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An accurate state of charge (SOC) estimation of the battery is one of the most important techniques in battery-based power systems, such as electric vehicles (EVs) and energy storage systems (ESSs). The Kalman filter is a preferred algorithm in estimating the SOC of the battery due to the capability of including the time-varying coefficients in the...
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... this research, the DP model consisting of an OCV-UOC, an Ohmic resistance Ri, and two RC networks, was selected as an ECM of the LFP battery, as shown in Figure 2. The charge transfer effect causing a first voltage drop UP on the electrode potential is presented by the charge transfer resistance RP and the double layer capacitance CP with a short time constant. ...
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... corresponding relationship between UOC and SOC is determined through a SOC-OCV test described in [19]. The electrical behavior of the LFP with the DP model, shown in Figure 2, can be expressed as Equation (1): ...
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... above function indicates the 2 nd -order ARX model of Equation (2) for the battery ECM in Figure 2, and the parameters of the system can be extracted by using a parameter identification method, such as the RLS method. ...
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... In addition, the equivalent-circuit models for battery overpotentials have been ubiquitously realized using the modal state-space representation, wherein the -matrix takes the diagonal form, and the state vector represents the collection of voltages across the resistor-capacitor networks. In this paper, the input-output model representation has been readily adopted as the starting point by noting the fact that an th-order state-space representation of an equivalent-circuit model in the LTI framework can be transformed into an th-order difference (or differential) equation of the form given by (4) using transfer-function-based approaches (see [28] as an example). Now, the scheduling-variable dependence discussed previously can be formally incorporated in the model structure by rendering the parameters { } =1 , { } =0 in (4) as functions of the variable . ...
This paper proposes a comprehensive approach to the identification of battery models in the linear parameter-varying (LPV) framework inspired by the equivalent-circuit model structures. The proposed LPV model structure is formulated using the input--output representation, wherein the model parameters are considered to depend on the state-of-charge, the current magnitude, and the current direction. The aforementioned dependence is explained using a suitable set of basis functions motivated with appropriate physical insight. Furthermore, the optimal experimental design problem is discussed to propose an improved input design for the model identification procedure. Subsequently, the Least Absolute Shrinkage and Selection Operator (LASSO) along with the ridge regression are employed for the selection of significant model terms and parameter estimation to yield a sparse model with adequate simulation capabilities. Finally, several battery models with varying model order and basis-function complexity are identified, which are subsequently validated and compared using a real drive-cycle dataset. The corresponding voltage simulation results yield the root-mean-squared error (RMSE) value for the best-performing model to be around 24.5 mV when a 1 Ah NMC battery gets discharged with the lower voltage cutoff as low as 2.5 V.
... Accurately tracking the trajectory of the actual battery SOC is an unsolved problem due to the time-varying and nonlinear characteristics of the battery SOC. Various SOC estimation methods exist including the open circuit voltage [5], ampere-hour integral [6], Kalman filter (KF) [7][8][9][10], and particle filter (PF) [11][12][13][14]. In recent years, data-driven estimation methods such as artificial neural networks [15][16][17] and support vector machines [18,19] have also been applied to the research of SOC estimation. ...
The estimation of the state of charge (SOC) in lithium-ion batteries is a crucial aspect of battery management systems, serving as a key indicator of the remaining available capacity. However, the inherent process and measurement noises created during battery operation pose significant challenges to the accuracy of SOC estimation. These noises can lead to inaccuracies and uncertainties in assessing the battery’s condition, potentially affecting its overall performance and lifespan. To address this problem, we propose a second-order central difference particle filter (SCDPF) method. This method leverages the latest observation data to enhance the accuracy and noise adaptability of SOC estimation. By employing an improved importance density function, we generate optimized particles that better represent the battery’s dynamic behavior. To validate the effectiveness of our proposed algorithm, we conducted comprehensive comparisons at both 25 °C and 0 °C under the new European driving cycle condition. The results demonstrate that the SCDPF algorithm exhibits a high accuracy and rapid convergence speed, with a maximum error which never exceeds 1.30%. Additionally, we compared the SOC estimations with both Gaussian and non-Gaussian noise to assess the robustness of our proposed algorithm. Overall, this study presents a novel approach to enhancing SOC estimation in lithium-ion batteries, addressing the challenges posed by the process itself and measurement noises.
... Sigma sampling is performed near the estimation points using an unscented transformation, and the Gaussian density function represented by these sampling points is utilized to approximate the state probability density operation, resulting in the prediction model's mean and variance. This method simplifies the computational complexity and has higher accuracy, but there is a problem of filtering divergence due to the adverse determination of the error covariance matrix [75]. The volumetric Kalman filtering algorithm samples are in accordance with the spherical radial criteria and variance of a nonlinear system using an equally weighted point set. ...
This study explores the challenges and advances in the estimation of the state of charge (SOC) of lithium-ion batteries (LIBs), which are crucial to optimizing their performance and lifespan. This review focuses on four main techniques of SOC estimation: experimental measurement, modeling approach, data-driven approach, and joint estimation approach, highlighting the limitations and potential inaccuracies of each method. This study suggests a combined approach, incorporating correction parameters and closed-loop feedback, to improve measurement accuracy. It introduces a multi-physics model that considers temperature, charging rate, and aging effects and proposes the integration of models and algorithms for optimal estimation of SOC. This research emphasizes the importance of considering temperature and aging factors in data-driven approaches. It suggests that the fusion of different methods could lead to more accurate SOC predictions, an important area for future research.
... The data-driven method includes Fuzzy Logic (FL) method (Singh et al., 2006;Lee et al., 2008;Hu et al., 2020), Neural Network (NN) method (Chemali et al., 2018b,a). The modelbased method needs to combine the corresponding battery model with the filter method, such as Kalman Filter (KF) (Benedikt et al., 2021;Oh et al., 2021;Zheng et al., 2018;Cui et al., 2022;Kim and Cho, 2013;Gholizadeh and Yazdizadeh, 2020;He et al., 2011;Xiong et al., 2013;Yu et al., 2017;Aung et al., 2015;Meng et al., 2016;Dong et al., 2017;Nguyen et al., 2020;Xiong et al., 2014;Qiao et al., 2021), Particle Filter (PF) (Zheng et al., 2020; The weight of particle for ith particle at time k w i ps,k ...
... The UKF was applied in Ref. Yu et al. (2017), Aung et al. (2015), Meng et al. (2016), Dong et al. (2017), because it does not need to calculate the Jacobi matrix during its linearization procedure. Besides, a combination of the UKF with other methods was employed to improve SOC estimation accuracy and robustness (Li and Bei, 2019;Dong et al., 2017;Nguyen et al., 2020;Xiong et al., 2014;Qiao et al., 2021). ...
The echelon utilization of retired lithium-ion battery with remaining capacity of 80%, is considered as one of the most promising ways to reduce battery cost by extending their service life. The accurate state of charge (SOC) estimation for retired lithium-ion batteries is of great significance for less-stressful demanding applications. The H-infinity filter (HIF) is widely used to identify the battery model parameters and correspondingly to estimate the SOC online assisted with the Thevenin model. But the estimation accuracy cannot be ensured due to the overly simple algorithm structure. In this paper, H-infinity particle filter (HIPF) is proposed to further improve the SOC estimation accuracy. It is a particle filter (PF) improved by HIF and can suppress the particle depletion during the execution of the standard particle filter. HIPF estimated the SOC after the weights of particles were compromised. The joint estimation of model parameters by HIF and the SOC by HIPF was simulated to verify the model accuracy. In the experiment, the retired lithium–iron phosphate battery in BAIC EV150 vehicle was tested under FUDS cycle and DST cycle. The verification result shows that the mean error of the estimated SOC by HIPF is 0.63% in FUDS cycle and 0.59% in DST cycle. And in FUDS cycle and DST cycle, respectively, the proposed method’s SOC estimation accuracy was increased by 65% and 63% compared with when particle weights were not compromised.
... Moreover, the EKF algorithm needs to calculate the Jacobian matrix once in each iteration process, which increases the amount of calculations. The UKF algorithm [24][25][26] can also be used for the state estimation of nonlinear systems. Its core method is unscented transformation (UT) [27,28], in which sampling points are used to approximate the distribution of nonlinear state variables, without the linearization of nonlinear functions and Jacobian matrix solution. ...
With the increasing demand for intelligence and automation, and the continuous strengthening of safety and efficiency requirements, the disadvantages of traditional “blind use” of nickel–cadmium batteries have become increasingly prominent, and the lack of state-of-charge (SOC) estimation needs to be changed urgently. For this purpose, a dynamic model of nickel–cadmium battery is established, and an SOC estimation method of nickel–cadmium battery based on adaptive untraced Kalman filter is proposed. Firstly, the experimental platform was built, and the open-circuit voltage and polarization characteristics of nickel–cadmium batteries were analyzed. On this basis, an equivalent circuit model is constructed to reflect the characteristics of nickel–cadmium batteries, and the model parameters were identified by the hybrid pulse power characteristic test; Then, based on the dynamic model, the SOC of the nickel–cadmium battery was estimated by combining with the Sage–Husa adaptive untrace Kalman filtering algorithm. Finally, the SOC estimation effect was verified under two operating conditions: Hybrid pulse power characteristic (HPPC) and constant cyclic charging and discharging power. The experimental results show that the proposed estimation method is insensitive to the initial value of SOC, and can still converge to the real value even if there is 30% error in the initial value. The mean absolute error and root mean square deviation of the final SOC estimation results are both less than 1%. The dynamic model and the proposed SOC estimation method provide valuable reference for the operation control, maintenance, and replacement of nickel–cadmium batteries in the use process.
... SOC estimation for LFP batteries using an improved battery model and KF was conducted by Xu et al. [13]. SOC estimation using Unscented Kalman Filter (UKF) and a Particle Filter was conducted by Nguyen et al. [14]. SOC estimation using an Extended Kalman filter (EKF) combined with Auto regressive exogenous (ARX) and recursive least square (RLS) was conducted by Ko et al. [15]. ...
p>This work has been submitted to the IEEE OA for publication. Copyrights may be transferred without notice, after which this version may no longer be accessible.</p
... SOC estimation for LFP batteries using an improved battery model and KF was conducted by Xu et al. [13]. SOC estimation using Unscented Kalman Filter (UKF) and a Particle Filter was conducted by Nguyen et al. [14]. SOC estimation using an Extended Kalman filter (EKF) combined with Auto regressive exogenous (ARX) and recursive least square (RLS) was conducted by Ko et al. [15]. ...
p>This work has been submitted to the IEEE OA for publication. Copyrights may be transferred without notice, after which this version may no longer be accessible.</p
... For SOC estimates of a single cell, a variety of methods have been presented, ranging from coulomb counting to machine learning approaches [44]. For SOC estimation, model-based techniques have been used in conjunction with various versions of Kalman Filtering (KF) [45][46][47][48][49][50][51], with the process and measurement noise in the model taken into account. Particularly, extended KFs (EKFs) [46,47] [48][49][50] determine the covariance of updated SOC. ...
... For SOC estimation, model-based techniques have been used in conjunction with various versions of Kalman Filtering (KF) [45][46][47][48][49][50][51], with the process and measurement noise in the model taken into account. Particularly, extended KFs (EKFs) [46,47] [48][49][50] determine the covariance of updated SOC. Furthermore, adaptive Kalman filters (AKF) [45,49] can provide better SOC estimation by dynamically updating the measurement and process covariance. ...
The continuously growing population and urban growth rates are responsible for the sharp rise in energy consumption , which leads to increased CO 2 emissions and demand-supply imbalances. The power sector is switching to alternative energy sources, including renewable energy resources (RES) such as Photovoltaic (PV) and wind power (WP) and battery energy storage systems (BESS), among others, due to an increase in the use of fossil fuels and their shortage. Since the power generation of these resources is uncertain due to climatic fluctuations and the direct integration of these resources into the power grid is very complex due to the issues such as; voltage and frequency regulation, overloading of active transmission lines, and supply-demand disparity, the research on system uncertainties is receiving increasing attention. This study provides a comprehensive analysis of the several parameters of uncertainty, approaches for dealing with the uncertainty in battery energy storage (BES)-based RES integrated grid, and the advantages and disadvantages of each method. Moreover, various analytical and numerical approaches were developed for integrating RES and BESS into the power grid, including proba-bilistic methods, possibilistic methods, robust optimization-based techniques, and machine learning algorithms. The comparative analysis of these approaches highlights their relative strengths and weaknesses, providing a valuable resource for researchers and utility planners. Additionally, this review paper identifies several issues and challenges associated with the integration of RES and BESS into the power grid, such as power quality, economical effect, battery aging effect, and environmental effect. Furthermore, the paper suggests a few future research directions, including the development of novel models for analyzing uncertainty in power systems, coordination of uncertainty parameters, integration of BESS into RES and grid, power electronics integration, and environmental factor. Overall, this article's novel contributions include a comprehensive analysis of uncertainty parameters, a comparative analysis of uncertainty modeling approaches, an identification of critical issues and challenges, and the suggestion of future research directions to promote a sustainable and reliable power system. This article will aid in defining the requirements and specifications for novel models for analyzing uncertainty in power systems. The discussion and analysis will assist researchers and utility planners in selecting a suitable uncertainty modeling approach with significant penetrations of distributed RESs, which can lead to achieving a reliable and sustainable power system.
... ECM is used with various battery components to depict the dynamic characteristics of the captured battery, and various ECM models have been proposed for lithium battery SOC estimation, including Rint [15], Thevenin, and partnership for new generation of vehicles (PNGV) models [15]. The model-based estimation methods that are widely used are mainly the Kalman filter (KF), particle filter (PF) [16], H infinity filter (HIF), other state observers, etc. Because of the highly nonlinear nature of the battery, Fengchun Sun et al. proposed an adaptive unscented Kalman filter (UKF) to estimate the battery SOC and approximate this highly nonlinear system [17]. ...
A battery management system (BMS) is an important link between on-board power battery and electric vehicles. The BMS is used to collect, process, and store important information during the operation of a battery pack in real time. Due to the wide application of lithium-ion batteries in electric vehicles, the correct estimation of the state of charge (SOC) of lithium-ion batteries (LIBS) is of great importance in the battery management system. The SOC is used to reflect the remaining capacity of the battery, which is directly related to the efficiency of the power output and management of energy. In this paper, a new long short-term memory network with attention mechanism combined with Kalman filter is proposed to estimate the SOC of the Li-ion battery in the BMS. Several different dynamic driving plans are used for training and testing under different temperatures and initial errors, and the results show that the method is highly reliable for estimating the SOC of the Li-ion battery. The average root mean square error (RMSE) reaches 0.01492 for the US06 condition, 0.01205 for the federal urban driving scheme (FUDS) condition, and 0.00806 for the dynamic stress test (DST) condition. It is demonstrated that the proposed method is more reliable and robust, in terms of SOC estimation accuracy, compared with the traditional long short-term memory (LSTM) neural network, LSTM combined with attention mechanism, or LSTM combined with the Kalman filtering method.
... A PF offers the highest accuracy and fastest response (state update) when there are large initial state errors. However, with a correct initial state when the estimated state totally converges to the actual state, the accuracy of a PF is same or even lower than both the EKF and UKF, especially in the range of SOC when SOC-V OC curve is almost flat because the weight of all samples is almost the same [48]. In terms of processing complexity, a PF is more complex than a UKF and requires a high-performance microcontroller to be applied because the Monte Carlo method employs a large number of weighted samples to form the distribution. ...
Lithium-ion batteries have become the most appropriate batteries to use in modern electric vehicles due to their high-power density, long lifecycle, and low self-discharge rate. The precise estimation of the state of charge (SOC) in lithium-ion batteries is essential to assure their safe use, increase the battery lifespan, and achieve better management. Various methods of SOC estimation for lithium-ion batteries have been used. Among these methods, the model-based estimation method is the most practical and reliable. The accuracy of the utilized model is a crucial factor in realizing better SOC estimation in the model-based method. In this paper, an enhanced battery model is proposed to estimate the SOC precisely via an optimized extended Kalman filter. The model considers the most influencing factors on the estimation accuracy, such as temperature, aging, and self-discharge. The parameterization of the model has defined the dependency of sensitive parameters on state estimation. As a fundamental step before estimating the SOC, the capacity degradation is evaluated using a straightforward approach. Later, a particle swarm optimization algorithm is utilized to optimize the vector of process noise covariance to enhance the state estimation. The performance of the proposed method is compared to recent techniques in the literature. The results indicate the effectiveness of the proposed approach in terms of both accuracy and computational simplicity.
