Reduced Order Impedance Models of Lithium Ion Batteries

This paper develops reduced order, linear models of lithium ion batteries that can be used for model-based power train simulation, design, estimation, and controlling in hybrid and electric vehicles (HEV). First, a reduced order model is derived from the fundamental governing electrochemical charge and Li⁺ conservation equations that are linearized at the operating state of charge and low current density. The equations are solved using analytical and numerical techniques to produce the transcendental impedance or transfer function from input current to output voltage. This model is then reduced to a low order state space model using a system identification technique based on least squares optimization. Given the prescribed current, the model predicts voltage and other variables such as electrolyte and electrode surface concentration distributions. The second model is developed by neglecting electrolyte diffusion and modeling each electrode with a single active material particle. The transcendental particle transfer functions are discretized using a Padé Approximation. The explicit form of the single particle model impedance can be realized by an equivalent circuit with resistances and capacitances related to the cell parameters. Both models are then tuned to match experimental electrochemical impedance spectroscopy (EIS) and pulse current-voltage data.