Embedded real-time fractional-order equivalent circuit model for internal resistance estimation of lithium-ion cells

This paper introduces a new on-board capable method for model-based estimation of the internal resistance of lithium-ion cells. The method relates to a fractional-order electrical Equivalent-Circuit-Model (ECM) consisting of ohmic resistances, ZARC and Warburg elements. Based on a Begin-of-Life (BOL) model parameterization by means of Electrochemical-Impedance-Spectroscopy (EIS), a subset of the model parameters is tracked offline over cell aging to generate End-of-Life (EOL) model parameters, using time domain measurements and a nonlinear optimization routine. The model parameters over lifetime are trained in quadratic polynomials for on-board application on the Battery-Management-System (BMS). The on-board aging estimation uses filtering algorithms and feedback control of the difference between the measured and calculated cell voltages during dynamical driving. An embedded real-time implementation, combining float-and fixed-point arithmetic, is carried out for a state-of-the-art BMS. Validation tests using a vehicle with an aged battery containing 108 cells confirm fast and stable convergence of all cell's State-of-Health-Resistance (SOHR). The SOHR estimation convergence is reached within at most one hour of dynamical driving with an estimation error under 3.5 %. Furthermore, a proposed model-based Open-Circuit-Voltage (OCV) estimation is validated with relaxation experiments, confirming an estimation error of less than 1 mV.