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

Global Sensitivity Methods for Design of Experiments in Lithium-ion Battery Context

Battery management systems may rely on mathematical models to provide higher performance than standard charging protocols. Electrochemical models allow us to capture the phenomena occurring inside a lithium-ion cell and therefore, could be the best model choice. However, to be of practical value, they require reliable model parameters. Uncertainty quantification and optimal experimental design concepts are essential tools for identifying systems and estimating parameters precisely. Approximation errors in uncertainty quantification result in sub-optimal experimental designs and consequently, less-informative data, and higher parameter unreliability. In this work, we propose a highly efficient design of experiment method based on global parameter sensitivities. This novel concept is applied to the single-particle model with electrolyte and thermal dynamics (SPMeT), a well-known electrochemical model for lithium-ion cells. The proposed method avoids the simplifying assumption of output-parameter linearization (i.e., local parameter sensitivities) used in conventional Fisher information matrix-based experimental design strategies. Thus, the optimized current input profile results in experimental data of higher information content and in turn, in more precise parameter estimates.Comment: Accepted for 21st IFAC World Congres

Optimal design of experiments for a lithium-ion cell: parameters identification of an isothermal single particle model with electrolyte dynamics

Advanced battery management systems rely on mathematical models to guarantee optimal functioning of Lithium-ion batteries. The Pseudo-Two Dimensional (P2D) model is a very detailed electrochemical model suitable for simulations. On the other side, its complexity prevents its usage in control and state estimation. Therefore, it is more appropriate the use of simplified electrochemical models such as the Single Particle Model with electrolyte dynamics (SPMe), which exhibits good adherence to real data when suitably calibrated. This work focuses on a Fisher-based optimal experimental design for identifying the SPMe parameters. The proposed approach relies on a nonlinear optimization to minimize the covariance parameters matrix. At first, the parameters are estimated by considering the SPMe as the real plant. Subsequently, a more realistic scenario is considered where the P2D model is used to reproduce a real battery behavior. Results show the effectiveness of the optimal experimental design when compared to standard strategies.Comment: Published in Ind. Eng. Chem. Res. 2019, 58, 3, 1286-129

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

Nonlinear electrochemical impedance spectroscopy for lithium-ion battery model parameterization

In this work we analyse the local nonlinear electrochemical impedance spectroscopy (NLEIS) response of a lithium-ion battery and estimate model parameters from measured NLEIS data. The analysis assumes a single-particle model including nonlinear diffusion of lithium within the electrode particles and asymmetric charge transfer kinetics at their surface. Based on this model and assuming a moderately-small excitation amplitude, we systematically derive analytical formulae for the impedances up to the second harmonic response, allowing the meaningful interpretation of each contribution in terms of physical processes and nonlinearities in the model. The implications of this for parameterization are explored, including structural identifiability analysis and parameter estimation using maximum likelihood, with both synthetic and experimentally measured impedance data. Accurate fits to impedance data are possible, however inconsistencies in the fitted diffusion timescales suggest that a nonlinear diffusion model may not be appropriate for the cells considered. Model validation is also demonstrated by predicting time-domain voltage response using the parameterized model and this is shown to have excellent agreement with measured voltage time-series data (11.1 mV RMSE).Comment: 40 pages (excluding supplementary material). Submitted to the Journal of the Electrochemical Societ

One-Shot Parameter Identification of the Thevenin's Model for Batteries: Methods and Validation

Parameter estimation is of foundational importance for various model-based battery management tasks, including charging control, state-of-charge estimation and aging assessment. However, it remains a challenging issue as the existing methods generally depend on cumbersome and time-consuming procedures to extract battery parameters from data. Departing from the literature, this paper sets the unique aim of identifying all the parameters offline in a one-shot procedure, including the resistance and capacitance parameters and the parameters in the parameterized function mapping from the state-of-charge to the open-circuit voltage. Considering the well-known Thevenin's battery model, the study begins with the parameter identifiability analysis, showing that all the parameters are locally identifiable. Then, it formulates the parameter identification problem in a prediction-error-minimization framework. As the non-convexity intrinsic to the problem may lead to physically meaningless estimates, two methods are developed to overcome this issue. The first one is to constrain the parameter search within a reasonable space by setting parameter bounds, and the other adopts regularization of the cost function using prior parameter guess. The proposed identifiability analysis and identification methods are extensively validated through simulations and experiments

Detection and Isolation of Small Faults in Lithium-Ion Batteries via the Asymptotic Local Approach

This contribution presents a diagnosis scheme for batteries to detect and isolate internal faults in the form of small parameter changes. This scheme is based on an electrochemical reduced-order model of the battery, which allows the inclusion of physically meaningful faults that might affect the battery performance. The sensitivity properties of the model are analyzed. The model is then used to compute residuals based on an unscented Kalman filter. Primary residuals and a limiting covariance matrix are obtained thanks to the local approach, allowing for fault detection and isolation by chi-squared statistical tests. Results show that faults resulting in limited 0.15% capacity and 0.004% power fade can be effectively detected by the local approach. The algorithm is also able to correctly isolate faults related with sensitive parameters, whereas parameters with low sensitivity or linearly correlated are more difficult to precise.Comment: 8 pages, 2 figures, 3 tables, conferenc