A Fractional-Order Kinetic Battery Model of Lithium-Ion Batteries Considering a Nonlinear Capacity
Abstract
:1. Introduction
2. Kinetic Battery Model (KiBaM)
3. The Proposed Fractional-Order KiBaM (FO-KiBaM)
3.1. Fractional Calculus Theory
3.2. Fractional-Order KiBaM
4. Parameter Identification and Experiment Verification
4.1. Experimental Platform and Test Results
4.2. Parameter Identification
4.3. Experiment Verification
5. Conclusions
6. Patents
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Abbreviations
LIB | lithium-ion battery |
EchM | electrochemical model |
AM | analytical model |
SM | stochastic model |
NNM | neural network model |
ECM | equivalent circuit model |
U-I | voltage-current |
KiBaM | kinetic battery model |
T-KiBaM | temperature-dependent kinetic battery model |
FO-KiBaM | fractional-order kinetic battery model |
BMS | battery management system |
Ah | ampere hours |
SOC | state of charge |
SOH | state of health |
SOP | state of peak power |
SOF | state of function |
SOE | state of energy |
C-rate | current rate |
CCCV | constant-current and constant-voltage |
CC | constant current |
CV | constant voltage |
FDD | fractional derivative definition |
GL-FDD | Grunwald-Letnikov fractional derivative definitions |
RL-FDD | Riemann-Liouville fractional derivative definitions |
MAE | mean absolute error |
Nomenclature | |
y1 | directly available capacity |
h1 | height of directly available capacity |
y2 | temporary capacity |
h2 | height of temporary capacity well |
the height difference of two wells | |
k | rate that the charge flows from y2 into y1 |
c | capacity proportion of two wells |
i | discharge current |
I | the constant discharge current |
the initial time | |
the discharge end time | |
the recovery end time | |
Cav | available capacity of battery |
Cunav | unavailable capacity of battery |
Crem | remaining available capacity of battery |
Cmax | the maximum available capacity of battery |
Ct0 | initial capacity of battery |
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Parameter | Value | Parameter | Value |
---|---|---|---|
Type | LR1865SZ | Series-parallel | 1S-13P |
Nominal voltage | 3.6 V | Rated capacity | 2.5 Ah |
End-of-charge voltage | 4.2 V | End-of-discharge voltage | 3.0 V |
Discharge Rate (C) | Discharge Current (A) | Discharge Time (min) | Released Capacity (Ah) | Proportion (%) |
---|---|---|---|---|
0.2 | 6.410 | 292.5 | 31.24 | 96.12 |
0.67 | 21.26 | 87.34 | 30.95 | 95.23 |
1 | 31.88 | 57.81 | 30.72 | 94.52 |
1.5 | 47.83 | 37.56 | 29.94 | 92.12 |
2 | 63.78 | 27.39 | 29.11 | 89.57 |
3 | 95.69 | 17.30 | 27.59 | 84.89 |
Discharge Current (A) | Available Capacity (Ah) | Improve Accuracy (%) | ||
---|---|---|---|---|
Experimental Data | KiBaM | FO-KiBaM | ||
6.410 | 31.24 | 32.12 | 32.04 | 0.26 |
21.26 | 30.95 | 31.27 | 31.03 | 0.78 |
47.83 | 29.94 | 30.10 | 29.90 | 0.67 |
63.78 | 29.11 | 29.66 | 29.50 | 0.55 |
95.69 | 27.59 | 29.11 | 29.04 | 0.25 |
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Zhang, Q.; Li, Y.; Shang, Y.; Duan, B.; Cui, N.; Zhang, C. A Fractional-Order Kinetic Battery Model of Lithium-Ion Batteries Considering a Nonlinear Capacity. Electronics 2019, 8, 394. https://doi.org/10.3390/electronics8040394
Zhang Q, Li Y, Shang Y, Duan B, Cui N, Zhang C. A Fractional-Order Kinetic Battery Model of Lithium-Ion Batteries Considering a Nonlinear Capacity. Electronics. 2019; 8(4):394. https://doi.org/10.3390/electronics8040394
Chicago/Turabian StyleZhang, Qi, Yan Li, Yunlong Shang, Bin Duan, Naxin Cui, and Chenghui Zhang. 2019. "A Fractional-Order Kinetic Battery Model of Lithium-Ion Batteries Considering a Nonlinear Capacity" Electronics 8, no. 4: 394. https://doi.org/10.3390/electronics8040394
APA StyleZhang, Q., Li, Y., Shang, Y., Duan, B., Cui, N., & Zhang, C. (2019). A Fractional-Order Kinetic Battery Model of Lithium-Ion Batteries Considering a Nonlinear Capacity. Electronics, 8(4), 394. https://doi.org/10.3390/electronics8040394