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An accurate state of charge (SOC) can provide effective judgment for the BMS, which is conducive for prolonging battery life and protecting the working state of the entire battery pack. In this study, the first-order RC battery model is used as the research object and two parameter identification methods based on the least square method (RLS) are a...
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The accurate estimation of a lithium-ion battery’s state of charge (SOC) plays an important role in the operational safety and driving mileage improvement of electrical vehicles (EVs). The Adaptive Extended Kalman filter (AEKF) estimator is commonly used to estimate SOC; however, this method relies on the precise estimation of the battery’s model p...
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... Considering different requirements of accuracy, convergence speed or robustness, H ∞ algorithm [23,24], sliding mode observer [25], particle filter [26][27][28], and proportional integral-based observer [29] have been explored as the alternatives of the Kalman filter (KF) family methods [30,31] to estimate battery states. Furthermore, model parameters are incorporated into the state vectors [32], and the EKF algorithm is utilized to estimate the parameters and states simultaneously. With the help of online adapted model parameters, the modelling and estimation accuracy of these methods are remarkably improved. ...
State of charge (SOC) and state of health (SOH) constitute pivotal factors in the efficient and secure management of lithium‐ion batteries, particularly within the context of electric vehicles. A highly‐robust co‐estimation method is proposed in this paper to accurately assess the SOC and SOH under strong electromagnetic interference environment. First, the 1‐RC equivalent circuit model is adopted and the model parameters are identified in a real‐time manner using the recursive total least‐square method to improve the accuracy and adaptivity of the battery model. Subsequently, the SOH estimation is reframed as capacity estimation and an unscented Kalman filter is designed to co‐estimate the SOC and capacity based on the battery model. The results suggest that the proposed method has strong robustness against the measurement noises on current and voltage. The average estimation errors of SOC and capacity are 1.57% and 0.11 Ahr, respectively.
... Here, the AFFRLS algorithm will be used to determine the online parameters of the equivalent circuit model. Compared with the RLS algorithm, the addition of the forgetting factor makes the algorithm avoid being influenced too much by the old data and avoids data saturation problems [46,47]. Compared with the FFRLS algorithm, the adaptive forgetting factor is added here. ...
In the battery management system (BMS), the state of charge (SOC) of lithium-ion batteries is an indispensable part, and the accuracy of SOC estimation has attracted wide attention. Accurate SOC estimation can improve the efficiency of battery use while ensuring battery safety and improving battery life. Taking ternary lithium battery as the research object, this paper proposes a parameter identification method using adaptive forgetting factor recursive least squares and an improved joint unscented particle filter algorithm to estimate SOC. Firstly, an adaptive method is used to select the appropriate forgetting factor value to improve the accuracy of the forgetting factor recursive least squares (FFRLS) method. Meanwhile, the improved particle swarm (IPSO) optimization algorithm that incorporates variable weights and shrinkage factors is utilized to make the best choice of the noise for the unscented Kalman filter (UKF) algorithm in order to improve the estimation accuracy of the UKF algorithm. At the same time, the UKF algorithm is used as the suggestion density function of the particle filter (PF) algorithm to form the unscented particle filter (UPF) algorithm. In this paper, the AFFRLS algorithm and IPSO-SDUPF algorithm are combined to estimate the SOC of Li-ion batteries in real time. Experimental results under different working conditions show that the proposed algorithm has good convergence and high stability for SOC estimation of lithium-ion batteries. The maximum estimation errors of this algorithm are 1.137% and 0.797% for BBDST and DST conditions at 25 °C, and 1.015% and 1.029% for BBDST and DST conditions at 35 °C, which are lower than those of the commonly used algorithms of EKF, SDUKF, IPSO-SDUKF, and SDUPF, and provide a reference for future. The maximum estimation errors are lower than those of the commonly used EKF, SDUKF, IPSO-SDUKF, and SDUPF algorithms, which provide a reference for the future high-precision SOC estimation of Li-ion batteries.
... Another set of strategies employs dual estimation, where two parallel filters are used to observe the model parameters and battery states concurrently. This way facilitates addressing the slow-varying model parameters and the fast dynamics of SoC [213][214][215][216][217][218][219][220]. Additionally, some researchers focus on data-model fusion methods, where model parameters are identified online using data-driven techniques like RLS while simultaneously estimating the SoC using advanced filters [221][222][223][224][225][226]. ...
... [ [213][214][215][216][217][218][219][220][221][222][223][224][225][226]258,259,261,262,[345][346][347][348]. ...
Energy storage has become one of the most critical issues of modern technology. In this regard, lithium-ion batteries have proven effective as an energy storage option. To optimize its performance and extend its lifetime, it is essential to monitor the battery's state of charge. Due to the distinct nonlinear behavior of batteries over their lifetime, the state of charge estimation is challenging. The challenge has been establishing a relationship between accuracy, robustness, and low implementation complexity. Over the last decade, numerous attempts have been made to effectively analyze and compare the state of charge estimation methods for commercial lithium-ion batteries. However, they seldom reflect on the state of charge estimation techniques based on a control-oriented viewpoint for a Li-ion battery system. To fill this gap, this paper reviews the most up-to-date battery state of charge estimation methods applied to lithium-ion battery systems. They are broadly classified as open-loop-based, closed-loop-based, and hybrid approaches. Finally, the paper concludes by providing an analysis of the positive and negative aspects of the reviewed techniques and some suggestions for future research.
... The EKF algorithm can linearize nonlinear systems by performing a first-order Taylor expansion on the nonlinear functions in the system and neglecting the higher-order terms above the second order, thereby approximating the nonlinear system as a linear system. The main steps of the recursive equations of the EKF algorithm are as follows [20]. ...
... Step 1: Initialize the system parameter θ 0 , the parameter variance matrix P θ 0 , the system state x 0,0 , and the state variance matrix P 0,0 , as in Equations (9), (10), (20) and (21). ...
State-of-charge (SoC) estimation is one of the core functions of battery energy management systems. An accurate SoC estimation can guarantee the safe and reliable operation of the batteries system. In order to overcome the practical problems of low accuracy, noise uncertainty, poor robustness, and adaptability in parameter identification and SoC estimation of lithium-ion batteries, this paper proposes a joint estimation method based on the adaptive extended Kalman filter (AEKF) algorithm and the adaptive unscented Kalman filter (AUKF) algorithm in multiple time scales for 18,650 ternary lithium-ion batteries. Based on the slowly varying characteristics of lithium-ion batteries’ parameters and the quickly varying characteristics of the SoC parameter, firstly, the AEKF algorithm was used to online identify the parameters of the model of batteries with a macroscopic time scale. Secondly, the identified parameters were applied to the AUKF algorithm for SoC estimation of lithium-ion batteries with a microscopic time scale. Finally, the comparative simulation experiments were implemented, and the experimental results show the proposed joint algorithm has higher accuracy, adaptivity, robustness, and self-correction capability compared with the conventional algorithm.
... Shi et al. [28] estimated the Li-ion battery SOC using an adaptive extended Kalman filter, while the recursive least square approach with a forgetting factor was employed to estimate the optimal parameters of the battery equivalent circuit. Duan et al. [29] used the first-order RC model with parameters identified via the least square method of an extended Kalman filter to simulate the battery equivalent circuit. Moreover, a multi-time scale prediction model of an adaptive unscented Kalman filter was introduced to estimate the battery SOC. ...
Constructing a reliable equivalent circuit of Li-Ion batteries using real operating conditions by estimating optimal parameters is mandatory for many engineering applications, as it controls the energy management of the battery in a hybrid system. However, model parameters can vary according to the electrochemical nature of the battery, so improving the accuracy of the battery model parameters is essential to obtain reliable and accurate equivalent circuits. Therefore, this paper proposes a new efficient hybrid optimization approach for determining the proper parameters of Li-ion battery Shepherd model equivalent circuits. The proposed algorithm comprises a white shark optimizer (WSO) and the whale optimization approach (WOA) for modifying the stochastic behavior of the WSO while searching for food sources. Minimizing the root mean square error between the estimated and measured battery voltages is the objective function considered in this work. The hybrid variant of the WSO (HWSO) was examined with two different types of batteries. Moreover, the proposed HWSO was validated versus a set of recent meta-heuristic approaches including the sea horse optimizer (SHO), artificial gorilla troops optimizer (GTO), coyote optimization algorithm (COA), and the basic version of the WSO. Furthermore, statistical analyses, mean convergence, and fitting curves were conducted for the comparisons. The proposed HWSO succeeded in achieving the least fitness values of 2.6172 × 10−4 and 5.6118 × 10−5 with standard deviations of 9.3861 × 10−5 and 3.2854 × 10−4 for battery 1 and battery 2, respectively. On the other hand, the worst fitness values were 6.5230 × 10−2 and 6.6197 × 10−5 via SHO and WSO for both considered batteries. The proposed HWSO results prove the efficiency of the proposed approach in providing highly accurate battery model parameters with high consistency and a unique convergence curve compared to the other methods.
... Lithiumion batteries with superior power and energy density, durability, and environmental protection have been widely applied in energy storage, and power systems such as water power, thermal power, wind power, and solar power stations, and so on. A high-efficiency battery management system (BMS) is usually deployed [4] to facilitate a safe and wide range of battery operations. Accurate battery state-of-charge (SOC), state-of-health (SOH), and remaining useful life (RUL) estimation are key modules within BMS for ensuring the reliability, durability, and performance of batteries. ...
Accurate co-estimations of battery states, such as state-of-charge (SOC), state-of-health (SOH,) and remaining useful life (RUL), are crucial to the battery management systems to assure safe and reliable management. Although the external properties of the battery charge with the aging degree, batteries' degradation mechanism shares similar evolving patterns. Since batteries are complicated chemical systems, these states are highly coupled with intricate electrochemical processes. A state-coupled co-estimation method named Deep Inter and Intra-Cycle Attention Network (DIICAN) is proposed in this paper to estimate SOC, SOH, and RUL, which organizes battery measurement data into the intra-cycle and inter-cycle time scales. And to extract degradation-related features automatically and adapt to practical working conditions, the convolutional neural network is applied. The state degradation attention unit is utilized to extract the battery state evolution pattern and evaluate the battery degradation degree. To account for the influence of battery aging on the SOC estimation, the battery degradation-related state is incorporated in the SOC estimation for capacity calibration. The DIICAN method is validated on the Oxford battery dataset. The experimental results show that the proposed method can achieve SOH and RUL co-estimation with high accuracy and effectively improve SOC estimation accuracy for the whole lifespan.
... If an improper noise covariance is used, it may lead to a significant error or even wrong results. To address the issue, in References Duan et al., 2020;He et al., 2021;Peng et al., 2021;Sun et al., 2020;Xiong et al., 2013), improved or adaptive EKF was proposed to adaptively adjust the state and measurement noise covariance. Furthermore, unscented Kalman filter (UKF) and their variants Lv et al., 2020;Zhang et al., 2020), as well as nonlinear observers (Kim et al., 2015;Qiao et al., 2017) were employed to estimate the battery SOC. ...
... Besides the estimation algorithm, the battery model accuracy also influences the accuracy of SOC estimation. To improve the accuracy of the battery model, thus further enhancing the SOC estimation accuracy, some techniques based on double/dual filters or joint estimators (Duan et al., 2020;Guo et al., 2016;Guo et al., 2019;Pavkovic et al., 2017;Xing et al., 2022) were proposed for estimating the SOC and simultaneously updating the model parameters online. Moreover, fractional-order battery models (FOMs) are gradually popular in recent years and have been used to improve the accuracy of battery modelling. ...
It is challenging for a battery management system to estimate the State-Of-Charge (SOC) of batteries. A novel model-based method, using a Dual Extended Kalman Filtering algorithm (DEKF) and Back Propagation Neural Network (BPNN), is proposed to estimate and correct lithium-ion batteries. The results of acceptable SOC estimation are achieved using the DEKF to estimate the battery SOC and simultaneously update model parameters online, while the SOC estimation error is in real-time predicted by the trained BPNN. To further reduce the SOC estimation error, the SOC estimated by the DEKF is corrected by adding the predicted estimation error. The SOC estimation results between the original DEKF and BPNN-based updated DEKF methods under the Federal Urban Driving Schedule (FUDS), the Dynamic Stress Test (DST), the Beijing Dynamic Stress Test (BJDST) and the US06 Highway Driving Schedule are compared. Experimental results show that the SOC error reduces considerably after correcting the estimated SOC. The corrected SOC Root-Mean Square Errors (RMSEs) decrease by an average of seven times compared with the case of no correction. The constant current discharge test verifies the generality and robustness of the proposed method. The modification to the SOC estimation results using ordinary EKF under the above four sophisticated dynamic tests verifies the effectiveness of the proposed method.
... A lot of research has been carried out on estimation algorithms. Except for studying the estimation performance of various filtering algorithms, some auxiliary algorithms are also introduced to improve these filters, such as adaptive algorithms [26,27] and multi-innovation algorithm [28,29]. The establishment of a battery model can be divided into two parts: fitting the OCV model and identifying the lumped parameter elements in EECMs. ...
Model-based methods are widely used for online states estimation of electric vehicles (EVs) due to its accuracy and robustness. Current research mainly focuses on improving estimation filters. However, there is less discussion on the parameters identification methods. In this work, the parameters identification method is divided into two parts: formulation of the regression model and application of identification algorithms. First, two methods of formulation of the regression model are studied, respectively. Then, performances on parameters identification of forgetting factor recursive least squares (FFRLS), optimal bounding ellipsoid (OBE), and linear Kalman filter (LKF) are discussed. Besides, cubature Kalman filter (CKF) is selected for state of charge (SOC) estimation. In order to obtain the experimental data and verify the parameters identification and states estimation accuracy, the Hybrid Pulse Power Characteristic (HPPC) test, urban dynamometer driving schedule (UDDS) test, and new European driving cycle (NEDC) test are carried out. In addition, the maximum absolute error (MAE), mean absolute error (MaE), and root mean square error (RMSE) are calculated for evaluating the SOC estimation accuracy. When the parameters are identified by LKF, the best performance in MAE, MaE, and RMSE of SOC estimation is obtained. Considering the estimated peak power fluctuation and the identified parameters fluctuation, the OBE algorithm is more suitable for co-estimation of SOC and state of power (SOP).
... 24, 25 Duan et al use extended Kalman filter (EKF) to update model parameters and adaptive unscented Kalman filter (AUKF) to predict battery SOC; the results prove that EKF-AUKF has high estimation accuracy. 26 Yang et al proposed a long short-term memory (LSTM)-cyclic neural network to simulate complex battery behavior at different temperatures and estimate the battery SOC based on voltage, current, and temperature variables, combined with UKF to filter out the noise and further reduce estimation errors. 27, 28 Hu et al adopted a novel SOC estimation method for series-connected battery packs based on the fuzzy adaptive federated filtering, which combines the SOC estimation value of the cell average model and the standard deviation of the SOC estimation with the fuzzy system to determine their fusion weight. ...
Accurate estimation of the state of charge (SOC) of lithium-ion batteries is quite crucial to battery safety monitoring and efficient use of energy; to improve the accuracy of lithium-ion battery SOC estimation under complicated working conditions, the research object of this study is the ternary lithium-ion battery; the forgetting factor recursive least square (FFRLS) method optimized by particle swarm optimization (PSO) and adaptive H-infinity filter (HIF) algorithm are adopted to estimate battery SOC. The PSO algorithm is improved with dynamic inertia weight to optimize the forgetting factor to solve the contradiction between FFRLS convergence speed and anti-noise ability. The noise covariance matrixes of the HIF are improved to realize adaptive correction function and improve the accuracy of SOC estimation. To verify the rationality of the joint algorithm, a second-order Thevenin model is established to estimate the SOC under three complex operating conditions. The experimental results show that the absolute value of the maximum estimation error of the improved algorithm under the three working conditions is 0.0192, 0.0131, and 0.0111, respectively, which proves that the improved algorithm has high accuracy and offers a theoretical basis for the safe and efficient operation of the battery management system.
... [23]- [25] presented SOC estimation approaches based on dual Kalman filters, one of which was used for the SOC estimation and the other for online parameter identification. In order to reduce the computational burden, some dual Kalman filters were operated at different timescales [26], [27]. The relationship between the OCV and SOC is a critical parameter for the model-based SOC estimation methods, while in fact it exhibits high dependence of ambient temperature [28]. ...
Accurate state-of-charge (SOC) estimation of batteries is of great significance for electric vehicles. Ambient temperature influences the relationship between open-circuit voltage (OCV) and SOC as well as model parameter and, accordingly, influences the accuracy of the battery SOC estimation for model-based methods. To address the temperature dependence of battery modeling and SOC estimation, an SOC estimation method for lithium-ion batteries based on a temperature-based fractional first-order RC circuit model and dual fractional-order Kalman filter (DFOKF) was proposed. The OCV-SOC look-up table corresponding to ambient temperature and an offset function regarding to ambient temperature were applied to the developed model for improving modeling accuracy. One of dual filters was used to estimate the SOC, and the other was employed to update the model parameters online for addressing the temperature dependence of model parameter. Comparisons of the SOC estimation results between the developed model and the original model that ignores the influence of ambient temperature under the US06 Highway Driving Schedule and the Federal Urban Driving Schedule (FUDS) tests at eight specified temperatures were performed. The results show that the developed model combined with the DFOKF algorithm improves the accuracy of SOC estimation. For the application of SOC estimation at untested temperature, we proposed to construct the corresponding OCV-SOC look-up table by linear interpolation of the measured OCV-SOC look-up table at the tested temperature. Comparisons of results between using the two kinds of look-up tables to estimate the SOC demonstrate the effectiveness of the proposed approach.
