Consumer electronics, wearable and personal health devices, power networks, microgrids, and hybrid electric vehicles (HEVs) are some of the many applications of lithium-ion batteries. Their optimal design and management are important for safe and profitable operations. The use of accurate mathematical models can help in achieving the best performance. This article provides a detailed description of a finite volume method (FVM) for a pseudo-two-dimensional (P2D) Li-ion battery model suitable for the development of model-based advanced battery management systems. The objectives of this work are to provide: (i) a detailed description of the model formulation, (ii) a parametrizable Matlab framework for battery design, simulation, and control of Li-ion cells or battery packs, (iii) a validation of the proposed numerical implementation with respect to the COMSOL MultiPhysics commercial software and the Newman's DUALFOIL code, and (iv) some demonstrative simulations involving thermal dynamics, a hybrid charge-discharge cycle emulating the throttle of an HEV, a model predictive control of state of charge, and a battery pack simulation. The increasing demand for portable devices (e.g., smartphones) and hybrid electric vehicles (HEVs) calls for the design and management of storage devices of high power density and reduced size and weight. During the many decades of research, different chemistries of batteries have been developed, such as Nickel Cadmium (NiCd), Nickel Metal Hydride (NiMH), Lead Acid and Lithium ion (Li-ion) and Lithium ion Polymer (Li-Poly) (e.g., see Refs. 1-4). Among electrochemical accumulators, Li-ion batteries provide one of the best tradeoff in terms of power density, low weight, cell voltage, and low self-discharge. 5 Mathematical models can support the design of new batteries as well as the development of new advanced battery management systems (ABMS). [6][7][8] According to the literature, mathematical models for Li-ion battery dynamics fall within two main categories: Equivalent Circuit Models (ECMs) and Electrochemical Models (EMs). ECMs use only electrical components to model the dynamic behavior of the battery. ECMs include (i) the R int model where only a resistance and a voltage source are used to model the battery, (ii) the RC model (introduced by the company SAFT 9 ) where capacitor dynamics have been added to the R int model, 10 and (iii) the Thevenin model, which is an extension of the RC model (e.g., see Refs. 11, 12 and references therein). In contrast, EMs explicitly represent the chemical processes that take place in the battery. While ECMs have the advantage of simplicity, EMs are more accurate due to their ability to describe detailed physical phenomena. 13 The most widely used EM in the literature is the porous electrode theory-based pseudo-two-dimensional (P2D) model, 14 which is described by a set of tightly coupled and highly nonlinear partial differential-algebraic equations (PDAEs). In order to exploit the model for simulation and design purposes, the set of PDAEs are reformu...

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A novel maximum likelihood solution to the problem of identifying parameters of a nonlinear model under missing observations is presented. If the observations are missing, then it is difficult to build a partial likelihood function consisting of only the available observations. Hence, an expectation-maximization (EM) algorithm, which uses the expected value of the complete log-likelihood function including the missing observations, is developed. The expected value of the complete log-likelihood (E-step) in the EM algorithm is approximated using particle filters and smoothers. New expressions for particle filters and smoothers under missing observations are derived. In order to reduce the variance on the smoothed states, a point-wise (as opposed to path-based) state estimation procedure is used. The maximization step (M-step) in the EM algorithm is performed using standard optimization routines. The proposed nonlinear identification approach is illustrated through numerical examples.On présente une nouvelle solution de vraisemblance maximum au problème d'identification des paramètres d'un modèle non linéaire avec des observations manquantes. Si des observations manquent, il est alors difficile d'établir une fonction de vraisemblance partielle seulement sur les observations disponibles. En conséquence, on a mis au point un algorithme de maximation des attentes (EM), qui utilise la valeur attendue de la fonction de vraisemblance logarithmique complète incluant les observations manquantes. La valeur attendue de la vraisemblance logarithmique complète (étape E) dans l'algorithme EM est approchéeà l'aide de filtres et d'algorithmes de lissage. De nouvelles expressions pour les filtres et les algorithmes de lissage avec des observations manquantes sont calculées. Afin de réduire la variance desétats lissés, on fait appelà une méthode d'estimation desétats ponctuels (par oppositionà une méthode basée sur les trajectoires). L'étape de maximisation (étape M) dans l'algorithme EM est réalisée au moyen de méthodes d'optimisation standards. La méthode d'identification non linéaire proposée est illustrée par des exemples numériques.

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Accurate capacity estimation is crucial for the reliable and safe operation of lithium-ion batteries. In particular, exploiting the relaxation voltage curve features could enable battery capacity estimation without additional cycling information. Here, we report the study of three datasets comprising 130 commercial lithium-ion cells cycled under various conditions to evaluate the capacity estimation approach. One dataset is collected for model building from batteries with LiNi0.86Co0.11Al0.03O2-based positive electrodes. The other two datasets, used for validation, are obtained from batteries with LiNi0.83Co0.11Mn0.07O2-based positive electrodes and batteries with the blend of Li(NiCoMn)O2 - Li(NiCoAl)O2 positive electrodes. Base models that use machine learning methods are employed to estimate the battery capacity using features derived from the relaxation voltage profiles. The best model achieves a root-mean-square error of 1.1% for the dataset used for the model building. A transfer learning model is then developed by adding a featured linear transformation to the base model. This extended model achieves a root-mean-square error of less than 1.7% on the datasets used for the model validation, indicating the successful applicability of the capacity estimation approach utilizing cell voltage relaxation.