A Phenomenological Model of Bulk Force in a Li-Ion Battery Pack and Its Application to State of Charge Estimation

A phenomenological model of the bulk force exerted by a lithium ion cell during various charge, discharge, and temperature operating conditions is developed. The measured and modeled force resembles the carbon expansion behavior associated with the phase changes during intercalation, as there are ranges of state of charge (SOC) with a gradual force increase and ranges of SOC with very small change in force. The model includes the influence of temperature on the observed force capturing the underlying thermal expansion phenomena. Moreover the model is capable of describing the changes in force during thermal transients, when internal battery heating due to high C-rates or rapid changes in the ambient temperature, which create a mismatch in the temperature of the cell and the holding fixture. It is finally shown that the bulk force model can be very useful for a more accurate and robust SOC estimation based on fusing information from voltage and force (or pressure) measurements.