Rapid Impedance Modeling via Potential Step and Current Relaxation Simulations

Abstract

We present a fast computational technique for the electrochemical impedance of solid oxide fuel cells ͑SOFCs͒ based on detailed electrochemistry and transport models. The technique is based on the transient numerical simulation of a fast, submicrosecond potential step followed by current relaxation. The impedance is reconstructed by applying a Fourier transform to the resulting current and potential traces. The successful application of this technique is based on the combination of ͑i͒ numerical time integration of the governing equations using a time-adaptive solution algorithm, and ͑ii͒ a Fourier transform algorithm for arbitrarily spaced time points. Results are presented for a two-dimensional model of a symmetrical SOFC including gas-phase transport, pore phase transport, surface chemistry, and elementary kinetic charge transfer. Calculation speed is increased by a factor of 10-200 in comparison to a conventional simulation technique based on frequency-resolved sinusoidal excitation, depending on the frequency resolution of the conventional technique and the imposed precision of the numerical solver. The technique is an important tool for a model-based interpretation of experimental impedance data without using equivalent circuits.

Insight into lithium–sulfur batteries: Elementary kinetic modeling and impedance simulation

“…For the impedance simulation, a voltage step/current relaxation technique is used [15]. Starting from opencircuit voltage (OCV), the voltage is increased by 1 mV within 0.1 µs and the resulting current transient is simulated over 1000 s. The resulting time traces of voltage and current are Fourier-transformed in the range of 10 7 to 10 −3 Hz in order to obtain the complex impedance Z in the frequency domain.…”

“…Electrochemistry is described with an elementary kinetic approach (no Butler-Volmer equation, no Nernst equation, cf. [15]). As no information on temperaturedependent kinetic coefficients is available, the model is assumed isothermal, and the activation energies are assumed to be zero for all reactions.…”

Modeling Impedance Response of SOFC Cathodes Prepared by Infiltration

“…Frequency domain data, identical to that which would be measured using sine wave testing, can then be obtained by performing a Fourier Transform of the time-dependent current and voltage profiles, i(t) and U(t), followed by complex division. [70][71][72][73] For the simulations in this work, we modeled the current responses to step changes in the cathode overpotential. For t < 0, the system was assumed to be at "open-circuit" voltage, with no overpotential applied to the YSZ fin.…”

Lifetime and Performance Prediction of SOFC Anodes Operated with Trace Amounts of Hydrogen Sulfide

“…Spatial derivatives of the PDE system are discretized by the finite volume method and the resulting differential algebraic equation (DAE) system is integrated by means of the semi-implicit extrapolation solver LIMEX (25). Experimental electrochemical impedance spectra were simulated using a potential step and current relaxation technique (26). The impedance is obtained in the frequency domain of interest (10 -3 to 10 6 Hz) by a Fourier transformation of the resulting time-domain traces of current and potential.…”