# Fuzzy Prediction of Power Lithium Ion Battery State of Function Based on the Fuzzy c-Means Clustering Algorithm

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Selection of Relevant Variables of SOF

#### 2.1. SOC

#### 2.2. SOH

#### 2.3. Maximum C-Rate (Charge–Discharge Rate)

## 3. Prediction of SOF Based on the Fuzzy Inference System Optimized by the FCM Algorithm

#### 3.1. Fuzzy c-Means Clustering

#### 3.2. Estimate the SOF

(L,L,L,L), (L,L,M,L), (L,L,H,L), (L,M,L,L), (L,M,M,M), (M,L,L,M), (M,L,M,M), (M,M,H,H), (L,M,H,M), (L,H,L,L), (L,H,M,M), (L,H,H,M), (M,L,L,M), (M,L,M,M), (M,L,H,M), (M,M,L,M), (M,M,M,M), (M,M,H,H), (M,H,L,M), (M,H,M,M), (M,H,H,H), (H,L,L,M), (H,L,M,M), (H,L,H,M), (H,M,L,M), (H,M,M,M), (H,M,H,H), (H,H,L,M), (H,H,M,H), (H,H,H,H).

## 4. SOF Measurement

- (1)
- Leave the battery for two hours to make sure that it stays in a stable state;
- (2)
- Adjust the instrument to ensure that correct readings of the current voltage and the current of the battery are obtained;
- (3)
- Set the discharge working mode as the cyclic test mode. The parameters of the starting current, termination current, termination voltage, step interval and time-step interval are set, respectively. Then, start the measurement.
- (4)
- Measure the maximum discharge current while the voltage drops to the termination voltage. At this time, the product of the voltage and current is taken as the current SOF of the battery.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Voltage curve under 1A constant current discharge using batteries with different state of health (SOH). From (

**a)**–(

**d**), the SOH of the battery decreases in turn. (

**a**) is the voltage vs. 1A-constant current curve of the battery with the best SOH, while (

**d**) is of the lowest one.

**Figure 3.**Voltage curve of the battery under different discharge currents. The discharge currents are 0.5A (

**a**), 1A (

**b**), 2A (

**c**) and 3A (

**d**), respectively.

**Figure 5.**Input variable membership functions and three-dimensional graphs of fuzzy relations. (

**a)**–(

**c**) are input variable membership functions of state of charge (SOC), SOH and charge–discharge rate (C-rate), respectively. (

**d**)–(

**f**) are three-dimensional graphs of fuzzy relations of every two input variables of three corresponding to SOF.

**Figure 7.**SOF measurement under the step-increasing discharge current. (

**a**)–(

**d**) represent voltage vs step-increasing current curves of four different batteries.

Index | Voltage | Current | SOH | SOF-ESTIMATED | Index | Voltage | Current | SOH | SOF-ESTIMATED |
---|---|---|---|---|---|---|---|---|---|

1 | 3.90 | 0.1 | 0.849 | 0.817 | 12 | 3.67 | 1.2 | 0.849 | 0.799 |

2 | 3.85 | 0.2 | 0.849 | 0.795 | 13 | 3.67 | 1.3 | 0.849 | 0.84 |

3 | 3.84 | 0.3 | 0.849 | 0.802 | 14 | 3.66 | 1.4 | 0.849 | 0.825 |

4 | 3.80 | 0.4 | 0.849 | 0.832 | 15 | 3.65 | 1.5 | 0.849 | 0.788 |

5 | 3.78 | 0.5 | 0.849 | 0.840 | 16 | 3.64 | 1.6 | 0.849 | 0.803 |

6 | 3.77 | 0.6 | 0.849 | 0.787 | 17 | 3.62 | 1.7 | 0.849 | 0.866 |

7 | 3.74 | 0.7 | 0.849 | 0.817 | 18 | 3.61 | 1.8 | 0.849 | 0.825 |

8 | 3.74 | 0.8 | 0.849 | 0.794 | 19 | 3.60 | 1.9 | 0.849 | 0.773 |

9 | 3.72 | 0.9 | 0.849 | 0.793 | 20 | 3.60 | 2.0 | 0.849 | 0.810 |

10 | 3.69 | 1.0 | 0.849 | 0.811 | 21 | 3.59 | 2.1 | 0.849 | 0.803 |

11 | 3.68 | 1.1 | 0.849 | 0.829 | 22 | 3.62 | 2.2 | 0.849 | 0.800 |

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Wang, D.; Yang, F.; Gan, L.; Li, Y.
Fuzzy Prediction of Power Lithium Ion Battery State of Function Based on the Fuzzy c-Means Clustering Algorithm. *World Electr. Veh. J.* **2019**, *10*, 1.
https://doi.org/10.3390/wevj10010001

**AMA Style**

Wang D, Yang F, Gan L, Li Y.
Fuzzy Prediction of Power Lithium Ion Battery State of Function Based on the Fuzzy c-Means Clustering Algorithm. *World Electric Vehicle Journal*. 2019; 10(1):1.
https://doi.org/10.3390/wevj10010001

**Chicago/Turabian Style**

Wang, Dasong, Feng Yang, Lin Gan, and Yuliang Li.
2019. "Fuzzy Prediction of Power Lithium Ion Battery State of Function Based on the Fuzzy c-Means Clustering Algorithm" *World Electric Vehicle Journal* 10, no. 1: 1.
https://doi.org/10.3390/wevj10010001