1.23 V at 25 °C; in practice the open-circuit voltage stays at 0.95–1.0 V because of mixed potential and gas crossover. As current is drawn the voltage falls through three losses: activation (at low current, logarithmic; mainly cathode ORR), ohmic (at mid current, linear; membrane + contact) and mass transport (at high current, sharp drop; water management/gas diffusion). The polarisation curve is modelled as E = E₀ − b·log(i) − R·i − m·exp(n·i); the maximum of the power curve defines the nominal operating point.
Measuring the polarisation curve
Galvanostatic steps (with a settling time at each step, typically 1–5 min) are preferred; a slow potentiodynamic scan is also used but creates hysteresis. Temperature, humidity, stoichiometry and pressure must be fixed and reported. High current (tens to hundreds of amperes) requires a booster/electronic load, low cell voltage (0.3–1 V) high-resolution voltage measurement.
Separating the losses with EIS
EIS taken at the operating point (under DC load) gives the membrane+contact resistance (HFR) at the high-frequency intercept, the cathode charge-transfer semicircle at mid frequency and the mass-transport arc at low frequency. Following the HFR with current shows membrane hydration, growth of the low-frequency arc flooding. The current-interrupt method is the fast alternative for HFR. In stacks the EIS of every cell is measured simultaneously to find the weak cell.
Electrolyser and reversible operation
In a PEM water electrolyser the curve is inverted: above 1.23 V the activation (OER, Ir/Ru oxide), ohmic and mass-transport (bubble) overpotentials are added; current densities of the order of A/cm² around 2 V are common. Durability tests follow the long-term voltage rise (hundreds to thousands of hours) at constant current.
2 Application in measurement
The polarisation (I–V) curve consists of activation, ohmic and mass-transport regions; each region represents a different loss. Galvano-EIS at operating points separates membrane resistance, charge-transfer and diffusion contributions; the high-frequency resistance (HFR) is used to monitor membrane humidification.
Control of gas flow, humidity, temperature and pressure is part of the measurement: BluPEM stations combine this control with an integrated potentiostat/EIS. For high current densities the HCP-803 (80 A) or FlexP (200–800 A) is used; the Entek FCT is a domestic two-channel test instrument up to 25 V/100 A.
In stack measurement the voltage and EIS of every cell are taken simultaneously (VMP-3e + SAM-50).
Key equations
Cell voltage: V = E_rev − η_act − I·R_ohm − η_mass
3 Applicability
Where it applies
- MEA/catalyst-layer development, stack validation, optimisation of operating conditions (humidity, temperature, stoichiometry), accelerated durability tests.
Limits and caveats
- Single-cell results do not scale directly to the stack; flow distribution and thermal gradients create different losses in the stack.
- EIS requires steady-state conditions; at high current, where water management fluctuates, NSD rises.
4 What did the application notes find?
- Fuel Cell AN31 — Shows the general framework of fuel-cell testing and I/E (polarisation) characterisation with galvanostatic steps; identification of the loss regions on the curve.
- Fuel Cell AN32 — Shows the separation of membrane resistance, charge transfer and mass transport by EIS under DC load; interpretation of the spectrum change at different currents.
- Electrolyzer AN63 — Shows DC polarisation and EIS measurement at high current (with a booster) on a PEM electrolyser; the change of HFR and OER charge-transfer resistance with current.
- Battery AN16 — Shows the simultaneous impedance measurement of series cells in a stack and the detection of the problematic cell; applies directly to fuel-cell stacks.
5 Which instruments perform this measurement?
References
- book F. Barbir. PEM Fuel Cells: Theory and Practice (2nd ed.). Academic Press / Elsevier, 2013.
- article X. Yuan, H. Wang, J. C. Sun, J. Zhang. AC impedance technique in PEM fuel cell diagnosis — A review. Int. J. Hydrogen Energy 32, 4365–4380, 2007. doi:10.1016/j.ijhydene.2007.05.036
- article K. R. Cooper, M. Smith. Electrical test methods for on-line fuel cell ohmic resistance measurement. J. Power Sources 160, 1088–1095, 2006. doi:10.1016/j.jpowsour.2006.02.086

