# State-of-Health Estimate for the Lithium-Ion Battery Based on Constant Voltage Current Entropy and Charging Duration

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## Abstract

**:**

## 1. Introduction

- (1)
- An original SOH combination indicator is proposed to estimate the battery SOH when it starts charging at a non-zero SOC. By employing information entropy to quantify the current sequence, the current entropy and charging duration is deduced from the CV–charging current curve.
- (2)
- The computational burden and precision of the SOH estimation are compared with four other traditional methods of employing a different number of input features. Although the amount of the calculation burden of the proposed method increases, the precision of the SOH estimation value has been greatly improved.
- (3)
- The adaptability and effectiveness of the proposed approach for the battery pack and cell SOH estimation are verified based on two different types of batteries: battery cell and battery pack.

## 2. The Battery SOH

## 3. Feature Extraction

#### 3.1. Current Entropy

#### 3.2. Charging Time

## 4. SSA-SVM

#### 4.1. Support Vector Machine

_{i}represents the error value of regression. The Lagrange equation is established through the above constraint conditions:

_{i}represents Lagrange multiplier. After finding first-order partial derivative of each variable based on Karush–Kuhn–Tucker (KKT) equations, arranging and converting the optimal solution into the following linear equations.

_{n}is a unit vector of order n, u = [u

_{1}, u

_{2},…, u

_{n}], K is the matrix of kernel function and it is described as follows:

#### 4.2. Sparrow Search Algorithm

_{2}∈ (0, 1], ST ∈ [0.5, 1.0], Q ∈ [−1, 1] is a random number, L denotes a matrix.

^{+}denotes a matrix.

_{i}represents the fitness of the ith sparrow, f

_{g}and f

_{w}represent the best and worst fitness of the current generation, respectively, and ε denotes the small number.

#### 4.3. The Process of SSA Optimizing SVM

## 5. Experimental Steps and Results Analysis

#### 5.1. Battery Data

#### 5.2. Experimental Procedures

#### 5.3. Experimental Results Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**Iterative optimization processes of battery pack and cell. (

**a**) Battery pack; (

**b**) battery cell.

**Figure 8.**The SOH bar errors between estimation and measurement. (

**a**) Battery pack; (

**b**) battery cell.

**Figure 10.**The absolute SOH estimation error values of the comparative experiment. (

**a**) Battery pack; (

**b**) battery cell.

Battery Type | Penalty Coefficient | Width Factor |
---|---|---|

Battery pack | 24.5285 | 0.0914 |

Battery cell | 6.7407 | 0.0610 |

Method | Input | Estimation Method |
---|---|---|

Proposed method | Current entropy and charging time | SSA-SVM |

Compared method 1 | Current entropy | SSA-SVM |

Compared method 2 | Current entropy and charging time | SVM |

Compared method 3 | Current entropy and charging time | Elman |

Compared method 4 | Current entropy and charging time | ELM |

Method | Error | Battery Pack | Battery Cell | Time (s) |
---|---|---|---|---|

Proposed method | MAE (%) ME (%) | 0.2364 1.2924 | 0.1939 0.6502 | 7.3965 |

Compared method 1 | MAE (%) ME (%) | 0.6482 1.5650 | 0.2525 1.1040 | 7.3620 |

Compared method 2 | MAE (%) ME (%) | 0.7139 1.6599 | 0.3251 1.2058 | 0.0121 |

Compared method 3 | MAE (%) ME (%) | 0.7963 3.2696 | 0.7426 2.1865 | 4.0970 |

Compared method 4 | MAE (%) ME (%) | 0.7212 2.3906 | 0.4594 1.5180 | 0.0105 |

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**MDPI and ACS Style**

Luo, L.; Zhang, C.; Tian, Y.; Liu, H.
State-of-Health Estimate for the Lithium-Ion Battery Based on Constant Voltage Current Entropy and Charging Duration. *World Electr. Veh. J.* **2022**, *13*, 148.
https://doi.org/10.3390/wevj13080148

**AMA Style**

Luo L, Zhang C, Tian Y, Liu H.
State-of-Health Estimate for the Lithium-Ion Battery Based on Constant Voltage Current Entropy and Charging Duration. *World Electric Vehicle Journal*. 2022; 13(8):148.
https://doi.org/10.3390/wevj13080148

**Chicago/Turabian Style**

Luo, Laijin, Chaolong Zhang, Youhui Tian, and Huihan Liu.
2022. "State-of-Health Estimate for the Lithium-Ion Battery Based on Constant Voltage Current Entropy and Charging Duration" *World Electric Vehicle Journal* 13, no. 8: 148.
https://doi.org/10.3390/wevj13080148