To slow down the fossil fuel depletion and promote the hybridization and electrification of vehicle propulsion systems, electric vehicles (EVs) and hybrid electric vehicles (HEVs) are occupying more and more market share. Both of them need a battery management system (BMS) to guarantee safe and reliable battery operations. The key technology of a BMS is to monitor online the battery states, mainly including state of charge (SOC), state of health (SOH), remaining useful life (RUL) and state of power (SOP). As a fundamental parameter of BMS, SOC determines the remaining energy in the battery pack and informs the driver how far the vehicle can still run at the current state. Since SOC cannot be measured directly during normal operation, a method to obtain accurate, real-time and robust SOC estimation is necessary and thus a hot research topic [1
]. SOH describes the physical health condition of a battery compared to a fresh battery, and is usually defined as the ratio of the available capacity of a battery over its rated value. When its value is reduced to below 80%, the battery is considered to be an unreliable power source and should be replaced [3
]. Also indicating the battery degradation, RUL is defined as the period from the current time until the system or component fails. Estimation of the RUL contributes to the maintenance activities and prevents any accidents due to battery failure [4
]. SOP is the parameter used to describe the maximum charging and discharging capabilities of the battery, and is very useful to formulate an optimal energy management strategy for vehicles. In this paper, we focus on SOC estimation.
The Ampere-Hour integral is the most widely used method to calculate SOC in real application, but uncertain initial SOC and the accumulated measurement errors are the accompanying weaknesses of this method [1
]. The open circuit voltage (OCV) method makes use of the OCV-SOC relationship to find the SOC [6
]. This method is accurate and reliable, but the battery needs a long time to relax so the method is thus unsuitable for real applications. Xing et al.
] took the effect of temperature on the OCV-SOC curves into account and developed a temperature-based model to estimate SOC, and verified its higher accuracy at various ambient temperatures. Besides, the artificial neural network (ANN) [8
], and support vector machine (SVM) [9
] methods have been applied to construct black-box models for SOC estimation. The similar disadvantages of the above methods are the requirement for extensive experimental data to train the models. The most popular algorithm for SOC estimation is the extended Kalman filter (EKF) method, which combines the Ampere-Hour integral with open circuit voltage correction [10
]. This method realizes the closed-loop estimation of SOC, and a variety of the analogous improved algorithms have been proposed, such as the adaptive extended Kalman filter (AEKF) [11
], unscented Kalman filtering (UKF) [12
] and adaptive unscented Kalman filtering (AUKF) [14
]. The Kalman filter (KF) assumes the process and measurement noise are Gaussian, and the stable estimation can also be ensured, even when the noises are not exactly Gaussian. However, non-Gaussian noises have a negative influence on the convergence behavior and accuracy of the filter. To avoid this, Schwunk et al.
] employed the particle filter (PF) to estimate the SOC and SOH of batteries and good accuracy was observed. It is noted that the SOC estimation accuracy of EKF strongly depends on the accuracy of the battery model as well as the noise covariance matrixes. According to the principle of the KF, the Kalman gain determines the confidence coefficient of the battery model by adjusting the weight of the open circuit voltage correction and has a strong correlation with the measurement noise covariance (R
). Lee et al.
] demonstrated that the R can compensate the intrinsic model error taken by simplifying the battery model. They took the effect of battery current, current change and SOC value on the model error into consideration, and established a measurement noise model and data rejection method to continuously adjust R
, and eventually improve the SOC estimation accuracy. As for obtaining noise covariance matrixes estimations, the AEKF based on covariance matching has been proposed and immediately offers superiority [17
]. This method is simple in theory and with the advantage of small computational demand. Fuzzy logic has been used to establish the relationship between SOC and the electrochemical impedance spectroscopy (EIS) [18
], and also estimate some battery parameters [20
]. The fuzzy adaptive Kalman filter has been applied in inertial navigation systems and global positioning systems [21
], and in this paper fuzzy models are mainly used to acquire accurate noise covariance, not to compensate the intrinsic model error.
In order to model the dynamic characteristics of battery, different forms of equivalent circuit models (ECMs) have been proposed [16
]. Considering the trade-off between estimation accuracy and computational complexity, the Thevenin model has been widely used to realize SOC estimation. In terms of acquiring real battery parameters under different operation conditions and aging levels, positive strategies, namely online identification methods, are applied. The recursive least squares (RLS) algorithm [24
], and EKF [26
] have been employed to identify online the parameters of ECMs. The RLS algorithm does not require complex matrix operations such as inversion, but cannot be efficiently applied for strongly nonlinear battery models. The EKF can be used to estimate the parameters of nonlinear battery models, but needs more computing power, and it is sensitive to the initial parameters. Xiong et al.
] derived a discrete time expression of the Thevenin model and employed the RLS method to identify online the model parameters. It is noted that the authors took the OCV as a known parameter, which is obtained by looking up the OCV-SOC curves, but the existing SOC deviations might lead to the identification of unreliable parameters. In our previous study [25
], the OCV was regarded as a parameter needing identification, and the recursive extended least squares (RELS) algorithm was implemented to consider the existing colored noises and finally improve the accuracy of the model parameters.