Accurate State Of Charge Estimation Research Articles

An Ensemble Learning Method for SOC Estimation of Lithium-Ion Batteries Using Machine Learning

Accurately assessing the State of Charge (SOC) is paramount for optimizing battery management systems, a cornerstone for ensuring peak battery performance and safety across diverse applications, encompassing vehicle powertrains and renewable energy storage systems. Confronted with the challenges of traditional SOC estimation methods, which often struggle with accuracy and cost-effectiveness, this research endeavors to elevate the precision of SOC estimation to a new level, thereby refining battery management strategies. Leveraging the power of integrated learning techniques, the study fuses Random Forest Regressor, Gradient Boosting Regressor, and Linear Regression into a comprehensive framework that substantially enhances the accuracy and overall performance of SOC predictions. By harnessing the publicly accessible National Aeronautics and Space Administration (NASA) Battery Cycle dataset, our analysis reveals that these integrated learning approaches significantly outperform traditional methods like Coulomb counting and electrochemical models, achieving remarkable improvements in SOC estimation accuracy, error reduction, and optimization of key metrics like R2 and Adjusted R2. This pioneering work propels the development of innovative battery management systems grounded in machine learning and deepens our comprehension of how this cutting-edge technology can revolutionize battery technology.

Research on SOC Prediction of Lithium-Ion Batteries Based on OLHS-DBO-BP Neural Network

Accurately estimating the state of charge (SOC) of lithium-ion batteries is of great significance for extending battery lifespan and enhancing the efficiency of energy management. Regarding the issue of the relatively low estimation accuracy of SOC by the backpropagation neural network (BPNN), an enhanced dung beetle optimizer (DBO) algorithm is proposed to optimize the initial weights and thresholds of the BPNN. This overcomes the drawback of a single BP neural network being prone to local optimum and accelerates the convergence rate. Simulation analyses on the experimental data of NCM and A123 lithium batteries were conducted in Matlab R2022a. The results indicate that the proposed algorithm in this paper has an average SOC estimation error of less than 1.6% and a maximum error within 2.9%, demonstrating relatively high estimation accuracy and robustness, and it holds certain theoretical research significance.

Discrete-time Luenberger observer design for Lithium-ion battery state-of-charge with stability guarantee

State-of-charge (SOC) estimation is particularly important as it provides information about the remaining energy capacity of the battery, allowing for better planning and utilization. Accurate SOC estimation is challenging because it cannot be directly measured from the battery. Instead, it is estimated by analyzing measurable variables such as current and voltage. To address this challenge, a discrete-time observer-based SOC estimation approach is proposed in this paper. This approach utilizes a second-order equivalent circuit model and a piecewise linear approximation to represent the relationship between SOC and open circuit voltage (OCV). The proposed observer-based approach utilizes these models to estimate the SOC with assured asymptotic stability under specific assumptions to simplify the design process. Simulations in Python are conducted to evaluate the performance of the designed observer. In the simulations, the SOC estimation under various conditions, such as model uncertainty, disturbances, and measurement noise, is also covered. In addition, three different observer gains are considered in the simulations. Lastly, simulation studies indicate that the estimated SOC values converge to the real SOC values, with some different behavior depending on the regarded situations.

State-of-Charge Estimation Method for Lithium Batteries Based on Adaptive Fusion Factors

Abstract Accurate estimation of the state of charge is significant for battery safety. To improve robustness, computational efficiency, and noise stability in state of charge estimation for lithium batteries, we propose a method based on adaptive fusion factors. Based on the methodological properties of the open circuit voltage method and the ampere hour method, we designed a fusion factor function to combine the strong correction ability of the open circuit voltage method with the smoothing advantages of the ampere hour method. The proposed method utilizes an adaptive forgetting factor recursive least squares approach to address the limitation of the traditional open circuit voltage method, which cannot estimate state of charge online. It corrects the battery capacity using historical data to achieve accurate state of charge estimation. The effectiveness and robustness of the proposed method are validated using self-tests and a public dataset. The results demonstrate that the mean absolute error in state of charge estimation is approximately 1%, even when the initial state of charge value deviates from the actual value and the dataset contains noise.

Lithium-Ion Battery Health Management and State of Charge (SOC) Estimation Using Adaptive Modelling Techniques

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%.

Robust Estimation of Lithium Battery State of Charge with Random Missing Current Measurement Data

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.

State of Charge Estimation of Lithium Battery Utilizing Strong Tracking H-Infinity Filtering Algorithm

The ability to quickly and accurately estimate the state of charge (SOC) of lithium batteries is a key function of the battery management system (BMS). To enhance the accuracy of SOC estimation for lithium batteries, we propose a method that combines the dynamic factor recursive least squares (DFFRLS) algorithm and the strong tracking H-infinity filtering (STF-HIF) algorithm. To address the issue of fixed forgetting factors in recursive least squares (RLS) that struggle to maintain both fast convergence and stability in battery parameter identification, we introduce dynamic forgetting factors. This approach adjusts the forgetting factor based on the residuals between the model’s estimated and actual values. To improve the H-infinity filtering (HIF) algorithm’s poor performance in tracking sudden state changes, we propose a combined STF-HIF algorithm, integrating HIF with strong tracking filtering (STF). Simulation experiments indicate that, compared to the HIF algorithm, the STF-HIF algorithm achieves a maximum absolute SOC estimation error (MaxAE) of 0.69%, 0.72%, and 1.22%, with mean absolute errors (MAE) of 0.27%, 0.25%, and 0.38%, and root mean square errors (RMSE) of 0.33%, 0.30%, and 0.46% under dynamic stress testing (DST), federal urban driving schedules (FUDS), and Beijing dynamic stress testing (BJDST) conditions, respectively.

An Adaptive Combined Method for Lithium‐Ion Battery State of Charge Estimation Using Long Short‐Term Memory Network and Unscented Kalman Filter Considering Battery Aging

AbstractThe accurate estimation of battery state of charge (SOC) enables the reliable and safe operation of lithium‐ion batteries. Data‐driven SOC estimation is considered an emerging and effective solution. However, existing data‐driven SOC estimation methods typically involve direct estimation and lack effective feedback correction. Moreover, battery degradation poses additional challenges to accurate SOC estimation. Therefore, this study proposes an adaptive combined method for battery SOC estimation based on a long short‐term memory (LSTM) network and unscented Kalman filter (UKF) algorithm considering battery aging status. First, an LSTM model is constructed to characterize the battery's dynamic performance instead of traditional battery models. Then, the UKF algorithm is employed to perform SOC estimation through the feedback of terminal voltage prediction. To enhance estimation accuracy under different aging statuses, a proportional‐integral‐derivative controller is employed to correct the capacity fading during the SOC estimation process. Validation results indicate that the terminal voltage prediction model demonstrates exceptional robustness against interference from current and voltage noise. Compared to the traditional estimation method combining the deep learning model and Kalman filter algorithm, the proposed method demonstrates superior estimation accuracy under various complex operating conditions. Furthermore, the proposed method outperforms the traditional method in estimation performance during battery aging.

Estimation of Lithium-Ion Battery SOC Based on IFFRLS-IMMUKF

The state of charge (SOC) is a characteristic parameter that indicates the remaining capacity of electric vehicle batteries. It plays a significant role in determining driving range, ensuring operational safety, and extending the service life of battery energy storage systems. Accurate SOC estimation can ensure the safety and reliability of vehicles. To tackle the challenge of precise SOC estimation in complex environments, this study introduces an improved forgetting factor recursive least squares (IFFRLS) method, which integrates the Golden Jackal optimization (GJO) algorithm with the traditional FFRLS method. This integration is grounded in the formulation of a lithium battery state equation derived from a second-order RC equivalent circuit model. Additionally, the research utilizes the interactive multiple model unscented Kalman filter (IMMUKF) algorithm for SOC estimation, with experimental validation conducted under various conditions, including hybrid pulse power characterization (HPPC), urban dynamometer driving schedule (UDDS), and real underwater scenarios. The experimental results demonstrate that the SOC estimation method of lithium batteries based on IFFRLS-IMMUKF exhibits high accuracy and a favorable temperature applicability range.

Multi-innovation adaptive Kalman filter algorithm for estimating the SOC of lithium-ion batteries based on singular value decomposition and Schmidt orthogonal transformation

The state of charge (SOC) of lithium battery is a key parameter for effective management of battery management systems (BMS). To address the problems of low precision, complex computation and poor robustness of traditional charging state estimation methods, an enhanced algorithm based on Unscented Kalman filter (UKF) is proposed. The singular value decomposition (SVD) method is adopted to ensure the normal operation of the Unscented Kalman Filter (UKF) algorithm even when the matrix P lacks positive semi-definiteness from a mathematical perspective. This enhancement significantly improves the theoretical robustness of UKF. Schmidt orthogonal transformation is concurrently used to reduce the computational complexity in the sampling point selection process, and the multi-innovation theory is combined with adaptive noise control to further improve the accuracy of SOC estimation. The algorithm is validated using the Urban Dynamometer Driving Schedule (UDDS) condition. The simulation results are excited using Singular value decomposition-multi-innovation adaptive Schmidt orthogonal unscented Kalman filter method (SVD-MIASOUKF). 0.95 % and 1.29 % of maximum errors are obtained at 25 °C and −10 °C, while the maximum errors are 2.46 %–2.99 % using SVD-UKF and UKF. The proposed approach shows faster convergence speed and higher estimation accuracy in comparison to traditional algorithms.

An accurate state-of-charge estimation of lithium-ion batteries based on improved particle swarm optimization-adaptive square root cubature kalman filter

The state of charge (SOC) of lithium-ion batteries (LIBs) is regarded as the fundamental parameter of the battery management system (BMS). In this paper, a parameter optimization method for mobile estimation windows based on particle swarm optimization-adaptive square root cubature Kalman filter (PSO-ASRCKF) is established to improve the SOC estimation ability and accuracy of LIBs. The filtering algorithm parameters are optimized to achieve high-precision SOC estimation. An improved ASRCKF with the PSO algorithm to optimize the moving estimation window is constructed to obtain the best adaptive window value. Different temperatures and initial SOC values are used to verify the proposed method under dynamic stress test (DST) and other conditions. The results show that the relative error is mainly distributed within 0.5 % when the SOC is stable. In addition, robustness and adaptability are verified with the root mean square error (RMSE) and the mean absolute error (MAE) values of 0.0019 and 0.0017, respectively, under the DST working condition. The experimental results show that the proposed method can achieve accurate SOC estimation under different temperatures, operating conditions, and initial SOC values.

State of Charge Estimation for Lithium-Ion Batteries Using Optimized Model Based on Optimal HPPC Conditions Created Using Taguchi Method and Multi-Objective Optimization

This study proposes a comprehensive methodology for accurate State of Charge (SOC) estimation in lithium-ion batteries by optimizing equivalent circuit model (ECM) parameters under varying temperature conditions using the Taguchi method. Analysis of Variance (ANOVA) was employed to evaluate the influence of these parameters on ECM accuracy. Experiments were conducted at −10 °C, 25 °C, and 40 °C to evaluate the effects of pulse time gap, discharge pulse time, and C-rate on SOC estimation accuracy. A genetic algorithm-based multi-objective optimization technique was employed to minimize RMSE in the extended Kalman filter (EKF) SOC estimation process. The results showed that temperature significantly impacts SOC prediction, with deviations most pronounced at low (−10 °C) and high (40 °C) temperatures. When assessments are conducted for different SOC levels (SOC90, SOC50, SOC30), the key results highlight the substantial influence of pulse time gap and discharge pulse time on model accuracy. Also, it was observed that there is a significant reduction in RMSE, indicating improved performance under optimized conditions. The findings are particularly relevant for real-time applications, such as electric vehicles, where accurate SOC estimation is crucial for battery management.

Self-attention network-based state of charge estimation for lithium-ion batteries with gapped temperature data

The accurate estimation of the state of charge (SOC), a critical indicator of the energy stored in lithium-ion batteries, is essential for ensuring reliable and safe battery management. The influence of temperature on the battery characteristics substantially affects the SOC estimation accuracy. Owing to the broad operational temperature range of batteries, it is vital to address the various temperature conditions. This study proposes a model structure for data-driven SOC estimation to enhance accuracy under diverse temperature conditions. The model leverages the analysis of the SOC characteristics derived from the measured data. The proposed structure incorporates parallel-connected self-attention and long-short-term memory modules, thus providing an innovative approach for effectively capturing intricate features in SOC estimation. This study primarily focused on evaluating the capability of the proposed model to achieve satisfactory SOC estimation for untrained temperature conditions when trained with gapped temperature data, thus emphasizing its practicality. To assess the feasibility of the proposed method, experiments were performed under a broad range of fixed and varying temperature conditions, including seasonal and daily changes. The experimental results demonstrated that the root-mean-square errors of the estimated SOC were 0.4101% and 1.5611% at fixed and time-varying temperatures, respectively, including the subzero ranges. These results highlight the robustness of the proposed model under various temperature conditions and its applicability to real-world battery operational temperatures.

Battery state of charge estimation for electric vehicle using Kolmogorov-Arnold networks

Accurate estimation of the state of charge (SoC) in electric vehicle (EV) batteries is essential for effective battery management and optimal performance. This study investigates the application of Kolmogorov-Arnold Networks (KAN) for SoC estimation, comparing its performance against Artificial Neural Networks (ANN) and a hybrid Barnacles Mating Optimizer-deep learning model (BMO-DL). The dataset, derived from simulations involving a lithium polymer cell model (ePLB C020) in an electric car similar to Nissan Leaf EV, encompasses 68,741 instances, divided into training and testing sets. Three KAN models were developed and evaluated based on root mean square error (RMSE), mean absolute error (MAE), maximum error (MAX), and coefficient of determination (R2). Residual analysis indicates that KAN-Model 1 performs the best, with residuals closely clustered around zero and no significant patterns, suggesting reliable and unbiased predictions. KAN-Model 2 also performs well but exhibits some nonlinear trends in the residuals. ANN and BMO-DL models show larger deviations and less consistent performance. These findings highlight the potential of KAN for enhancing SoC estimation accuracy in EV applications.

Review Paper for SOC Estimation Techniques: Challenges and Future Areas for Improvement

This paper explores the advancements and challenges in State of Charge (SOC) estimation techniques for lithium-ion batteries, particularly within the context of electric vehicles (EVs) and renewable energy systems. As the global demand for sustainable energy solutions grows, accurate SOC estimation becomes essential for optimizing battery performance, enhancing safety, and extending battery life. The paper categorizes various SOC estimation methods into three primary approaches: direct measurement techniques, model-based methods, and data-driven algorithms. Direct measurement techniques, such as Coulomb counting and Open Circuit Voltage (OCV), are straightforward but often lack precision under dynamic conditions. Model-based methods, including Equivalent Circuit Models (ECM) and electrochemical models, provide detailed insights into battery behavior but can be computationally intensive. In contrast, data-driven approaches utilizing machine learning algorithms exhibit promising adaptability and accuracy, albeit relying heavily on large datasets. Despite these advancements, several limitations persist. Current SOC estimation methods are hindered by their dependence on accurate battery models and quality data, which can degrade over time. Furthermore, hybrid methods, which combine strengths from various techniques, introduce complexity and demand substantial computational resources. The integration of SOC estimation techniques in EV applications poses additional challenges due to varying operational conditions, necessitating efficient processing of real-time data from multiple sensors. Emerging trends in Battery Management Systems (BMS) are also examined, highlighting the role of AI and machine learning in improving real-time SOC computations and predictive capabilities. Cloud-based BMS systems are identified as a significant development for remote monitoring and control, enhancing the overall reliability of battery systems. This paper aims to provide a comprehensive overview of SOC estimation techniques, identify ongoing challenges, and suggest future research directions to enhance the effectiveness of battery management strategies in the evolving landscape of energy systems. DOI: https://doi.org/10.52783/pst.906

Robustness estimation for state-of-charge of a lithium-ion battery based on feature fusion

State of charge (SOC) of the lithium-ion battery stands as one of the crucial parameters of the battery management system. To enhance the robustness and accuracy of data-driven methods for estimating SOC, in this study, a novel framework based on feature selection and closed-loop estimation framework is proposed for estimating the SOC of a battery. Firstly, the maximum mutual information coefficient is used to correlate the data collected from the battery experiments. Secondly, an improved least squares support vector machine model (LSSVM) is proposed for SOC estimation using the sine cosine optimization algorithm for parameter optimization of LSSVM. Furthermore, based on the Sage-Husa adaptive Kalman filter, this study constructed a closed-loop estimation model. Finally, we conduct experiments on batteries with variable temperatures and working conditions, to verify its robustness and generalization. The results indicate that the proposed method has great SOC estimation accuracy compared to the control group. Even under simulated measurement noise conditions, the proposed method achieves the root mean square error 1.28 % and 1.12 % respectively, demonstrating strong robustness.

Mechanism and Data-Driven Fusion SOC Estimation

An accurate assessment of the state of charge (SOC) of electric vehicle batteries is critical for implementing frequency regulation and peak shaving. This study proposes mechanism- and data-driven SOC fusion calculation methods. First, a second-order Thevenin battery model is developed to obtain the physical parameters of the battery. Second, data from the Thevenin battery model and data from four standard cycling conditions in the electric vehicle industry are added to the dataset of the feed-forward neural network data-driven model to construct the test and training sets of the data-driven model. Finally, the error of the mechanism and data-driven fusion modeling method is quantitatively analyzed by comparing the estimation error of the method for the battery SOC at different temperatures with the accuracy of the data-driven SOC estimation method. The simulation results show that the root mean square error, the mean age absolute error, and the maximum error of mechanism and data-driven method for the estimation error of battery SOC are lower than those of the data-driven method by 0.9%, 0.65%, and 1.3%, respectively. The results show that the mechanism and data-driven fusion SOC estimation method has better generalization performance and higher SOC estimation accuracy.

Data-driven state-of-charge estimation of a lithium-ion battery pack in electric vehicles based on real-world driving data

State-of-charge (SOC) is one of the most important indicators in the battery management system (BMS) of electric vehicles (EVs). Accurate online estimation of battery pack SOC is essential for ensuring safety by preventing overcharging and overdischarging, as well as for facilitating proper operation and efficient energy utilization. This paper proposes a deep learning model, CNN-BiLSTM-Attention, to drive the battery pack SOC estimation by datasets collected from actual operating EVs. Multivariate time series (MVTS) signals such as vehicle speed, battery voltage, current and temperature are carefully selected as inputs to the model. Additionally, a three-parameter Weibull probability model is used to model the terminal voltage distribution of all cells within the investigated battery pack, and the evolution of cell terminal voltage inconsistency concerning depth of discharge (DOD) is described from the perspective of dispersion and symmetry. By adding these distribution features to the input dimension of the CNN-BiLSTM-Attention model, the estimation accuracy of battery pack SOC has been further improved. Experimental results indicate that when the window length (WL) is set to 25 sampling time steps and the window overlap rate is >72 %, the SOC estimation error is <3 % and the root mean square error (RMSE) is <1.12 % within the maximum DOD variation range experienced by the battery pack. Especially when the battery pack is in the discharge platform period of 30 %–100 % SOC, the SOC estimation error is reduced to <2 %. After adding the Weibull distribution features that reflect the cell inconsistency evolution into the model's input dimensions, the overall SOC estimation RMSE is reduced by about 31 %, especially by about 51 % at lower SOC levels (below 31 %).

Estimation of state of charge for polymer solid-state batteries: Ensemble learning models and temperature impact study

In addition to the research and development of solid electrolytes to improve battery performance, an efficient battery management system (BMS) is a must to ensure safe use and extend battery life, and state of charge (SOC) estimation is critical in the BMS. This paper presents a novel temperature-influenced method for estimating the SOC of polymer-based solid-state batteries in real-time, using machine learning to capture the relationship between SOC and battery characteristics at different temperatures. The results show that accurate SOC estimation results can be achieved at different temperatures, with an average root mean square error of 1.42 %. Furthermore, the method uses Shapley Additive explanation (SHAP) to reduce the degree of black box nature of the model and analyzes the electrochemical processes inside the battery at different temperatures through relaxation time distribution. Accurate estimates of SOC and guidelines for appropriate operating temperatures can serve as a basis for BMS decision-making and improve the lifetime of polymer-based solid-state batteries.

Adaptive optimal observer for real-time state of charge estimation of lithium-ion batteries in robotic systems

PurposeThis study aims to address the challenge of the real-time state of charge (SOC) estimation for lithium-ion batteries in robotic systems, which is critical for monitoring remaining battery power, planning task execution, conserving energy and extending battery lifespan.Design/methodology/approachThe authors introduced an optimal observer based on adaptive dynamic programming for online SOC estimation, leveraging a second-order resistor–capacitor model for the battery. The model parameters were determined by fitting an exponential function to the voltage response from pulse current discharges, and the observer's effectiveness was verified through extensive experimentation.FindingsThe proposed optimal observer demonstrated significant improvements in SOC estimation accuracy, robustness and real-time performance, outperforming traditional methods by minimizing estimation errors and eliminating the need for iterative steps in the adaptive critic and actor updates.Originality/valueThis study contributes a novel approach to SOC estimation using an optimal observer that optimizes the observer design by minimizing estimation errors. This method enhances the robustness of SOC estimation against observation errors and uncertainties in battery behavior, representing a significant advancement in battery management technology for robotic applications.