Enhancing Stability and Robustness of State-of-Charge Estimation for Lithium-Ion Batteries by Using Improved Adaptive Kalman Filter Algorithms
Abstract
:1. Introduction
2. Experiments
3. Description of the Adaptive Kalman Filter
3.1. Adaptive Sage-Husa Kalman Filter
3.2. Adaptive Kalman Filter Based on the Maximum Likelihood Criterion
3.3. State-of-Charge Estimation
4. Results and Discussion
4.1. State-of-Charge Estimation Using the Improved Sage-Husa Algorithm
4.2. Estimation Using the Improved Maximum Likelihood Criterion Algorithm
4.3. Effects of the State Variable Error Covariance on the Estimation
4.4. Effects of the Noise Covariance on the Estimation
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AEKF | Adaptive extend Kalman filter |
BMS | Battery Management System |
CCD | Constant current discharge |
CDKF | Central difference Kalman filter |
DEKF | Dual extended Kalman filter |
DP | Dual polarization |
EV | Electric vehicles |
EKF | Extend Kalman filter method |
FUDS | Federal Urban Driving Schedule |
HPPC | Hybrid pulse power characteristic |
IIAE | Improved innovation-based adaptive estimation |
ISH I | Improved Sage-Husa 1 |
ISH II | Improved Sage-Husa 2 |
PNGV | Partnership for a new generation of vehicles |
RMSE | Root mean square error |
SOC | State of charge |
SOP | State of power |
SRUKF | Square-root unscented Kalman filter |
UKF | Unscented Kalman filter |
UDDS | Urban Dynamometer Driving Schedule |
List of Notations
b | Forgetting factor |
covariance | |
The rated capacity of the battery | |
Concentration capacitance | |
Electrochemical capacitance | |
covariance | |
Adaptive factors | |
Kalman gain | |
M | Moving average window length |
The initial error covariance | |
The auto-covariance of SOC | |
covariance matrix | |
covariance matrix | |
Ohmic internal resistance | |
Concentration resistance | |
Electrochemical resistance | |
The innovation as a residual sequence | |
Open circuit voltage | |
The terminal voltage of the battery | |
Concentration polarization voltage | |
Electrochemical polarization voltage | |
System excitation | |
Measurement noise | |
State vector | |
Filtered value of the state variable | |
Predicted value of the state variable | |
Predicted value of the measured variable | |
Process noise | |
The discharge efficiency |
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Step 2 Computation: for k = 1, 2, 3… Time update: | |
Kalman gain: | |
Measurement update: | |
Adaptive factor: | |
Process noise covariance and measurement noise covariance update: | |
ISH I: | |
ISH II: | |
Step 2 Computation: For k = 1, 2, 3… Time update: |
Kalman gain: |
Measurement update: |
Judgement: |
If (estimated step size < M) |
Else |
Process noise covariance and measurement noise covariance update: |
Algorithm | Operating Conditions | Max(%) | Mean(%) | RMSE(%) | Convergence Time/s |
---|---|---|---|---|---|
SH | CCD | 16.72 | 1.652 | 3.693 | 98 |
ISH I | 2.929 | 1.562 | 3.311 | 96 | |
ISH II | 5.345 | 1.856 | 3.603 | 63 | |
ISH I | FUDS | 2.306 | 0.822 | 1.857 | 87 |
ISH II | 3.257 | 0.952 | 2.009 | 59 |
Algorithm | Max(%) | Mean(%) | RMSE(%) | Convergence Time/s |
---|---|---|---|---|
IAE (M = 100) | 4.218 | 0.841 | 2.982 | 36 |
IIAE (M = 100) | 1.377 | 1.234 | 2.857 | 29 |
IIAE (M = 10) | 1.438 | 1.263 | 2.828 | 21 |
Initial SOC | Test | Algorithm | Max (%) | Mean(%) | RMSE(%) | Convergence Time/s |
---|---|---|---|---|---|---|
SOC = 0.2 | CCD | ISH I | 2.929 | 1.557 | 3.312 | 109 |
IIAE | 1.437 | 1.264 | 2.828 | 22 | ||
SOC = 0.4 | CCD | ISH I | 2.919 | 1.548 | 3.327 | 97 |
IIAE | 1.383 | 1.213 | 2.245 | 19 | ||
SOC = 0.6 | CCD | ISH I | 2.921 | 1.544 | 2.5 | 92 |
IIAE | 1.363 | 1.206 | 1.68 | 15 | ||
SOC = 0.8 | CCD | ISH I | 2.952 | 1.514 | 1.721 | 16 |
IIAE | 1.354 | 1.154 | 1.302 | 6 | ||
50% error | DST | Ref. [39] | 2.49 | 0.63 | - | 6 |
No error | nonstandard | Ref. [40] | - | 0.12 | 3.50 | - |
No error | B-DST | Ref. [41] | 2 | 1.24 | 1.35 | - |
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Zhang, F.; Yin, L.; Kang, J. Enhancing Stability and Robustness of State-of-Charge Estimation for Lithium-Ion Batteries by Using Improved Adaptive Kalman Filter Algorithms. Energies 2021, 14, 6284. https://doi.org/10.3390/en14196284
Zhang F, Yin L, Kang J. Enhancing Stability and Robustness of State-of-Charge Estimation for Lithium-Ion Batteries by Using Improved Adaptive Kalman Filter Algorithms. Energies. 2021; 14(19):6284. https://doi.org/10.3390/en14196284
Chicago/Turabian StyleZhang, Fan, Lele Yin, and Jianqiang Kang. 2021. "Enhancing Stability and Robustness of State-of-Charge Estimation for Lithium-Ion Batteries by Using Improved Adaptive Kalman Filter Algorithms" Energies 14, no. 19: 6284. https://doi.org/10.3390/en14196284