Abstract

The paper characterizes dynamics and modelling of a Lithium-ion battery. Theoretical formulation and literature review are combined to derive the necessary battery characterization. The three main dynamics for modeling the battery are: direct-current electrical equivalent circuit, state-ofcharge (SOC) and thermal dynamic. Furthermore, the capacity fade caused by degradation is considered as a fourth dynamic. Degradation is considered as the sum of calendar aging and cycling loss dynamics. The modeling procedure has general validity and can be used for different battery chemistries by changing specific parameters. The model is tailored for a 40 kWh Lithium Nickel Manganese Cobalt (NMC) Oxide battery, which is currently used in the Nissan LEAF 2018. Considering a user driving 45 km/day and the temperature of the years 2017 and 2018 in Denmark, the battery capacity fade is found to be between 2 and 5% of the battery capacity after two years of use."br/"Degradation is highly dependent on the average level of SOC during the years.

Abstract

This paper presents an efficient method for estimating capacity-fade uncertainty in lithium-ion batteries (LIBs) in order to integrate them into the battery-management system (BMS) of electric vehicles, which requires simple and inexpensive computation for successful application. The study uses the pseudo-two-dimensional (P2D) electrochemical model, which simulates the battery state by solving a system of coupled nonlinear partial differential equations (PDEs). The model parameters that are responsible for electrode degradation are identified and estimated, based on battery data obtained from the charge cycles. The Bayesian approach, with parameters estimated by probability distributions, is employed to account for uncertainties arising in the model and battery data. The Markov Chain Monte Carlo (MCMC) technique is used to draw samples from the distributions. The complex computations that solve a PDE system for each sample are avoided by employing a polynomial-based metamodel. As a result, the computational cost is reduced from 5.5 h to a few seconds, enabling the integration of the method into the vehicle BMS. Using this approach, the conservative bound of capacity fade can be determined for the vehicle in service, which represents the safety margin reflecting the uncertainty. Document type: Article