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Nonlinear Double-Capacitor Model for Rechargeable Batteries: Modeling, Identification and Validation

Ning Tian, Huazhen Fang, Jian Chen, Yebin Wang

TL;DR

A new equivalent circuit model for rechargeable batteries is proposed by modifying a double-capacitor model by introducing a nonlinear-mapping-based voltage source and a serial RC circuit that offers excellent accuracy and predictive capability.

Abstract

This paper proposes a new equivalent circuit model for rechargeable batteries by modifying a double-capacitor model proposed in [1]. It is known that the original model can address the rate capacity effect and energy recovery effect inherent to batteries better than other models. However, it is a purely linear model and includes no representation of a battery's nonlinear phenomena. Hence, this work transforms the original model by introducing a nonlinear-mapping-based voltage source and a serial RC circuit. The modification is justified by an analogy with the single-particle model. Two parameter estimation approaches, termed 1.0 and 2.0, are designed for the new model to deal with the scenarios of constant-current and variable-current charging/discharging, respectively. In particular, the 2.0 approach proposes the notion of Wiener system identification based on maximum a posteriori estimation, which allows all the parameters to be estimated in one shot while overcoming the nonconvexity or local minima issue to obtain physically reasonable estimates. An extensive experimental evaluation shows that the proposed model offers excellent accuracy and predictive capability. A comparison against the Rint and Thevenin models further points to its superiority. With high fidelity and low mathematical complexity, this model is beneficial for various real-time battery management applications.

Nonlinear Double-Capacitor Model for Rechargeable Batteries: Modeling, Identification and Validation

TL;DR

A new equivalent circuit model for rechargeable batteries is proposed by modifying a double-capacitor model by introducing a nonlinear-mapping-based voltage source and a serial RC circuit that offers excellent accuracy and predictive capability.

Abstract

This paper proposes a new equivalent circuit model for rechargeable batteries by modifying a double-capacitor model proposed in [1]. It is known that the original model can address the rate capacity effect and energy recovery effect inherent to batteries better than other models. However, it is a purely linear model and includes no representation of a battery's nonlinear phenomena. Hence, this work transforms the original model by introducing a nonlinear-mapping-based voltage source and a serial RC circuit. The modification is justified by an analogy with the single-particle model. Two parameter estimation approaches, termed 1.0 and 2.0, are designed for the new model to deal with the scenarios of constant-current and variable-current charging/discharging, respectively. In particular, the 2.0 approach proposes the notion of Wiener system identification based on maximum a posteriori estimation, which allows all the parameters to be estimated in one shot while overcoming the nonconvexity or local minima issue to obtain physically reasonable estimates. An extensive experimental evaluation shows that the proposed model offers excellent accuracy and predictive capability. A comparison against the Rint and Thevenin models further points to its superiority. With high fidelity and low mathematical complexity, this model is beneficial for various real-time battery management applications.

Paper Structure

This paper contains 19 sections, 50 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Review of Battery Modeling
  4. Review of Battery Model Identification
  5. Statement of Contributions
  6. Organization
  7. NDC Model Development
  8. Parameter Identification 1.0: Constant-Current Charging/Discharging
  9. Identification of $h(\cdot)$
  10. Identification of Impedance and Capacitance
  11. Terminal Voltage Response Analysis
  12. Data-Fitting-Based Identification of $\bm \theta$
  13. Parameter Identification 2.0: Variable-Current Charging/Discharging
  14. Wiener-Type Strucutre of the NDC Model
  15. MAP-Based Wiener Identification
  16. ...and 4 more sections

Figures (13)

  • Figure 1: (a) The original double-capacitor model; (b) the proposed NDC model.
  • Figure 2: The single-particle model (top), and a particle (bottom) subdivided into two volumes, core and shell, which correspond to $R_b$-$C_b$ and $R_s$-$C_s$, respectively.
  • Figure 3: The Wiener-type structure of the nonlinear double-capacitor (NDC) model.
  • Figure 4: PEC® SBT4050 battery tester.
  • Figure 5: Identification 1.0: parameter identification of $h(\cdot)$ that defines SoC-OCV relation.
  • ...and 8 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5