An Online State of Charge Estimation Algorithm for Lithium-Ion Batteries Using an Improved Adaptive Cubature Kalman Filter

2018 Energies  
An accurate state of charge (SOC) estimation of the on-board lithium-ion battery is of paramount importance for the efficient and reliable operation of electric vehicles (EVs). Aiming to improve the accuracy and reliability of battery SOC estimation, an improved adaptive Cubature Kalman filter (ACKF) is proposed in this paper. The battery model parameters are online identified with the forgetting factor recursive least squares (FRLS) algorithm so that the accuracy of SOC estimation can be
more » ... r improved. The proposed method is evaluated by two driving cycles, i.e., the New European Driving Cycle (NEDC) and the Federal Urban Driving Schedule (FUDS), and compared with the existing unscented Kalman filter (UKF) and standard CKF algorithms to verify its superiority. The experimental results reveal that comparing with the UKF and standard CKF, the improved ACKF algorithm has a faster convergence rate to different initial SOC errors with higher estimation accuracy. The root mean square error of SOC estimation without initial SOC error is less than 0.5% under both the NEDC and FUDS cycles. The non-model based methods typically include the look-up table method, the Ampere-hour integral or Coulomb counting method [11, 12] , the open-circuit voltage method [13] , the electrochemical impedance spectroscopy method [14] , and machine learning based methods (e.g., artificial neural networks [15, 16] , fuzzy logic models, and support vector machines [17, 18] ). For example, Dang et al. [15] investigated open-circuit voltage-based SOC estimation by using a dual neural network fusion battery model. Anto'n et al. [17] studied the usage of a support vector machine in lithium-ion battery SOC estimation. Li et al. [19] combined a 12-input-2-level merged fuzzy neural network with a reduced-form generic algorithm to predict battery SOC. These non-model-based methods are featured with open-loop estimators, so they have several shortcomings. Firstly, they are incapable of correcting errors caused by factors regardless of inaccurate initial SOC values, measurement noises, or model uncertainties. Secondly, a large number of training data covering all of the driving conditions is required in order to improve the estimation accuracy of the machine learning-based methods, otherwise a large prediction error will be caused by the uncertainty of the new data set. However, it is a huge challenge and time-consuming to collect the large amount of training data needed. Compared with the non-model-based methods, the model-based filtering estimation approaches featured with closed-loop estimators can online correct estimating deviation caused by initial SOC errors, measurement noises, and parameter uncertainties. Among the model-based methods, the Kalman filter (KF)-based SOC estimation methods have the merits of self-correction, online computation, and the availability of dynamic SOC estimation. They have accordingly been widely studied and commonly used in online SOC estimation. The Kalman filter was originally proposed to estimate the state of linear systems. Later, in order to introduce the KF estimator into nonlinear systems, the extended Kalman filter (EKF) and the unscented Kalman filter (UKF) were developed. The EKF-based and UKF-based methods for battery SOC estimation have been investigated in , respectively. However, some intrinsic shortcomings of the EKF limit its application in practice. For instance, large errors are possibly caused by the linearizing process of the highly nonlinear battery system. Furthermore, computation of the Jacobian matrix is complicated and may lead to filter instability. Compared with the EKF, the UKF can reduce the estimation error and does not need to calculate the complicated Jacobian matrix. Nevertheless, the EKF and UKF algorithms are both subject to divergence or the curse of dimensionality or both [41] . Later, the cubature Kalman filter (CKF), which is suitable for state estimation of high-order nonlinear systems, was proposed on the basis of the radial-spherical cubature rule [42, 43] . In the CKF algorithm, a set of 2n points (where n represents the state-vector dimension) is employed to simulate the mean and covariance of states of nonlinear systems suffering from additive Gaussian noise. The process noise covariance and measurement noise covariance are well-known to have a distinct influence on the filtering performance and stability of the KF algorithms. In standard EKF, UKF, and CKF, both the process noise covariance and measurement noise covariance are considered to be constant and their values need to be pre-specified by a trial-and-error process which is time-consuming, laborious, and error-prone. Additionally, for battery SOC estimation, inappropriate values of the noise covariance are very likely to result in a large estimation error. Therefore, an adaptive cubature Kalman filter (ACKF) was presented in [44] to improve the SOC estimation accuracy through the voltage residual-based updating law. However, the converged root mean square error (RMSE) of SOC estimation wildly fluctuates with different initial SOC errors. In addition, the battery model parameters are determined by an offline identification method. In fact, however, the battery parameters are changeable during the discharge or charge process. It is accordingly essential to identify the battery model parameters online. Aiming to improve the SOC estimation accuracy, in this paper, an adaptive cubature Kalman filter is presented based on the improved Sage-Husa estimator. The values of the process noise covariance matrix and the measurement noise covariance matrix are both adaptively updated according to the output voltage residual sequence of the battery model. Besides, the process noise variance matrix and the measurement noise variance matrix can be ensured to always be non-negative, qualitative, and symmetric, preventing deviation of the SOC estimation results. To establish an accurate battery
doi:10.3390/en11010059 fatcat:6rzgudi33rhizm6c4db5x5yg7u