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Improved covariance matching-electrical equivalent modeling for accurate internal state characterization of packing lithium‐ion batteries.

Wang, Shunli; Fan, Yongcun; Yu, Chunmei; Jin, Siyu; Fernandez, Carlos; Stroe, Daniel‐Ioan


Shunli Wang

Yongcun Fan

Chunmei Yu

Siyu Jin

Daniel‐Ioan Stroe


As for the cell-to-cell inconsistency of packing lithium-ion batteries, accurate equivalent modeling plays a significant role in the working characteristic monitoring and improving the safety protection quality under complex working conditions. In this work, a novel covariance matching–electrical equivalent circuit modeling method is proposed to realize the adaptive working state characterization by considering the internal reaction features, and an improved adaptive weighting factor correction-differential Kalman filtering model is constructed for the iterative calculation process. A new parameter named state of balance is introduced to describe the cell-to-cell variation mathematically by forming an effective influence correction strategy. An adaptive covariance matching method is investigated to update and transmit the noise matrix for high-power energy supply conditions, in which the weighting factor correction is conducted by considering the coupling relationship to improve the prediction accuracy. Experimental tests are conducted to verify the estimation effect, in which the closed-circuit voltage responds well corresponding to the battery state variation. The maximum closed-circuit voltage traction error is 1.80%, and the maximum SOC estimation error for packing lithium-ion batteries is 1.114% for the long-term experimental tests with the MAE value of 0.00481 and RMSE value of 5.44085E-5. The improved covariance matching-electrical equivalent circuit modeling method provides a theoretical foundation for the reliable application of lithium-ion batteries.


WANG, S., FAN, Y., YU, C., JIN, S., FERNANDEZ, C. and STROE, D.-I. 2021. Improved covariance matching-electrical equivalent modeling for accurate internal state characterization of packing lithium-ion batteries. International journal of energy research [online], Early View. Available from:

Journal Article Type Article
Acceptance Date Oct 9, 2021
Online Publication Date Nov 8, 2021
Deposit Date Nov 22, 2021
Publicly Available Date Nov 9, 2022
Journal International Journal of Energy Research
Print ISSN 0363-907X
Electronic ISSN 1099-114X
Publisher Wiley Open Access
Peer Reviewed Peer Reviewed
Keywords Adaptive covariance matching; Cell-to-cell variation; Electrical equivalent circuit modeling; Packing lithium-ion batteries; State of balance; Weighting factor correction
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