Efficiency of Cycled Batteries Analyzed Through Voltage-Current Phase Differences

Ageing of rechargeable batteries is routinely characterized in the frequency domain by electrochemical impedance spectroscopy, but the technique requires laboratory measurements to be made on a time scale of days. However, the normal cycling of a battery as it is used in situ provides equivalent information in the time domain, though extracting robust frequency information from a time series is challenging. In this work, we explore, in the time domain, the relationship between instantaneous voltage-current phase difference and cycle efficiency. Moreover, we demonstrate that phase measures can be used to identify battery ageing. We have cycled a 250 mA h Nickel-Cobalt cell several hundred times and used Hilbert Transforms to identify phase difference between voltage and current. This phase difference becomes closer to zero as the battery ages, commensurate with a drop in energy cycle efficiency. In another experiment, we applied a synthetic current profile mimicking behaviour of an electric car cell, to a 3.2 A h LiNiMnCoO2 cell, for ~100 days. For this more complicated profile with a wide range of frequency content, we used wavelet analysis to identify changes in phase difference and impedance as the battery aged. For this cell, drop in cycle efficiency was associated with a rise in internal resistance. The results imply that time-series analysis of in situ measurements of voltage and current, when applied with equivalent circuit models and underlying theory, can identify markers of battery ageing.