To achieve an accurate estimate of losses in a battery it is necessary to consider the reversible entropic losses, which may constitute more than 20% of the peak total loss. In this work, a procedure for experimentally determining the entropic heating coefficient of a lithium-ion battery cell is developed. The entropic heating coefficient is the rate of change of the cell’s open-circuit voltage (OCV) with respect to temperature; it is a function of state-of-charge (SOC) and temperature and is often expressed in mV/K. The total cell losses are the sum of the reversible and irreversible losses, where reversible losses are the product of current and the entropic heating coefficient and irreversible losses consist of ohmic electrode losses, ion transport losses, and other irreversible chemical reactions.
The entropic heating coefficient is determined by exposing the cell to a range of temperatures at each SOC value of interest. The OCV is recorded at each combination of SOC and temperature, and ∂OCV/∂T is calculated from the measurements. Since a ∆T of 20℃ may result in a ∆OCV of 100µV or less, it is critical to have a high accuracy and high input impedance voltage sensor. Additionally, the measurement is sensitive to self-discharge, relaxation of the battery terminal voltage, and the amount of time spent soaking at each test point. A test methodology is developed which achieves an accurate OCV measurement, corrects for self-discharge and relaxation, and utilizes the minimum necessary soak time, resulting in a high-quality measurement without excessive testing time.
Once determined experimentally, the entropic heating coefficient map is used to model losses during several charges with rates from 1C to 5C, and the results are compared with a constant current loss model derived from experimental data for a lithium nickel manganese cobalt oxide (NMC) cell.