Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State
Abstract
:1. Introduction
2. Experimental Methods
2.1. Test Equipment
2.2. Cycle Life Tests
- The battery with no degradation treatment (referred to as the normal cell) had good initial consistency.
- The battery that underwent the initial capacity degradation treatment (referred to as the degraded cell) had the same degree of degradation.
3. Results
3.1. Unbalance Analysis in the Charge–Discharge Cycle
- The series configuration that primarily reflected the voltage difference:
- 2.
- The parallel configuration that primarily reflected the current difference:
- 3.
- The series–parallel configuration that reflected both the current and voltage differences:
- 4.
- The parallel–series configuration that reflected both the current and voltage differences:
- For the series circuit, the voltage value of the degraded battery is significantly higher than that of the normal battery. Moreover, due to the higher internal resistance, the degraded battery increases the load in the circuit and accelerates the energy consumption of the battery pack, and there is also the risk of reverse voltage;
- For the parallel circuit, due to the lower discharge capacity of the degraded battery and the higher resistance, the normal battery must make up for its insufficient discharge, causing the current of the normal battery to become higher than the set value.
3.2. Degradation Process and Dependency Analysis
3.2.1. Capacity Degradation Process Analysis
- When the normal cell was connected in series with the degraded cell, the degradation rate did not show a large difference.
- When the normal cell was connected in parallel with the degraded cell, the degradation rate of the normal cell was significantly smaller than that of the degraded cell.
- The degradation rates of Pack A and its cells were not significantly different. The degradation rates of Pack B and Pack C were significantly higher than the rates of their cells.
3.2.2. Dependency Analysis of the Battery Packs
- Cell-1 and Cell-2 in Pack A had the same effect on the battery degradation and temperature.
- The effect of Cell-3 on the capacity of the battery pack in Pack B was significantly higher than that of Cell-4. However, for the impact on temperature, Cell-4 is higher than Cell-3. Based on previous analysis and test results, in the unbalanced state, the normal cell in the parallel structure will demonstrate an over-current phenomenon because it must compensate for the insufficient discharge capacity of the degraded cell. As the cycle increases, the difference between the cells becomes greater, and the current load of the normal battery also becomes greater. It can be seen from the formula that the heat of the battery increases with the current squared. Therefore, when the difference between batteries reaches a certain level, the influence of normal batteries on temperature plays a leading role.
- Pack C combined the characteristics of Pack A and Pack B, and the battery in series had the same degree of influence. In addition, there was a significant difference in the degree of influence of the parallel battery.
- The temperature of the degraded cells was affected by the cells more than it was by the normal cells.
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Glossary
Variable | |
Discharge capacity | |
Capacity degradation rate | |
Capacity degradation mAh | |
Correlation coefficient | |
Charge–discharge cycle | |
Matrix containing the independent variables | |
Matrix containing the dependent variables | |
Principal component vector of A | |
Principal component vector of B | |
Score vector of | |
Score vector of | |
Regression coefficient for independent variables | |
Regression coefficient for dependent variables | |
Cross-validity test coefficient |
Appendix A
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Item | Specification |
---|---|
Typical Capacity | 2150 mAh |
Minimum Capacity | 2050 mAh |
Charging Voltage | 4.2 V ± 0.05 V |
Nominal Voltage | 3.62 V |
Charging Method | Constant voltage with limited current |
Charging Current | Standard charge: 1075 mA Rapid charge: 2150 mA |
Charging Time | Standard charge: 3 h Rapid charge: 2.5 h |
Max. Charge Current | 2150 mA |
Max. Discharge Current | 10 A (Continuous discharge) |
Discharge Cut-Off Voltage | 2.75 V |
Cell Weight | 44.5 g max. |
Cell Dimension | Diameter (max.): Φ 18.40 mm Height: 65 mm max. |
Operating Temperature | Charge: 0 to 45 °C−10 to 0 °C (Charging voltage: 4.10 V/Cell, Charging Current: Under 0.5 C) (2 *) Discharge: −20 to 60 °C |
Storage Temperature | 1 year: −20~25 °C (1 *); 3 months: −20~45 °C (1 *) |
Cell-1 | Cell-2 | Cell-3 | Cell-4 | Cell-5 | Cell-6 | |
Initial capacity (mAh) | 2100 | 2095 | 2103 | 2110 | 2100 | 2090 |
Cell-7 | Cell-8 | Cell-9 | Cell-10 | Cell-11 | Cell-12 | |
Initial capacity (mAh) | 2103 | 2104 | 2101 | 2115 | 2099 | 2110 |
Cell | Initial Capacity (mAh) | Degraded Capacity (mAh) |
---|---|---|
Cell-1 | 2100 | 1995 |
Cell-3 | 2103 | 1997 |
Cell-5 | 2100 | 1996 |
Cell-9 | 2101 | 1995 |
Pack No. | Configuration | Cell No. |
---|---|---|
Pack A | Series | Cell 1, 2 |
Pack B | Parallel | Cell 3, 4 |
Pack C | Series–parallel | Cell 5, 6, 7, 8 |
Pack D | Parallel–series | Cell 9, 10, 11, 12 |
(a) | YCell-1 | YCell-2 | YPack-A | ||||
YCell-1 | 1 | 0.9995 | 0.9910 | ||||
YCell-2 | 1 | 0.9906 | |||||
YPack-A | 1 | ||||||
(b) | YCell-3 | YCell-4 | YPack-B | ||||
YCell-3 | 1 | 0.9887 | 0.9750 | ||||
YCell-4 | 1 | 0.9123 | |||||
YPack-B | 1 | ||||||
(c) | YCell-5 | YCell-6 | YCell-7 | YCell-8 | YPack-C | ||
YCell-5 | 1 | 0.9995 | 0.9188 | 0.9178 | 0.9856 | ||
YCell-6 | 1 | 0.9181 | 0.9171 | 0.9857 | |||
YCell-7 | 1 | 0.9990 | 0.8999 | ||||
YCell-8 | 1 | 0.8991 | |||||
YPack-C | 1 | ||||||
(d) | YCell-9 | YCell-10 | YCell-11 | YCell-12 | YPack-D | ||
YCell-9 | 1 | 0.5767 | 0.3264 | 0.5750 | 0.4570 | ||
YCell-10 | 1 | 0.3664 | 0.4711 | 0.2647 | |||
YCell-11 | 1 | −0.5109 | 0.1485 | ||||
YCell-12 | 1 | 0.2640 | |||||
YPack-D | 1 |
Pack-A | Cell-1 | Cell-2 | |||||
---|---|---|---|---|---|---|---|
mu | 0.6789 | 0.7545 | 0.7712 | ||||
sigma | 5.0358 | 6.3175 | 6.7718 | ||||
p-value | >0.05 | >0.05 | >0.05 | ||||
Pack-B | Cell-3 | Cell-4 | |||||
mu | 1.0801 | 0.8617 | 0.4764 | ||||
sigma | 13.7966 | 12.5706 | 6.1109 | ||||
p-value | >0.05 | >0.05 | >0.05 | ||||
Pack-C | Cell-5 | Cell-6 | Cell-7 | Cell-8 | |||
mu | 1.2921 | 0.6813 | 0.6822 | 0.4124 | 0.4112 | ||
sigma | 24.4506 | 7.5422 | 7.4526 | 7.7252 | 7.6654 | ||
p-value | >0.05 | >0.05 | >0.05 | >0.05 | >0.05 |
Pack No. | Degradation Rate | Cell No. | Degradation Rate |
---|---|---|---|
Pack-A | 0.7998 | Cell-1 | 0.8019 |
Cell-2 | 0.8020 | ||
Pack-B | 1.2681 | Cell-3 | 0.8613 |
Cell-4 | 0.5543 | ||
Pack-C | 1.3131 | Cell-5 | 0.9024 |
Cell-6 | 0.9055 | ||
Cell-7 | 0.4931 | ||
Cell-8 | 0.4930 | ||
Pack-D | 0.3970 | Cell-9 | 0.0103 |
Cell-10 | 0.3730 | ||
Cell-11 | 0.6448 | ||
Cell-12 | −0.2737 |
Pack-A | YPack-A | TCell-1 | TCell-2 | ||||
YCell-1 | 0.4936 | −0.4968 | −0.1104 | ||||
YCell-2 | 0.4936 | −0.4967 | −0.1104 | ||||
Ncomp | 2 | ||||||
R2 | 0.9824 | 0.8323 | 0.9405 | ||||
Pack-B | YPack-B | TCell-3 | TCell-4 | ||||
YCell-3 | 0.5391 | −0.1781 | −0.0797 | ||||
YCell-4 | 0.4664 | −0.2226 | −0.1875 | ||||
Ncomp | 2 | ||||||
R2 | 0.9521 | 0.9082 | 0.9378 | ||||
Pack-C | YPack-C | TCell-5 | TCell-6 | TCell-7 | TCell-8 | ||
YCell-5 | 0.2240 | −0.1681 | −0.0424 | −0.0345 | −0.0114 | ||
YCell-6 | 0.2241 | −0.1681 | −0.0424 | −0.0345 | −0.0114 | ||
YCell-7 | 0.2100 | −0.2019 | −0.0742 | −0.0658 | −0.0417 | ||
YCell-8 | 0.2100 | −0.2019 | −0.0742 | −0.0658 | −0.0417 | ||
Ncomp | 2 | ||||||
R2 | 0.9300 | 0.9018 | 0.9068 | 0.9133 | 0.9050 |
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Wang, X.; Li, S.; Wang, L.; Sun, Y.; Wang, Z. Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State. Energies 2020, 13, 5934. https://doi.org/10.3390/en13225934
Wang X, Li S, Wang L, Sun Y, Wang Z. Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State. Energies. 2020; 13(22):5934. https://doi.org/10.3390/en13225934
Chicago/Turabian StyleWang, Xiaohong, Shixiang Li, Lizhi Wang, Yaning Sun, and Zhongxing Wang. 2020. "Degradation and Dependence Analysis of a Lithium-Ion Battery Pack in the Unbalanced State" Energies 13, no. 22: 5934. https://doi.org/10.3390/en13225934