State of Charge Estimation of Lithium-Ion Batteries Based on Fuzzy Fractional-Order Unscented Kalman Filter
Abstract
:1. Introduction
2. Theory and Method Research
2.1. Fractional-Order Calculus
2.2. Fractional-Order Model
2.3. Model Parameter Identification and Validation
3. Fuzzy Controller
4. SOC Estimation
- 1
- Initialization
- (1)
- Give the initial state , Q, R and state error covariance P.
- 2
- Time updating
- (1)
- Calculate sigma points using the singular value decomposition:
- (2)
- Transform the sigma sampling points using the nonlinear function :
- (3)
- Update the prior states estimation. The mean and covariance of and can be calculated by:
- 3
- Observation updating
- (1)
- Calculate sigma points using the singular value decomposition. The weight of the sigma points is obtained using (20):
- (2)
- Transform the sigma sampling points using the nonlinear function :
- (3)
- Estimate the observation-error covariance matrix:
- (4)
- Calculate the theoretical and actual covariances:
- (5)
- Update the observation noise variance:
- (6)
- Update the posterior states estimation:
5. Numerical Verification and Discussion
5.1. Experimental Results at 25 °C
5.2. Experimental Results at 0 °C
5.3. Experimental Results at 45 °C
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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0.5975 | 264.25 | 1.2679 | 448.54 | 0.4325 | 0.4380 |
Input fuzziness | NB | NS | Z | PS | PB |
Output fuzziness | NB | NS | Z | PS | PB |
RMSE | EKF | FUKF | FFUKF |
---|---|---|---|
FUDS | 0.87% | 0.67% | 0.20% |
BJDST | 1.95% | 0.68% | 0.13% |
RMSE | EKF | FUKF | FFUKF |
---|---|---|---|
FUDS | 0.88% | 0.85% | 0.20% |
BJDST | 1.49% | 1.04% | 0.32% |
RMSE | EKF | FUKF | FFUKF |
---|---|---|---|
FUDS | 1.49% | 1.08% | 0.51% |
BJDST | 2.18% | 1.20% | 0.58% |
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Chen, L.; Chen, Y.; Lopes, A.M.; Kong, H.; Wu, R. State of Charge Estimation of Lithium-Ion Batteries Based on Fuzzy Fractional-Order Unscented Kalman Filter. Fractal Fract. 2021, 5, 91. https://doi.org/10.3390/fractalfract5030091
Chen L, Chen Y, Lopes AM, Kong H, Wu R. State of Charge Estimation of Lithium-Ion Batteries Based on Fuzzy Fractional-Order Unscented Kalman Filter. Fractal and Fractional. 2021; 5(3):91. https://doi.org/10.3390/fractalfract5030091
Chicago/Turabian StyleChen, Liping, Yu Chen, António M. Lopes, Huifang Kong, and Ranchao Wu. 2021. "State of Charge Estimation of Lithium-Ion Batteries Based on Fuzzy Fractional-Order Unscented Kalman Filter" Fractal and Fractional 5, no. 3: 91. https://doi.org/10.3390/fractalfract5030091