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The estimation accuracy of State-of-Charge (SOC) has great significance for cell charge/discharge management, balance control, and safety management. However, some inconsistencies among cells may lead to model mismatch, which will have a significant impact on the estimation results. Furthermore, it is difficult to achieve an accurate SOC estimation with less computational burden when the battery pack contains hundreds (or thousands) of cells. This paper constructs a battery pack model that consists of a mean-model and several difference-models. The mean-model represents the overall performance of the battery pack. The difference-model describes the inconsistencies of SOC, internal resistance, and coulombic efficiency among cells. In addition, a joint algorithm is proposed to estimate SOC with low complexity. It includes a dual time-scale adaptive extended Kalman filter (AEKF) and a SOC correction method. Comparing with the conventional filter method of SOC estimation, it can effectively simplify a large number of matrix operations, and greatly reduce the overall computational complexity. The experimental results show that the established model can well describe the dynamic characteristics of the battery pack, and the proposed method can track the changing of SOC at a low computational cost. ● The CE inconsistency among cells is further considered in modeling. ● The estimated SOC tracks the changing of actual value well. ● The method is proposed to estimate the SOCs of many cells rapidly. ● The method requires low computation cost. ● The method is suitable for the real-time application. [ABSTRACT FROM AUTHOR]

This paper proposes an H∞ observer based on descriptor systems to estimate the state of charge (SOC). The battery's open-current voltage is chosen as a generalized state variable, thereby avoiding the artificial derivative calculation of the algebraic equation for the SOC. Furthermore, the observer's dynamic performance is saved. To decrease the impacts of the uncertain noise and parameter perturbations, nonlinear H∞ theory is implemented to design the observer. The sufficient conditions for the H∞ observer to guarantee the disturbance suppression performance index are given and proved by the Lyapunov stability theory. This paper systematically gives the design steps of battery SOC H∞ observers. The simulation results highlight the accuracy, transient performance, and robustness of the presented method.

State-of-charge (SOC) estimation of lithium-ion battery is one of the core functions of battery management system. In order to improve the estimation accuracy of SOC, this paper proposes a long short-term memory neural network based on particle swarm optimization (PSO-LSTM). Firstly, the key parameters of LSTM are optimized by PSO algorithm, so that the data characteristics of lithium-ion battery can match the network topology. In addition, random noise is added to the input layer of PSO-LSTM neural network to improve the anti-interference ability of the network. Finally, experiments show that the proposed method can achieve accurate estimation under different conditions. The estimates based on PSO-LSTM converge to the real state-of-charge within an error of 0.5%. • A PSO-LSTM model is established for SOC estimation of lithium-ion battery. • PSO is applied to optimize the hyper-parameters of LSTM. • Random noises are added to the sampled data, so as to prevent over-fitting of the PSO-LSTM model. • Results show that the proposed method has high estimation accuracy and robustness. [ABSTRACT FROM AUTHOR]

Accurate estimation of the state of charge (SOC) of lithium batteries is paramount to ensuring consistent battery pack operation. To improve SOC estimation accuracy and suppress colored noise in the system, a fractional order model based on an unscented Kalman filter and an H-infinity filter (FOUHIF) estimation algorithm was proposed. Firstly, the discrete state equation of a lithium battery was derived, as per the theory of fractional calculus. Then, the HPPC experiment and the PSO algorithm were used to identify the internal parameters of the second order RC and fractional order models, respectively. As discovered during working tests, the parameters identified via the fractional order model proved to be more accurate. Furthermore, the feasibility of using the FOUHIF algorithm was evaluated under the conditions of NEDC and UDDS, with obvious colored noise. Compared with the fractional order unscented Kalman filter (FOUKF) and integer order unscented Kalman filter (UKF) algorithms, the FOUHIF algorithm showed significant improvement in both the accuracy and robustness of the estimation, with maximum errors of 1.86% and 1.61% under the two working conditions, and a terminal voltage prediction error of no more than 5.29 mV. [ABSTRACT FROM AUTHOR]

The traditional Kalman filter algorithms have disadvantages of poor stability (the program cannot converge or crash), robustness (sensitive to the initial errors) and accuracy, partially resulted from the fact that noise covariance matrices in the algorithms need to be set artificially. To overcome the above problems, some adaptive Kalman filter (AKF) algorithms are studied, but the problems still remain unsolved. In this study, two improved AKF algorithms, the improved Sage-Husa and innovation-based adaptive estimation (IAE) algorithms, are proposed. Under the different operating conditions, the estimation accuracy, filter stability, and robustness of the two proposed algorithms are analyzed. Results show that the state of charge (SOC) Max error based on the improved Sage-Husa and the improved IAE is less than 3% and 1.5%, respectively, while the Max errors of the original algorithms is larger than 16% and 4% The two proposed algorithms have higher filter stability than the traditional algorithms. In addition, analyses of the robustness of the two proposed algorithms are carried out by changing the initial parameters, proving that neither are sensitive to the initial errors. [ABSTRACT FROM AUTHOR]

The state of charge (SOC) estimation and battery equalization method are essential in battery management system (BMS). In this paper, an improved H infinity filter algorithm based on the reverse recursion of historical data which could update the inner parameters of algorithm online is proposed. The battery life decay experiment result shows that open circuit voltage (OCV)–SOC relationship and the actual capacity of battery have a great impact on the SOC estimation accuracy based on H infinity, and the max SOC estimation error can exceed 15%. The improved H infinity algorithm proposed in this paper can keep the SOC error within 3% and its convergence to the true SOC is faster than the sliding mode observer algorithm. On this basis, a novel equalization strategy based on shunting is proposed. The equalization strategy model is simulated in SIMULINK, and as compared with the general cell bypass methods, the proposed method utilizes a redundant cell to achieve a high efficiency beyond 99%. The analysis results show that the 6Ah redundant cell could decrease the inconsistence of SOCs to 2%. • The SOC estimation based on H infinity filter algorithm is introduced for equalization strategy. • An improved H infinity filter algorithm based on reverse recursion of historical data is proposed. • The equilibrium efficiency higher than 99% is achieved using the proposed balancing method. • A 6Ah redundant cell could improve the in consistence of SOCs to 1.5%. [ABSTRACT FROM AUTHOR]

An accurate state of charge (SOC) estimation of the lithium iron phosphate battery (LiFePO4) is one of the most important functions for the battery management system (BMS) for electric vehicles (EVs) and energy storage systems (ESSs). However, an accurate estimation of the SOC of LiFePO4 is challenging due to the hysteresis phenomenon occurring during the charge and discharge. Therefore, an accurate modeling of the hysteresis phenomenon is essential for reliable SOC estimation. The conventional hysteresis modeling methods, such as one-state hysteresis modeling and parallelogram modeling, are not good enough to achieve high-accuracy SOC estimation due to their errors in the approximation of the hysteresis contour. This paper proposes a novel method for accurate hysteresis modeling, which can provide a significant improvement in terms of the accuracy of the SOC estimation compared with the conventional methods. The SOC estimation is performed by using an extended Kalman filter (EKF) and the parameters of the battery are estimated by using auto regressive exogenous (ARX) model and the recursive least square (RLS) filter. The experimental results with the conventional and proposed methods are compared to show the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Under the actual operating conditions of electric vehicle, the temperature of the battery system changes with the ambient temperature, its influence is rarely considered on state of charge (SOC) estimation. Aiming at this problem, this work explores the relationship between temperature and battery discharge capacity, capacity loss, coulomb efficiency and open circuit voltage, and establishes a temperature correction model. Then, a temperature-based coulomb counting (TBCC) method is proposed. To eliminate the cumulative errors of SOC estimation, a TBCC combined adaptive particle filter (APF) combination estimation method is proposed, which can update the temperature-related variables, and estimates the system state with the identified model parameters. The estimation method adapts to the temperature change of the power lithium battery while taking into account the superiority of the APF in non-linear and non-Gaussian systems, so as to improve the accuracy of the SOC estimation in the changing temperature range. Simulations under urban dynamometer driving schedule (UDDS) are conducted, and the results show that compared with the method without temperature correction, the proposed combination method can improve the accuracy and convergence ability of SOC estimation under the influence of temperature. • Relationship between temperature and typical discharge parameters is explored. • A correction model considering the influence of temperature change is established. • Combination estimation method with Temperature-based coulomb counting is proposed. [ABSTRACT FROM AUTHOR]

Accurate determination of the continuous and instantaneous load capability is important for safety, durability, and energy deployment of lithium-ion batteries. It is also a crucial challenge for the battery-management-system to determine the load capability of a pack due to inevitable differences among in-pack cells. To overcome these challenges, a flexible battery equivalent-circuit-model is first developed without prior knowledge of in-pack cells' capacity and internal resistance. Then, a method for determining the load capability of a pack is proposed based on a two time-scale filter using a combination of recursive-least-square-method and Kalman-filter. Distinguished from traditional model-based state-of-charge estimation strategies, only the terminal voltages and currents are used to estimate the open-circuit-voltages of each cell. The temperature and hysteresis effects are compensated to improve estimation accuracy. To reduce the computational complexity, a two time-scale scheme is designed to monitor the state-of-charge and model parameters of in-pack cells, which are further used to determine the peak power of the battery pack. Experiments and simulations conducted on LiFePO 4 battery pack are employed to verify the performance of the proposed approach under dynamic operating currents and temperatures. The results indicate that the proposed approach is suitable for determining the load capability of a battery pack. • A two time-scale co-estimator for determining battery load capability is proposed. • A peak power prediction framework for series-connected battery pack is proposed. • The analysis for influential mechanisms of peak power constraints are performed. • The advancements of the proposed method are verified under dynamic conditions. [ABSTRACT FROM AUTHOR]

The state of charge (SOC) of a battery indicates its useable capacity. In the case of lithium-ion batteries, an accurate estimate improves their performance. With the recent tendency in the increased use of lithium-ion batteries in electric vehicles, the estimation of SOC has become even a more critical issue than before. In this paper, the combination of an Autoencoder neural network and a Long Short-Term Memory (LSTM) neural network is proposed for the estimation of the SOC of a battery with high precision. The Dynamic Stress Test (DST) drive cycle and the Federal Urban Driving Schedule (FUDS) drive cycle datasets are used to test the proposed algorithm at three different temperatures. To reveal the performance of the proposed method, the results are compared with several other methods from the literature. It is observed that the SOC estimation by the proposed method yields to a significantly better accuracy at all three temperatures. • New features extracted from SOC data using autoencoder neural network. • LSTM neural network is used to estimates SOC from the extracted features. • The effect of temperature is considered in the simulations. • The performance of proposed model is tested by simulation on two different data set. • Comparison with some well-known methods reveals the efficiency of proposed method. [ABSTRACT FROM AUTHOR]

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 model and its superior performance in the SOC estimation. However, since its performance highly depends on the measurement noise (MN) and process noise (PN) values, it is difficult to obtain highly accurate estimation results with the battery having a flat plateau OCV (open-circuit voltage) area in the SOC-OCV curve, such as the Lithium iron phosphate battery. In this paper, a new integrated estimation method is proposed by combining an unscented Kalman filter and a particle filter (UKF-PF) to estimate the SOC of the Lithium iron phosphate battery. The equivalent circuit of the battery used is composed of a series resistor and two R-C parallel circuits. Then, it is modeled by a second-order autoregressive exogenous (ARX) model, and the parameters are identified by using the recursive least square (RLS) identification method. The validity of the proposed algorithm is verified by comparing the experimental results obtained with the proposed method and the conventional methods. [ABSTRACT FROM AUTHOR]

State of charge (SOC) estimation plays a crucial role in battery management systems. Among all the existing SOC estimation approaches, the model-driven extended Kalman filter (EKF) has been widely utilized to estimate SOC due to its simple implementation and nonlinear property. However, the traditional EKF derived from the mean square error (MSE) loss is sensitive to non-Gaussian noise which especially exists in practice, thus the SOC estimation based on the traditional EKF may result in undesirable performance. Hence, a novel robust EKF method with correntropy loss is employed to perform SOC estimation to improve the accuracy under non-Gaussian environments firstly. Secondly, a novel robust EKF, called C-WLS-EKF, is developed by combining the advantages of correntropy and weighted least squares (WLS) to improve the digital stability of the correntropy EKF (C-EKF). In addition, the convergence of the proposed algorithm is verified by the Cramér–Rao low bound. Finally, a C-WLS-EKF method based on an equivalent circuit model is designed to perform SOC estimation. The experiment results clarify that the SOC estimation error in terms of the MSE via the proposed C-WLS-EKF method can efficiently be reduced from 1.361% to 0.512% under non-Gaussian noise conditions. [ABSTRACT FROM AUTHOR]

Accurate estimation of the state of charge (SOC) is an important criterion to prevent the batteries from being over-charged or over-discharged, and this assures an electric vehicle's safety and reliability. To investigate the effect of different operating conditions on the SOC estimation results, a dual-polarization model (DPM) and a fractional-order model (FOM) are established in this study, taking into account the prediction accuracy and structural complexity of a battery model. Based on these two battery equivalent circuit models (ECMs), a hybrid Kalman filter (HKF) algorithm is adopted to estimate the SOC of the battery; the algorithm comprehensively utilizes the ampere-hour (Ah) integration method, the Kalman filter (KF) algorithm, and the extended Kalman filter (EKF) algorithm. The SOC estimation results of the DPM and FOM, under the dynamic stress test (DST), federal urban driving schedule (FUDS), and hybrid pulse power characteristic (HPPC) cycle conditions, are compared and analyzed through six sets of experiments. Simulation results show that the SOC estimation accuracy of both the models is high and that the errors are within the range of ±0.06. Under any operating conditions, the SOC estimation error, based on the FOM, is always lower than the SOC estimation error of the DPM, but the adaptability of the FOM is not as high as that of the DPM. [ABSTRACT FROM AUTHOR]

• Adaptive federated Kalman filter is used for enhanced battery pack SOC estimation. • A fuzzy system is used to adapt to various cell SOC inconsistency distributions. • Accuracy is evaluated under SOC inconsistencies against conventional methods. • Fault tolerance is evaluated under the influence of measurement errors. Inconsistencies among battery cells and measurement errors have significant impacts on the accuracy and reliability of state of charge (SOC) estimations for series-connected battery packs. The aim of this paper is to propose a novel SOC estimation method for series-connected battery packs based on the fuzzy adaptive federated filtering. The mean-plus-difference model is employed to characterize the inconsistencies among battery cells. The fuzzy system is designed to improve the accuracy and adaptability of SOC estimation under cell inconsistencies. The SOC estimation value from a cell mean model and the standard deviation of SOC estimation are combined with a fuzzy system to determine their fusion weights. The master filter adaptively adjusts the information distribution coefficient according to the local filter estimation accuracy to improve reliability. Through simulation and experimentation on series-connected battery packs with different SOC distributions, the estimation accuracy of the proposed method is compared between the proposed method and the conventional methods. The SOC estimation accuracy of each battery cell is evaluated. The results show that, over the full SOC range, the root-mean-square error (RMSE) of the battery pack SOC estimation is less than 0.6% and 1.5% using online and offline parameters, respectively. The SOC estimation RMSEs of the battery cells using online and offline parameters are less than 0.4% and 1%, respectively. The fault tolerance is verified by artificially adding measurement errors. These accurate and reliable results show a strong prospect for the design and optimization of future clean and sustainable mobility. [ABSTRACT FROM AUTHOR]

State of charge (SOC) estimation plays a critical role in the operation of an electric vehicle (EV) power battery. In this Letter, the authors propose machine learning (ML) algorithms as alternate to the existing filtering algorithms used for SOC estimation of an EV battery. The SOC estimation approach is evaluated by the simulation experiments in advanced vehicle simulator (ADVISOR). For the modelling of ML algorithms, the input parameters that affect the SOC estimation are battery current, battery module temperature, power out of the battery (available and requested), battery power loss and heat removed from the battery. Training and testing stages of the models are carried out using the data collected from ADVISOR. As the drive cycle conditions provided by ADVISOR are universal therefore present method is applicable to all kinds of batteries used in EVs including lithium ion, nickel metal hydride and lead acid batteries. Thus, the proposed models for SOC estimation provide an alternative approach in SOC estimation. [ABSTRACT FROM AUTHOR]

This paper focuses on an efficient fundamental approach of the electrochemical model of lithium-ion batteries (LIBs), especially considering the effect of Electrical Double Layer (EDL) potential on the over-potential of batteries. Firstly, the electrode solid phase and electrolyte liquid phase in LIBs are modelled by electrochemical theory, especially emphasizing the influence of EDL structure. Three-parameter parabola method is effectively employed to simplify the model. Furthermore, a parameter identification method based on genetic algorithm is proposed according to the structure characteristics of EDL model. The accuracy of model is verified by comparing the output voltage of the EDL model under 0.1∼2C charging/discharging, 1C pulse discharging and New European Driving Cycle (NEDC) condition with the experimental terminal voltage. Finally, the battery SOC estimation method is developed by using the extended Kalman filter (EKF) algorithm based on EDL model and is verified by the 1C pulse discharge and the NEDC condition experiments. The results show that the proposed algorithm can accurately estimate the SOC value of LIBs. In addition, the algorithm has a strong correction effect on the initial SOC error and convergence. [ABSTRACT FROM AUTHOR]

In this paper, a new approach to modeling the hysteresis phenomenon of the open circuit voltage (OCV) of lithium-ion batteries and estimating the battery state of charge (SoC) is presented. A characterization procedure is proposed to identify the battery model parameters, in particular, those related to the hysteresis phenomenon and the transition between charging and discharging conditions. A linearization method is used to obtain a suitable trade-off between the model accuracy and a low computational cost, in order to allow the implementation of SoC estimation on common hardware platforms. The proposed characterization procedure and the model effectiveness for SoC estimation are experimentally verified using a real grid-connected storage system. A mixed algorithm is adopted for SoC estimation, which takes into account both the traditional Coulomb counting method and the developed model. The experimental comparison with the traditional approach and the obtained results show the feasibility of the proposed approach for accurate SoC estimation, even in the presence of low-accuracy measurement transducers. [ABSTRACT FROM AUTHOR]

State-of-charge estimation and on-line model modification of lithium-ion batteries are more urgently required because of the great impact of the model accuracy on the algorithm performance. This study aims to propose an improved DUKF based on the state-parameter separation. Its characteristics include: (1) State-Of-Charge (SoC) is treated as the only state variable to eliminate the strong correlation between state and parameters. (2) Two filters are ranked to run the parameter modification only when the state estimation has converged. First, the double polarization (DP) model of battery is established, and the parameters of the model are identified at both the pulse discharge and long discharge recovery under Hybrid Pulse Power Characterization (HPPC) test. Second, the implementation of the proposed algorithm is described. Third, combined with the identification results, the study elaborates that it is unreliable to use the predicted voltage error of closed-loop algorithm as the criterion to measure the accuracy of the model, while the output voltage obtained by the open-loop model with dynamic parameters can reflect the real situation. Finally, comparative experiments are designed under HPPC and DST conditions. Results show that the proposed state-parameter separated IAUKF-UKF has higher SoC estimation accuracy and better stability than traditional DUKF. [ABSTRACT FROM AUTHOR]

Accurate estimation of battery state of charge (SOC) is of great significance for extending battery life, improving battery utilization, and ensuring battery safety. Aiming to improve the accuracy of SOC estimation, in this paper, a temperature-dependent second-order RC equivalent circuit model is established for lithium-ion batteries, based on the battery electrical characteristics at different ambient temperatures. Then, a dual Kalman filter algorithm is proposed to estimate the battery SOC, using the proposed equivalent circuit model. The SOC estimation results are compared with the SOC value obtained from experiments, and the estimation errors under different temperature conditions are found to be within ±0.4%. These results prove that the proposed SOC estimation algorithm, based on a temperature-dependent second-order RC equivalent circuit model, provides accurate SOC estimation performance with high temperature adaptability and robustness. [ABSTRACT FROM AUTHOR]

State of charge (SOC) estimation of lithium batteries is one of the most important unresolved problems in the field of electric vehicles. Due to the changeable working environment and numerous interference sources on vehicles, it is more difficult to estimate the SOC of batteries. Particle filter is not restricted by the Gaussian distribution of process noise and observation noise, so it is more suitable for the application of SOC estimation. Three main works are completed in this paper by taken LFP (lithium iron phosphate) battery as the research object. Firstly, the first-order equivalent circuit model is adapted in order to reduce the computational complexity of the algorithm. The accuracy of the model is improved by identifying the parameters of the models under different SOC and minimum quadratic fitting of the identification results. The simulation on MATLAB/Simulink shows that the average voltage error between the model simulation and test data was less than 24.3 mV. Secondly, the standard particle filter algorithm based on SIR (sequential importance resampling) is combined with the battery model on the MATLAB platform, and the estimating formula in recursive form is deduced. The test data show that the error of the standard particle filter algorithm is less than 4% and RMSE (root mean square error) is 0.0254. Thirdly, in order to improve estimation accuracy, the auxiliary particle filter algorithm is developed by redesigning the importance density function. The comparative experimental results of the same condition show that the maximum error can be reduced to less than 3.5% and RMSE is decreased to 0.0163, which shows that the auxiliary particle filter algorithm has higher estimation accuracy. [ABSTRACT FROM AUTHOR]

The remaining discharge energy prediction of the battery pack is an important function of a battery management system. One of the key factors contributing to the inaccuracy of battery pack remaining discharge energy prediction is the inconsistency of the state and model parameters. For a batch of lithium-ion batteries with nickel cobalt aluminum oxide cathode material, after analyzing the characteristics of battery model parameter inconsistency, a "specific and difference" model considering state of charge and R0 inconsistency is established. The dual time-scale dual extended Kalman filter algorithm is proposed to estimate the state of charge and R0 of each cell in the battery pack, and the remaining discharge energy prediction algorithm of the battery pack is established. The effectiveness of the state estimation and remaining discharge energy prediction algorithm is verified. The results show that the state of charge estimation error of each cell is less than 1%, and the remaining discharge energy prediction error of the battery pack is less than 1% over the entire discharge cycle. The main reason which causes the difference between the "specific and difference" and "mean and difference" models is the nonlinearity of the battery's state of charge - open circuit voltage curve. When the nonlinearity is serious, the "specific and difference" model has higher precision. [ABSTRACT FROM AUTHOR]

State of charge (SOC) estimation is a key issue in battery management systems. The challenge lies in balancing the trade-off between accuracy and computation cost. To this end, we propose an alternate method by combining the ampere-hour integral (AHI) method which has low computation cost, and the adaptive extended Kalman filter (AEKF) method, which has high accuracy. The technical viability of this alternate method is verified on a LiMnO2-LiNiO2 battery module with a nominal capacity of 130 Ah under the New European Driving Cycle (NEDC) condition. Drifts in current and voltage measurement are considered. The experimental results show that the absolute SOC error using the AHI method monotonously increases from 0% to 7.2% with the computation time of 10 s while the calculation time is obtained on a ThinkPad E450 PC with an Intel Core i7-5500U CPU @2.40 GHz and 16.0 GB RAM. The absolute SOC error of the AEKF method maintains within 3.5% with the computation time of 49 s. Therefore, the alternate method almost maintains the same SOC accuracy compared to the AEKF method which reduces the maximum absolute SOC error by 50% compared to the AHI method. Therefore, the alternate method almost has the same computation time compared with the AHI method which reduces the computation time by nearly 75% compared to the AEKF method. [ABSTRACT FROM AUTHOR]

As an effective computing technique, Kalman filter (KF) currently plays an important role in state of charge (SOC) estimation in battery management systems (BMS). However, the traditional KF with mean square error (MSE) loss faces some difficulties in handling the presence of non-Gaussian noise in the system. To ensure higher estimation accuracy under this condition, a robust SOC approach using correntropy unscented KF (CUKF) filter is proposed in this paper. The new approach was developed by replacing the MSE in traditional UKF with correntropy loss. As a robust estimation method, CUKF enables the estimate process to be achieved with stable and lower estimation error performance. To further improve the performance of CUKF, an adaptive update strategy of the process and measurement error covariance matrices was introduced into CUKF to design an adaptive CUKF (ACUKF). Experiment results showed that the proposed ACUKF-based SOC estimation method could achieve accurate estimate compared to CUKF, UKF, and adaptive UKF on real measurement data in the presence of non-Gaussian system noises. [ABSTRACT FROM AUTHOR]

In recent years, the fractional order model has been employed to state of charge (SOC) estimation. The non integer differentiation order being expressed as a function of recursive factors defining the fractality of charge distribution on porous electrodes. The battery SOC affects the fractal dimension of charge distribution, therefore the order of the fractional order model varies with the SOC at the same condition. This paper proposes a new method to estimate the SOC. A fractional continuous variable order model is used to characterize the fractal morphology of charge distribution. The order identification results showed that there is a stable monotonic relationship between the fractional order and the SOC after the battery inner electrochemical reaction reaches balanced. This feature makes the proposed model particularly suitable for SOC estimation when the battery is in the resting state. Moreover, a fast iterative method based on the proposed model is introduced for SOC estimation. The experimental results showed that the proposed iterative method can quickly estimate the SOC by several iterations while maintaining high estimation accuracy. [ABSTRACT FROM AUTHOR]