Stochastic spectral projection of electrochemical thermal model for lithium-ion cell state estimation

Abstract A novel approach for integrating a pseudo-two dimensional electrochemical thermal (P2D-ECT) model and data assimilation algorithm is presented for lithium-ion cell state estimation. This approach refrains from making any simplifications in the P2D-ECT model while making it amenable for online state estimation. Though deterministic, uncertainty in the initial states induces stochasticity in the P2D-ECT model. This stochasticity is resolved by spectrally projecting the stochastic P2D-ECT model on a set of orthogonal multivariate Hermite polynomials. Volume averaging in the stochastic dimensions is proposed for efficient numerical solution of the resultant model. A state estimation framework is developed using a transformation of the orthogonal basis to assimilate the measurables with this system of equations. Effectiveness of the proposed method is first demonstrated by assimilating the cell voltage and temperature data generated using a synthetic test bed. This validated method is used with the experimentally observed cell voltage and temperature data for state estimation at different operating conditions and drive cycle protocols. The results show increased prediction accuracy when the data is assimilated every 30s. High accuracy of the estimated states is exploited to infer temperature dependent behavior of the lithium-ion cell.

[1]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[2]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[3]  Chaoyang Wang,et al.  Control oriented 1D electrochemical model of lithium ion battery , 2007 .

[4]  T. A. Zang,et al.  Uncertainty Propagation for a Turbulent, Compressible Nozzle Flow Using Stochastic Methods , 2004 .

[5]  Marc Doyle,et al.  Mathematical Modeling of the Lithium Deposition Overcharge Reaction in Lithium‐Ion Batteries Using Carbon‐Based Negative Electrodes , 1999 .

[6]  Maxime Montaru,et al.  From a novel classification of the battery state of charge estimators toward a conception of an ideal one , 2015 .

[7]  Bhaskar Saha,et al.  Prognostics Methods for Battery Health Monitoring Using a Bayesian Framework , 2009, IEEE Transactions on Instrumentation and Measurement.

[8]  N. Wiener,et al.  Nonlinear Problems in Random Theory , 1964 .

[9]  Jay Lee,et al.  Review and recent advances in battery health monitoring and prognostics technologies for electric vehicle (EV) safety and mobility , 2014 .

[10]  John Red-Horse,et al.  Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach , 1999 .

[11]  Taejung Yeo,et al.  A physics based reduced order aging model for lithium-ion cells with phase change , 2014 .

[12]  Valerie H. Johnson,et al.  Battery performance models in ADVISOR , 2002 .

[13]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[14]  Xiaosong Hu,et al.  A comparative study of equivalent circuit models for Li-ion batteries , 2012 .

[15]  V. Senthil Kumar,et al.  Reduced order model for a lithium ion cell with uniform reaction rate approximation , 2013 .

[16]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[17]  Taejung Yeo,et al.  A reduced order electrochemical thermal model for lithium ion cells , 2015 .

[18]  Neil J. Gordon,et al.  A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking , 2002, IEEE Trans. Signal Process..

[19]  Gregory L. Plett.  Battery Management Systems , 2015 .

[20]  J. Newman,et al.  Heat‐Generation Rate and General Energy Balance for Insertion Battery Systems , 1997 .

[21]  N. Zabaras,et al.  Stochastic inverse heat conduction using a spectral approach , 2004 .

[22]  Taejung Yeo,et al.  Recursive Bayesian filtering framework for lithium-ion cell state estimation , 2016 .

[23]  D. Xiu,et al.  Modeling uncertainty in flow simulations via generalized polynomial chaos , 2003 .

[24]  John McPhee,et al.  A survey of mathematics-based equivalent-circuit and electrochemical battery models for hybrid and electric vehicle simulation , 2014 .

[25]  Ralph E. White,et al.  Online Estimation of the State of Charge of a Lithium Ion Cell , 2006 .

[26]  Stephen Duncan,et al.  Lithium-ion battery thermal-electrochemical model-based state estimation using orthogonal collocation and a modified extended Kalman filter , 2015, ArXiv.

[27]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[28]  Dean Patterson,et al.  Use of lithium-ion batteries in electric vehicles , 2000 .

[29]  M. Doyle,et al.  Modeling of Galvanostatic Charge and Discharge of the Lithium/Polymer/Insertion Cell , 1993 .

[30]  Min Chen,et al.  Accurate electrical battery model capable of predicting runtime and I-V performance , 2006, IEEE Transactions on Energy Conversion.

[31]  A. Jazwinski.  Stochastic Processes and Filtering Theory , 1970 .

[32]  Xiaodong Luo.  Recursive Bayesian Filters for Data Assimilation , 2009, 0911.5630.

[33]  Taejung Yeo,et al.  Bayesian calibration for electrochemical thermal model of lithium-ion cells , 2016 .

[34]  M. Doyle,et al.  Simulation and Optimization of the Dual Lithium Ion Insertion Cell , 1994 .

[35]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[36]  Cecilio Blanco Viejo,et al.  Support Vector Machines Used to Estimate the Battery State of Charge , 2013 .

[37]  Thomas A. Zang,et al.  Stochastic approaches to uncertainty quantification in CFD simulations , 2005, Numerical Algorithms.

[38]  Gan Ning,et al.  Cycle Life Modeling of Lithium-Ion Batteries , 2004 .

[39]  N. Wiener.  The Homogeneous Chaos , 1938 .

[40]  Ralph E. White,et al.  Single-Particle Model for a Lithium-Ion Cell: Thermal Behavior , 2011 .

[41]  Gregory L. Plett,et al.  Electrochemical state and internal variables estimation using a reduced-order physics-based model of a lithium-ion cell and an extended Kalman filter , 2015 .

[42]  S. Gunn.  Support Vector Machines for Classification and Regression , 1998 .

[43]  Dominic A. Notter,et al.  Contribution of Li-ion batteries to the environmental impact of electric vehicles. , 2010, Environmental science & technology.

[44]  Jianqiu Li,et al.  A review on the key issues for lithium-ion battery management in electric vehicles , 2013 .

[45]  Terry Hansen,et al.  Support vector based battery state of charge estimator , 2005 .

[46]  Habib N. Najm,et al.  Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics , 2009 .

[47]  Dongbin Xiu,et al.  A generalized polynomial chaos based ensemble Kalman filter with high accuracy , 2009, J. Comput. Phys..

[48]  Pol D. Spanos,et al.  Spectral Stochastic Finite-Element Formulation for Reliability Analysis , 1991 .

[49]  Christopher D. Rahn,et al.  Model-Based Electrochemical Estimation and Constraint Management for Pulse Operation of Lithium Ion Batteries , 2010, IEEE Transactions on Control Systems Technology.

[50]  Mohammad Farrokhi,et al.  State-of-Charge Estimation for Lithium-Ion Batteries Using Neural Networks and EKF , 2010, IEEE Transactions on Industrial Electronics.

[51]  Richard D. Braatz,et al.  Optimal Charging Profiles with Minimal Intercalation-Induced Stresses for Lithium-Ion Batteries Using Reformulated Pseudo 2-Dimensional Models , 2014 .

[52]  R. Ghanem,et al.  A stochastic projection method for fluid flow. I: basic formulation , 2001 .

[53]  Michael Pecht,et al.  A generic model-free approach for lithium-ion battery health management , 2014 .

[54]  Gregory L. Plett,et al.  Controls oriented reduced order modeling of lithium deposition on overcharge , 2012 .

[55]  George Em Karniadakis,et al.  Predictability and uncertainty in CFD , 2003 .

[56]  James L. Lee,et al.  Extended operating range for reduced-order model of lithium-ion cells , 2014 .

[57]  Ralph E. White,et al.  Review of Models for Predicting the Cycling Performance of Lithium Ion Batteries , 2006 .

[58]  Yanqing Shen,et al.  Adaptive online state-of-charge determination based on neuro-controller and neural network , 2010 .

[59]  Oliver G. Ernst,et al.  Analysis of the Ensemble and Polynomial Chaos Kalman Filters in Bayesian Inverse Problems , 2015, SIAM/ASA J. Uncertain. Quantification.

[60]  William H. Press,et al.  Numerical recipes in C (2nd ed.): the art of scientific computing , 1992 .