The state of charge (SOC) for a lithium-ion battery is a key index closely related to battery performance and safety with respect to the power supply system of electric vehicles. The Kalman filter (KF) or extended KF (EKF) is normally employed to estimate SOC in association with the relatively simple and fast second-order resistor-capacitor (RC) equivalent circuit model for SOC estimations. To improve the stability of SOC estimation, a two-stage method is developed by combining the second-order RC equivalent circuit model and the eXogenous Kalman filter (XKF) to estimate the SOC of a lithium-ion battery. First, approximate SOC estimation values are observed with relatively poor accuracy by a stable observer without considering parameter uncertainty. Second, the poor accuracy SOC results are further fed into XKF to obtain relative stable and accurate SOC estimation values. Experiments demonstrate that the SOC estimation results of the present method are superior to those of the commonly used EKF method. It is expected that the present two-stage XKF method will be useful for the stable and accurate estimation of SOC in the power supply system of electric vehicles.
This work analyzes the causes of the slip phenomenon in the impeller on the basis of the internal flow mechanism. Detailed optical measurements of the flow inside the rotation passages of a five-bladed centrifugal pump impeller are obtained through particle image velocimetry (PIV). On the basis of experimental data, the deviation coefficient of slip velocity is proposed and then revised according to the slip factor calculation formula of Stechkin. Results show that, at the same rotation speed, the slip factor increases with the flow rate and reaches the maximum value at 1.0 QBEP flow rate. At different rotation speeds, the slip factor increases with the rotation speed and shows a relatively large variation range. Moreover, a revised slip factor formula is proposed. The modified model is suitable for the correction of slip factor at part-load flow rates and serves as a guide for the hydraulic performance design and prediction of centrifugal pumps.
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