State-space representation of Li-ion battery porous electrode impedance model with balanced model reduction

Abstract This paper presents an approximate time-domain solution for physics-based electrochemical lithium-ion cell battery models. The time-domain solution is represented in state-space form and can be easily used for the design of a state estimator or controller. It uses an interconnection-of-system approach to derive a state-space representation of a battery impedance model and provides a reduced order model based via the balanced truncation method. Simulation results are also provided to show the performance of the proposed model in the frequency domain.

[1]  Bruce A. Francis,et al.  Feedback Control Theory , 1992 .

[2]  J. Newman,et al.  Double‐Layer Capacitance in a Dual Lithium Ion Insertion Cell , 1999 .

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

[4]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[5]  Jasim Ahmed,et al.  Algorithms for Advanced Battery-Management Systems , 2010, IEEE Control Systems.

[6]  Chaoyang Wang,et al.  Solid-state diffusion limitations on pulse operation of a lithium ion cell for hybrid electric vehicles , 2006 .

[7]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[8]  Georg Brasseur,et al.  Modeling of high power automotive batteries by the use of an automated test system , 2003, IEEE Trans. Instrum. Meas..

[9]  Ralph E. White,et al.  An approximate solution for solid-phase diffusion in a spherical particle in physics-based Li-ion cell models , 2012 .

[10]  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.

[11]  Andrew Chemistruck,et al.  One-dimensional physics-based reduced-order model of lithium-ion dynamics , 2012 .

[12]  T. Jacobsen,et al.  Diffusion impedance in planar, cylindrical and spherical symmetry , 1995 .

[13]  James L. Lee,et al.  Discrete-time realization of transcendental impedance models, with application to modeling spherical solid diffusion , 2012 .

[14]  Ralph E. White,et al.  Reduction of Model Order Based on Proper Orthogonal Decomposition for Lithium-Ion Battery Simulations , 2009 .

[15]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[16]  M. Verbrugge,et al.  Electrochemical and Thermal Characterization of Battery Modules Commensurate with Electric Vehicle Integration , 2002 .

[17]  B. Moore.  Principal component analysis in linear systems: Controllability, observability, and model reduction , 1981 .

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

[19]  Ian Postlethwaite,et al.  Multivariable Feedback Control: Analysis and Design , 1996 .

[20]  K.A. Smith,et al.  Electrochemical Control of Lithium-Ion Batteries [Applications of Control] , 2010, IEEE Control Systems.

[21]  John McPhee,et al.  Simplification and order reduction of lithium-ion battery model based on porous-electrode theory , 2012 .

[22]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .

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