State Of Charge Estimation For Lithium-ion Batteries Research Articles

Research on SOC estimation of lithium-ion batteries based on robust full order proportional integral observer

Accurate state of charge (SOC) estimation of lithium-ion batteries is vital for the reliable and safe operation of electric vehicles. This paper introduces a novel SOC estimation method, the robust full-order proportional integral observer (RF-PIO), designed to overcome SOC estimation misalignment challenges in electric vehicles during high load shocks and temperature fluctuations. These challenges arise from the degradation of proportional integral observer stability. The RF-PIO method incorporates a novel proportional link into the disturbance estimation, significantly improving the observer's robustness without increasing computational complexity. This enhancement allows for more accurate tracking of model parameters under dynamic conditions. Extensive comparison experiments, in conjunction with a variety of driving data, validate the RF-PIO method. The results indicate that the SOC estimation error remains below 2.11%, even amidst unknown model parameters and high-frequency noise interference.

A hybrid network of NARX and DS-attention applied for the state estimation of lithium-ion batteries

Monitoring the state of the battery, including the state of charge (SOC) and state of health (SOH), is crucial for ensuring the safety and reliability of electrical equipment. The paper presents a novel hybrid network that combines nonlinear autoregressive model with exogenous inputs (NARX) and DS-attention. The proposed DS-attention method establishes a robust mapping relationship between inputs and outputs, it is a specialized method of the recurrent neural network that enhances the estimation performance by incorporating division function and self-adaptive function into the attention mechanism. The division function is designed to efficiently differentiate between exogenous inputs and state outputs, thereby minimizing the potential for cross-interference between them, and the self-adaptive function optimizes the query features within the attention mechanism. The results demonstrate that the hybrid method of NARX and DS-attention achieves higher prediction accuracy for SOH and SOC estimation of lithium-ion batteries. Specifically, compared with the best-performing similar methods, the proposed hybrid method enhanced the prediction accuracy by 22.9%, 60.7%, and 51.2% across three different SOH datasets, respectively. In terms of long sequence SOC forecasting, the improvements in prediction accuracy under two different working conditions are 82.5% and 60.5%, respectively. The proposed algorithm optimizes the attention mechanism based on the characteristics of the NARX, resulting in higher estimation accuracy for predicting the state of lithium batteries.

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.

An improved Cauchy robust correction-sage Husa extended Kalman filtering algorithm for high-precision SOC estimation of Lithium-ion batteries in new energy vehicles

The accurate estimation of battery State of Charge (SOC) is a key technology in the research of electric vehicle battery management systems. In order to solve the problem of inaccurate noise estimation in nonlinear systems, an improved Cauchy robust correction-Sage Husa extended Kalman filtering (CRC-SHEKF) algorithm is proposed for high-precision SOC estimation of lithium-ion batteries in new energy vehicles. Considering the polarization effect of the battery, the FFRLS algorithm is used for online parameter identification of the Dual Polarization model. Using robust data correction methods, the Cauchy robust function is simplified for real-time correction of the covariance matrix Q of system state noise and the covariance matrix R of the observed noise in the filtering process and combined with SHEKF for SOC estimation. The experimental results show that under different temperature conditions and complex working conditions, the proposed CRC-SHEKF algorithm has the minimum mean absolute error (MAE), root mean square error (RMSE), and maximum error (MAX). Under the condition of the Beijing bus dynamic stress test (BBDST) at 15 °C, the MAE, RMSE, and MAX of the CRC-SHEKF algorithm are 0.392 %, 0.716 %, and 0.945 %, with the computing time of only 4.839 s. The algorithm proposed in this article has high accuracy and robustness, and has practical application value, providing a reference for the application of lithium battery condition monitoring.

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.

Open circuit voltage - state of charge curve calibration by redefining max–min bounds for lithium-ion batteries

The relationship between open circuit voltage (OCV) and state of charge (SoC) is essential for SoC estimation of lithium-ion batteries, which can be secured by either low-current OCV test or incremental OCV test, with incremental OCV test demonstrating better results. Nevertheless, low current always leads to a discharge capacity that is inconsistent with maximum available capacity, which is a key parameter in SoC estimation. Therefore, the resultant OCV-SoC curve fails to provide a consistent SoC range and thus affects SoC estimation. In this paper, OCV-SoC curves obtained from low-current OCV tests are calibrated by redefining max–min bounds to improve SoC estimation accuracy. Max–min bounds of SoC are redefined by measuring, calculating and resetting upper and lower cut-off voltages of the OCV-SoC curve. Based on second-order RC model, model parameters are identified online and adaptive square-root unscented Kalman filter (ASRUKF) algorithm is introduced to perform SoC estimation, which is proved to be precise and adaptive. The calibrated OCV-SoC curve achieves an overall better SoC estimation performance than that obtained from the low-current OCV test and incremental OCV test, which is validated by experiments of LiNiMnCoO2 (NMC) batteries at 0°C and 25°C.

An Adaptive Extended Kalman Filter for Model-Based Fault Diagnosis and State of Charge Estimation of Lithium-Ion Batteries

Precisely gauging the state of charge (SOC) of a lithium-ion battery poses a considerable obstacle due to the battery's intricate electrochemical properties, which are highly dynamic and nonlinear. The effectiveness of the control strategy employed in electric vehicles heavily hinges on the precise estimation of the battery's SOC. Among the crucial elements, the accurate assessment of SOC for power lithium-ion batteries stands out. Ensuring the durability and reliability of battery management systems in electric vehicles to predict SOC is a multifaceted endeavor. Given the inherently nonlinear degradation pattern of batteries, achieving precise forecasting of SOC while minimizing degradation proves to be a demanding task. The accurate determination of battery SOC holds significant significance for both battery electric vehicles and hybrid electric vehicles. Lithium-ion batteries have gained extensive usage in various facets of daily life due to their positive environmental and resource-related attributes. The precise determination of SOC is pivotal in ensuring proper battery operation. Nonetheless, the challenges of SOC estimation under low temperatures have received limited attention. To tackle this issue, this study introduces an adaptive extended Kalman Filter for model-based fault diagnosis and SOC estimation of lithium-ion batteries.

A hybrid-aided approach with adaptive state update for estimating the state-of-charge of LiFePO4 batteries considering temperature uncertainties

Developing an accurate state of charge (SOC) estimation method is crucial for proper monitoring and management of electric vehicles (EVs). As deep learning methods advance, it is critical to design a network structure for SOC estimation that is accurate, flexible, and adaptable to different driving conditions. However, these methods are hindered by high computational costs and trial-and-error training approaches, which compromise their performance. Therefore, this paper proposes a variational epoch selector for a multi-layered long short-term memory (LSTM) network with an adaptive weighted extended Kalman filter (AWEKF) for SOC estimation of lithium-ion batteries. First, a random weight (RW) algorithm is proposed to variably select the required number of training epochs suitable to train the LSTM network for SOC estimation using three domain knowledge, which improves stability, accuracy, robustness against uncertainties, etc., with a significant reduction in model computational training costs and errors. Second, the AWEKF with feedback correction ability is proposed to optimize the estimations of the network to map the nonlinear characteristics and minimize the output SOC fluctuations and errors. The estimations critically investigate the various key factors for the proposed RWLSTM strategy at different temperatures under real-world simulated driving cycles using a lithium iron phosphate battery. Finally, the results show that the mean absolute error and root mean square error of the proposed RWLSTM and RWLSTM-AWEKF strategies are <0.6% and 0.2%, respectively, under various driving conditions, showing their efficiency in estimating the SOC by utilizing battery domain knowledge for BMS applications.

SOC estimation for lithium-ion battery based on AGA-optimized AUKF

The window size for covariance matching (CM) of the adaptive unscented Kalman filter (AUKF) affects the state of charge (SOC) estimation performance due to changes with time in the distribution of error innovation sequence (EIS). A new adaptive genetic algorithm (AGA) to address this problem is proposed in this paper. The proposed AUKF (AGA-AUKF1) obtains its best window size determined by the AGA. A novel AUKF (AGA-AUKF2) is proposed to prevent the uncertainty caused by time-varying EIS with the combination of AGA and CM methods. Firstly, the influence of different temperatures on the prediction performance of the algorithm is investigated by FUDS data. The influence of various parameters on the algorithm is further analyzed by FUDS. For different temperatures, initial SOC values, and initial measurement noise covariance, the SOC estimation results show that the accuracy of AGA-AUKFs is better than AUKF. The population size and termination algebra simulation results indicate that the proposed AGA performs well in parameter optimization. Subsequently, the SOC estimation capability of two proposed methods in different working conditions is analyzed by BJDST and US06. The results show that AGA-AUKF2 has better accuracy and robustness than AGA-AUKF1.

State of Charge Estimation of Lithium-Ion Battery Based on IDRSN and BiGRU

Abstract The estimation of state of charge (SOC) is a critical issue in the energy management of electric vehicle (EV) power batteries. However, the current accuracy of SOC estimation methods does not meet the requirements of practical applications. Therefore, this study proposes an improved lithium-ion battery SOC estimation method that combines deep residual shrinkage network (DRSN) and bidirectional gated recurrent unit (BiGRU) to enhance the SOC estimation accuracy. First, we insert the bidirectional gated recurrent unit neural network between the global average pooling layer and the output fully connected layer of the deep residual shrinkage network. This improvement enhances the model’s expressiveness, robustness, and data learning effect. Second, we develop a new activation function called “∂_swish” to replace the original ReLU activation function in the deep residual shrinkage network. The ∂_swish activation function improves the accuracy of the deep network model and reduces the risk of overfitting by utilizing its regularization effect. Finally, we conduct experimental tests at three different temperatures using the FUDS driving cycle dataset and the DST-US06-FUDS continuous driving cycle dataset. The algorithm model’s convergence speed is verified by comparing it with other models. The results show that compared to other models, the proposed method significantly improves SOC estimation accuracy at three different temperatures. In addition, the method demonstrates a high convergence speed.

SOC estimation of lithium-ion batteries based on the improved Kalman filter

Nowadays, the environmental crisis and energy crisis have been known by people around the world as issues that have to be taken seriously. It is recognized that electric vehicles are more environmentally friendly than traditional fuel cars, but there are still many immature aspects of electric vehicle technology. Battery technology is one of them, and lithium battery is a common power storage tool for electric vehicles. Therefore, it is very important to monitor the status of the battery pack in real-time. Improving the practical capacity, safety, and service life of lithium batteries all have an important impact on the development of electric vehicles. In battery management systems (BMS), the accurate prediction of the battery state of charge (SOC) is particularly important. In this paper, the 18650 lithium battery was selected for the research experiment, and the circuit model of second-order RC was selected. Modeling by MATLAB, the SOC-OCV curve of the battery was determined through the data obtained from the charging and discharging experiment (HPPC), the original least squares method was improved, the forgetting factor was introduced, and the model was identified by the parameters based on the experimental data. The traditional SOC prediction method added noise adaptive rules and iterative theory in the extended Kalman filter(EKF), formed the adaptive Kalman filter (AIEKF) to estimate the SOC of lithium battery, and estimated the SOC using the American urban road cycle (UDDS) data. The results show that the AIEKF algorithm has fewer errors and advantages than the traditional EKF algorithm.

Improved noise bias compensation-equivalent circuit modeling strategy for battery state of charge estimation adaptive to strong electromagnetic interference

Strong electromagnetic interference, which has a significant impact on the performance and safety of the lithium-ion battery, usually affects the accurate state of charge (SOC). Different optimization strategies are used to estimate the model parameters and the SOC due to the unknown nonlinear characteristics caused by noise. However, the impact of sensor and model errors is treated separately. To express the sensor and model uncertainties, a noise bias compensation-equivalent circuit model (NBC-ECM) is proposed, in which sensor noise and model error voltages are employed in the model structure and the SOC estimation process of the lithium-ion battery. For parameter identification, a singular value decomposition-bias compensation recursive least squares (SVD-BCRLS) algorithm is proposed to identify the characteristic micro-parameters of the battery. Then, a moving window adaptive extended Kalman filtering (MWAEKF) algorithm based on window functions is proposed for accurate SOC estimation of lithium-ion batteries. The stability of the model parameters and the reliability of the proposed algorithm in estimating the SOC are evaluated using different noise factors: current and voltage sensor noises of 10 and 50 mA. Using the proposed SVD-BCRLS-MWAEKF algorithm, the maximum SOC error is 1.3 %, the root mean square error (RMSE) is 0.3972 %, and the mean absolute error (MAE) is 0.2316 % using the noise of 0.05 V/A under the hybrid power pulse characterization (HPPC) operating condition. With the same noise value under the Beijing bus dynamic stress test (BBDST) operating condition, the proposed algorithm SOC has a maximum SOC error of 1.57 %, an RMSE of 0.5638 %, and an MAE of 0.4475 %. Under noise interference conditions, estimation is more accurate compared to static conditions, proving that the proposed algorithm can overcome the uncertainties encountered by lithium-ion batteries for real-time BMS applications.

A NARX network optimized with an adaptive weighted square-root cubature Kalman filter for the dynamic state of charge estimation of lithium-ion batteries

Due to the high nonlinearities and unstable working conditions, accurately estimating the state of charge (SOC) by the battery management system (BMS) is a major challenge in ensuring the safety and reliability of lithium-ion batteries in electric vehicles. This paper presents a deep learning network, a nonlinear autoregressive model with exogenous inputs (NARX) network with a closed-loop architecture and transfer learning mechanism, which is optimized using a proposed adaptive weighted square-root cubature Kalman filter (AWSCKF) with a moving sliding window and an adaptive weighing coefficient for SOC estimation of lithium-ion batteries. The proposed AWSCKF method is established through square-root and cubature updates to optimize the statistical value of the state estimate, error covariance, and measurement noise covariance matrices, with the ability to incorporate high nonlinearities to filter out the noise, stabilize, and optimize the final SOC. To evaluate the effectiveness of the optimized NARX network and verify the proposed AWSCKF method, battery tests are carried out using a lithium cobalt oxide battery at various charge-discharge rates and a lithium nickel cobalt manganese oxide battery at temperatures of 0 and 45 °C under five complex working conditions. The SOC accuracy of lithium-ion batteries is enhanced by the hybrid method estimation process, which is based on sensitivity analysis and adaptation to various working conditions. The comprehensive results show that the proposed NARX-AWSCKF model achieves the overall best mean absolute error, root mean square error, and mean absolute percentage error values of 0.07293%, 0.0912%, and 0.40356%, respectively, under various complex conditions. By effectively utilizing battery domain knowledge for real-world BMS applications, the proposed model outperforms other existing methods in terms of high effectiveness, robustness, and potential to boost the NARX performance.

State of charge estimation of lithium-ion batteries using improved BP neural network and filtering techniques

The state of charge (SOC) is a critical parameter in the battery management system (BMS), and its accurate estimation is essential for ensuring the safety and reliability of batteries. This paper presents a lithium-ion battery SOC estimation method that combines an improved neural network with a filtering algorithm. Firstly, the backpropagation (BP) algorithm is chosen as the architecture of the neural network in the hybrid method due to its strong nonlinear approximation ability, and the particle swarm optimization (PSO) algorithm is used to optimize it to avoid falling into local optimal solutions. By combining the search ability of PSO with the learning ability of the BP neural network, the accuracy of the neural network model is improved. The proposed method integrates the PSO-BP model with the extended Kalman filter based on minimum error entropy (MEE-EKF). PSO-BP is utilized as the measurement equation for MEE-EKF, while the ampere-hour integration method is employed as the state equation to achieve closed-loop SOC estimation. Finally, experimental validation is conducted under four typical operating conditions and one random condition across a wide temperature range. The results demonstrate that the proposed method achieves high accuracy across all conditions compared with the results of other algorithms, with a maximum absolute error of not exceeding 3.13%, a mean absolute error of less than 0.54%, and a root mean square error of no more than 0.66%.

An Improved Multi-Timescale AEKF–AUKF Joint Algorithm for State-of-Charge Estimation of Lithium-Ion Batteries

State-of-charge (SoC) estimation is one of the core functions of battery energy management systems. An accurate SoC estimation can guarantee the safe and reliable operation of the batteries system. In order to overcome the practical problems of low accuracy, noise uncertainty, poor robustness, and adaptability in parameter identification and SoC estimation of lithium-ion batteries, this paper proposes a joint estimation method based on the adaptive extended Kalman filter (AEKF) algorithm and the adaptive unscented Kalman filter (AUKF) algorithm in multiple time scales for 18,650 ternary lithium-ion batteries. Based on the slowly varying characteristics of lithium-ion batteries’ parameters and the quickly varying characteristics of the SoC parameter, firstly, the AEKF algorithm was used to online identify the parameters of the model of batteries with a macroscopic time scale. Secondly, the identified parameters were applied to the AUKF algorithm for SoC estimation of lithium-ion batteries with a microscopic time scale. Finally, the comparative simulation experiments were implemented, and the experimental results show the proposed joint algorithm has higher accuracy, adaptivity, robustness, and self-correction capability compared with the conventional algorithm.

A time-series Wasserstein GAN method for state-of-charge estimation of lithium-ion batteries

Estimating the state-of-charge (SOC) of lithium-ion batteries is essential for maintaining secure and reliable battery operation while minimizing long-term service and maintenance expenses. In this work, we present a novel Time-Series Wasserstein Generative Adversarial Network (TS-WGAN) approach for SOC estimation of lithium-ion batteries, characterized by a well-designed data preprocessing process and a distinctive WGAN-GP architecture. In the data preprocessing stage, we employ the Pearson correlation coefficient (PCC) to identify strongly associated features and apply feature scaling techniques for data normalization. Moreover, we leverage polynomial regression to expand the original features and utilize principal component analysis (PCA) to reduce the computational load and retain essential information by projecting features into a lower-dimensional subspace. Within the WGAN-GP architecture, we originally devise a Transformer as the generator and a Convolution Neural Network (CNN) as the critic to make the most of local (CNN) and global (Transformer) variables. The overall model is trained with the WGAN, incorporating gradient penalty loss for training purposes. Simulation outcomes using real-road dataset and laboratory dataset reveal that TS-WGAN surpasses all baseline methods with enhanced accuracy, stability, and robustness. The coefficient of determination (R2) for both datasets exceeds 99.50%, demonstrating its potential for practical application.

State-of-Charge Estimation of Lithium-Ion Batteries Based on Dual-Coefficient Tracking Improved Square-Root Unscented Kalman Filter

Accurate state of charge (SOC) estimation is helpful for battery management systems to extend batteries’ lifespan and ensure the safety of batteries. However, due to the pseudo-positive definiteness of the covariance matrix and noise statistics error accumulation, the SOC estimation of lithium-ion batteries is usually inaccurate or even divergent using Kalman filters, such as the unscented Kalman filter (UKF) and the square-root unscented Kalman filter (SRUKF). To resolve this problem, an SOC estimation method based on the dual-coefficient tracking improved square-root unscented Kalman filter for lithium-ion batteries is developed. The method is composed of an improved square-root unscented Kalman filter (ISRUKF) and a dual-coefficient tracker. To avoid the divergence of SOC estimation due to the covariance matrix with pseudo-positive definiteness, an ISRUKF based on the QR decomposition covariance square-root matrix is presented. Moreover, the dual-coefficient tracker is designed to track and correct the state noise error of the battery, which can reduce the SOC estimation error caused by the accumulation of the battery model error using the ISRUKF. The accuracy and robustness of the SOC estimation method using the developed method are validated by the comparison with the UKF and SRUKF. The developed algorithm shows the highest SOC estimation accuracy with the SOC error within 1.5%.

Improved Feature Decoupling Transfer Network Modeling based on Singular Value Decomposition for SOC Estimation in Energy-Storage Lithium-ion Batteries

Deep learning (DL) methods is applied extensively in the field of state of charge (SOC) estimation, which require training data and test data to have similar distribution. Discrepancies in data distribution arising from the complexity and diversity of lithium-ion batteries under operational conditions in practice, as well as the difficulty in obtaining data labels, make it enormously challenging to access sufficient battery data to train a specific deep estimator. Aiming to improve the performance of cross-domain SOC estimation for lithium-ion batteries, a model for SOC estimation which combines transfer learning with singular value decomposition (SVD) is proposed. To begin with, a gated recurrent unit (GRU) network is employed to avail the nonlinear dynamic characteristics of the battery from the source and target domains. Then, the features are decoupled by using SVD method to extract task-relevant, important and minor information in the network. Further, the amount of transferred information over the source network to the target network is automatically tuned by the maximum mean discrepancy (MMD) to determine the different degrees of similarity in domain, and the cosine discrepancy to measure the discrepancy on the same domain, which achieves the optimized performance of the target network.

State of charge estimation of lithium-ion battery based on improved adaptive boosting algorithm

State of charge (SOC) is a crucial battery state to calibrate the remaining charge of lithium-ion batteries in electric vehicles. Accurate battery SOC estimation is one of the keys and difficult issues for lithium-ion batteries. To achieve SOC estimation accurately, an improved adaptive boosting algorithm called AdaBoost.RT algorithm, which is a regression ensemble algorithm and uses the extreme learning machine (ELM) as weak learners, is applied to estimate the SOC of lithium-ion batteries in this paper. And a two-step method is also proposed to denoise experimental data, which are used as the input data of the proposed SOC estimation method, to further enhance the accuracy of SOC estimation. Firstly, a complementary ensemble empirical mode decomposition with adaptive noise method (CEEMDAN) is utilized to decompose the experimental data including battery voltage and current according to the frequency of the signals to form different frequency components. Secondly, a wavelet threshold denoising method (WTD) is combined to denoise these components. The denoised components trend to form a new battery signal by the linear superposition principle and input into the proposed SOC method in this paper. The combined SOC estimation method can be called CEEMDAN-WTD-AdaBoost-ELM (CWAELM) method. To verify the proposed method, experiments are conducted under Beijing dynamic stress test (BJDST), dynamic stress test (DST), federal urban driving schedule (FUDS), and highway driving schedule (US06) conditions at 0 °C, 25 °C and 45 °C temperatures, respectively. The results show that the proposed model has good robustness and accuracy in the SOC estimation of lithium-ion batteries under various working conditions at different temperatures.

An ASTSEKF optimizer with nonlinear condition adaptability for accurate SOC estimation of lithium-ion batteries

Safe and reliable operations of lithium-ion batteries in electric vehicles (EVs), etc., highly depend on the accurate state of charge (SOC) estimated by the battery management system (BMS). However, due to the battery's nonlinear operating conditions and complex electrochemistry, accurately estimating SOC is a major challenge. In this paper, an adaptive strong tracking square-root extended Kalman filter (ASTSEKF) with nonlinear condition adaptability is proposed for the recursive correction, denoising, and op4timization of the SOC estimation of lithium-ion batteries. The proposed ASTSEKF optimizer introduces an adaptive fading factor, a weight adjustor, and a strong tracking filter to recursively update the posteriori error covariance matrix using a Cholesky decomposition and corrects the uncertainties of the EKF method. The effectiveness of the ASTSEKF method is demonstrated by utilizing it to refine and enhance the estimations of a closed-loop nonlinear autoregressive model with exogenous input (NARX) and a deep feed-forward neural network (DFFNN) utilizing deep transfer learning techniques. The Levenberg-Marquardt and adaptive moment estimation approaches are employed to address gradient issues and stabilize the networks. Battery tests are carried out at different charge-discharge rates, temperatures, complex working conditions, and aging levels. The comparative SOC results show that the proposed ASTSEKF optimizer ensures an overall maximum mean absolute error, mean square error, and root mean square error improvements of 89.82%, 91.67%, and 90.76%, respectively. Additionally, it denoises, stabilizes, optimizes, and quickly converges the final SOC with a good balance between optimal accuracy and computational complexity. In comparison to other existing methods, the proposed ASTSEKF optimizer can overcome nonlinearities encountered by the BMS under various operating conditions to provide accurate SOC estimation in EVs.