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.

I. Introduction

As the major industrialised nations are becoming more concerned about global warming and fossil fuel depletion, they outline their plans for electric vehicles (EV) development and production in detriment of combustion engines. Battery technology has been one of the bottlenecks in EV, making the research on battery management systems (BMS) extremely important, especially for the battery state-of-charge (SoC) estimation — the current capacity of a battery expressed as a percentage of the fully-charged capacity. Factors that mainly affect battery SoC are: charge/discharge rate and times, polarisation effect, temperature, self-discharge or battery ageing. In fact, batteries are very complex due to their strong time-varying and non-linear properties, what makes the accurate estimate of SoC a challenging task. During the last years EV powered by lithium batteries have become popular since significant improvements in energy density and power capability have made Li-ion batteries [4], [19] the preferred solution for nowadays low carbon mobility. The change in behaviour of the batteries throughout a vehicle lifetime can have a significant detrimental effect on the whole vehicle performance and existence. Thence, exploring the causes of battery ageing, as well as developing mitigation strategies to avoid premature degradation becomes of paramount importance to vehicle manufacturers. In [24] various representative patents and papers related to SoC estimation methods for an electric vehicle battery are reviewed. According to their theoretical and experimental characteristics, the estimation methods were divided into traditional, based on battery experiments, and modern, based on control theory, especially intelligent algorithms.