Observer design for an electrochemical model of lithium ion batteries based on a polytopic approach

International audienceSmart battery management systems require reliable state information, which is unavailable through direct measurements. Electrochemical models are relevant in this context as these describe the internal phenomena, which govern the battery. These models can thus be used to design observers and hence to estimate the state variables on-line. We propose an electrochemical model of a lithium ion battery given by a set of ordinary differential equations built from the spatial discretisation of partial differential equations that locally describe mass and charge transport of the lithium. We then design an observer and analyse its stability via a polytopic approach, which relies on the satisfaction of linear matrix inequalities. The latter are shown to be verified for standard model parameters values. Simulation results on the original infinite-dimensional model are presented, which show the good performance of the observer

Modelling and estimation in lithium-ion batteries: a literature review

Lithium-ion batteries are widely recognised as the leading technology for electrochemical energy storage. Their applications in the automotive industry and integration with renewable energy grids highlight their current significance and anticipate their substantial future impact. However, battery management systems, which are in charge of the monitoring and control of batteries, need to consider several states, like the state of charge and the state of health, which cannot be directly measured. To estimate these indicators, algorithms utilising mathematical models of the battery and basic measurements like voltage, current or temperature are employed. This review focuses on a comprehensive examination of various models, from complex but close to the physicochemical phenomena to computationally simpler but ignorant of the physics; the estimation problem and a formal basis for the development of algorithms; and algorithms used in Li-ion battery monitoring. The objective is to provide a practical guide that elucidates the different models and helps to navigate the different existing estimation techniques, simplifying the process for the development of new Li-ion battery applications.This research received support from the Spanish Ministry of Science and Innovation under projects MAFALDA (PID2021-126001OB-C31 funded by MCIN/AEI/10.13039/501100011033/ ERDF,EU) and MASHED (TED2021-129927B-I00), and by FI Joan Oró grant (code 2023 FI-1 00827), cofinanced by the European Union.Peer ReviewedPostprint (published version

Identifiability and parameter estimation of the single particle lithium-ion battery model

This paper investigates the identifiability and estimation of the parameters of the single particle model (SPM) for lithium-ion battery simulation. Identifiability is addressed both in principle and in practice. The approach begins by grouping parameters and partially non-dimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that, excluding open circuit voltage, there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearised SPM is unique. It is found that the model is unique provided that the electrode open circuit voltage functions have a known non-zero gradient, the parameters are ordered, and the electrode kinetics are lumped into a single charge transfer resistance parameter. We then demonstrate the practical estimation of model parameters from measured frequency-domain experimental electrochemical impedance spectroscopy (EIS) data, and show additionally that the parametrised model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between model and experiment over a 10 minute dynamic discharge.Comment: 16 pages, 9 figures, pre-print submitted to the IEEE Transactions on Control Systems Technolog

State of Charge Estimation of Parallel Connected Battery Cells via Descriptor System Theory

This manuscript presents an algorithm for individual Lithium-ion (Li-ion) battery cell state of charge (SOC) estimation when multiple cells are connected in parallel, using only terminal voltage and total current measurements. For battery packs consisting of thousands of cells, it is desirable to estimate individual SOCs by only monitoring the total current in order to reduce sensing cost. Mathematically, series connected cells yield dynamics given by ordinary differential equations under classical full voltage sensing. In contrast, parallel connected cells are evidently more challenging because the dynamics are governed by a nonlinear descriptor system, including differential equations and algebraic equations arising from voltage and current balance across cells. An observer with linear output error injection is formulated, where the individual cell SOCs and local currents are locally observable from the total current and voltage measurements. The asymptotic convergence of differential and algebraic states is established by considering local Lipschitz continuity property of system nonlinearities. Simulation results on LiNiMnCoO$_2$/Graphite (NMC) cells illustrate convergence for SOCs, local currents, and terminal voltage.Comment: 7 pages, 4 figures, 1 table, accepted by 2020 American Control Conferenc

A review of fractional-order techniques applied to lithium-ion batteries, lead-acid batteries, and supercapacitors

Electrochemical energy storage systems play an important role in diverse applications, such as electrified transportation and integration of renewable energy with the electrical grid. To facilitate model-based management for extracting full system potentials, proper mathematical models are imperative. Due to extra degrees of freedom brought by differentiation derivatives, fractional-order models may be able to better describe the dynamic behaviors of electrochemical systems. This paper provides a critical overview of fractional-order techniques for managing lithium-ion batteries, lead-acid batteries, and supercapacitors. Starting with the basic concepts and technical tools from fractional-order calculus, the modeling principles for these energy systems are presented by identifying disperse dynamic processes and using electrochemical impedance spectroscopy. Available battery/supercapacitor models are comprehensively reviewed, and the advantages of fractional types are discussed. Two case studies demonstrate the accuracy and computational efficiency of fractional-order models. These models offer 15–30% higher accuracy than their integer-order analogues, but have reasonable complexity. Consequently, fractional-order models can be good candidates for the development of advanced b attery/supercapacitor management systems. Finally, the main technical challenges facing electrochemical energy storage system modeling, state estimation, and control in the fractional-order domain, as well as future research directions, are highlighted

Advances in Batteries, Battery Modeling, Battery Management System, Battery Thermal Management, SOC, SOH, and Charge/Discharge Characteristics in EV Applications

The second-generation hybrid and Electric Vehicles are currently leading the paradigm shift in the automobile industry, replacing conventional diesel and gasoline-powered vehicles. The Battery Management System is crucial in these electric vehicles and also essential for renewable energy storage systems. This review paper focuses on batteries and addresses concerns, difficulties, and solutions associated with them. It explores key technologies of Battery Management System, including battery modeling, state estimation, and battery charging. A thorough analysis of numerous battery models, including electric, thermal, and electro-thermal models, is provided in the article. Additionally, it surveys battery state estimations for a charge and health. Furthermore, the different battery charging approaches and optimization methods are discussed. The Battery Management System performs a wide range of tasks, including as monitoring voltage and current, estimating charge and discharge, equalizing and protecting the battery, managing temperature conditions, and managing battery data. It also looks at various cell balancing circuit types, current and voltage stressors, control reliability, power loss, efficiency, as well as their advantages and disadvantages. The paper also discusses research gaps in battery management systems.publishedVersio

A cell-in-the-loop approach to systems modelling and simulation of energy storage systems

This research is aligned with the engineering challenge of scaling-up individual battery cells into a complete energy storage system (ESS). Manufacturing tolerances, coupled with thermal gradients and the differential electrical loading of adjacent cells, can result in significant variations in the rate of cell degradation, energy distribution and ESS performance. The uncertain transition from cell to system often manifests itself in over-engineered, non-optimal ESS designs within both the transport and energy sectors. To alleviate these issues, the authors propose a novel model-based framework for cell-in-the-loop simulation (CILS) in which a physical cell may be integrated within a complete model of an ESS and exercised against realistic electrical and thermal loads in real-time. This paper focuses on the electrical integration of both real and simulated cells within the CILS test environment. Validation of the CILS approach using real-world electric vehicle data is presented for an 18650 cell. The cell is integrated within a real-time simulation model of a series string of similar cells in a 4sp1 configuration. Results are presented that highlight the impact of cell variability (i.e., capacity and impedance) on the energy available from the multi-cell system and the useable capacity of the physical cell

On-chip implementation of Extended Kalman Filter for adaptive battery states monitoring

This paper reports the development and implementation of an adaptive lithium-ion battery monitoring system. The monitoring algorithm is based on the nonlinear Dual Extended Kalman Filter (DEKF), which allows for simultaneous states and parameters estimation. The hardware platform consists of an ARM cortex-M0 processor with six embedded analogue-to-digital converters (ADCs) for data acquisition. Two definitions for online state-of-health (SOH) characterisation are presented; one energy-based and one power-based. Moreover, a method for online estimation of battery's capacity, which is used in SOH characterisation is proposed. Two definitions for state-of-power (SOP) are adopted. Despite the presence of large sensor noise and incorrect filter initialisation, the DEKF algorithm poses excellent SOC and SOP tracking capabilities during a dynamic discharge test. The SOH prediction results are also in good agreement with actual measurements