Analytical transfer function for the blocked-diffusion warburg impedance with frequency dispersion. Simulation of the impedance spectrum and voltage response of a lithium-ion battery

The frequency-impedance spectrum of the blocked-diffusion Warburg (BDW) impedance is represented by a 45-degree angle straight-line at high frequencies followed by a vertical line at low frequencies in the Nyquist plot. On the contrary, the impedance spectrum of the blocked-diffusion Warburg impedance with frequency dispersion (BDWf) is represented by a straight-line with slope < 45-degree angle at high frequencies followed by a constant phase element (CPE) response at low frequencies. In this study, the mathematical treatment reported in a previous study for the transfer function of the BDW impedance is extended for the derivation of a transfer function representing the BDWf impedance. The new transfer function representing the BDWf impedance is able to reveal the contribution of the diffusion process which is overlapped with the CPE behaviour in the BDWf impedance spectrum. The transfer function representing the BDWf impedance developed in this study and the transfer function representing the finite-length Warburg (FLW) impedance presented in a different study have been considered in an equivalent electrical circuit (EEC) configuration constructed in MATLAB/Simulink environment to simulate the frequency-impedance spectrum and output voltage response of a Lithium-ion battery. The effect of the electrode diffusion distance of lithium ions on the frequency-impedance spectrum and output voltage response of a Li-ion battery is simulated through the Simulink model of the battery. This study could assist other studies focusing on the simulation of the diffusion phenomena in modern batteries with different particle sizes considering the EIS measurements as a baseline.