Real-time SOC co-estimation algorithm for Li-ion batteries based on fast square-root unscented Kalman filters
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摘要: 針對標準無跡卡爾曼濾波(Unscented Kalman filter, UKF) 算法本身存在著因狀態誤差協方差矩陣無法實現Cholesky分解而導致濾波發散的隱患，以及在電池狀態估計過程中由離線標定的電池等效模型參數而造成的累積誤差的問題，本文發展了一種平方根無跡卡爾曼濾波(Square-root unscented Kalman filter, SR-UKF)算法，并設計了一種電池狀態聯合估計策略。首先快速SR-UKF算法通過對觀測方程進行準線性化處理，降低了每次無跡變換時的計算開銷；然后在迭代過程中，用狀態誤差協方差矩陣的平方根代替狀態誤差協方差矩陣，該平方根是由QR分解與 Cholesky因子的一階更新得到，解決了UKF 算法迭代過程中可能由計算累積誤差引起狀態誤差協方差矩陣負定而導致濾波結果發散的問題，保證了電池荷電狀態(State of charge，SOC)在線滾動估計的數值穩定性；最后采用聯合估計策略，對電池等效模型參數進行實時辨識，保證了電池等效模型的準確性與有效性，從而提高了電池SOC的估計精度。仿真對比結果驗證了快速SR-UKF算法以及電池狀態聯合估計策略的可行性與魯棒性。
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關鍵詞:
- 荷電狀態 /
- 健康狀態 /
- 平方根無跡卡爾曼濾波 /
- 聯合估計 /
- 鋰離子動力電池
Abstract: The Li-ion battery is an important energy source for electric vehicles (EVs), and the accurate estimation of the battery power state provides a reliable reference for balancing the battery packing and battery management system (BMS). It also has great practical significance for making full and reasonable utilization of batteries, and improving the battery life cycle and vehicle operation efficiency. Practical issues that must be addressed include the filtering divergence caused by the non-positive definite error covariance matrix in the standard unscented Kalman filter (UKF) and the state estimation errors that accumulate from the simplified mathematical modeling of the Li-ion battery, with its inherently strong non-linearity, time variation, and uncertainty. To resolve these issues, in this article, a real-time state co-estimation algorithm was proposed based on a fast square-root unscented Kalman filter (SR-UKF) framework. First, during the iteration process, the non-linear measurement function, which describes the propagation of each sigma point, is called by an unscented transform. A reduction in computational complexity can be achieved if the non-linear measurement function is quasi-linearized. Second, instead of a state error covariance matrix, the square root of the state error covariance matrix is used, which is obtained by QR decomposition and first-order updating of the Cholesky factor. This step deals with the problem that arises if the state error covariance matrix is negative definite due to the computational errors accumulated while performing recursive estimation with the standard UKF. This guarantees the numerical stability of the battery’s estimated state of charge (SOC) in real time. Third, the inner ohmic resistance and nominal capacity that indirectly characterize the state of health can be estimated online, and a highly precise SOC estimation can be realized due to the accuracy and efficiency of the battery model. Comparative experimental results confirm and validate the feasibility and robustness of the proposed fast SR-UKF algorithm and co-estimation strategy. -
圖 7 SOC初值標定偏差為5%情況下的SOC估計曲線對比
Figure 7. Comparison of SOC estimations when the calibration deviation of initial SOC value is 5%
圖 9 放電過程中端電壓的峰谷壓差曲線
Figure 9. Peak–valley difference in terminal voltage during discharge process
圖 11 SOC初值標定偏差為4%情況下的SOC估計曲線對比
Figure 11. Comparison of SOC estimations when the calibration deviation of initial SOC value is 4%
表 1 基于二階RC網絡的模型參數
Table 1. Parameters of 2nd-order RC model
Re/mΩ Rs/mΩ Rl/mΩ Q0/(A·h) Cs/F Cl /F 5.9 2.0 3.8 29.3 36000 68400 
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