# Battery State-of-Health Evaluation for Roadside Energy Storage Systems in Electric Transportation

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## Abstract

**:**

## 1. Introduction

## 2. Case Study of a Roadside Energy Storage System

#### 2.1. Data Collection

#### 2.2. Data Screening

#### 2.3. Data Processing

#### 2.3.1. Battery-Pack Consistency Assessment

_{i}and the rest voltage in the group is ${U}_{j}$($j\le N,j\ne i)$. The average voltage of the rest battery cell in the battery pack is ${u}_{av}$, which is defined as Equation (1):

#### 2.3.2. Internal Resistance Balance

#### 2.3.3. The Temperature Balance

#### 2.3.4. The Battery-Cell Balance

_{max}and the minimum voltage is ${V}_{\mathrm{min}}$. A proper voltage analysis interval is chosen to obtain the voltage interval points: [V

_{max}, V

_{max-1}× V

_{interval}, V

_{max-2}× V

_{interval}, V

_{max-3}× V

_{interval}, …, V

_{max-(k-1)}× V

_{interval}]. Then, the data between each interval were checked by comparing the difference between the maximum and minimum current, I

_{d}. An I

_{d}that is greater than the threshold was deleted from the data sets. The average current $\overline{I}$ of the segment was calculated. Therefore, the segments in the ${C}_{1}^{th}$ cycle and in the ${C}_{2}^{th}$ cycle are described as $\left[\right({V}_{c2}^{1},{I}_{c2}^{1}),({V}_{c2}^{2},{I}_{c2}^{2}),\dots ,({V}_{c2}^{N},{I}_{c2}^{N}\left)\right]$, and N is the number of collected segments. The amp-hour integrator method was used to calculate the electric capacity Q

_{d}. The Q series changes in each segment and the Q-series are provided in Equations (5)–(7):

#### 2.4. SOH Calculation

## 3. State-of-Health Evaluation

#### 3.1. Health State Segmentation

#### 3.1.1. K-Means Algorithm

- (1)
- For all n objects, randomly select k objects as the center of a class, representing the k classes to be generated;
- (2)
- Calculate the distance from other objects to the cluster center, and assign objects to the nearest cluster;
- (3)
- Calculate the average value of all objects for each class as the new central value of all objects;
- (4)
- Reassign data according to the principle of nearest distance;
- (5)
- Return to (3) until there is no change and end the clustering.

#### 3.1.2. Gaussian Mixture Model

- (1)
- Judge whether a model fits well by observing the proximity between the sampling probability value and the model probability value;
- (2)
- Calculate the expected value of the data through the model and update the mean and standard deviation (parameters) of the distribution, i.e., $\mu $ and $\sigma $;
- (3)
- Repeat the process many times until the two probability values are very close;
- (4)
- Stop updating and complete model training.

#### 3.1.3. K-Means++ Algorithm

- (1)
- Select a point randomly from the set of input data points as the first cluster center;
- (2)
- For each point x in the data set, calculate the distance D(x) from the nearest cluster center (the selected cluster center);
- (3)
- Select a new data point as the new cluster center. The selection criterion is the point with larger D(x) has a higher probability of being selected as the cluster center;
- (4)
- Repeat steps 2 and 3 until k cluster centers are selected.

#### 3.2. Results and Performance of the Methods

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Label | Maximum | Minimum | Mean | Std |
---|---|---|---|---|

Total operating voltage (V) | 57,268 | 0 | 52,321.73 | 2921.62 |

Single cell voltage (V) | 15.3 | 0 | 5.2 | 1.35 |

Single row battery pack voltage (V) | 81.29 | 0 | 25.15 | 28.10 |

Total voltage (V) | 57,653 | 0 | 32,486.98 | 25,496.05 |

Mainboard temperature (°C) | 65 | 0 | 43.25 | 5.92 |

Environment temperature (°C) | 41 | 0 | 31.70 | 4.63 |

Main battery electricity (mA) | 316 | 0 | 90.44 | 89.73 |

Legend | Parameter | Interpretation |
---|---|---|

Temperature | Max TEn_{c} | The maximum of temperature entropy in the Cth iteration |

Avg TEn_{c} | The average value of temperature entropy | |

Var TEn_{c} | The variance of temperature entropy | |

Avg ${T}_{c}$ | The average value of the Cth iteration | |

Avg ${T}_{c}^{max}$ | The minimum temperature at Cth iteration | |

Voltage | Max VEn_{c1} | The maximum value of the voltage entropy |

Avg VEn_{c1} | The average value of the voltage entropy | |

Var VEn_{c1} | The variance of the voltage entropy | |

Max ${\text{}V}_{c1}^{diff}$ | The maximum value of the voltage difference of the four cells | |

Avg ${V}_{c1}^{diff}$ | The average value of the voltage difference of the four cells | |

Avg ${V}_{c1}^{max}$ | The maximum value of the voltage of the four cells | |

Capacity | Var_{c1,c2} | Variance: Var_{c1,c2} = Min(Q_{c2} − Q_{c1}) |

Resistance | ${R}_{internal}$ | The value of internal resistance |

Input Parameters | Output Parameter | |||
---|---|---|---|---|

Index | Voltage (V) | Resistance (Ω) | Temperature (°C) | State of Health |

1 | 10.497 | 0.094 | 30.9 | 95.1 |

2 | 10.497 | 0.092 | 31.3 | 95.2 |

3 | 10.497 | 0.095 | 31.3 | 95.1 |

4 | 10.497 | 0.091 | 31.0 | 95.0 |

5 | 10.497 | 0.091 | 31.1 | 94.8 |

6 | 10.497 | 0.088 | 31.0 | 94.5 |

7 | 10.497 | 0.092 | 31.2 | 94.1 |

8 | 10.497 | 0.093 | 31.5 | 93.9 |

9 | 10.498 | 0.091 | 30.8 | 93.0 |

Clustering Algorithms | Advantages | Disadvantages | Silhouette Coefficient |
---|---|---|---|

K-Means | Low time complexity; high computing efficiency | Number of clusters needed to be preset; not suitable for nonconvex data | 0.63 |

Gaussian Mixture Model | each class probability; high computing speed | Inflexible shape; limited accuracy; lack of robustness | 0.80 |

K-Means++ | Improved K-Means algorithm; improve the final error; reduce the calculation time | Internal orderliness; low scalability; high time complexity | 0.75 |

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## Share and Cite

**MDPI and ACS Style**

Deng, K.; Shen, K.; Dong, Z.; Liang, Z.; Zhao, L.; Xu, T.; Yin, S.
Battery State-of-Health Evaluation for Roadside Energy Storage Systems in Electric Transportation. *Future Transp.* **2023**, *3*, 1310-1325.
https://doi.org/10.3390/futuretransp3040072

**AMA Style**

Deng K, Shen K, Dong Z, Liang Z, Zhao L, Xu T, Yin S.
Battery State-of-Health Evaluation for Roadside Energy Storage Systems in Electric Transportation. *Future Transportation*. 2023; 3(4):1310-1325.
https://doi.org/10.3390/futuretransp3040072

**Chicago/Turabian Style**

Deng, Kailong, Kaiyuan Shen, Zihao Dong, Zekai Liang, Lei Zhao, Ting Xu, and Shunde Yin.
2023. "Battery State-of-Health Evaluation for Roadside Energy Storage Systems in Electric Transportation" *Future Transportation* 3, no. 4: 1310-1325.
https://doi.org/10.3390/futuretransp3040072