A Methodology for Characterizing Lithium-Ion Batteries Under Constant-Current Charging Based on Spectral Analysis
Abstract
:1. Introduction
- Electrochemical models;
- Equivalent circuit models;
- Performance-based models;
- Analytical models with empirical fitting;
- Statistical approaches.
2. The Methodology Based on Spectra Generation and the Experimental Setup
- Divide the complete voltage curve U(t) into two distinct phases (see Figure 1). The first (primary) phase includes data from the starting point up to the inflection point, while the secondary phase covers the data from the inflection point to the endpoint.
- Calculate the discrete spectrum using the experimental data from the first phase of the curve.
- Subtract the theoretically modeled curve (approximated over the entire range, from the starting point to the endpoint) from the experimental curve. This results in a monotonically increasing curve that includes data from the time range between the inflection point and the endpoint. We refer to this as the secondary curve.
- Calculate the discrete spectrum for the newly obtained curve.
Experimental Setup
3. Numerical Calculations and Error Analysis
3.1. Fitting the Primary Phase of the Voltage Curve
3.2. Fitting Secondary Phase of the Voltage Curve
4. Final Results of the Modeling
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Genetic Algorithm | Levenberg–Marquardt | |||
---|---|---|---|---|
71,914.9 [s/V] | 505,370 [s/V] | |||
[s] | [V] | [s] | [V] | |
1 | 8.913004 × 10−3 | 3.033364 × 10−1 | 9.000 × 10−3 | 3.134 × 10−1 |
2 | 8.461603 × 10−2 | 7.481855 × 10−2 | 1.769 × 10−1 | 7.540 × 10−2 |
3 | 2.566468 × 100 | 1.743974 × 10−1 | 3.074 × 100 | 1.765 × 10−1 |
4 | 4.409065 × 101 | 2.054043 × 10−1 | 6.371 × 101 | 3.442 × 10−1 |
5 | 1.173434 × 102 | 2.032495 × 10−1 | 2.810 × 102 | 5.520 × 10−2 |
6 | 4.526886 × 103 | 4.813059 × 10−2 | 5.088 × 103 | 1.141 × 10−1 |
SSE | 6.8 × 10−4 | 2.0 × 10−4 |
Error Estimation | |||||
---|---|---|---|---|---|
SSE | 0.1132 | 0.0048 | 0.0034 | 0.0007 | 0.0002 |
R-square | 0.9859 | 0.9994 | 0.9996 | 0.9999 | 1.0000 |
RMSE | 0.0295 | 0.0061 | 0.0052 | 0.0024 | 0.0013 |
[s] | [V] | |
---|---|---|
1 | 239.5 | 1.103 × 10−3 |
2 | 1999 | 3.369 × 10−3 |
3 | 2597 | 1.4610 × 10−2 |
4 | 3097 | 2.585 × 10−3 |
5 | 3597 | 1.475 × 10−2 |
SSE | 8.585 × 10−5 | |
R-square | 0.9982 | |
RMSE | 1.721 × 10−3 |
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Nikonov, A.; Nagode, M.; Klemenc, J. A Methodology for Characterizing Lithium-Ion Batteries Under Constant-Current Charging Based on Spectral Analysis. World Electr. Veh. J. 2025, 16, 308. https://doi.org/10.3390/wevj16060308
Nikonov A, Nagode M, Klemenc J. A Methodology for Characterizing Lithium-Ion Batteries Under Constant-Current Charging Based on Spectral Analysis. World Electric Vehicle Journal. 2025; 16(6):308. https://doi.org/10.3390/wevj16060308
Chicago/Turabian StyleNikonov, Anatolij, Marko Nagode, and Jernej Klemenc. 2025. "A Methodology for Characterizing Lithium-Ion Batteries Under Constant-Current Charging Based on Spectral Analysis" World Electric Vehicle Journal 16, no. 6: 308. https://doi.org/10.3390/wevj16060308
APA StyleNikonov, A., Nagode, M., & Klemenc, J. (2025). A Methodology for Characterizing Lithium-Ion Batteries Under Constant-Current Charging Based on Spectral Analysis. World Electric Vehicle Journal, 16(6), 308. https://doi.org/10.3390/wevj16060308