# Research on Calendar Aging for Lithium-Ion Batteries Used in Uninterruptible Power Supply System Based on Particle Filtering

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## Abstract

**:**

## 1. Introduction

#### 1.1. Research Background and Motivation

#### 1.2. Literature Review

#### 1.3. Main Contributions

#### 1.4. Outline of the Article

## 2. Battery Calendar Aging Modeling

## 3. Methodology

#### 3.1. Battery Cell SOH Estimation Algorithm

- (1)
- Update the particles: for any i, generate a new sample of states (particles) for the current k moments according to the state Equation (7) and the previous moment particle population: ${\widehat{x}}_{k}^{i}=\mathrm{A}{\widehat{x}}_{k-1}^{i}+B{u}_{k}+{\omega}_{k}$. The battery capacity decay rate at moment k can be obtained according to Equation (8): ${\widehat{y}}_{k}^{i}=f\left[{\widehat{x}}_{k}^{i},{u}_{k}\right]+{\upsilon}_{k}$.
- (2)
- Generating weights: based on the measured value of the battery capacity decay rate at moment k, the importance weights are generated according to the following equation: ${q}_{k}^{i}=\frac{1}{\sqrt{2\pi {Q}_{v}}}\mathrm{exp}\left(\frac{1}{2{Q}_{v}}\left({y}_{k}-{\widehat{y}}_{k}^{i}\right)\right)$ (where ${Q}_{v}$ is the measurement noise covariance).
- (3)
- Weight normalization: ${\overline{q}}_{k}^{i}={q}_{k}^{i}/{\displaystyle {\sum}_{i=1}^{{N}_{s}}{q}_{k}^{i}}$

#### 3.2. Battery Pack and Group SOH Estimation Algorithm

#### 3.3. Battery Cell RUL Estimation Algorithm

#### 3.4. Battery Pack and Group RUL Estimation Algorithm

## 4. Results and Discussion

#### 4.1. Experimental Testbench

- (1)
- Charge the battery cell at a constant current of 0.3 C (30 A) and reach the charging cutoff voltage of 3.6 V when the current voltage is recorded as the terminal voltage corresponding to SOC = 100%;
- (2)
- Discharge the battery with a constant current of 0.5 C (50 A) and record the corresponding terminal voltage change to 2.6 V, and stop discharging when the discharge cut-off voltage is reached;
- (3)
- Create a capacity discrimination table. According to the end voltage curve obtained in step (2), starting from the discharge moment. The corresponding voltage value is taken every 12 min as the end voltage corresponding to SOC = [90%, 80%, 70%, 60%. 50%, 40%, 30%, 20%, 10%, 0%].

- (1)
- Start the experiment by charging the battery at a constant current of 0.3 C (30 A) and stop charging when the charging cut-off voltage of 3.6 V is reached to ensure that the battery is fully charged, i.e., SOC = 1.0;
- (2)
- Record the float voltage of each individual cell (note: voltage at the end of the cell that is not offline);
- (3)
- Start the constant current discharge, and record the starting voltage of each single battery (Note: offline battery terminal voltage; do not rest; immediately measure); the discharge current size is 0.5 C (50 A), and the battery discharge is 1 h (discharge 50%). Do not rest; immediately record the end voltage at the end of discharge to determine whether the single battery voltage is lower than 2.6 V. If it is lower than 2.6 V, stop the experiment and replace the substandard qualified battery. Otherwise, continue the experiment;
- (4)
- Determine the capacity of the battery according to the capacity discrimination table in the constant capacity test.

- (1)
- Conduct constant current and voltage charging with a charge current of 0.3 C (30 A) and a charge cut-off voltage of 3.6 V, ensuring that the battery is fully charged, i.e., SOC = 1.0;
- (2)
- Check the battery cell voltage. If it is not lower than 3.35 V, then continue to store at 25 °C and check the battery. If the cell voltage is lower than 3.35 V, the battery is charged at a 0.3 C constant current;
- (3)
- Detect the battery cell voltage. If the battery cell voltage does not reach 3.6 V and the total battery pack voltage does not reach 580 V, then continue to charge. If the voltage of the battery cell reaches 3.6 V or the total voltage of the battery pack reaches 580 V, then stop charging and continue to store at 25 °C;
- (4)
- Conduct battery capacity testing every half month. If the aging time reaches one month, conduct capacity verification test and judge whether the aging test termination condition is reached, i.e., if the battery capacity decays to 50% of the rated capacity. If the test termination condition is not reached, return to step (3); if the test termination condition is reached, end the experiment. If the aging time does not reach one month, continue to store the battery at 25 °C and return to step (3).

#### 4.2. Results and Analysis

#### 4.2.1. Battery SOH Estimation

^{−2}, and ${\upsilon}_{k}$ is set to 1 × 10

^{−5}. The initial particle Ns is set to 200. As shown in Figure 5, the SOH estimation results are given for 12 single-cells in a pack. The horizontal coordinate is the cell SOH estimated using the PF algorithm, and the vertical coordinate is the experimentally measured value. The root mean square error (RMSE) and mean absolute percentage error (MAPE) of the prediction are given in Table 1.

#### 4.2.2. Battery RUL Estimation

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Topological relationship between the battery pack and the battery cells. (

**b**) Topology of the battery group and battery pack.

**Figure 5.**Battery cell SOH estimation results. (

**a**–

**l**) Battery SOH estimation for 12 single-cells in a pack.

Cell | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

RMSE (%) | 1.87 | 7.26 | 2.97 | 3.12 | 3.58 | 1.8 | 0.15 | 6.37 | 3.1 | 3.15 | 9.07 | 2.06 |

MAPE (%) | 1.18 | 5.37 | 1.85 | 2.17 | 2.79 | 0.97 | 0.16 | 5.42 | 1.96 | 2.07 | 6.85 | 1.58 |

Cell | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

RUL (Days) | 1231 | 1179 | 1950 | 1150 | 1759 | 1027 | 194 | 1099 | 1330 | 1841 | 1295 | 1425 |

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**MDPI and ACS Style**

Xu, W.; Tan, H.
Research on Calendar Aging for Lithium-Ion Batteries Used in Uninterruptible Power Supply System Based on Particle Filtering. *World Electr. Veh. J.* **2023**, *14*, 209.
https://doi.org/10.3390/wevj14080209

**AMA Style**

Xu W, Tan H.
Research on Calendar Aging for Lithium-Ion Batteries Used in Uninterruptible Power Supply System Based on Particle Filtering. *World Electric Vehicle Journal*. 2023; 14(8):209.
https://doi.org/10.3390/wevj14080209

**Chicago/Turabian Style**

Xu, Wei, and Hongzhi Tan.
2023. "Research on Calendar Aging for Lithium-Ion Batteries Used in Uninterruptible Power Supply System Based on Particle Filtering" *World Electric Vehicle Journal* 14, no. 8: 209.
https://doi.org/10.3390/wevj14080209