Effects of undercharge and internal loss on the rate dependence of battery charge storage efficiency

Battery charge efficiency across a range of input powers is an important performance parameter in variable charging systems. Here we use equivalent circuit theory to model the inherent trade-off between battery charging power and energy stored and compare our model to the existing Ragone model for discharge power and energy. An additional parameter is included to account for undercharge and underdischarge of the battery due to premature arrival at the battery's voltage limits. At a given power, energy efficiency is predicted to be higher for charging than discharging when only accounting for energy dissipated by internal resistance. We experimentally determine charge and discharge energy-power curves for lithium-ion batteries and find they exhibit a reduction in energy stored or withdrawn as power increases. We isolate the effects of undercharge and underdischarge from energy lost to internal resistance, and find the former outweighs the latter effect. Furthermore, the shallow shape of the voltage curve near the charge voltage cutoff results in a more limited range of charging powers than discharging powers. The model is expected to help inform operational parameters for battery charging for variable power sources.