Modeling and Identification of Li-ion Cells

To develop a full battery model in view to accurate battery management, Li-ion cell dynamics is modelled by a capacitor in series with a simplified Randles circuit. The open circuit voltage is the voltage at the capacitor terminals, allowing, in this way, for the dependence of the open circuit voltage on the state-of-charge to be embedded in its capacitance. The Randles circuit is recognised as a trusty description of a cell dynamics. It contains a semi-integrator of the current, known as the Warburg impedance, that is a special case of a fractional integrator. To enable the formulation of a time-domain system identification algorithm, the Warburg impedance impulse response was calculated and normalised, in order to derive a finite order state-space approximation, using the Ho-Kalman algorithm. Thus, this Warburg impedance LTI model, with known parameters (normalised impedance) in series with a gain block, is suitable for system identification, since it has only one unknown parameter. A LTI System identification Algorithm was formulated to estimate the model parameters and the initial values of both the open circuit voltage and the states of the normalised Warburg impedance. The performance of the algorithm was very satisfactory on the whole state-of-charge region and when compared with low order Thévenin models. Once it is understood the parameters variability on the state-of-charge, temperature and ageing, we envisage to continue the work using parameter-varying algorithms.