Accurate State Of Charge Estimation Research Articles

Lithium-ion point-of-care ultrasound battery joint state of charge estimation

With recent advances in ultrasound technology, including accessibility and portability, point-of-care ultrasound systems (POCUS) are becoming ubiquitous in urban and rural health services. The efficient use of POCUS battery power is necessary due to the limited access to electricity in rural locations. Accurate estimation of the state-of-charge (SOC) of the onboard lithium-ion battery is crucial in ensuring the safe, efficient, and reliable operation of the battery management system (BMS). This research suggests a novel approach for striking a reasonable balance between the POCUS battery management systems computation time and SOC estimate accuracy. Given that the lithium-ion battery is a non-linear and time-varying system, it is modelled by a second-order RC equivalent circuit model (2-RC ECM). Real-time parametric identification is carried out using the method of recursive least squares with respect to an adaptive forgetting factor (AFFRLS). The joint SOC evaluation technique, ordering the results of real-time identification and the Extended Kalman Filter (EKF) recommended for estimating battery SOC at temperatures between 0 and 45 °C. Simulations were carried out using experimental data from the DST (Dynamic Stress Test), incremental current and, the Federal Urban Driving Program (FUDS) of the CALCE research group to evaluate the proposed approach. Based on the monitoring of dynamic changes in model parameters and the computational complexity of existing algorithms, the results reveal that the joint AFFRLS-EKF estimation proposed for the SOC strategy achieves good accuracy, high adaptability and rapid convergence of SOC estimation.

A novel suppressing Kalman filter divergence method for the state of charge estimation of lithium-ion batteries under complex conditions

The estimation method for state of charge (SOC) of lithium-ion batteries based on the Extended Kalman Filter (EKF) is prone to losing the ability to track sudden changes under complex driving conditions. Thus, this method cannot guarantee estimation accuracy and robustness. To overcome this deficiency, fading factors are introduced into the error covariance to enhance the effect of newly generated measurement data on the current filtering estimation. A Suboptimal Multiple Fading EKF (SMFEKF) SOC estimation method is proposed herein. The fading factors are solved by forcing the new error sequence of the predicted and actual terminal voltage values to remain orthogonal. The new error sequence that remains orthogonal undergoes transitions from strong autocorrelation in the original stable state to weak autocorrelation. Through real-time adjustment of the Kalman gain matrix, the effective tracking ability of the system in the event of sudden changes gets enhanced. To verify the effectiveness of the proposed method, first, a battery dynamic condition test library covering multiple driving scenarios (such as cities, suburbs, and highways) is established through ADVISOR advanced vehicle simulator driving condition tests. Second, a second-order equivalent circuit model is established and the recursive least squares method is used for parameter identification. Finally, a detailed comparison is made between SMFEKF and EKF in terms of SOC estimation accuracy and robustness under driving conditions with different levels of complexity. It is found that four operating conditions are the main reasons for filtering divergence in EKF. The results show that the root mean square errors of SMFEKF are 63.72 %, 54.20 %, and 21.30 % those of EKF under the three complex conditions, respectively. The new method effectively reduces SOC estimation error and solves the problem of EKF filtering divergence under complex conditions.

Study on the estimation of the state of charge of lithium-ion battery

Lithium-ion battery (LIB) occupies a major position in rechargeable batteries. However, if the state of charge (SOC) estimation of LIB is not accurate, it will lead to the decline of battery life. SOC is often estimated by the extended Kalman filter (EKF) algorithm, but this method depends on the accuracy of model parameters. The sampling point interval time can affect the accuracy of SOC estimation. In this paper, the first-order RC model parameters are identified by two methods and the SOC is estimated by the EKF algorithm. Using this method, the battery parameters are received more accurate and the SOC estimation error is smaller. When the sampling interval is 0.03 s, the SOC estimation error is the smallest. And the second-order RC model can receive the same result. When the sampling interval is 0.03 s, the SOC estimation error of the 1RC-1 method is less than 1.4 %, the SOC estimation error of the 1RC-2 method is less than 0.017, and the root mean square error (RMSE) is 0.0087 and 0.01084. The conclusion is also used in the second-order RC model and contributes to the improvement of the SOC estimation accuracy. An effective method to estimate the battery SOC range is also proposed. This paper provides an effective method for obtaining more accurate SOC.

State-of-charge estimation of lithium-ion battery: Joint long short-term memory network and adaptive extended Kalman filter online estimation algorithm

With the widespread use of lithium-ion batteries, estimating the State of Charge (SOC) has been one of the most critical tasks in the battery management system (BMS). In this paper, a joint long short-term memory recurrent neural network (LSTM-RNN) and adaptive extended Kalman filter (AEKF) algorithm is proposed to achieve accurate SOC estimation. The proposed algorithm generates an initial SOC estimation value through a trained LSTM-RNN with a sliding time window signal sequence as input. The initial estimation value is then used as a feedback input to the AEKF. The results show that only a 30-s time series as the input of the LSTM-RNN can achieve satisfactory estimation results. Compared with traditional adaptive extended Kalman filter and unscented Kalman filter (UKF), the proposed algorithm has a better performance of estimation accuracy under various discharging conditions, especially when applied at low temperatures. Finally, the SOC estimation results under four operating conditions and various temperatures show that the maximum error is less than 2.5 %, in particular, the root mean square error (RMSE) and the mean absolute error (MAE) are below 1.01 % and 0.64 %. The proposed algorithm is an effective SOC estimation method with good robustness and high estimation accuracy.

Second-Order Central Difference Particle Filter Algorithm for State of Charge Estimation in Lithium-Ion Batteries

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.

A self-attention-based CNN-Bi-LSTM model for accurate state-of-charge estimation of lithium-ion batteries

In the quest for clean and efficient energy solutions, lithium-ion batteries have emerged at the forefront of technological innovation. Accurate state-of-charge (SOC) estimation across a broad temperature range is essential for extending battery longevity, and enduring effective management of overcharge and over-discharge conditions. However, prevailing challenges persist in achieving precise SOC estimates and generalizing across a wide temperature range, particularly at lower temperatures. Our comparative analysis reveals that, while a single-layer bidirectional LSTM model with a self-attention mechanism achieves remarkable SOC estimation accuracy at room temperature, the intricacies of SOC estimation at lower temperatures necessitate the incorporation of more hidden layers and more complex network architecture to capture intricate features influencing battery dynamics. Hence, we propose a deep learning model, based on convolutional neural networks integrating bidirectional long short-term memory and self-attention mechanism (CNN-Bi-LSTM-AM), specifically designed to tackle the challenges of achieving accurate SOC estimations across a wide temperature range. The proposed model demonstrates proficiency in capturing both spatial and temporal dependencies critical for lithium-ion battery SOC estimation. Furthermore, the integration of a self-attention mechanism enhances the model’s adeptness to discern pertinent features and patterns within the dataset, thereby improving its overall performance and robustness, even in sub-room temperature environments.

The LiFePO4 battery lifespan SoC estimation using Ham-Informer and internal pressure

The goal of this study is to use the Ham-Informer to accurately and reliably estimate state of charge (SoC) throughout the LiFePO4 battery lifespan. First, Pearson heat map is used to study the correlation between different parameters and SoC, and found that the correlation between internal pressure is as high as 0.97. Hence， internal pressure is introduced to improve the accuracy of SoC estimation. The Informer model is refined using Hampel filter and Multi-head ProbeHamSparse to reduce the computational complexity and improve its feature extraction ability. The use of internal pressure and Ham-Informer can reduce the MAE (Mean Absolute Error) of the estimated SoC values of LFP batteries with light, mild, and severe degradation by 75 %, 74 %, and 86 %, respectively, compared to the absence of internal pressure. Compared with the unimproved Informer, the MAE of SoC estimates at different life stages decreased by 76 %, 68 %, and 84 %. The model exhibiting an average decrease of 89 % in MAE when compared to the LSTM model, and a 77 % decrease when compared to the GRU model. The incorporation of internal pressure and Ham-Informer can enhance the accuracy and reliability of battery lifespan SoC estimation. Compared with other methods, the computational complexity of Ham-Informer is smaller. Therefore, it can be applied to battery management systems, enabling accurate and dependable SoC estimation throughout the battery's lifespan.

State-of-charge estimation for lithium-ion batteries based on modified unscented Kalman filter using improved parameter identification

The full and single hybrid pulse power characterization (HPPC) experiments are conducted on nickel cobalt manganese (NCM) and lithium iron phosphate (LFP) batteries to obtain the accurate relationship between state of charge (SOC) and open circuit voltage (OCV). The pseudo random number generated by the RAND function is used as the initial value of the parameter identification equation for the second-order equivalent circuit model (ECM), and the parameter identification of lithium-ion batteries is achieved through least squares fitting. The unscented Kalman filter (UKF) simulation model is modified by the first order low pass filtering (FOLPF) algorithm to improve the accuracy of SOC estimation of batteries. The results show that the goodness of fit between the real and estimated HPPC pulse voltage values at different SOC values is above 0.99 for both NCM and LFP batteries. Based on the parameter identification results, the maximum error of the HPPC voltage estimated by the second-order ECM is within 0.045 V under both full pulse and single pulse testing conditions while the maximum error of SOC estimation is within 0.025. The UKF model modified by the FOLPF algorithm provides a reference for the accurate SOC estimation of batteries.

A Bayesian optimized machine learning approach for accurate state of charge estimation of lithium ion batteries used for electric vehicle application

In recent times, battery technology used in electric vehicles has drawn numerous researchers' attention. Monitoring the battery condition, particularly the State of charge, is required to ensure the battery's safe and reliable performance. Despite the fact that many SOC estimation methods have been proposed, further research is necessary to identify an approach that adapts versatile lithium-ion battery chemistries. In the recent study it has been demonstrated that Machine Learning approaches have better prediction accuracy compared to conventional methods. To maximize the performance of Machine learning models, it is imperative to select the optimal hyperparameters and employ appropriate input parameters. At present, researchers employ, established heuristics methods to select hyperparameters, which may involve manual tuning or exhaustive search techniques such as random search and grid search. These techniques make the models less accurate and inefficient. In this paper, a systematic, automated process for selecting hyperparameters with a Bayesian optimization algorithm is proposed. In addition, along with the battery parameters (voltage, current and temperature), vehicle velocity, road condition, motor characteristics and environmental conditions are used as the input parameters for accurate SOC prediction. The highly correlated input features are selected through the MRMR algorithm. The performance of six ML algorithms, namely SVM, ANN, GPR, Ensembler, linear regression and Decision Tree, is tested and validated with and without hyperparameter tuning for different data sets. The experimental results demonstrate that the hyperparameter-tuned model outperforms the standard model in estimating the State of charge (SOC). In addition, the model's estimation error is <1 % across a range of vehicle velocity, road condition, motor torque, battery voltage, current, and temperature.

Enhancing SOC estimation accuracy via incremental learning techniques for second-life batteries

The available options for retired batteries include recycling or finding a secondary application. Repurposing the batteries for applications like stationary systems or low-speed vehicles may present a viable alternative. However, Second-Life Batteries (SLB) entail unique challenges since a battery pack comprises cells with diverse resistance and capacity characteristics. It makes the operation of BMS less efficient as the battery undergoes degradation. In light of these challenges, this study introduces an application of Incremental Learning in conjunction with a Random Forest model employing twenty estimators to predict a battery’s state of charge (SOC) at various levels of state of health. The proposed model was trained using the first three cycles and applied in real time during subsequent discharges. After each discharge cycle, the model underwent further training to refine its understanding of the underlying problem. Compared to other models, the implementation is more straightforward because the model learns with the data and does not require cell rest, actual capacity, or a battery model, such as known models in the literature. To validate the model, it has been applied for sixty discharge cycles for first-life batteries (Exp1), stationary (Exp2), and dynamic SLB systems (Exp3). The results demonstrated a consistently low RMSE SOC variation of less than 2% for Exp1 and Exp2 and less than 4% for Exp3, validating the use of it for first-life batteries and SLB with constant and dynamic loads.

State of Charge Estimation of Flooded Lead Acid Battery Using Adaptive Unscented Kalman Filter

Flooded Lead Acid (FLA) batteries remain a cost-effective choice in various industries. Accurate State of Charge (SOC) estimation is crucial for effective battery management systems. This paper thoroughly examines the behavior of Open-Circuit Voltage (OCV) during hysteresis in FLA batteries, proposing a novel hysteresis modeling approach based on this behavior to enhance the SOC estimation accuracy. Additionally, we introduce an Adaptive Unscented Kalman Filter (AUKF) to further refine the SOC estimation precision. Experimental validation confirms the effectiveness of the proposed hysteresis modeling. A comparative analysis against the traditional Unscented Kalman Filter (UKF) under random charge/discharge profiles underscores the superior performance of AUKF, showcasing an improved convergence to the correct SOC value and a significant reduction in the SOC estimation error to approximately 2%, in contrast to the 5% error observed with the traditional UKF.

An adaptive fractional-order extended Kalman filtering approach for estimating state of charge of lithium-ion batteries

This paper proposes an adaptive fractional-order extended Kalman filter (AFEKF) approach for estimating state of charge (SOC) of a lithium-ion battery. Firstly, the fractional-order model (FOM) with a constant phase element module is established to describe the fractional-order characteristics inside a lithium-ion battery. Then, the augmented state equation including SOC is built by using the augmented vector approach. To avoid the calculation of the coefficients of the measurement equation, a linear adaptive integer-order Kalman filter is adopted. The AFEKF approach with the Sage-Husa filter is proposed to update the unknown parameters and unknown noises on the basis of augmented state equations. Finally, the comparison experiment between AFEKF approach and adaptive integer-order extended Kalman filter (AIEKF) approach is designed. Besides, the applicability of the AFEKF approach under different working conditions is also tested. The experimental tests indicate that the SOC estimation accuracy of the AFEKF approach is higher than that of the AIEKF approach, and the AFEKF approach can also be applicable in complex environments.

A novel hybrid deep learning model for accurate state of charge estimation of Li-Ion batteries for electric vehicles under high and low temperature

This paper presents a novel architecture, termed Fusion-Fission Optimisation (FuFi) based Convolutional Neural Network with Bi-Long Short Term Memory Network (FuFi-CNN-Bi-LSTM), to enhance state of charge (SoC) estimation performance. The proposed FuFi-CNN-Bi-LSTM model leverages the power of both Convolutional Neural Networks (CNN) and Bi-Long Short Term Memory Networks (Bi-LSTM) while utilizing FuFi optimization to effectively tune the hyperparameters of the network. This optimization technique facilitates efficient SoC estimation by finding the optimal configuration of the model. A comparative analysis is conducted against FuFi Algorithm-based models, including FuFi-CNN-LSTM, FuFi-Bi-LSTM, FuFi-LSTM, and FuFi-CNN. The comparison involves assessing performance on SoC estimation tasks and identifying the strengths and limitations of models. Furthermore, the proposed FuFi-CNN-Bi-LSTM model undergoes rigorous testing on various drive cycle tests, including HPPC, HWFET, UDDS, and US06, at different temperatures ranging from -20 to 25 degrees Celsius. The model’s robustness and reliability are assessed under different real-world operating conditions using well-established evaluation indexes, including Relative Error (RE),Mean Absolute Error (MAE), R Square (R2), and Granger Causality Test. The results demonstrate that the proposed FuFi-CNN-Bi-LSTM model achieves efficient SoC estimation performance across a wide range of temperatures at higher and lower ranges. This finding signifies the model’s efficacy in accurately estimating SoC in various operating conditions.

Reduce state of charge estimation errors with an extended Kalman filter algorithm

Li-ion batteries (LiBs) are accurately estimated under varying operating conditions and external influences using extended Kalman filtering (EKF). Estimating the state of charge (SOC) is essential for enhancing battery efficiency, though complexities and unpredictability present obstacles. To address this issue, the paper proposes a second-order resistance-capacitance (RC) battery model and derives the EKF algorithm from it. The EKF approach is chosen for its ability to handle complex battery behaviors. Through extensive evaluation using a Simulink MATLAB program, the proposed EKF algorithm demonstrates remarkable accuracy and robustness in SOC estimation. The root mean square error (RMSE) analysis shows that SOC estimation errors range from only 0.30% to 2.47%, indicating substantial improvement over conventional methods. These results demonstrate the effectiveness of an EKF-based approach in overcoming external influences and providing precise SOC estimations to optimize battery management. In addition to enhancing battery performance, the results of the study may lead to the development of more reliable energy storage systems in the future. This will contribute to the wider adoption of LiBs in various applications.

A multi-scale SOC estimation method for lithium-ion batteries incorporating expansion force

Electric vehicles (EVs) have become a viable alternative to fuel vehicles, and accurate State of Charge (SOC) estimation of the lithium-ion battery is the key to guarantee EVs' safe operation. However, small data sampling interval like 1 s is usually required for exiting SOC estimation techniques, which cannot be achieved in practical EVs operation scenarios. This paper proposes a novel SOC evaluation method through the fusion of expansion force with voltage and current measurements. Specifically, long-term estimation (i.e., global trend) of SOC are established by extracting information from expansion force and voltage data with long short-term memory (LSTM) algorithm, while short-term estimation (i.e., local variation) of SOC are obtained by extracting information from current and voltage measurements with Support Vector Regression (SVR). After that, long-term and short-term (i.e. multi-scale) SOC estimations are fused to provide final SOC estimation. Various test data under different driving profiles are utilized to validate the proposed method, including NEDC, and results are compared to those from widely used SOC estimation techniques like LSTM. Results demonstrate that with sampling interval increases from 1 s to 10s, the multi-scale SOC estimation method can maintain maximum absolute error (ME) less than 2.84 %, while mean absolute error (MAE) changes from 0.32 % to 0.48 % and root mean squared error (RMSE) changes from 0.44 % to 0.64 %. It demonstrates that the proposed method can effectively alleviate the dependence on small data sampling interval, thus can provide accurate SOC estimation with various sampling intervals.

The State of Charge Estimation of LiFePO4 Batteries Performance Using Feed Forward Neural Network Model

Lithium-ion batteries like LiFePO4 become a new choice for electrical energy sources in the world and can be used on electric vehicles. Battery packs monitoring by Battery Management System in electric vehicles require accurate monitoring. The inaccuracy of monitoring such property can lead to low safety, low efficiency and battery’s life reduction. Estimating state of charge (SoC) to prevent battery damage from overcharging and over discharging. Some of the methods used to estimate SoC such as Coulomb Counting have errors during the charge and discharge process. This research proposes a counting method for measuring SoC with the artificial neural networks (ANN) to provide more precise estimation. Feed Forward Neural Network (FFNN) is an ANN model that can give an accurate estimation of SoC by learning data of the charge-discharge process performed on sample batteries. The sample batteries are tested with a battery analyzer to get its charging-discharging data consisting of variables such as voltage, current, capacity, and time with C-Rate variations. These variables data are then learned by the modeled FFNN to predict SoC value. The FFNN model consisted of 16 neurons in the first layer, 8 neurons in the second layer, and 4 neurons in the third layer. The predicted SoC value from FFNN has a similar value with its real SoC value. The relationship between SoC and battery voltage is plotted in a curve and shows an identical characteristic with how the SoC-Voltage curve of a battery should be and have a low mae value. This FFNN model can be applied further such as in electric vehicles to maintain its safety and for longer use.

Fractional calculus-based modeling and state-of-charge estimation of supercapacitor

Supercapacitors (SCs) are becoming a well-accepted energy storage device in many industrial applications for their high power density and remarkably long life span. The SC-powered systems require an accurate estimation of the state of charge (SOC) to ensure the proper energy management of the system. SOC estimation accuracy is significantly affected by SC leakage current, particularly in low-duty cycle applications like wireless sensor nodes. Considering the memory effect of the electrochemical energy storage systems, the fractional calculus-based SC model accurately characterizes the device’s electrical dynamics. This paper proposes a fractional order (FO) equivalent circuit model of SC considering the leakage effect of the device. The model parameters are experimentally identified, considering the commercially available 5F Maxwell SC cell. Based on the proposed model, a fractional order Extended Kalman Filter (FOEKF) has been designed and implemented to estimate the SOC of the SCs. A state initialization method has been proposed to address the convergence issue of the estimator under unknown initial conditions. The performance of the proposed estimation scheme has been illustrated through simulation and experimental studies. Finally, the performance of the proposed fractional order estimation has been compared with the integer-order approach.

Robust state of charge estimation of LiFePO4 batteries based on Sage_Husa adaptive Kalman filter and dynamic neural network

Robust and accurate state of charge estimation for LiFePO4 batteries has tremendous significance, since they are constituted the basis of reliable operation for battery management system. However, the nature flat voltage curve poses challenges in both the accuracy and robustness of state of charge estimation. Here, we present a state of charge estimation framework for LiFePO4 batteries with integrating physics calculation, adaptive Kalman filter, and machine learning, where nonlinearity of flat voltage curve can be captured with strong robustness by optimized machine learning. To address the parameter sensitivity problem for dynamic neural network, the sine cosine algorithm is adopted to obtain the optimal parameters. Then, the offline training model is established based on nonlinear autoregressive models with exogenous inputs and sine cosine algorithm, and the adaptive Kalman filter is selected for online estimation. The observed data from 26,650 and 18,650 LiFePO4 batteries at 25 and 40 °C has been used to verify the accuracy and robustness of the proposed method under four working conditions. Compared to the existing methods, the proposed method can achieve strong robustness and higher accuracy in state of charge estimation with a maximum relative error below 2 %.

An Improved Model Combining Machine Learning and Kalman Filtering Architecture for State of Charge Estimation of Lithium-Ion Batteries

Accurate state of charge (SOC) estimation of lithium-ion batteries is a fundamental prerequisite for ensuring the normal and safe operation of electric vehicles, and it is also a key technology component in battery management systems. In recent years, lithium-ion battery SOC estimation methods based on data-driven approaches have gained significant popularity. However, these methods commonly face the issue of poor model generalization and limited robustness. To address such issues, this study proposes a closed-loop SOC estimation method based on simulated annealing-optimized support vector regression (SA-SVR) combined with minimum error entropy based extended Kalman filter (MEE-EKF) algorithm. Firstly, a probability-based SA algorithm is employed to optimize the internal parameters of the SVR, thereby enhancing the precision of original SOC estimation. Secondly, utilizing the framework of the Kalman filter, the optimized SVR results are incorporated as the measurement equation and further processed through the MEE-EKF, while the ampere-hour integral physical model serves as the state equation, effectively attenuating the measurement noise, enhancing the estimation accuracy, and improving generalization ability. The proposed method is validated through battery testing experiments conducted under three typical operating conditions and one complex and random operating condition with wide temperature variations under only one condition training. The results demonstrate that the proposed method achieves a mean absolute error below 0.60% and a root mean square error below 0.73% across all operating conditions, showcasing a significant improvement in estimation accuracy compared to the benchmark algorithms. The high precision and generalization capability of the proposed method are evident, ensuring accurate SOC estimation for electric vehicles.

A Bayesian Optimized Deep Learning Approach for Accurate State of Charge Estimation of Lithium Ion Batteries Used for Electric Vehicle Application

A Bayesian Optimized Deep Learning Approach for Accurate State of Charge Estimation of Lithium Ion Batteries Used for Electric Vehicle Application