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State estimation for parallel-connected batteries via inverse dynamic modeling

Hannah Lee, Casey Casten, Hosam Fathy

Abstract

This paper examines the problem of estimating the states, including state of charge, of battery cells connected in parallel. Previous research highlights the importance of this problem, and presents multiple approaches for solving it. Algorithm scalability and observability analysis can both be challenging, particularly because the underlying pack dynamics are governed by differential algebraic equations. Our work addresses these challenges from a novel perspective that begins by inverting the causality of parallel pack dynamics, which breaks the pack model's underlying algebraic loop. This simplifies observability analysis and observer design significantly, leading to three novel contributions. First, the paper derives mathematical conditions for state observability that apply regardless of the number of battery cells and the order of their individual dynamics. Second, the paper presents an approach for grouping battery cells such that their lumped dynamics are observable. Finally, the paper presents a novel pack state estimator that achieves computational tractability by employing inverse dynamic modeling. We conclude by presenting a Monte Carlo simulation study of this estimator using experimentally-parameterized models of two battery chemistries. The simulation results highlight the computational benefits of both the clustering strategy and inverse dynamics approach for state estimation.

State estimation for parallel-connected batteries via inverse dynamic modeling

Abstract

This paper examines the problem of estimating the states, including state of charge, of battery cells connected in parallel. Previous research highlights the importance of this problem, and presents multiple approaches for solving it. Algorithm scalability and observability analysis can both be challenging, particularly because the underlying pack dynamics are governed by differential algebraic equations. Our work addresses these challenges from a novel perspective that begins by inverting the causality of parallel pack dynamics, which breaks the pack model's underlying algebraic loop. This simplifies observability analysis and observer design significantly, leading to three novel contributions. First, the paper derives mathematical conditions for state observability that apply regardless of the number of battery cells and the order of their individual dynamics. Second, the paper presents an approach for grouping battery cells such that their lumped dynamics are observable. Finally, the paper presents a novel pack state estimator that achieves computational tractability by employing inverse dynamic modeling. We conclude by presenting a Monte Carlo simulation study of this estimator using experimentally-parameterized models of two battery chemistries. The simulation results highlight the computational benefits of both the clustering strategy and inverse dynamics approach for state estimation.
Paper Structure (17 sections, 1 theorem, 17 equations, 7 figures, 1 table)

This paper contains 17 sections, 1 theorem, 17 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. Parallel-Connected Pack Modeling
  3. Model Structure
  4. Forward Causality Model
  5. Inverse Causality Model
  6. Observability Analysis
  7. Model Linearization
  8. Observability Analysis without RC Dynamics
  9. Observability Analysis with RC Dynamics
  10. Kalman Filter
  11. Model Identification
  12. Clustering Criterion
  13. Design of Kalman Filter
  14. Monte Carlo Simulation Studies
  15. Simulation of Pack
  16. ...and 2 more sections

Key Result

Theorem 1

The observability of the state-space model in Eq. eq:ssMatrices2 has the necessary and sufficient conditions that: (i) the slopes of all cells' characteristic OCV-SOC curves, $\gamma_{1,...,N}$, are nonzero; (ii) the series Ohmic resistances of all cells, $R_{1...s,N}$ are finite; and (iii) the pote

Figures (7)

  • Figure 1: Configuration of a parallel-connected battery pack.
  • Figure 2: Equivalent circuit models of a single cell and cells in parallel.
  • Figure 3: CCCV cycling results for OCV as a function of SOC.
  • Figure 4: NMC and LFP cell clusters, capacity vs. Ohmic resistance.
  • Figure 5: Simulated current and voltage for 4 packs with 1st or 3rd-order NMC or LFP cells.
  • ...and 2 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof