Identifiability of generalised Randles circuit models

The Randles circuit (including a parallel resistor and capacitor in series with another resistor) and its generalised topology have widely been employed in electrochemical energy storage systems such as batteries, fuel cells and supercapacitors, also in biomedical engineering, for example, to model the electrode-tissue interface in electroencephalography and baroreceptor dynamics. This paper studies identifiability of generalised Randles circuit models, that is, whether the model parameters can be estimated uniquely from the input-output data. It is shown that generalised Randles circuit models are structurally locally identifiable. The condition that makes the model structure globally identifiable is then discussed. Finally, the estimation accuracy is evaluated through extensive simulations

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

Structural identifiability of equivalent circuit models for Li-Ion batteries

Structural identifiability is a critical aspect of modelling that has been overlooked in the vast majority of Li-ion battery modelling studies. It considers whether it is possible to obtain a unique solution for the unknown model parameters from experimental data. This is a fundamental prerequisite of the modelling process, especially when the parameters represent physical battery attributes and the proposed model is utilised to estimate them. Numerical estimates for unidentifiable parameters are effectively meaningless since unidentifiable parameters have an infinite number of possible numerical solutions. It is demonstrated that the physical phenomena assignment to a two-RC (resistor–capacitor) network equivalent circuit model (ECM) is not possible without additional information. Established methods to ascertain structural identifiability are applied to 12 ECMs covering the majority of model templates used previously. Seven ECMs are shown not to be uniquely identifiable, reducing the confidence in the accuracy of the parameter values obtained and highlighting the relevance of structural identifiability even for relatively simple models. Suggestions are proposed to make the models identifiable and, therefore, more valuable in battery management system applications. The detailed analyses illustrate the importance of structural identifiability prior to performing parameter estimation experiments, and the algebraic complications encountered even for simple models. View Full-Tex

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

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

Advanced Diagnostics for Lithium-ion Batteries: Decoding the Information in Electrode Swelling

Lithium-ion batteries exhibit mechanical expansion and contraction during cycling, consisting of a reversible intercalation-induced expansion and an irreversible expansion as the battery ages. Prior experimental studies have shown that mechanical expansion contains valuable information that correlates strongly with cell aging. However, a number of fundamental questions remain on the usability of the expansion measurement in practice. For example, it is necessary to determine whether the expansion measurements provide information that can help the estimation of the electrode state of health (eSOH), given limits on data availability and sensor noise in the field. Furthermore, the viability of using expansion for cell diagnostics also needs more investigation considering the broad range of aging conditions in real-world applications. This dissertation focuses on the experimental and modeling study of the expansion measurements during aging in order to assess its ability in helping battery diagnostics. To this end, mechanistic voltage and expansion models based on the underlying physics of phase transitions are developed. For the first time, the identifiability of eSOH parameters is explored by incorporating the expansion/force measurement. It is shown that the expansion measurements enhance the estimation of eSOH parameters, especially with a limited data window, since it has a better signal-to-noise ratio compared to the voltage. Moreover, the increased identifiability is closely related to the phase transitions in the electrodes. A long-term experimental aging study of the expansion of the graphite/NMC pouch cells is conducted under a variety of conditions such as temperature, charging rate, and depth of discharge. The goals here are to validate the results of the identifiability analysis and record the reversible and irreversible expansion correlated with capacity loss for informing the electrochemical models. Firstly, the advantages of the expansion concerning the eSOH identifiability are confirmed. Secondly, the results of the expansion evolution reveal that the features in the reversible expansion are an excellent indicator of health and, specifically, capacity retention. The expansion feature is robust to charge conditions. Namely, it is mostly insensitive to the hysteresis effects of the various initial state of charge, and it is detectable at higher C-rates up to 1C. Additionally, the expansion feature occurs near the half-charged point and therefore diagnostics can be performed more often during naturalistic use cases. Thus, the expansion measurement facilitates more frequent capacity checks in the field. Furthermore, an electrochemical and expansion model suitable for model-based estimation is developed. In particular, a multi-particle modeling approach for the graphite electrode is considered. It is demonstrated that the new model is able to capture the peak smoothing effect observed in the differential voltage at higher C-rates above C/2. Model parameters are identified using experimental data from the graphite/NMC pouch cell. The proposed model produces an excellent fit for the observed electric and mechanical swelling response of the cells and could enable physics-based data-driven degradation studies at practical charging rates. Finally, a fast-charging method based on the constant current constant voltage (CC-CV) charging scheme, called CC-CVησT (VEST), is developed. The new approach is simpler to implement and can be used with any model to impose varying levels of constraints on variables pertinent to degradation, such as plating potential and mechanical stress. The capabilities of the new CC-CVησT charging are demonstrated using the physics-based model developed in this dissertation.PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/169953/1/pmohtat_1.pd

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