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Comparing Mass-Preserving Numerical Methods for the Lithium-Ion Battery Single Particle Model

Joseph N. E. Lucero, Le Xu, Simona Onori

Abstract

The single particle model (SPM) is a reduced electrochemical model that holds promise for applications in battery management systems due to its ability to accurately capture battery dynamics; however, the numerical discretization of the SPM requires careful consideration to ensure numerical stability and accuracy. In this paper, we present a comparative study of two mass-preserving numerical schemes for the SPM: the finite volume method and the control volume method. Using numerical simulations, we systematically evaluate the performance of these schemes, after independently calibrating the SPM discretized with each scheme to experimental data, and find a tradeoff between accuracy (quantified by voltage root-mean-square error) and computational time. Our findings provide insights into the selection of numerical schemes for the SPM, contributing to the advancement of battery modeling and simulation techniques.

Comparing Mass-Preserving Numerical Methods for the Lithium-Ion Battery Single Particle Model

Abstract

The single particle model (SPM) is a reduced electrochemical model that holds promise for applications in battery management systems due to its ability to accurately capture battery dynamics; however, the numerical discretization of the SPM requires careful consideration to ensure numerical stability and accuracy. In this paper, we present a comparative study of two mass-preserving numerical schemes for the SPM: the finite volume method and the control volume method. Using numerical simulations, we systematically evaluate the performance of these schemes, after independently calibrating the SPM discretized with each scheme to experimental data, and find a tradeoff between accuracy (quantified by voltage root-mean-square error) and computational time. Our findings provide insights into the selection of numerical schemes for the SPM, contributing to the advancement of battery modeling and simulation techniques.

Paper Structure

This paper contains 13 sections, 18 equations, 4 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Single Particle Model
  3. Numerical methods
  4. Finite Volume Method
  5. Control Volume Method
  6. Choice of integrator
  7. Results
  8. Model Calibration -- Procedure
  9. Model Calibration -- Results
  10. Model Validation
  11. Volume number variation
  12. Perspective
  13. Conclusion

Figures (4)

  • Figure 1: Validation of FVM method with Hermite polynomial extrapolation using UDDS data. (a) Voltage comparison. (b) SoC comparison. Solid lines denote experimental data. Dashed lines denote model outputs. Top plots show the error (difference) between model output and experimental data..
  • Figure 2: Validation of CVM method using UDDS data. Similar visualization as Fig. \ref{['fig:FVM_UDDS_results']}.
  • Figure 3: RMSE between model output of using a given method and reference solution. (a,d) Voltage RMSE. (b, e) Negative electrode SoC RMSE. (c, f) Positive electrode SoC RMSE. (a-c) are associated with an HPPC input while (d-f) are associated with a UDDS input.
  • Figure 4: Ratio of CVM computational time to FVM computational time as a function of the number of node points $N_{r}$ for an (a) HPPC profile and (b) a UDDS profile. Error bars denote the standard error of the mean and are present but are as small as the points.