An online SOC and capacity estimation method for aged lithium-ion battery pack considering cell inconsistency

•Propose a “Special and Difference” model for the battery pack.•Construct a multi-time scale algorithm framework in the aged battery pack.•Monitor the cell with extreme capacity for the battery pack consistency management. For lithium-ion battery packs, especially aged lithium-ion batteries, the inconsistencies in State-of-Charge (SOC), model parameter and capacity between cells cannot be ignored. In order to accurately estimate the SOC and capacity of each cell in the lithium-ion battery pack online, a "Special and Difference (S&D)" model, i.e. a serial-connected battery pack model, is established based on a second-order equivalent circuit model as cell model. The multi-time scale extended Kalman filter algorithm is proposed based on “S&D” model to estimate the SOC, model parameter and capacity of each cell in the battery pack. The proposed algorithm involves three time dimensions: a short time scale which contains special cell's SOC and model parameter estimation, a middle time scale which contains the remaining cells’ SOC and model parameter estimation, and a long time scale which contains all cells’ capacity estimation. The multi-time scale extended Kalman filter algorithm for aged battery pack is verified under two dynamic conditions. The results show that the SOC estimation error of each cell in the battery pack is within 5% in the whole testing period and it is within 3% when the later capacity estimation process keeps stable. In addition, the number of the cells with maximum and minimum capacity can be accurately identified after the middle stage of the capacity estimation process, which is significant for the consistency management of the battery pack.