State of Charge (SOC) Estimation Based on Extended Exponential Weighted Moving Average H∞ Filtering
Abstract
:1. Introduction
2. Battery Modeling
2.1. Model Establishment
2.2. Acquisition of SOC-OCV Curve
2.3. Model Parameters Identification
3. SOC Estimation
3.1. HIF Algorithm
3.2. EE-HIF Algorithm
4. Experimental Verification
4.1. Comparative Analysis of the EWMA and HIF Algorithms
4.2. Comparative Analysis of Three Estimation Methods of the EE-HIF, EWMA, and HIF Algorithms
4.3. Comparative Analysis of the Three Estimation Methods (EE-HIF, EWMA, and HIF) When the Model Error Increases
4.4. Estimation under Variable Current
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclatures
SOC | state of charge |
BMS | battery management system |
OCV | open circuit voltage |
KF | Kalman filter |
EKF | extended Kalman filter |
UKF | unscented Kalman filter |
HIF | H∞ algorithm |
EV | electric vehicle |
EE-HIF | extended exponential weighted moving average H∞ algorithm |
EWMA | exponential weighted moving average H∞ algorithm |
RC | resistor–capacitor |
system matrix | |
input matrix | |
output matrix | |
direct transfer matrix | |
filter gain vector | |
second-order prediction covariance matrix | |
unit matrix | |
symmetric positive definite matrix that can be customized | |
full rank custom matrix | |
covariance of | |
covariance of | |
errormax | maximum error |
RMSE | root mean square error |
system noise | |
observation noise | |
constant weighting coefficient | |
exponential weighting coefficient | |
the standard deviation of the Gaussian function | |
time constant of network | |
the state variable of the system | |
exponential weighted estimation value | |
the prior value of | |
the posterior value of | |
the output of the lithium battery system | |
control input of the battery system | |
resistance of lithium battery system | |
capacitance of lithium battery system | |
sampling period | |
operating current of the lithium battery | |
the rated capacity of the lithium battery |
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Algorithm | H∞ (HIF) | Exponential Weighted Moving Average (EWMA) | Extended Exponential Weighted Moving Average H∞ (EE-HIF) |
---|---|---|---|
errormax | 3.24% | 2.23% | 1.91% |
Root mean square error (RMSE) | 1.02% | 0.87% | 0.48% |
Convergence speed | 6.9 s | 4.8 s | 3.6 s |
Computational time | 4.23 s | 4.56 s | 5.08 s |
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Zhang, S.; Wan, Y.; Ding, J.; Da, Y. State of Charge (SOC) Estimation Based on Extended Exponential Weighted Moving Average H∞ Filtering. Energies 2021, 14, 1655. https://doi.org/10.3390/en14061655
Zhang S, Wan Y, Ding J, Da Y. State of Charge (SOC) Estimation Based on Extended Exponential Weighted Moving Average H∞ Filtering. Energies. 2021; 14(6):1655. https://doi.org/10.3390/en14061655
Chicago/Turabian StyleZhang, Shuaishuai, Youhong Wan, Jie Ding, and Yangyang Da. 2021. "State of Charge (SOC) Estimation Based on Extended Exponential Weighted Moving Average H∞ Filtering" Energies 14, no. 6: 1655. https://doi.org/10.3390/en14061655