Search Results (115)

With the increasing application of sodium-ion batteries in energy storage systems, accurate state of charge (SOC) estimation plays a vital role in ensuring both available battery capacity and operational safety. Traditional Kalman-filter-based methods often suffer from limited model expressiveness or oversimplified physical assumptions, making it difficult to balance accuracy and robustness under complex operating conditions, which may lead to unreliable estimation results. To address these challenges, this paper proposes a hybrid framework that combines an unscented Kalman filter (UKF) with a long short-term memory (LSTM) neural network for SOC estimation. Under various driving conditions, the UKF—based on a second-order equivalent circuit model with online parameter identification—provides physically interpretable estimates, while LSTM effectively captures complex temporal dependencies. Experimental results under CLTC, NEDC, and WLTC cycles demonstrate that the proposed LSTM-UKF approach reduces the mean absolute error (MAE) by an average of 2% and the root mean square error (RMSE) by an average of 3% compared to standalone methods. The proposed framework exhibits excellent adaptability across different scenarios, offering a precise, stable, and robust solution for SOC estimation in sodium-ion batteries. Full article

The rapid advancement of electric vehicles (EVs) and renewable energy storage systems has significantly increased the demand for reliable and efficient battery technologies. Lithium iron phosphate (LFP) batteries are particularly suitable for these applications due to their superior thermal stability and long cycle life. A critical parameter in optimizing the performance of LFP batteries is the open-circuit voltage (OCV), essential for accurate state of charge (SoC) estimation. The accurate determination of the OCV is challenging due to relaxation effects post-charging/discharging, causing voltage changes for up to 24 h or even more until stabilization. This paper presents a novel statistical model for OCV estimation that employs an online observer to detect the knee/elbow point in the voltage relaxation curve. By utilizing the voltage at the knee/elbow point and the initial voltage, the model accurately computes the OCV at the stabilization point. The proposed method, validated with extensive experimental data, achieves high accuracy, with a computed error of less than 0.26% for charging and under 1.2% for discharging. Full article

Thermal management is pivotal for ensuring the safe and efficient operation of LIBs under dynamic conditions. Accurate core temperature monitoring remains a key BTMS challenge for predicting thermal distributions and mitigating TR risks. This study proposes a real-time core temperature estimation framework integrating joint EKF with an electro-thermal-aging model (ECM-1D). Using only surface temperature and voltage measurements, it simultaneously estimates core temperature, SOC, and capacity with bidirectional electro-thermal coupling. The hybrid approach pre-calibrates temperature/SOC/SOH-dependent parameters offline while updating capacity online. Validation under extreme conditions (high-rate cycling, aging, and ISCs) demonstrates 60% lower core temperature RMSE during high-rate cycling, a maximum estimation error below 0.9 K, and 58.9% reduction in SOC estimation error under aging conditions versus existing methods. The framework reliably tracks core temperature trends despite parasitic heat and signal noise, enabling earlier critical temperature warnings. This provides a foundation for TR prevention, advancing battery safety for EV and grid storage applications. Future extensions could integrate physical aging mechanisms and enhance fault detection capabilities. Full article

Kalman filter (KF) is an effective way to estimate the state-of-charge (SOC), but its performance is heavily dependent on the state-space model parameters. One of the factors that causes the model parameters to change is battery aging, which is individually and non-uniformly experienced by the cells inside the battery pack. To mitigate this issue, this paper proposes an online calibration method considering the impact of cell aging and cell inconsistency. In this method, the state-of-health (SOH) levels of the individual cells are estimated using the deep learning method, and the historical parameter loop-up table is constructed to update the state-space model. The proposed calibration framework provides enhanced accuracy for cell-by-cell SOC estimation by lightweight computing devices. The SOC estimation errors of the calibrated EKF reduce to 1.81% compared to 12.1% of the uncalibrated algorithms. Full article

State estimation of batteries is crucial in battery management systems (BMSs), particularly for accurately predicting the state of charge (SOC), which ensures safe and efficient battery operation. This paper proposes a joint SOC estimation method based on a fractional-order model, utilizing a multi-innovation full-tracking adaptive unscented Kalman filter (FOMIST-AUKF-EKF) combined with an extended Kalman filter (EKF) for online parameter updates. The fractional-order model more effectively represents the battery’s dynamic characteristics compared to traditional integer-order models, providing a more precise depiction of electrochemical processes and nonlinear behaviors. It offers superior modeling for long-memory effects, complex dynamics, and aging processes, enhancing adaptability to aging and nonlinear characteristics. Comparative results indicate a maximum end-voltage error reduction of 0.002 V with the fractional-order model compared to the integer-order model. The multi-innovation technology increases filter robustness against noise by incorporating multiple historical observations, while the full-tracking adaptive strategy dynamically adjusts the noise covariance matrix based on real-time data, thus enhancing estimation accuracy. Furthermore, EKF updates battery parameters (e.g., resistance and capacitance) in real time, correcting model errors and improving SOC prediction accuracy. Simulation and experimental validation show that the proposed method significantly outperforms traditional UKF-based SOC estimation techniques in accuracy, stability, and adaptability. Specifically, under varying conditions such as NEDC and DST, the method demonstrates excellent robustness and practicality, with maximum SOC estimation errors of 0.27% and 0.67%, respectively. Full article

Effective health management and accurate state of charge (SOC) estimation are crucial for the safety and longevity of lithium-ion batteries (LIBs), particularly in electric vehicles. This paper presents a health management system (HMS) that continuously monitors a 4s2p LIB pack’s parameters—current, voltage, and temperature—to mitigate risks such as overcurrent and thermal runaway while ensuring balanced charge distribution between cells. An improved online battery model (IOBM) is developed to enhance SOC estimation accuracy. The system utilises forgetting factor recursive least squares (FFRLS) for real-time parameter updates, an adaptive nonlinear sliding mode observer (ANSMO) for SOC estimation, and a long short-term memory (LSTM) network to dynamically adjust capacity based on operating conditions. Validation using the urban dynamometer driving schedule (UDDS) test demonstrated high accuracy, with the proposed battery model achieving a root mean square error (RMSE) of 12.13 mV and the LSTM achieving an RMSE of 0.0118 Ah. Regular updates to the battery’s current capacity, along with the proposed IOBM, significantly improved SOC estimation performance, maintaining estimation errors within 1.08%. Full article

For the Battery Management System (BMS) to manage and control the battery, State of Charge (SOC) is an important battery performance indicator. In order to identify the parameters of the LiFePO₄ battery, this paper employs the forgetting factor recursive least squares (FFRLS) method, which considers the computational volume and model correctness, to determine the parameters of the LiFePO₄ battery. On this basis, the two resistor-capacitor equivalent circuit model is selected for estimating the SOC of the Li-ion battery by combining the extended Kalman filter (EKF) with the Sage–Husa adaptive algorithm. The positivity is improved by modifying the system noise estimation matrix. The paper concludes with a MATLAB 2016B simulation, which serves to validate the SOC estimation algorithm. The results demonstrate that, in comparison to the conventional EKF, the enhanced EKF exhibits superior estimation precision and resilience to interference, along with enhanced convergence during the estimation process. Full article

The precise estimation of the state of charge (SOC) in lithium batteries is crucial for enhancing their operational lifespan. To address the issue of reduced accuracy in SOC estimation caused by the random missing values of lithium battery current measurements, a joint estimation method which combines recursive least squares with missing input data (MIDRLS) and the unscented Kalman filter (UKF) algorithm is proposed, called the MIDRLS-UKF algorithm. Firstly, the equivalent circuit model of a Thevenin battery is formulated. Then, the current imputation model is designed to interpolate the missing data, based on which the MIDRLS algorithm is derived by solving the unbiased estimation of the gradient of the objective function, thus realizing the online high-precision identification of the circuit model parameters. Furthermore, the proposed algorithm is combined with the UKF algorithm to facilitate the online precise estimation of SOC. The simulation results indicate a marked decrease in the SOC estimation error when employing the proposed joint algorithm, as opposed to the conventional forgetting factor recursive least squares (FFRLS) algorithm combined with the UKF joint estimation algorithm, which verifies the precision and effectiveness of the proposed joint algorithm. Full article

For the safe and efficient use of lithium-ion batteries, the state of charge (SOC) is a particularly important state variable. In this paper, we propose a method for the online estimation of SOC and model parameters based on a fractional-order equivalent circuit model. Firstly, we constructed a fractional-order battery model that includes pseudo-capacitance and determined the values of the circuit elements offline using the least squares method from actual input–output data based on the driving profile of an automobile. Compared to the integer-order battery model, we confirmed that the proposed fractional-order battery model has higher accuracy. Secondly, we constructed a fractional-order Kreisselmeier-type adaptive observer as an observer that performs state estimation and parameter adjustment simultaneously. Applying the general adaptive law to the battery model results in a redundant design with many adjustable parameters, so we proposed an adaptive law that reduces the number of adjustable parameters without compromising the stability of the observer. The effectiveness of the proposed method was verified through numerical simulations. As a result, the high estimation accuracy and convergence of the proposed adaptive law were confirmed. Full article

This paper presents a method to validate state of charge (SOC) estimations in batteries for their use in remotely manned aerial vehicles (UAVs). The SOC estimation must provide the mission control with a measure of the available range of the aircraft, which is critical for extended missions such as search and rescue operations. However, the uncertainty about the initial state and depth of discharge during the mission makes the estimation challenging. In order to assess the estimation provided to mission control, an a posteriori re-estimation is performed. This allows for the assessment of estimation methods. A reverse-time Kalman estimator is proposed for this task. Accurate SOC estimations are crucial for optimizing the utilization of multiple UAVs in a collaborative manner, ensuring the efficient use of energy resources and maximizing mission success rates. Experimental results for LiFePO4 batteries are provided, showing the capabilities of the proposal for the assessment of online SOC estimators. Full article

Accurate estimation of State-of-Charge (SoC) is essential for ensuring the safe and efficient operation of electric vehicles (EVs). Currently, second-order RC equivalent circuit models do not account for the influence of battery charging and discharging states on battery parameters. Additionally, offline parameter identification becomes inaccurate as the battery ages. Online identification requires real-time parameter updates during the SoC estimation process, which increases the computational complexity and reduces the computational efficiency of real vehicle Battery Management System (BMS) chips. To address these issues, this paper proposes a SoC estimation method that combines online and offline identification based on an optimized second-order RC equivalent circuit model, which distinguishes it from existing methods in the field. On the basis of the traditional second-order RC model, the Ohmic resistance (R0), polarization resistance (R1), polarization capacitance (C1), diffusion resistance (R2), and diffusion capacitance (C2) during the charging and discharging processes are discussed separately. R0, which does not change frequently, is identified offline, while R1, R2, C1, and C2, which dynamically change with time and current, are identified online. To thoroughly verify the feasibility of the proposed method, we construct an SoC estimation test bench, which allows us to adjust the battery’s surface temperature in real time using a temperature control chamber. Experimental validation under Federal Urban Driving Schedule (FUDS) (−10 °C to 45 °C, 80% battery capacity) and Dynamic Stress Test (DST) (−10 °C to 45 °C, 8% battery capacity) conditions demonstrate that our method improves SoC estimation accuracy by 16.28% under FUDS and 28.2% under DST compared to the improved GRU-based transfer learning method, while maintaining system SoC estimation efficiency. Full article

A new optimization method for estimating the State of Charge (SOC) of battery charge state is proposed. This method incorporates the Levenberg–Marquardt Algorithm (LMA) for online parameter identification and the Extended Kalman Filter (EKF) for SOC. On the one hand, the LMA efficiently alleviates the ’Data saturation’ problem experienced by least squares methods by dynamically adjusting weights of data. On the other hand, the EKF improves the robustness and adaptability of SOC estimation. Simulation results under Hybrid Pulse Power Characteristic (HPPC) conditions demonstrate that this new approach offers superior performance in SOC estimation in batteries for electric vehicles compared to existing methods, with better tracking of the true SOC curve, reduced estimation error, and improved convergence. Full article

With the increase in the amount of actual operating data on electric vehicles, how to analyze and process useful information from existing battery charging and discharging data and apply it to subsequent state estimation is worthy of in-depth thinking and practice by researchers. This article proposes a collaborative estimation architecture for SOC and SOH based on the 1RC equivalent circuit model, recursive least squares, and adaptive extended Kalman filtering algorithms (AEKF), which combine offline data processing with online applications. By applying offline data processing, OCV–SOC polynomial fitting and average polarization resistance were determined, which reduced the time required for basic data measurement and improved the accuracy of model parameter identification, while a recursive estimation combining micro- and macro-time-scales of AEKF was used for the online real-time estimation of the SOC and actual available capacity of batteries, in order to eliminate interference from measurement and process noise. The results of the simulated and experimental data validation indicate that the proposed algorithm is applicable to the lithium-ion batteries studied in this paper, the average SOC deviation is less than 1.5%, the maximum deviation is less than 2.02%, and the SOH estimation deviation is less than 1% under different driving conditions in the multi-temperature range. This study lays the foundation for further utilizing offline data and improving SOC and SOH collaborative estimation algorithms. Full article

In order to improve the accuracy of internal temperature estimation in batteries, a 10-parameter time-varying multi-surface heat transfer model including internal heat production, heat transfer and external heat transfer is established based on the structure of a lithium iron phosphate pouch battery and its three directional anisotropic heat conduction characteristics. The entropy heat coefficient, internal equivalent heat capacity and internal equivalent thermal resistance related to the SOC and temperature state of the battery were identified using experimental tests and the least square fitting method, and were then used for online calculation of internal heat production and heat transfer in the battery. According to the time-varying and nonlinear characteristics of the heat transfer between the surface and the environment of the battery, an internal temperature estimation algorithm based on the square root cubature Kalman filter was designed and developed. By iteratively calculating the estimated surface temperature and the measured value, dynamic tracking and online correction of the internal temperature of the battery can be achieved. The verification results using FUDS and US06 dynamic working condition data show that the proposed method can quickly eliminate the influence of initial temperature deviations and accumulated process errors and has the characteristics of a high estimation accuracy and good robustness. Compared with the estimation results of the adaptive Kalman filter, the proposed method improves the estimation accuracy of FUDS and US06 working conditions by 67% and 54%, respectively, with a similar computational efficiency. Full article

The open-circuit voltage (OCV) curve has a significant influence on the accuracy of the state of charge (SOC) estimation based on equivalent circuit models (ECMs). However, OCV curves are tested through offline experiments and are hard to be very accurate because they constantly change with the test method’s ambient temperature and aging status. Recently, researchers have attempted to improve the accuracy of OCV curves by increasing the volume of sample data or updating/reconstructing the curve combined with practical operation data. Still, prior offline tests are essential, and experimental errors inevitably exist. Consequently, a SOC estimation method without any offline OCV tests might be an efficient route to improve the accuracy of SOC. According to this idea, this paper presents a novel method for SOC estimation, which is based on online OCV curve construction. Meanwhile, a stepwise multi-timescale parameter identification algorithm is designed to improve the interpretability and precision of the estimated ECM parameters. The results demonstrate that the maximum SOC estimation error is only 0.05% at 25 °C, indicating good robustness under various ambient temperatures and operational conditions. Full article