Why your battery meter tells lies and it's hard to fix: Effect of pauses in cycling on submillihertz battery impedance

Abstract

Rechargeable lithium-ion batteries are an increasing part of our world, found in small devices such as medical implants and mobile phones, up to much larger applications in electric vehicles and the huge battery electric storage systems (BESS) that support the modern electricity grid. But despite the advances in design and manufacturing, your battery meter still does not tell you the truth: "75% charge remaining" most likely does not mean 75% charge remaining. On a trivial scale this means your phone battery goes flat unexpectedly; less trivially your car runs out of charge before you get home, and on a cold winter's morning the electricity grid might not actually be able to provide the peak power that its operators think it can. The reason that producing an accurate meter is so challenging is that battery history matters. A battery's response to an electrical stimulus doesn't just depend on its state now, but also on its state in the past. In mathematical terms, its behaviour is described by fractional differential equations, where the order of the equation is non-integer. In this presentation, we discuss an experiment where we have looked at the effect of a long (56 day) break in battery battery charge/discharge cycling on electrical properties of the battery. On recommencement of cycling, we can discern the effect of the pause on impedance for around 30 days after the break. To see the effect we have constructed the impedance spectrum at ultra-low frequencies (10 μHz - 10 mHz) by applying wavelet methods to time-series data of voltage and current. However, if uncontrolled, other factors such as the shape of stimulating waveforms will mask much of this history effect, and thus in practice history may only matter on the scale of a few days. Nonetheless, results show that answering a simple question "what is my battery charge" does not have a simple physical answer, and thus producing a battery meter that does not lie remains a real challenge for theoretical physicists and mathematicians.