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| State of Charge Estimation of Lithium-Ion Battery Based on Enhanced Extended Kalman Filter Algorithm with Observation Equation Reconstruction |
| Huang Kai1, Sun Kai1, Guo Yongfang2, Wang Zipeng1, Li Senmao1 |
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China;
2. School of Artificial Intelligence Hebei University of Technology Tianjin 300130 China |
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Abstract Lithium-ion batteries play a crucial role in energy storage, aerospace, new energy vehicles and other fields. However, over-charging and over-discharging will cause irreversible damage, consequently, to ensure the reliable and safe operation of batteries, it is very necessary to accurately estimate the state of charge (SOC) in real time. Considering that the observation equation of the dynamical system is an important factor affecting the SOC estimation result, an adaptive error correction strategy is put forward in the paper, furthermore, the observation equation is reconstructed. Combined with the extended Kalman filter (EKF), the enhanced EKF is established to estimate SOC.
Here, the widely used first-order RC model is adopted as the battery equivalent circuit model (ECM). In addition, it mainly studies the commonly used 20%~80% SOC working range.
Firstly, the effects of the parameter identification method, ambient temperature, SOC and current ratio on the offset between the output of the observation equation and the true measurement value are studied. The results show that: (1) at the same temperature and working condition, the probability density distribution of the output error of the observation equation produced by the two parameter identification methods (Recursive least squares of forgetting factor (FFRLS) and EKF) is very similar, more specifically, the difference of the average output error of them is less than 15%. (2) Temperature has a great influence on the output error of observation equation. Generally, the lower the temperature, the greater the output error. The higher the temperature, the closer and smaller the errors under the same SOC. (3) In general, the larger the current rate, the larger the output error of the observation equation. The extreme point of output error basically occurs when the current rate changes. (4) The output error of observation equation fluctuates with SOC, and its distribution has no obvious rule. Base on the experimental analysis, it is inferred that, the output error of the observation equation is mainly affected by the battery rate, temperature and SOC, and is less affected by the parameter identification algorithm, so it will be ignored in the paper. Secondly, according to the output error distribution and analysis results, an adaptive error correction model is generated, which is a second-order polynomial about SOC. In which, the coefficients of secondary and primary terms are affected by temperature and SOC, while the coefficient of the constant term are affected by temperature and current rate. As a result, the error correction model can adapt to current rate, SOC and temperature in practical applications. Finally, the adaptive error correction model is used to reconstruct the observation equation, combined with the EKF (named E-EKF) to update the SOC in real time.
DST and US06 conditions are used to verify the validity of the adaptive error correction model and the performance of E-EKF algorithm. In which, DST conditions at 0℃, 20℃ and 40℃ are used to train the adaptive error correction model, and US06 and DST at 0℃, 10℃, 20℃, 25℃, 30℃ and 40℃ are used to test the model. On the one hand, the accuracy of the observation equation of E-EKF and EKF is obtained, the results show that, compared with EKF, the average output error generated by the observed equation in E-EKF is reduced by 71.84% in DST condition and 60.92% in US06 condition. On the other hand, the SOC estimation accuracy of E-EKF, EKF and adaptive EKF (AEKF) is obtained. The results show that, compared with EKF and AEKF, the average SOC estimation error of E-EKF is reduced by 18.12% and 6.15% in DST condition and 73.64% and 30.00% in US06 condition respectively.
In summary, current rate, SOC working range and ambient temperature which influence the performance of Lithium-ion batteries are dynamic change in practical applications. Ignoring these factors, when using EKF to estimate SOC, there will be a large error (that is, a large innovation) between the output of the observation equation and the measurement value, resulting in lower SOC estimation accuracy. The adaptive error correction model proposed can help to reduce the innovation, so as to improve the accuracy of SOC estimation.
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Received: 13 January 2023
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2024, Vol. 39 
