Abstract
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 ≈ 11.6 μHz 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 μHz. Next, we present reliable impedance data extending to a lower frequency limit of 10 μHz. 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.
Highlights
A great many manuscripts appear in the literature describing rechargeable battery equivalent-circuit models of widelyvarying complexity
Researchers sometimes use time-domain I/V data to which to fit their model, but most carry out an ElectroImpedance Spectroscopy (EIS) measurement, yielding the complex impedance as a function of frequency
This method is superior because it can produce a signal with arbitrarily low frequency and the post-processing of the IV data is immune to offset drifts, imperfect waveshape, and distortions by virtue of the windowing and filtering
Summary
A great many manuscripts appear in the literature describing rechargeable battery equivalent-circuit models of widelyvarying complexity. Researchers sometimes use time-domain I/V data to which to fit their model, but most carry out an ElectroImpedance Spectroscopy (EIS) measurement, yielding the complex impedance as a function of frequency. Many references are not specific about their frequency range, and present only Nyquist, not Bode plots This is surprising, since many batteries are in appliances charged daily, corresponding to a frequency of ≈11.6μHz. Reference [22], over 20 years old, appears to be alone in arguing that data down to 1μHz may be useful, but even this manuscript presents data down to only 6.8μHz, and there is no discussion of how this data was obtained. This instrument is mentioned in several manuscripts, e.g. [21], [26], [27], and appears to be a popular choice for battery measurements, at which it is targeted by its makers
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