A New Method for State of Charge Estimation of Lithium-Ion Battery Based on Strong Tracking Cubature Kalman Filter
The estimation of state of charge (SOC) is a crucial evaluation index in a battery management system (BMS). The value of SOC indicates the remaining capacity of a battery, which provides a good guarantee of safety and reliability of battery operation. It is difficult to get an accurate value of the SOC, being one of the inner states. In this paper, a strong tracking cubature Kalman filter (STCKF) based on the cubature Kalman filter is presented to perform accurate and reliable SOC estimation.
... e STCKF algorithm can adjust gain matrix online by introducing fading factor to the state estimation covariance matrix. The typical second-order resistor-capacitor model is used as the battery's equivalent circuit model to dynamically simulate characteristics of the battery. The exponential-function fitting method accomplishes the task of relevant parameters identification. Then, the developed STCKF algorithm has been introduced in detail and verified under different operation current profiles such as Dynamic Stress Test (DST) and New European Driving Cycle (NEDC). Making a comparison with extended Kalman filter (EKF) and CKF algorithm, the experimental results show the merits of the STCKF algorithm in SOC estimation accuracy and robustness. sensitively influenced by discharge rate, ambient temperature, and aging degree of the battery, the accurate value of the SOC is difficult to obtain. To predict precise SOC values, numerous SOC estimation methods have been proposed, like Ampere-hour (Ah) counting method  , open-circuit voltage (OCV) method , artificial neural network (ANN) [5,6], particle filter (PF) [7, 8] , a series of algorithms based on Kalman filter          . The Ah counting method is the most common technique for the battery SOC determination in practice. The main idea of the method is integrating the current. However, this method dissatisfies estimation accuracy requirement because of initial value errors and the integral accumulation error caused by measurement current. The OCV method uses the relationship between the open circuit voltage and the SOC for the specific battery type, then, the SOC value can be obtained with interpolation method. However, this method is improper for online applications since the battery has to be left in open circuit mode for a long time to reach the steady-state before measuring the OCV. In addition, some kinds of batteries do not have a definite relationship between OCV and SOC, such as lithium iron phosphate batteries, which have voltage plateaus. Nevertheless, the method is effective for determining the SOC at the initial and end stages due to its simplicity. The ANN method predicts the SOC according to the nonlinear relationship between the battery SOC and its influencing factors obtained by the trained black-box battery models. This method has excellent performance if the training data is sufficient to cover the total loading conditions. Nevertheless, it is time-consuming and nearly impossible to collect training data covering all of the battery loading conditions. The PF method needs numerous matrix operations and has high requirement for hardware. Recently, a widely used method, Kalman filter (KF)  algorithm, which is originally developed to optimize the estimate state for linear systems, is applied to predict the battery SOC. The aim of the algorithm is to extract accurate information out of noisy measurements, and then correct it. Since lithium-ion batteries are a nonlinear system, extended Kalman filter (EKF) [10-13] and unscented Kalman filter (UKF) methods    have been developed to solve this problem. The EKF use a linearization process, namely a first-order Taylor series expansion, at every time step to approximate the nonlinear system. However, the instability of the filter and the lack of robustness due to the linearization process, and also the nontrivial, error-prone calculation of the Jacobian matrices can be listed as the shortcomings of the EKF approach. As an alternative, sigma-point Kalman filters (SPKF) have higher order accuracy in the error covariance of the state vector compared to EKF. The SPKF-based methods are comparable in terms of complexity with Jacobian matrix deploying EKF  , moreover, achieving a second-order accuracy compared to EKF's first order accuracy at the same complexity level is important to note  . The UKF introduces an unscented transformation to approximate the state distribution through a set of sample points called sigma points. It has been demonstrated that UKF has better performance than EKF in terms of accuracy and robustness. Even so, despite its derivative-free state estimation, the standard UKF has the possibility to suffer from performance degradation and instability problems in the case of a mismatch between the a priori assumptions, which include an accurate model, proper initial values and full information of the noise distribution. Many electrochemical model-based approaches    , which are derived from principles of electrochemistry, are proposed get precise knowledge of battery internal information like SOC. In , two nonlinear robust observer designs have been presented for SOC estimation of Li-ion cells using an uncertain reduced electrochemical model. Simulation studies and experiments are presented to show the effectiveness of the observer designs. According to  , an adaptive observer design based on a coupled electrochemical-thermal model, is presented for simultaneous state-parameter estimation of a Li-ion cell. Simulation studies show the effectiveness of the design where the states and parameters are estimated with a desired convergence rate and accuracy. Although electrochemical model-based techniques are arguably more accurate than the other modeling approaches, the complexity and computation cost will increase accordingly.