Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data
Abstract
1. Introduction
2. Battery Model and Parameter Identification
2.1. Battery Model
2.2. The Proposed MIDRLS Algorithm
Algorithm 1 The algorithm flow of the proposed MIDRLS |
. |
. |
End For |
2.3. Parameter Identification of the Battery Model
3. SOC Estimation Based on the Joint MIDRLS-UKF Algorithm
3.1. Equations of State and Measurement for the Battery Model
3.2. SOC Estimation Based on the UKF Algorithm
- (1)
- Initialize:
- (2)
- Obtain Sigma points at time :The weighting factors are
- (3)
- Calculate the forecasted values of the mean and covariance matrix:
- (4)
- Update the sigma sample points:
- (5)
- Calculate the estimated values of the output and the Kalman gain:
- (6)
- Update the state variables and error covariance matrix:
3.3. Implementation Flow of the MIDRLS-UKF Algorithm
4. Simulation Results and Analysis
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
SOC | state of charge |
UKF | unscented Kalman filter |
EKF | extended Kalman filter |
FFRLS | forgetting factor recursive least square |
MIDRLS | recursive least square with missing input data |
BMS | battery management system |
RMSE | root mean square error |
MAE | maximum absolute error |
Symbols | |
voltage of the ideal voltage source | |
battery equivalent internal resistance | |
polarization resistance | |
polarization capacitor | |
battery terminal voltage | |
load current | |
Bernoulli random variable | |
input data | |
input data with random missing values | |
probability that input data are not missing | |
constant times of imputation | |
output data | |
parameter vector to be identified | |
forgetting factor | |
objective function of the FFRLS algorithm | |
time step index | |
sampling time | |
maximum capacity of the battery | |
Coulombic efficiency | |
state vector | |
process noise | |
measurement noise | |
terminal voltage minus ideal voltage source voltage | |
measure vector | |
estimated value of the initial state | |
initial error covariance matrix | |
dimension of state variable | |
weighted value of the mean of the sampling points | |
weighted value of the error covariance matrices | |
estimated value of the state variable at moment | |
gain matrix |
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Parameters of the MIDRLS Algorithm | Parameters of the UKF Algorithm |
---|---|
Algorithm | RMSE (%) | MAE (%) |
---|---|---|
MIDRLS-UKF | 0.43% | 0.81% |
FFRLS-UKF | 8.12% | 14.64% |
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Li, X.; Zheng, Z.; Meng, J.; Wang, Q. Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data. Electronics 2024, 13, 4436. https://doi.org/10.3390/electronics13224436
Li X, Zheng Z, Meng J, Wang Q. Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data. Electronics. 2024; 13(22):4436. https://doi.org/10.3390/electronics13224436
Chicago/Turabian StyleLi, Xi, Zongsheng Zheng, Jinhao Meng, and Qinling Wang. 2024. "Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data" Electronics 13, no. 22: 4436. https://doi.org/10.3390/electronics13224436
APA StyleLi, X., Zheng, Z., Meng, J., & Wang, Q. (2024). Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data. Electronics, 13(22), 4436. https://doi.org/10.3390/electronics13224436