A robust extended Kalman filter (EKF) is proposed as a method for estimation of the state of charge (SOC) of lithium-ion batteries used in hybrid electric vehicles (HEVs). An equivalent circuit model of the battery, including its electromotive force (EMF) hysteresis characteristics and polarization characteristics is used. The effect of the robust EKF gain coefficient on SOC estimation is analyzed, and an optimized gain coefficient is determined to restrain battery terminal voltage from fluctuating. Experimental and simulation results are presented. SOC estimates using the standard EKF are compared with the proposed robust EKF algorithm to demonstrate the accuracy and precision of the latter for SOC estimation.

Fast capacity estimation is a key enabling technique for second-life of lithium-ion batteries due to the hard work involved in determining the capacity of a large number of used electric vehicle (EV) batteries. This paper tries to make three contributions to the existing literature through a robust and advanced algorithm: (1) a three layer back propagation artificial neural network (BP ANN) model is developed to estimate the battery capacity. The model employs internal resistance expressing the battery’s kinetics as the model input, which can realize fast capacity estimation; (2) an estimation error model is established to investigate the relationship between the robustness coefficient and regression coefficient. It is revealed that commonly used ANN capacity estimation algorithm is flawed in providing robustness of parameter measurement uncertainties; (3) the law of large numbers is used as the basis for a proposed robust estimation approach, which optimally balances the relationship between estimation accuracy and disturbance rejection. An optimal range of the threshold for robustness coefficient is also discussed and proposed. Experimental results demonstrate the efficacy and the robustness of the BP ANN model together with the proposed identification approach, which can provide an important basis for large scale applications of second-life of batteries.

Battery model identification is very important for reliable battery management as well as for battery system design process. The common problem in identifying battery models is how to determine the most appropriate mathematical model structure and parameterized coefficients based on the measured terminal voltage and current. This paper proposes a novel semiparametric approach using the wavelet-based partially linear battery model (PLBM) and a recursive penalized wavelet estimator for online battery model identification. Three main contributions are presented. First, the semiparametric PLBM is proposed to simulate the battery dynamics. Compared with conventional electrical models of a battery, the proposed PLBM is equipped with a semiparametric partially linear structure, which includes a parametric part (involving the linear equivalent circuit parameters) and a nonparametric part [involving the open-circuit voltage (OCV)]. Thus, even with little prior knowledge about the OCV, the PLBM can be identified using a semiparametric identification framework. Second, we model the nonparametric part of the PLBM using the truncated wavelet multiresolution analysis (MRA) expansion, which leads to a parsimonious model structure that is highly desirable for model identification; using this model, the PLBM could be represented in a linear-in-parameter manner. Finally, to exploit the sparsity of the wavelet MRA representation and allow for online implementation, a penalized wavelet estimator that uses a modified online cyclic coordinate descent algorithm is proposed to identify the PLBM in a recursive fashion. The simulation and experimental results demonstrate that the proposed PLBM with the corresponding identification algorithm can accurately simulate the dynamic behavior of a lithium-ion battery in the Federal Urban Driving Schedule tests.