State Of Charge Estimation Research Articles

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.

Distributed estimation of state-of-charge of supercapacitor packs: A consensus-based approach

It is crucial to estimate the state-of-charge (SoC) of a supercapacitor pack as cells are typically connected to form packs in practical applications. However, most of the existing studies adopted a centralized approach, which is to estimate all the single cells, and then calculate the overall SoC. When the total number of the cells comes to a high level, the burden of communication and the price of a single fault rise rapidly. To address this challenge, in this article, we propose a decentralized method for estimation of pack SoC, which is free of the central observer. We use the state space equation to model the supercapacitors in the physical modeling. In the cyber modeling, we construct their communication topology and apply a definition of pack SoC. A two-layer structure is proposed in which we design a Luenberger observer for each cell to estimate SoC of each cell. We propose a consensus-based algorithm to estimate its pack SoC. A laboratory testbed has been built to verify the effectiveness of the proposed method. Experimental results show that the proposed method can effectively implement the estimation and is more robust to communication failure than the centralized method.

Multi-temperature capable enhanced bidirectional long short term memory-multilayer perceptron hybrid model for lithium-ion battery SOC estimation

In this study, we propose a novel hybrid modeling framework for State of Charge (SOC) estimation across a broad temperature spectrum. First, we build a hybrid model to optimize stacked layers of stacked bidirectional long short term memory networks by introducing dropout mechanisms. At the same time, we also optimize the traditional multi-layer perceptron model to ResMLP, which is improved by introducing residual linkage, and then integrate the two optimization models. Finally, the synergistic effect and attention mechanism of genetic algorithm and particle swarm optimization are used to optimize its parameters. We then rigorously tested the model on nine datasets, including HPPC, DST and BBDST, at different temperatures of 5 °C, 15 °C and 35 °C. Using MAE, RMSE and MAXE benchmarks, our research results show that the proposed hybrid model outperforms the benchmark algorithm, achieving significantly enhanced performance and higher accuracy, and the maximum SOC estimation error is kept below 4.53 %. In addition, experimental evaluation at different temperatures shows the robustness and adaptability of the proposed algorithm.

A Novel Fitting Polynomial Approach for An Accurate Soc Estimation In Li-Ion Batteries Considering Temperature Hysteresis

Lithium-ion batteries are essential to modern technology, requiring accurate estimation of the state of charge (SOC) for optimal performance. Traditional methods such as Coulomb Counting (CC) are ineffective in the face of temperature variations, leading to inaccuracies in SOC estimation, which in turn cause obvious deformation of hysteresis curves. To address this, this paper introduces a novel method called Polynomial Fit State of Charge (FPSOC), for effective SOC estimation. This method incorporates a fifth-degree polynomial fitting that accounts for a wide range of temperature variations (from -10°C to +80°C), a feature that, according to the authors, has not been offered by all previously published methods. A series of simulation tests using the MATLAB/Simulink tool are conducted under various temperature profiles to evaluate the effectiveness of the FPSOC method. The results demonstrate the notable superiority of the FPSOC model compared to the CC method, with a significantly reduced RMSE of only 0.93% compared to 6.77% of the CC model. Particularly effective at low SOC levels (30%), the FPSOC model demonstrates precision up to six times higher compared to the CC model. Additionally, when evaluated against other recent SOC estimation techniques such as CM, RLSF, EKF, DST, BBDST, ASMO, LPM_H, LSTM-SA Group A and B, and baseline ECM-ID, The FPSOC method proves extremely accurate, with the lowest average error under different temperature conditions.

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.

Estimation of SOC for Li-ion battery-powered three-wheeled electric vehicle using machine learning methods

Abstract The Battery Management System (BMS) serves as the heart of the electric vehicle system, in which estimating the state of charge (SOC) is the crucial part of the BMS to ensure the durability, reliability, and sustainability of the battery pack. Due to its nonlinear characteristics, accurately estimating the SOC for a slow degradation of the charge is highly cumbersome. The literature provides a series of machine learning algorithms (MLA) to estimate and predict the SOC of lithium-ion (Li-ion) battery systems for electric vehicle (EV) applications. The literature has proposed various MLA, coulomb counting, and different Kalman filter methods to address this challenge and estimate the SOC of Li-ion battery systems for EV applications. This research looks at the differences and similarities between the coulomb counting method, the unscented Kalman filter method, and a number of machine learning algorithms. These include linear regression, polynomial linear regression, support vector regression, decision trees, random forests, artificial neural networks (ANN), and long short-term memory (LSTM). The goal is to assess the MLAs' accuracy in estimating battery SOC. Analyzing model errors optimizes the battery's performance parameter. We identify ANN and LSTM as the two most efficient methods for accurate SOC estimation in an EV-operated BMS system by evaluating the performance indices of the aforementioned machine learning methodologies. Once again, the LSTM model for SOC estimation has proven to be highly accurate in analyzing the discrepancy between the actual and predicted traveling ranges of the designed prototype. We design a MATLAB/SIMULINK EV powertrain by collecting realtime data from the Li-ion battery pack, analyzing the SOC variation data, and using the previously mentioned MLA in the Python platform to estimate the SOC and its accuracy. It highlights the effectiveness of advanced MLAs in improving SOC estimation, thereby enhancing the performance and reliability of EV battery systems.

Enhancing the state-of-charge estimation of lithium-ion batteries using a CNN-BiGRU and AUKF fusion model

Accurate estimation of lithium-ion batteries’ state of charge (SOC) is crucial for the safety of energy storage devices, preventing issues such as overcharging or discharging. This paper introduces a fusion model combining convolutional neural network (CNN), bidirectional gated recurrent unit (BiGRU), and adaptive unscented Kalman filter (AUKF). This method's advantage lies in integrating Kalman filtering with the benefits of neural networks, eliminating the need for complex hyperparameter tuning and battery model construction. Initially, CNN-BiGRU maps variables like voltage, current, and temperature to SOC for initial estimation. The AUKF algorithm then filters these SOC outputs, minimizing fluctuations and enhancing accuracy. This approach ultimately leads to precise and stable SOC estimates. To validate the model's effectiveness, lithium-ion battery datasets across various temperatures were extensively trained and tested. The CNN-BiGRU-AUKF model demonstrated consistent performance under these conditions, with a maximum MSE of 0.00011, MAE under 0.0092, Max AE around 0.02, and a maximum RMSE of 0.017. Compared to similar methods, the proposed approach demonstrates superior SOC estimation accuracy and computational efficiency. Additionally, the model's scalability was validated using training and testing data for SOC estimates from a different type of lithium battery.

Impact of Data Corruption and Operating Temperature on Performance of Model-Based SoC Estimation

Electric vehicles (EVs) are becoming popular around the world. Making a lithium battery (LIB) pack with a robust battery management system (BMS) for an EV to operate under different complex environments is both a challenge and a requirement for engineers. A BMS can intelligently manage LIB systems by estimating the battery state of charge (SoC). Due to the nonlinear characteristics of LIB, influenced by factors such as the harsh environment and data corruption caused by electromagnetic interference (EMI) inside electric vehicles, SoC estimation should consider available capacity, model parameters, operating temperature and reductions in data sampling time. The widely used model-based algorithms, such as the extended Kalman filter (EKF) have limitations. Therefore, a detailed review of the balance between temperature, data sampling time, and different model-based algorithms is necessary. Firstly, a state of charge—open-circuit voltage (SoC-OCV) curve of LIB is obtained by the polynomial curve fitting (PCF) method. Secondly, a first-order RC (1-RC) equivalent circuit model (ECM) is applied to identify the battery parameters using a forgetting factor-based recursive least squares algorithm (FF-RLS), ensuring accurate internal battery parameters for the next step of SoC estimation. Thirdly, different model-based algorithms are utilized to estimate the SoC of LIB under various operating temperatures and data sampling times. Finally, the experimental data by dynamic stress test (DST) is collected at temperatures of 10 °C, 25 °C, and 40 °C, respectively, to verify and analyze the impact of operating temperature and data sampling time to provide a practical reference for the SoC estimation.

Joint Model Parameter Identification and EKF Algorithm for the SOC Estimation of LFP Battery

Abstract Accurately estimating the state of charge (SOC) of batteries is crucial for achieving the safety and efficient driving of electric vehicles. To address the negative impact of voltage platform flatness and accumulated errors in current sampling, the SOC estimation method jointing model parameter identification and extended Kalman filter (EKF) algorithm is proposed and verified through simulation in this paper. Firstly, the parameter identification method is obtained based on the second-order dual polarization model, and effective identification of the parameters under different SOC is achieved using experimental conditions of hybrid pulse power characteristic and constant current discharge. On this basis, a function model with SOC as the independent variable and model parameters as the dependent variable is established by jointing model parameter identification and EKF algorithm, and the iterative estimation of SOC is achieved through the 1stopt and cftool methods. Finally, the SOC estimation accuracy of the proposed method is validated under three operating conditions that adopt the latest standards and are closer to the actual driving environment. The simulation results show that the SOC estimation method jointing model parameter identification and EKF algorithm has higher accuracy and smaller fluctuations than the traditional AH integration method, and the mean squared error (MSE) of estimation for the four test conditions are less than 0.29%, 0.72% and 0.25%, respectively.

A generic fusion framework integrating deep learning and Kalman filter for state of charge estimation of lithium-ion batteries: Analysis and comparison

Lithium-ion batteries (LIBs) are extensively utilized in power and energy storage systems. Accurately estimating state of charge (SOC) of LIBs using single methods is still challenging to fully address the problem associated with SOC. This paper proposes a novel generic fusion framework that integrates deep learning (DL) and Kalman filter (KF), characterized by an effective fusion of the results obtained by multiple-methods. Within the DL-based method, a spatial-temporal awareness model and an improved dung beetle optimizer are proposed to enhance the capture of spatial-temporal features and optimize hyperparameters. Additionally, three adaptive nonlinear KFs are employed for SOC estimation based on a simplified electrochemical model, with the adaptive cubature KF emerging as the most suitable following comparative analysis. Subsequently, the results from both approaches are integrated to derive the final result using various fusion methodologies. The effectiveness of the fusion framework is validated using experimental data, with kernel ridge regression emerging as the optimal fusion method. The best fusion results yield a mean absolute error of 0.2341% and a root mean square error of 0.3072%, demonstrating that proposed framework can effectively process and utilize multiple-source information, thereby enhancing accuracy and robustness compared to single methods and exhibiting adaptability to complex situations.

The state of charge predication of lithium-ion battery energy storage system using contrastive learning

The state of charge (SOC) is a critical state quantity that must be determined in real-time for a battery energy storage system (BESS). It is a prerequisite for the operation of a BESS. However, obtaining the precise value of SOC is challenging due to it being a hidden state quantity. Existing neural network models commonly employ an end-to-end prediction paradigm for SOC estimation, which fails to fully exploit the rich information present in the time-series battery data. Unlike most studies available in the literature, we propose a novel SOC prediction method named CLDMM. This method is the first to apply contrastive learning techniques from the image field to the SOC prediction of lithium batteries. The method utilizes data augmentation, a multi-scale encoder, and multi-layer perceptrons to learn latent representations and mix these with raw data proportionally for downstream predictive tasks. The performance of the proposed method is evaluated using the Panasonic NCR18650PF dataset, and ablation study were conducted. Experimental results show that CLDMM outperforms baseline methods, achieving an average mean absolute error (MAE) of 0.64% and an average maximum error (MAX) of 2.66%.

A Multi-Mechanism Fusion Method for Robust State of Charge Estimation via Bidirectional Long Short-Term Memory Model with Mixture Kernel Mean p-Power Error Loss Optimized by Golden Jackal Optimization Algorithm

Abstract Accurate state of charge (SOC) estimation is crucial for effective battery management in various applications. The bidirectional long short-term memory (BiLSTM) as an outstanding nonlinear regression model can be used for SOC estimation. This work develops a novel multi-mechanism fusion method based on BiLSTM to further enhance its estimation performance for SOC, in which the convolutional neural network (CNN), attention mechanism, and mixture kernel mean p-power error (MKMPE) loss are introduced into the BiLSTM framework for addressing different issues. First, the introduction of CNN components aims to extract essential features from battery data, enhancing the model's comprehension of complex information. Then, the attention mechanism is used to further refine the model's perceptual ability and a robust MKMPE loss is introduced into the BiLSTM framework to replace its original mean squared error loss, and a novel robust model is developed to suppress non-Gaussian noise interference. Finally, some key hyperparameters of the proposed model are fine-tuned using the golden jackal optimization algorithm, resulting in improved estimation performance. Comparative numerical experiments are meticulously conducted in various cases to evaluate the performance of the proposed method, and the experiment results demonstrate that it can perform outstanding effectiveness in handling non-Gaussian noise scenarios.

Improved whale optimization algorithm towards precise state-of-charge estimation of lithium-ion batteries via optimizing LSTM

Accurate state-of-charge (SOC) estimation is a crucial part of the battery management system (BMS). However, conventional estimation methods are unable to capture the extremely complex dynamic characteristics of lithium-ion batteries. Besides, manually setting the optimal hyperparameters of models has many drawbacks. To address the problems, an (improved whale optimization algorithm) IWOA- (long short-term memory) LSTM model is proposed in this work. Utilizing the whale optimization algorithm (WOA) improved with four enhancement strategies (Gaussian chaotic mapping initialization, Nonlinear weight update, Lévy flight mechanism, and Elite opposition-based learning) to optimize the number of hidden layer nodes, the learning rate, and the number of iterations of LSTM model. It not only overcomes the shortcomings of artificially setting LSTM hyperparameters but also further boosts the learning ability of the IWOA-LSTM model, making the model more suitable for SOC estimation under different scenarios. The evaluation results show that the MAE of the proposed model for SOC estimation results is lower than 0.8 % under different temperatures and dynamic conditions. Compared with SOTA models, all MAE, RMSE, and MAPE of the proposed model substantially decline. Furthermore, the R2 of the estimation results using the LG dataset in Experiment Ⅲ is 98.65 %, suggesting the applicability of the proposed model to Li-ion batteries from various manufacturers. The experimental results demonstrate the proposed IWOA-LSTM model is suitable for accurate SOC estimation.

A multi-dimensional machine learning framework for accurate and efficient battery state of charge estimation

Accurate state of charge (SOC) estimation is essential for battery safe and efficient utilization. As artificial intelligence technologies evolve, data-driven methods have become mainstream for estimating SOC. However, the technique can significantly deteriorate model performance when encountering poor or insufficient data quality. In this paper, we apply median filtering to eliminate extreme noise and utilize continuous wavelet transform to extract time-frequency features from voltage signals. Additionally, we generate novel features via feature crossing. We then apply dimensionality reduction via the random forest method to decrease computational expense. Finally, we select a convolutional neural network (CNN) as the base model to learn optimized features for more precise SOC estimation. To confirm the efficacy of our proposed method, this study compares it with CNN, long short-term memory (LSTM), bidirectional LSTM (BILSTM), and a CNN-BILSTM model combined with an attention mechanism. These comparisons are conducted under different temperatures and operating conditions. The results indicate that this method achieves a mean absolute error and a root mean square error of less than 2.89 % and 3.71 %, respectively, in SOC estimation, demonstrating superior accuracy compared to other models. This study underscores the significance of feature engineering techniques in SOC estimation.

Application of Deep Learning Techniques for the State of Charge Prediction of Lithium-Ion Batteries

This study proposes a deep learning-based long short-term memory (LSTM) model to predict the state of charge (SOC) of lithium-ion batteries. The purpose of the research is to accurately model the complex nonlinear behavior that occurs during the charging and discharging processes of batteries to predict the SOC. The LSTM model was trained using battery data collected under various temperature and load conditions. To evaluate the performance of the artificial intelligence model, measurement data from the CS2 lithium-ion battery provided by the University of Maryland College of Engineering was utilized. The LSTM model excels in learning long-term dependencies from sequence data, effectively modeling temporal patterns in battery data. The study trained the LSTM model based on battery data collected from various charge and discharge cycles and evaluated the model’s performance by epoch to determine the optimal configuration. The proposed model demonstrated high SOC estimation accuracy for various charging and discharging profiles. As training progressed, the model’s predictive performance improved, with the predicted SOC moving from 14.8400% at epoch 10 to 12.4968% at epoch 60, approaching the actual SOC value of 13.5441%. Simultaneously, the mean absolute error (MAE) and root mean squared error (RMSE) decreased from 0.9185% and 1.3009% at epoch 10 to 0.2333% and 0.5682% at epoch 60, respectively, indicating continuous improvement in predictive performance. In conclusion, this study demonstrates the effectiveness of the LSTM model for predicting the SOC of lithium-ion batteries and its potential to enhance the performance of battery management systems.

A Switching Observer for State-of-Charge Estimation of Reconfigurable Supercapacitors

While State-of-Charge (SOC) estimation for supercapacitors has been extensively studied, most research focuses on single units. However, the recent introduction of reconfigurable circuits significantly alters system dynamics, rendering existing SOC estimation techniques inadequate. This paper addresses this challenge by employing a switching systems approach to estimate the SOC of supercapacitors with reconfigurable circuits. We first establish an RC model for the supercapacitor integrated with the reconfigurable circuit and thoroughly analyze the state continuity and observability of the resulting switched system. Subsequently, we propose a switching observer and evaluate its convergence properties by comparing its performance against other observer techniques. Experimental validation on a hardware platform demonstrates the superiority of our proposed observer for accurate SOC estimation in this context.

Enhanced Second-Order RC Equivalent Circuit Model with Hybrid Offline–Online Parameter Identification for Accurate SoC Estimation in Electric Vehicles under Varying Temperature Conditions

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

State of charge estimation for the lithium-ion battery based on fractional-order multi-dimensional Taylor network

To accurately estimate the state of charge (SOC) of the lithium-ion battery (LiB), a fractional-order multi-dimensional Taylor network (FMTN) model was proposed in the study. With two open datasets of LiBs, the performance of the FMTN model on the SOC estimation is evaluated and compared with multi-dimensional Taylor network (MTN), back propagation neural network (BPNN), and dual-stage attention gate recurrent unit neural network (DA-GRUNN) models. With the datasets of B0005 and B0006 LiBs, the SOC estimation accuracy of the FMTN-6 model is 34 %, 32 %, and 37 %, 45 % higher than that of the MTN-6 and BPNN-3 models, respectively. The estimation time consumptions of the FMTN-6 model are increased by 2.8 % and 3.9 % and reduced by 49.5 % and 52.8 % compared with that of the MTN-6 and BPNN-3 models, respectively. With the open dataset of real driving conditions, the root-mean-square error of the SOC estimation of the FMTN model is reduced by 48 % compared with that of the MTN model. Besides, with the datasets at 25 °C and 45 °C, the SOC estimation accuracy of the FMTN model is improved by 17 % and 18 % compared with that of the DA-GRUNN model, respectively.