# A Review of Critical State Joint Estimation Methods of Lithium-Ion Batteries in Electric Vehicles

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Single-State Estimation

#### 2.1. Definition and Estimation Methods of SOC

#### 2.1.1. Definition of SOC

_{current}in its maximum available capacity Q

_{rate}[10], which is shown as follows:

#### 2.1.2. Estimation Methods of SOC

_{0}) is the initial state of charge, η denotes the coulombic efficiency, C

_{n}represents rated capacity, and I(t) is the instantaneous discharge current of the battery.

_{j,k}and θ

_{j,k}denote the weight and bias from the hidden layer to the output layer, respectively, O

_{j}is the output of the hidden layer, and f

_{i}represents the activation function.

#### 2.2. Definition and Estimation Methods of SOH

#### 2.2.1. Definition of SOH

- SOH is one of the important parameters of lithium-ion batteries, which is calibrated according to the change of battery capacity, as follows.

_{r}is the rated capacity, and Q

_{m}is the current maximum available capacity of the battery, which is measured under rated conditions.

- 2.
- SOH is defined according to the internal resistance of the battery, as follows.

_{e}is the internal resistance of the battery when it reaches the end of life, and R

_{n}is the internal resistance of the new battery.

#### 2.2.2. Estimation Methods of SOH

#### 2.3. Definition and Estimation Methods of SOP

## 3. Dual-State Estimation

#### 3.1. SOC/SOH Joint Estimation

#### 3.1.1. Model-Based Estimation

#### 3.1.2. Data-Driven Estimation

#### 3.1.3. Fusion Estimation Algorithm Based on Data-Driven Approach and Model

#### 3.2. SOC/SOP Joint Estimation

## 4. Key Issues and Future Work

#### 4.1. Key Issues

#### 4.1.1. Estimation Errors

#### 4.1.2. Estimation Robustness

#### 4.1.3. Division of Time Scale

#### 4.2. Future Work

#### 4.2.1. Joint Estimation of Battery Pack

#### 4.2.2. Joint Estimation under Intelligent Network Connection

#### 4.2.3. Integration Optimization

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Estimation Methods | Types | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|

Experimental based [23,24,25] | Ampere-time counting. Open-circuit voltage. AC impedance | Simple principle. Reliable. | Time-consuming. Cannot be estimated in real time. Cumulative error exists | <5% |

Model-based approaches [19,27,28] | Kalman filter. Particle filter. Sliding mode observer. | Closed-loop estimation. Low requirement for initial SOC values. | Difficult modeling. Difficult parameter identification. | <5% |

Data-driven approach [21,27] | Neural network class. Support vector machine. Fuzzy logic. | No modeling is required. | High level of data dependency. Time-consuming. | <1.5% |

Hybrid methods [28,29,30,31,32] | Data-model parallel mixture estimation. Data-model nested mixture model. | High estimation accuracy. Good robustness | Complex calculations. High energy consumption. Slow estimation speed. | <1% |

Estimation Methods | Types | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|

Traditional estimation methods [31,32,33,34] | Capacity measurement. Resistance measurement. Differential analysis. | Simple principle. Small calculation volume. Accurate. Reliable. | Time consuming. Cannot be estimated in real time. Cumulative error exists. | <5% |

Methods for filtering classe [32,33,34,35,36] | Kalman filter. Particle filter. Least squares. | Can be estimated in real time. High precision. Good robustness. | Difficult modeling. Difficult parameter identification. Large calculation volume. | <5% |

Data Driven [35,36,37,38,39,40,41] | Support vector machine. Convolutional neural network. | Real-time estimation. Highly adaptive. High accuracy. | High reliance on data accuracy. Time-consuming offline training. | <1% |

Estimation Methods | Types | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|

Interpolation method [14] | HPPC. | Estimation method is simple. | Requires extensive testing. No consideration of polarization and aging phenomena. | About 3% |

Model estimation methods [42,43] | Voltage constraint. SOC constraint. Multi-constraint dynamic method. | Simple. Efficient. | Single-state estimation methods have large errors, leading to threats to the safety of the battery. | <5% |

Data Driven [44,45] | BP neural networks. Adaptive fuzzy neural. Support vector machines. | Good self-learning ability. High accuracy. Good robustness. | Requires extensive experiments. Computationally complex and time-consuming to train offline. | <2.5% |

Algorithms | Model | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|

DEKF [53,54,55] | Thevenin model | High estimation accuracy. Faster convergence. Good robustness. | The effect of ambient temperature on the battery is not considered. Individual differences in batteries are not taken into account. Calculated losses exist. | <2% |

DUKF [9,56,57] | 2RC model | Smaller error. Higher precision. Reflects actual battery characteristics. | The effect of ambient temperature on the battery is not considered, and the individual differences of the battery are not taken into account. | <2% |

DAUKF [56,58] | 2RC model | Fast calculation speed. High estimation accuracy. Good convergence. | Not applicable to battery packs. Calculated losses exist. | <2% |

MIAUKF + VFFRLS [59,60,61] | 2RC model | High accuracy and robustness. | The effect of temperature on the estimation accuracy is not considered. There is a computational loss. | <2% |

FOEKF + AUKF [58,61,62] | 2RC fractional-order model | High precision. High self-adaptability. Fast convergence speed. | Highly influenced by temperature. Not applicable with battery packs. High calculation volume. | <1% |

Algorithms | Model | Scales | Disadvantages | Estimation Error |
---|---|---|---|---|

UPF + UPF [63,64] | 1RC model | SOH estimation scale is one charge/discharge cycle, SOC estimation interval is 0.1 s. | Higher precision. Lower computational volume. Low hardware requirements. | <1.5% |

ASREKF + EKF [64,65] | Thevenin model | SOH estimation scale is one charge/discharge cycle, SOC estimation interval is 1 s. | High accuracy and low calculation volume. | <1.5% |

FFRLS + DEKF [68,69,70] | 2RC model | SOH estimation scale is 2.5 s, SOC estimation interval is 1 s. | High stability and accuracy, saving calculation cost. | <1.5% |

Algorithms | Data Set | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|

Double Recurrent Neural Netwok [17,72,73] | NASA Lithium Battery Random Use Dataset | Independence of battery model. No decoupling required. | Need to keep updating data. | <1% |

LSTM [74] | Oxford Aging Dataset | Accuracy is higher than wavelet neural network and BP neural network, and the long-term dependency problem is solved. | No validation of effectiveness on battery packs. | <1% |

SWPSO-DRNN [22,75,76] | Customized data sets | Higher training effect than gradient descent algorithm. High generalization ability and robustness. | Not applicable to battery packs. | <1% |

GRN-RNN + CNN [77,78,79] | NASA Lithium Battery Random Use Dataset and Oxford Battery Aging Dataset | Avoid long-term dependence on new information, fast computation, high accuracy, and good robustness. | No validation of effectiveness on battery packs. | <1% |

Mogrifier LSTM-CNN [79] | NASA dataset and Oxford aging dataset | Solve the problem of large local errors of LSTM method, good adaptability and high robustness. | No validation of effectiveness on battery packs. | <1% |

Model | Estimation Method of SOC | Constraints | Advantages | Disadvantages | Estimation Error |
---|---|---|---|---|---|

2RC model | EKF | Voltage, current, SOC | The estimation accuracy is higher and more robust than that without considering SOC constraints. | No consideration of temperature and aging effects. | <5% |

2RC model | H infinity filter | Voltage, current, SOC | Better robustness and adaptability than EKF. | No consideration of temperature and aging effects. | <2.5% |

2RC model | UKF | Voltage, current, SOC | High estimation accuracy and good robustness. | No consideration of temperature and aging effects | <2% |

2RC fractional-order model | Fractional-order adaptive extended Kalman filter (FO-AEKF) | Voltage, current, SOC | Better robustness and adaptability than EKF. | No consideration of temperature and aging effects. | <3% |

2RC fractional-order model | Square-root unscented Kalman filter (SRUKF) | Voltage, current, SOC | High estimation accuracy and good robustness. | No consideration of temperature and aging effects. | <2% |

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## Share and Cite

**MDPI and ACS Style**

Hou, J.; Li, T.; Zhou, F.; Zhao, D.; Zhong, Y.; Yao, L.; Zeng, L.
A Review of Critical State Joint Estimation Methods of Lithium-Ion Batteries in Electric Vehicles. *World Electr. Veh. J.* **2022**, *13*, 159.
https://doi.org/10.3390/wevj13090159

**AMA Style**

Hou J, Li T, Zhou F, Zhao D, Zhong Y, Yao L, Zeng L.
A Review of Critical State Joint Estimation Methods of Lithium-Ion Batteries in Electric Vehicles. *World Electric Vehicle Journal*. 2022; 13(9):159.
https://doi.org/10.3390/wevj13090159

**Chicago/Turabian Style**

Hou, Junjian, Tong Li, Fang Zhou, Dengfeng Zhao, Yudong Zhong, Lei Yao, and Li Zeng.
2022. "A Review of Critical State Joint Estimation Methods of Lithium-Ion Batteries in Electric Vehicles" *World Electric Vehicle Journal* 13, no. 9: 159.
https://doi.org/10.3390/wevj13090159