New Results for Battery Impedance at Very Low Frequencies

In search of an equivalent circuit model for rechargeable batteries, many authors start with a measurement of battery impedance, spanning what is presumed to be the frequency range of interest. Various networks have been suggested in the literature to account for the measured impedance characteristic. Most incorporate two or more resistors, at least one capacitor, some include at least one Warburg element, and more recently "constant phase elements'' (CPE), otherwise identified as fractional-derivative capacitors. Networks that are more successful at reproducing the measured impedance have from five up to tens of degrees of freedom. The frequency range upon which most models are based extends only to 1mHz. This is surprising since many batteries see a daily or longer usage cycle, corresponding to a frequency of approximate to 11.6 mu Hz or lower. We show in this manuscript that the most-cited impedance measurement instrument, and one of the few that can operate below 1mHz, can be unreliable at and below this boundary. We present a novel impedance measurement algorithm robust against the issues present while measuring the impedance of electrochemical systems to as low as 1 mu Hz. Next, we present reliable impedance data extending to a lower frequency limit of 10 mu Hz. A remarkable characteristic appears at the lower frequencies, suggesting a surprisingly simple and elegant equivalent circuit consisting of a single fractional capacitor. A new model is proposed, which requires only four parameters to predict the measured impedance as a function of frequency.