# Multiscale Modelling Methodologies of Lithium-Ion Battery Aging: A Review of Most Recent Developments

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## Abstract

**:**

## 1. Introduction

## 2. Heat Generation in Battery Systems

#### 2.1. Electrode Particle Heat Generation Phenomenon

#### 2.2. Battery Cell Heat Generation Phenomenon

#### 2.3. Battery Pack Heat Generation Phenomenon

## 3. Aging Mechanisms

#### 3.1. Electrode Particle Aging Contributing Factors

_{2}) causes side reactions with the electrolyte to form additional gases such as carbon monoxide (CO) and carbon dioxide (CO

_{2}) [20]. Beyond electrolyte decomposition, if gas evolution is not mitigated, it increases the risk of a battery explosion and subsequent thermal runaway [21].

#### 3.2. Battery Cell Aging Mechanisms

#### 3.2.1. Production-Related Aging Mechanisms

#### 3.2.2. Calendar Aging Mechanisms

#### 3.2.3. Cycle Aging Mechanisms

#### 3.3. Battery Pack Aging Contributing Factors

#### 3.3.1. Cell Spreading

#### 3.3.2. External Stress Factors

#### 3.3.3. User Patterns Impact

## 4. Aging Modelling Strategies

- Model the cycle and calendar aging phenomena together;
- Reference electro-chemo-mechanical-related aging phenomena;
- Be scalable to multiple hierarchical scales;
- Validated experimentally under realistic operating conditions;
- Implementable online in a battery management system (BMS).

#### 4.1. Data-Based Models

#### 4.1.1. Empirical Models

- $\xi $: capacity degradation at non-ambient conditions;
- $\xi \delta \left(T\right)$: capacity degradation at ambient temperature T;
- $SO{C}_{avg},SO{C}_{dev}$: average SOC, deviation from average SOC;
- $Ah$: charge;
- ${k}_{s1},{k}_{s2},{k}_{s3},{k}_{s4}$: empirically derived coefficients.

#### 4.1.2. Equivalent Circuit Models

#### 4.1.3. Machine Learning Models

#### 4.1.4. Deep Learning Models

#### 4.1.5. Statistical Models

#### 4.2. Multiphysics-Based Modelling

#### 4.2.1. Pseudo-Two-Dimensional Model

#### 4.2.2. Single-Particle Model and Other Simplified Electrochemical Models

- Discrete-time realization algorithm (DRA) that converts functions to discrete-time unit pulse responses, and then uses either the Ho–Kalman or the eigensystem realization algorithm to generate an ROM;
- Continuous time realization algorithm (CRA) that converts the function to a continuous time state space model and then to a discrete-time state space model;
- Hybrid realization algorithm (HRA) that converts functions to discrete-time frequency response and then reduces the model order;
- Lagrange interpolation realization algorithm (LRA) that converts functions to a continuous state space model which approximates function values followed by a reduction in order and conversion to a discrete state space model.

#### 4.2.3. Thermal Modelling

#### 4.3. Combined Modelling Techniques

## 5. Battery Testing Strategies

#### 5.1. Test Types

- Formation or characterization tests to diagnose cell initial prognostics and variations;
- Duty cycle test to test the battery under the desired condition;
- Reference performance test (RPT) to characterize parameter evolution for the battery.

#### 5.1.1. Characterization Tests

#### 5.1.2. Aging Emulation Testing

#### 5.2. Aging Phenomena Diagnosis Techniques

#### 5.2.1. Electrochemical Impedance Spectroscopy

#### 5.2.2. Incremental Capacity Differential Voltage Analysis

## 6. Overview and Future Perspectives

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ANN | Artificial neural network |

BMS | Battery Management System |

BOL | Beginning of life |

BTMS | Battery thermal management system |

CRA | Continuous realization algorithm |

CEI | Cathodic electrolyte interphase |

CC-CV | Constant current - constant voltage |

CNN | Convolutional neural network |

DOD | Depth of discharge |

DRA | Discrete realization algorithm |

DST | Dynamic stress tests |

ECM | Equivalent circuit model |

EIS | Electrochemical impedance spectroscopy |

EMD | Empirical mode decomposition |

EOL | End of life |

EV | Electric vehicles |

FFLSRA | Forgetting factor recursive least squares algorithm |

FUDS | Federal urban driving schedules |

GM | General Motors |

HRA | Hybrid realization algorithm |

IC-DV | Incremental capacity/differential voltage |

ISPM+ | Improved SPM |

KRR | Kernel ridge regression |

LAM | Loss of active material |

LRA | Lagrange interpolation realization algorithm |

LCO | Lithium Cobalt Oxide |

LIB | Lithium-ion battery |

LLI | Loss of lithium inventory |

LFP | Lithium Iron Phosphate |

LMO | Lithium Manganese Oxide |

LSTM | Long short term memory |

LTO | Lithium Titante Oxide |

NCA | Nickel Cobalt Aluminum Oxide |

NEDC | New european driving cycle |

NMC | Nickel Manganese Cobalt Oxide |

OCV | Open circuit voltage |

OEM | Original equipment manufacturer |

P2D | Pseudo 2D model |

PCM | Phase change material |

PDE | Partial differential equation |

PHEV | Plug in hybrid electric vehicle |

pOCV | Pseudo OCV |

RDE | Remaining discharge energy |

RMSE | Root mean squared error |

RNN | Recurrent neural network |

ROM | Reduced order model |

RPT | Reference performance test |

SEI | Solid electrolyte interphase |

SPM | Single particle model |

SOC | State of charge |

SOH | State of health |

SVM | Support vector machine |

TEMA | Transport technology and mobility |

V2G | Vehicle to grid |

WLTP | World harmonized light duty vehicle test procedures |

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**Figure 1.**Lithium-ion battery aging schema relating contributing factors at the pack and particle scales to aging mechanisms at the cell scale.

**Figure 3.**Machine learning model development stages, where offline stages are stored in the cloud and online stages are deployed in the electric vehicle.

**Figure 4.**Battery aging neural network workflow: input typical test profile/characterization studies and output an aging trajectory model.

**Figure 5.**Pseudo-two-dimensional model graphical summary showing ion transport in cell and particle domains.

**Figure 6.**Electrochemical and thermal model coupling methodology to gauge thermal performance by linking heat generation rate and temperature distribution between models.

**Figure 8.**Generation of pseudo-open circuit voltage curve by averaging low C-rate charge and discharge curves (adapted from [161]).

**Figure 10.**Idealized Nyquist plot illustrating typical impedance responses to internal lithium-ion battery phenomena based on frequency range (adapted from [166]).

**Figure 11.**Equivalent circuit model illustrating the relationship between electrical elements and lithium-ion battery aging phenomena (adapted from [166]).

**Figure 12.**Incremental capacity (top), differential voltage (bottom) identification of aging mechanisms through peak shifts from the beginning to end of life (adapted from [166]).

**Figure 13.**Proposed modelling framework: 1: cell electrochemical characterization to extract properties for model development; 2: multiple model development/coupling—2a: electrochemical model gauging cell electrical performance, 2b: mechanical model gauging particle diffusion stress and relevant cell scale effects, 2c: thermal model gauging cell temperature distribution; 3: state of health and aging mechanism composition result—3a: cell-scale results, 3b: scale up to pack-scale results using Monte Carlo distribution of parameter measurements from 1; 4: comparing model results with experimental validation (proceed to 5 if experimental correlation achieved; otherwise, retune model at 2); 5: capturing generated model framework into a machine learning interface saved in the cloud.

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**MDPI and ACS Style**

Ali, M.A.; Da Silva, C.M.; Amon, C.H.
Multiscale Modelling Methodologies of Lithium-Ion Battery Aging: A Review of Most Recent Developments. *Batteries* **2023**, *9*, 434.
https://doi.org/10.3390/batteries9090434

**AMA Style**

Ali MA, Da Silva CM, Amon CH.
Multiscale Modelling Methodologies of Lithium-Ion Battery Aging: A Review of Most Recent Developments. *Batteries*. 2023; 9(9):434.
https://doi.org/10.3390/batteries9090434

**Chicago/Turabian Style**

Ali, Mir A., Carlos M. Da Silva, and Cristina H. Amon.
2023. "Multiscale Modelling Methodologies of Lithium-Ion Battery Aging: A Review of Most Recent Developments" *Batteries* 9, no. 9: 434.
https://doi.org/10.3390/batteries9090434