A Padé Approximate Model of Lithium Ion Batteries

Ngoc Tham Tran,San Shing Choi,Yang Li,Mahinda Vilathgamuwa,Troy Farrell,Joseph Teague

doi:10.1149/2.0651807jes

Ngoc Tham Tran, San Shing Choi + Show 4 more

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https://doi.org/10.1149/2.0651807jes

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Abstract

We present a reduced order model for a lithium ion battery in which Padé approximants are used to simplify complex, transcendental, transfer functions associated with the linearized, pseudo 2-dimensional (P2D) electrochemical model of the battery. The resulting transfer functions take the form of simple, rational polynomial functions, which can be used to compute any variable at any location within a one-dimensional representation of the battery domain. Corrections for nonlinear behavior are also incorporated into the reduced model. The results obtained using the reduced model compare favorably to those from the full (nonlinear) P2D model and the computational time required to produce these results is significantly reduced. Importantly, the form of the reduced model means that variables can be evaluated at specific discrete locations within the cell domain, without the need to compute all values of the variable at all discrete locations, as is the case with the spatial discretization methods most commonly used to implement the P2D model. We show that this results in further significant time savings and enhances the suitability of the model for variety of applications.

Highlights

Lithium ion batteries are commonly used for large renewable energy storage systems, as either as part of the power grid or in stand-alone installations.[1]
These transfer functions describe the electrochemical dynamics of the lithium ion battery and the corrections for nonlinear behavior are used to improve the accuracy of the linearized pseudo 2-dimensional (P2D) model.[5]
We presented a reduced order model for a lithium ion battery in which Padeapproximants were used to simplify complex, transcendental, transfer functions associated with the linearized, pseudo 2-dimensional (P2D) electrochemical model of the battery

Summary

A Pade Approximate Model of Lithium Ion Batteries

Ngoc Tham Tran, 1,∗,z Mahinda Vilathgamuwa,[1] Troy Farrell, 2 San Shing Choi,[1] Yang Li,[1] and Joseph Teague[2]. We propose an improvement to the previous SPM and extended SPM Padeapproximation models discussed above To do this we consider the transcendental transfer functions of the linearized P2D model and the corresponding corrections for nonlinear behavior given by Lee, Chemistruck and Plett.[5] These transfer functions describe the electrochemical dynamics of the lithium ion battery and the corrections for nonlinear behavior are used to improve the accuracy of the linearized P2D model.[5] We apply Padeapproximations to these complicated transcendental transfer functions in order to develop simpler, rational polynomial transfer functions, which form a reduced model of cell operation that is amenable to rapid computation and embedded BMS applications. J neg (z, s) Iapp (s) νneg (s) asneg F ALneg κnefefg + σenfefg σenfefg cosh (νneg (s) z) + κnefefg cosh (νneg (s) (z − 1)) . sinh (νneg (s))

F Rcnteg

Results and Discussion

Conclusions