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A Unified Model for Active Battery Equalization Systems

Quan Ouyang, Nourallah Ghaeminezhad, Yang Li, Torsten Wik, Changfu Zou

Abstract

Lithium-ion battery packs demand effective active equalization systems to enhance their usable capacity and lifetime. Despite numerous topologies and control schemes proposed in the literature, conducting quantitative analyses, comprehensive comparisons, and systematic optimization of their performance remains challenging due to the absence of a unified mathematical model at the pack level. To address this gap, we introduce a novel, hypergraph-based approach to establish the first unified model for various active battery equalization systems. This model reveals the intrinsic relationship between battery cells and equalizers by representing them as the vertices and hyperedges of hypergraphs, respectively. With the developed model, we identify the necessary condition for all equalization systems to achieve balance through controllability analysis, offering valuable insights for selecting the number of equalizers. Moreover, we prove that the battery equalization time is inversely correlated with the second smallest eigenvalue of the hypergraph's Laplacian matrix of each equalization system. This significantly simplifies the selection and optimized design of equalization systems, obviating the need for extensive experiments or simulations to derive the equalization time. Illustrative results demonstrate the efficiency of the proposed model and validate our findings.

A Unified Model for Active Battery Equalization Systems

Abstract

Lithium-ion battery packs demand effective active equalization systems to enhance their usable capacity and lifetime. Despite numerous topologies and control schemes proposed in the literature, conducting quantitative analyses, comprehensive comparisons, and systematic optimization of their performance remains challenging due to the absence of a unified mathematical model at the pack level. To address this gap, we introduce a novel, hypergraph-based approach to establish the first unified model for various active battery equalization systems. This model reveals the intrinsic relationship between battery cells and equalizers by representing them as the vertices and hyperedges of hypergraphs, respectively. With the developed model, we identify the necessary condition for all equalization systems to achieve balance through controllability analysis, offering valuable insights for selecting the number of equalizers. Moreover, we prove that the battery equalization time is inversely correlated with the second smallest eigenvalue of the hypergraph's Laplacian matrix of each equalization system. This significantly simplifies the selection and optimized design of equalization systems, obviating the need for extensive experiments or simulations to derive the equalization time. Illustrative results demonstrate the efficiency of the proposed model and validate our findings.
Paper Structure (22 sections, 2 theorems, 50 equations, 9 figures, 3 tables, 1 algorithm)

This paper contains 22 sections, 2 theorems, 50 equations, 9 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Active Equalization Systems and Their Analysis
  3. Overview of Battery Equalization Systems
  4. Equalization Current Analysis
  5. Equalization currents through CC equalizers
  6. Equalization currents through MM equalizers
  7. Equalization currents through CPC equalizers
  8. Equalization currents through CMC equalizers
  9. Unified Model Development for Active Battery Equalization Systems
  10. Hypergraph representation of equalizers and cells
  11. Application of hypergraphs to equalizer modeling
  12. Hypergraph-based modeling of CC equalizers
  13. Hypergraph-based models of other equalizers
  14. Hypergraph-based battery system modeling
  15. Equalization Performance Analysis based on the Unified Model
  16. ...and 7 more sections

Key Result

Lemma 1

For any battery system composed of $n$ series-connected cells with the state dynamics governed by 321, given a fixed incidence matrix $C$, defined in 3212, at least $n-1$ equalizers are required to achieve equalization of all the $n$ battery cells.

Figures (9)

  • Figure 1: The structures of six typical active equalization systems. Here, $B_i$ denotes battery $i$, and $e_i$ represents equalizer $i$. (a) Series-based CC, (b) module-based CC, (c) layer-based CC, (d) CPC, (e) module-based CPC, and (f) switch-based CPC equalization systems.
  • Figure 2: Electric circuit presentation and equivalent hyperedge of different equalizers: (a) CC, (b) MM, (c) CPC, and (d) CMC equalizers.
  • Figure 3: Hypergraphs and incidence matrices of (a) Series-based CC, (b) module-based CC, (c) layer-based CC, (d) CPC, (e) module-based CPC, and (f) switch-based CPC equalization systems for a battery pack containing $8$ series-connected cells.
  • Figure 4: Model validation results for a series-based CC equalization system. (a) The experimental result obtained in 6063871. (b) The simulation result from our proposed model (\ref{['321']}).
  • Figure 5: Model validation results for a layer-based CC equalization system. (a) The experimental result obtained in 6063871. (b) The simulation result from our proposed model (\ref{['321']}).
  • ...and 4 more figures

Theorems & Definitions (7)

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