State Of Charge Estimation Error Research Articles

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

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

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

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

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

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

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

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

Estimation of battery state of charge based on changing window adaptive extended Kalman filtering

Adaptive extended Kalman filter (AEKF) is commonly used for lithium-ion battery state of charge (SOC) estimation. However, it overlooks the impact of changes in the distribution of error innovation sequence (EIS) on the noise covariance, resulting in inaccurate state of charge estimates. To address this issue, this paper introduces a novel approach called changing window adaptive extended Kalman filter (CW-AEKF) algorithm. This algorithm uses variance ratio and Levene test to identify the change in the distribution of error innovation sequence, and adaptively updates the optimal noise window length based on the judgment result to achieve accurate noise estimation. Subsequently, the proposed algorithm is combined with a temperature-corrected second-order RC equivalent circuit model for state of charge estimation. The results of dynamic stress test (DST) at different temperatures show that the changing window adaptive extended Kalman filter algorithm can obtain higher accuracy in state of charge estimation results than other algorithms, with state of charge estimation errors remaining within 1 %. Finally, the state of charge estimation of the changing window adaptive extended Kalman filter algorithm in publicly available datasets is analyzed. The results demonstrate that the proposed algorithm maintains strong generalization ability when facing various working conditions.

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.

Mechanism and Data-Driven Fusion SOC Estimation

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

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

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

A new online SOC estimation method using broad learning system and adaptive unscented Kalman filter algorithm

The accurate estimation of lithium batteries’ state of charge (SOC) is important for extending battery life and preventing accidents. To improve the battery model’s adaptability to variations in actual operating conditions, this paper proposes a new hybrid SOC estimation method. The battery model is first built based on the broad learning system (BLS) to simulate the battery’s voltage characteristics. Subsequently, the adaptive unscented Kalman filter algorithm is applied for SOC estimation. We introduce the Bernstein inequality (BI) to guide the BLS model’s online update process. With the BI method, the redundant incremental data is not used for battery model updates, which improves the model’s online learning efficiency. Finally, dynamic test operation data is collected from different temperatures to validate the proposed SOC estimation algorithm. Experimental results manifest that the SOC estimation error can be limited to 0.51 %. In addition, the proposed method has satisfactory training and online learning time consumption.

Online state of charge estimation of LiFePO4 battery based on EKF-AUKF algorithm with reference compensation for estimation results

The state of charge(SOC) is an important index in Battery Management System(BMS) for smart grids and electric vehicles, whose accuracy is affected by model and sensor errors. In this paper, an online SOC estimation method based on EKF-AUKF algorithm with reference compensation for estimation results is proposed. Firstly, a joint estimation method based on extended Kalman filter(EKF) and adaptive unscented Kalman filter(AUKF) algorithm is adopted to estimate SOC under Beijing bus dynamic stress test(BBDST) condition. The result shows that the estimation error is within 2 %. Secondly, the characteristics of EKF-AUKF algorithm under voltage and current sampling errors are analyzed over the whole SOC range. The results indicate that voltage measurement error increases SOC estimation error. Then, an online reference is built by calculating the sum of the estimation result of ampere-hour counting(AHC) method and constant deviation, and then the difference between the estimation result of EKF-AUKF algorithm and online reference can be obtained. The absolute value of the difference is used to compare with limit deviation value and compensate the SOC of EKF-AUKF method by different compensation coefficients. Finally, the effectiveness of the proposed method is verified under different operating conditions. The experimental results show that the proposed method can greatly improve the SOC estimation accuracy under large voltage error.

Target decomposition-led light-weighted offline training strategy-aided data-driven state-of-charge online estimation during constant current charging conditions over battery entire lifespan

This paper develops a novel target decomposition-led light-weighted offline training strategy-aided data-driven state-of-charge (SOC) online estimation method during constant current (CC) charging conditions over battery entire lifespan. Firstly, real SOC is conceptually decomposed into base SOC and SOC error. Subsequently, taking voltage and real SOC of initial CC charging cycle as input and output, machine learning algorithm is adopted to offline establish base SOC acquisition model without considering battery aging. Thirdly, the errors between real SOC and acquired base SOC are calculated, where the extremely similar distribution of SOC error against different battery degradation with two aging-dependent peaks can be clearly observed. Following this precious characteristic, a SOC error calculation model is further built only via several typical CC charging cycles with base SOC and battery capacity as input. Finally, the acquired base SOC is compensated by the computed SOC error for real SOC calculation. The validation results demonstrate that the proposed target decomposition-led method has overwhelming advantages in light-weighted offline training and accurate SOC online estimation during CC charging conditions, where maximum mean absolute error and maximum root mean squared error of SOC estimation results over the same type of batteries’ entire lifespan are only 0.98 % and 1.2 %, respectively.

A comparative study on state-of-charge estimation for lithium-rich manganese-based battery based on Bayesian filtering and machine learning methods

In this paper, a comparative study on the state of charge (SOC) estimation of the lithium-rich manganese-based battery (LRMB) has been conducted by systematically considering the equivalent circuit model (ECM), aging state and algorithms. The results show that the first-order RC model combined with the Extended Kalman filter (EKF) is more suitable for the SOC estimation of the LRMB when the battery decays less severely. The maximum value of root mean square error of SOC estimation error no exceeds 1.6 % under various dynamic operating conditions, which can well meet the practical application. Besides, the first-order model based EKF algorithm occupies least computing resource and simultaneously possesses the best convergence velocity against the initial SOC value deviation. When the LRMB suffers a severe aging, the SOC estimation performance decreases significantly with the max error exceeding 6 %, to overcome this, a new algorithm combined deep learning and Extend Kalman filter (EKF) is proposed, which exhibit high SOC estimation accuracy with the RMSE less than 0.16 %. In summary, a systematic study about the SOC estimation of LRMB has been carried out, which can provide great guidance for the future engineering application of LRMB.

State of Charge Estimation of Lithium-ion Batteries Based on Online OCV Curve Construction

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

An improved electrochemical equivalent circuit model and precise state-of-charge estimation comparative study for lithium-rich manganese-based battery

State-of-charge (SOC) serves as a crucial metric for lithium-ion batteries. A precise battery model is an essential factor influencing the accuracy of SOC estimation. Notably, lithium-rich manganese-based (LRMB) layered oxide batteries exhibit distinct voltage characteristics that differentiate them from other battery types. Experimental findings reveal that traditional equivalent circuit models (ECMs) are not well-suited for capturing the behavior of LRMB batteries. To address the aforementioned problem and its attendant phenomenon of large SOC estimation error, in this paper, we proposed an improved electrochemical equivalent circuit model (IEECM) for LRMB batteries that concurrently enhances accuracy and mitigates error. The proposed model comprehensively accounts for the long-term diffusion process of lithium ions within the solid phase, thereby offering a more precise representation of the battery's behavior. The results indicate that under different operating conditions, the RMSE of voltage error remains below 31.3 mV. Notably, under UDDS conditions, the MAE and RMSE are merely 15.1 mV and 20.6 mV, respectively. To further validate its effectiveness, we utilize three common SOC estimation algorithms under various operation conditions. Experimental results show that the RMSEs of SOC estimation based on the proposed model under different algorithms are lower than 2.21 %, which is better than ECMs. Consistently, our findings indicate that this model is particularly well-suited for LRMB batteries, leading to a notable enhancement in SOC estimation accuracy.

Advancing state estimation for lithium-ion batteries with hysteresis through systematic extended Kalman filter tuning

Knowledge of remaining battery charge is fundamental to electric vehicle deployment. Accurate measurements of state-of-charge (SOC) cannot be obtained directly and estimation methods must be used instead. This requires both a good model of a battery and a well-designed state estimator. Here, hysteretic reduced-order battery models and adaptive extended Kalman filter estimators are shown to be highly effective, accurate predictors of SOC. A battery model parameterisation framework is proposed, which enhances standardised methods to capture hysteresis effects. The hysteretic model is parameterised for three independent NMC811 lithium-ion cells and is shown to reduce voltage RMS error by 50% across 18 h automotive drive-cycles. Parameterised models are used alongside an extended Kalman filter, which demonstrates the value of adaptive filter parameterisation schemes. When used alongside an extended Kalman filter, adaptive covariance matrices yield highly accurate SOC estimates, reducing SOC estimation error by 85%, compared to the industry standard battery model.

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.

State of Charge Estimation for Lithium Battery Based on Fractional Order Square Root Cubature Kalman Filter and Adaptive Multi-innovation Unscented Kalman Filter

Accurate state of charge (SOC) estimation of batteries is of great significance for electric vehicles. A SOC estimation method based on a fractional order square root cubature Kalman filter (FOSRCKF) and an adaptive multi-innovation unscented Kalman filter (AMIUKF) is proposed. The battery is modelled using fractional order calculus theory and the model parameters are identified by adaptive genetic algorithm. The FOSRCKF estimates the battery SOC, while the AMIUKF online updates the internal resistance in the model, and there exchanges information between two filters. The experimental results under the Urban Dynamometer Driving Schedule (UDDS) and the US06 Highway Driving Schedule show that the proposed method has lower SOC estimation error and lower terminal prediction error compared with the traditional SRCKF method based on integer order models, which demonstrates the effectiveness, accuracy and robustness of the proposed method.

Multi-interest adaptive unscented Kalman filter based on improved matrix decomposition methods for lithium-ion battery state of charge estimation

Accurately predicting the state of charge (SOC) is crucial to improving Li-ion battery performance. However, available model-based estimation approaches still face challenges in handling model uncertainty and measurement noise effects on parameter identification. Besides, the widely used unscented Kalman filter (UKF) algorithm has limitations in electric vehicles as it requires the error covariance matrix to maintain positive definiteness, limiting its applicability under certain conditions. This study introduces the bias-compensated forgetting factor recursive least squares (BCFFRLS) method for parameter estimation within the second-order RC equivalent circuit model specific to the INR18650-20R battery. Furthermore, we propose a novel algorithm named the optimization multi-interest adaptive unscented Kalman filter (O-MIAUKF). This algorithm is designed to address stability and robustness issues with traditional UKF encounters in dynamic environments. Experimental validation demonstrates that the O-MIAUKF algorithm excels in maintaining strong stability and robustness in various working conditions, accurately estimating SOC even with a non-positive covariance matrix. The SOC estimation error remains stable at 0.8 %, which is lower than that of the current Extended Kalman Filter (EKF), UKF, and Dual Extended Kalman Filter (DEKF).

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.