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

Accuracy versus simplicity in online battery model identification

This paper presents a framework for battery modeling in online, real-time applications where accuracy is important but speed is the key. The framework allows users to select model structures with the smallest number of parameters that is consistent with the accuracy requirements of the target application. The tradeoff between accuracy and speed in a battery model identification process is explored using different model structures and parameter-fitting algorithms. Pareto optimal sets are obtained, allowing a designer to select an appropriate compromise between accuracy and speed. In order to get a clearer understanding of the battery model identification problem, “identification surfaces” are presented. As an outcome of the battery identification surfaces, a new analytical solution is derived for battery model identification using a closed-form formula to obtain a battery’s ohmic resistance and open circuit voltage from measurement data. This analytical solution is used as a benchmark for comparison of other fitting algorithms and it is also used in its own right in a practical scenario for state-of-charge estimation. A simulation study is performed to demonstrate the effectiveness of the proposed framework and the simulation results are verified by conducting experimental tests on a small NiMH battery pack

On-board monitoring of 2-D spatially-resolved temperatures in cylindrical lithium-ion batteries: Part II. State estimation via impedance-based temperature sensing

Impedance-based temperature detection (ITD) is a promising approach for rapid estimation of internal cell temperature based on the correlation between temperature and electrochemical impedance. Previously, ITD was used as part of an Extended Kalman Filter (EKF) state-estimator in conjunction with a thermal model to enable estimation of the 1-D temperature distribution of a cylindrical lithium-ion battery. Here, we extend this method to enable estimation of the 2-D temperature field of a battery with temperature gradients in both the radial and axial directions. An EKF using a parameterised 2-D spectral-Galerkin model with ITD measurement input (the imaginary part of the impedance at 215 Hz) is shown to accurately predict the core temperature and multiple surface temperatures of a 32113 LiFePO$_4$ cell, using current excitation profiles based on an Artemis HEV drive cycle. The method is validated experimentally on a cell fitted with a heat sink and asymmetrically cooled via forced air convection. A novel approach to impedance-temperature calibration is also presented, which uses data from a single drive cycle, rather than measurements at multiple uniform cell temperatures as in previous studies. This greatly reduces the time required for calibration, since it overcomes the need for repeated cell thermal equalization.Comment: 11 pages, 8 figures, submitted to the Journal of Power Source

Model Reduction for Multiscale Lithium-Ion Battery Simulation

In this contribution we are concerned with efficient model reduction for multiscale problems arising in lithium-ion battery modeling with spatially resolved porous electrodes. We present new results on the application of the reduced basis method to the resulting instationary 3D battery model that involves strong non-linearities due to Buttler-Volmer kinetics. Empirical operator interpolation is used to efficiently deal with this issue. Furthermore, we present the localized reduced basis multiscale method for parabolic problems applied to a thermal model of batteries with resolved porous electrodes. Numerical experiments are given that demonstrate the reduction capabilities of the presented approaches for these real world applications

Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter

This paper investigates the state estimation of a high-fidelity spatially resolved thermal- electrochemical lithium-ion battery model commonly referred to as the pseudo two-dimensional model. The partial-differential algebraic equations (PDAEs) constituting the model are spatially discretised using Chebyshev orthogonal collocation enabling fast and accurate simulations up to high C-rates. This implementation of the pseudo-2D model is then used in combination with an extended Kalman filter algorithm for differential-algebraic equations to estimate the states of the model. The state estimation algorithm is able to rapidly recover the model states from current, voltage and temperature measurements. Results show that the error on the state estimate falls below 1 % in less than 200 s despite a 30 % error on battery initial state-of-charge and additive measurement noise with 10 mV and 0.5 K standard deviations.Comment: Submitted to the Journal of Power Source

Global sensitivity analysis of the single particle lithium-ion battery model with electrolyte

The importance of global sensitivity analysis (GSA) has been well established in many scientific areas. However, despite its critical role in evaluating a model’s plausibility and relevance, most lithium ion battery models are published without any sensitivity analysis. In order to improve the lifetime performance of battery packs, researchers are investigating the application of physics based electrochemical models, such as the single particle model with electrolyte (SPMe). This is a challenging research area from both the parameter estimation and modelling perspective. One key challenge is the number of unknown parameters: the SPMe contains 31 parameters, many of which are themselves non-linear functions of other parameters. As such, relatively few authors have tackled this parameter estimation problem. This is exacerbated because there are no GSAs of the SPMe which have been published previously. This article addresses this gap in the literature and identifies the most sensitive parameter, preventing time being wasted on refining parameters which the output is insensitive to

Advanced Battery Technologies: New Applications and Management Systems

In recent years, lithium-ion batteries (LIBs) have been increasingly contributing to the development of novel engineering systems with energy storage requirements. LIBs are playing an essential role in our society, as they are being used in a wide variety of applications, ranging from consumer electronics, electric mobility, renewable energy storage, biomedical applications, or aerospace systems. Despite the remarkable achievements and applicability of LIBs, there are several features within this technology that require further research and improvements. In this book, a collection of 10 original research papers addresses some of those key features, including: battery testing methodologies, state of charge and state of health monitoring, and system-level power electronics applications. One key aspect to emphasize when it comes to this book is the multidisciplinary nature of the selected papers. The presented research was developed at university departments, institutes and organizations of different disciplines, including Electrical Engineering, Control Engineering, Computer Science or Material Science, to name a few examples. The overall result is a book that represents a coherent collection of multidisciplinary works within the prominent field of LIBs

SoC estimation for lithium-ion batteries : review and future challenges

ABSTRACT: Energy storage emerged as a top concern for the modern cities, and the choice of the lithium-ion chemistry battery technology as an effective solution for storage applications proved to be a highly efficient option. State of charge (SoC) represents the available battery capacity and is one of the most important states that need to be monitored to optimize the performance and extend the lifetime of batteries. This review summarizes the methods for SoC estimation for lithium-ion batteries (LiBs). The SoC estimation methods are presented focusing on the description of the techniques and the elaboration of their weaknesses for the use in on-line battery management systems (BMS) applications. SoC estimation is a challenging task hindered by considerable changes in battery characteristics over its lifetime due to aging and to the distinct nonlinear behavior. This has led scholars to propose different methods that clearly raised the challenge of establishing a relationship between the accuracy and robustness of the methods, and their low complexity to be implemented. This paper publishes an exhaustive review of the works presented during the last five years, where the tendency of the estimation techniques has been oriented toward a mixture of probabilistic techniques and some artificial intelligence