State Of Charge Estimation Results Research Articles

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.

State-of-Charge Estimation of Lithium-Ion Battery Based on Convolutional Neural Network Combined with Unscented Kalman Filter

Estimation of the state-of-charge (SOC) of lithium-ion batteries (LIBs) is fundamental to assure the normal operation of both the battery and battery-powered equipment. This paper derives a new SOC estimation method (CNN-UKF) that combines a convolutional neural network (CNN) and an unscented Kalman filter (UKF). The measured voltage, current and temperature of the LIB are the input of the CNN. The output of the hidden layer feeds the linear layer, whose output corresponds to an initial network-based SOC estimation. The output of the CNN is then used as the input of a UKF, which, using self-correction, yields high-precision SOC estimation results. This method does not require tuning of network hyperparameters, reducing the dependence of the network on hyperparameter adjustment and improving the efficiency of the network. The experimental results show that this method has higher accuracy and robustness compared to SOC estimation methods based on CNN and other advanced methods found in the literature.

State-of-Charge Estimation of Nickel–Cadmium Batteries Based on Dynamic Modeling of Electrical Characteristics and Adaptive Untrace Kalman Filtering

With the increasing demand for intelligence and automation, and the continuous strengthening of safety and efficiency requirements, the disadvantages of traditional “blind use” of nickel–cadmium batteries have become increasingly prominent, and the lack of state-of-charge (SOC) estimation needs to be changed urgently. For this purpose, a dynamic model of nickel–cadmium battery is established, and an SOC estimation method of nickel–cadmium battery based on adaptive untraced Kalman filter is proposed. Firstly, the experimental platform was built, and the open-circuit voltage and polarization characteristics of nickel–cadmium batteries were analyzed. On this basis, an equivalent circuit model is constructed to reflect the characteristics of nickel–cadmium batteries, and the model parameters were identified by the hybrid pulse power characteristic test; Then, based on the dynamic model, the SOC of the nickel–cadmium battery was estimated by combining with the Sage–Husa adaptive untrace Kalman filtering algorithm. Finally, the SOC estimation effect was verified under two operating conditions: Hybrid pulse power characteristic (HPPC) and constant cyclic charging and discharging power. The experimental results show that the proposed estimation method is insensitive to the initial value of SOC, and can still converge to the real value even if there is 30% error in the initial value. The mean absolute error and root mean square deviation of the final SOC estimation results are both less than 1%. The dynamic model and the proposed SOC estimation method provide valuable reference for the operation control, maintenance, and replacement of nickel–cadmium batteries in the use process.

State of Charge Estimation of Lithium-Ion Batteries Based on Vector Forgetting Factor Recursive Least Square and Improved Adaptive Cubature Kalman Filter

Accurate online parameter identification and state of charge (SOC) estimation are both very crucial for ensuring the operating safety of lithium-ion batteries and usually the former is a base of the latter. To achieve accurate and stable SOC estimation results, this paper proposes a model-based method, which incorporates a vector forgetting factor least square (VFFLS) algorithm and an improved adaptive cubature Kalman filter (IACKF). Firstly, considering it is difficult for the traditional forgetting factor recursive least square (FFRLS) algorithm to balance the accuracy, convergence, and stability for multiple parameters with different time-varying periods, an improved VFFLS method is employed to determine the multiple parameters of the first-order RC battery model online. It supersedes the single forgetting factor in the FFRLS with multiple forgetting factors in a vector form for improving adaptive capability to multiple time-varying parameters. Secondly, aiming at the fact that the standard cubature Kalman filter (CKF) cannot operate properly when the error covariance matrix is non-positive definite, which is caused by disturbance, initial error, and the limit of the computer word length, the UR decomposition rather than the Cholesky decomposition is applied, thus improving the algorithm stability. In addition, an adaptive update strategy is added to the CKF to enhance accuracy and convergence speed. Finally, comparative experiments with different operating patterns, positive and non-positive definite error covariance matrices, and temperatures are carried out. Experimental results showed that the proposed method can estimate the SOC accurately and stably.

State of Charge Estimation for Lithium-Ion Battery Based on Unscented Kalman Filter and Long Short-Term Memory Neural Network

State of charge (SOC) estimation is the core algorithm of the battery management system. However, the commonly used model-based, data-driven, or experiment-based methods struggle to independently achieve accurate SOC estimation under different working conditions and temperatures, which affects battery performance and safety. To this end, this paper proposes an online SOC estimation method that combines the model-driven and double-data-driven approaches. The unscented Kalman filter (UKF) based on the first-order RC model is used to achieve robust SOC estimation, while the data-driven long short-term memory (LSTM) neural network is used to achieve fast SOC estimation. The former model has an excellent dynamic performance and the latter has high steady-state accuracy. The SOC estimation results are input into the SOC estimation model of series LSTM so that the stable but inaccurate SOC values estimated by UKF in the first part and the accurate but fluctuating SOC values estimated by LSTM can be correlated and corrected, achieving a fast and accurate SOC estimation under various working conditions. The estimation results show that the above method has strong robustness and high accuracy, and effectively reduces model complexity and data redundancy. In addition, the root mean square error of SOC estimation under different working conditions is controlled within 1–2.3% at 0 °C, 25 °C, and 45 °C, which is better than the traditional single-SOC estimation method.

State of charge estimation for lithium-ion batteries based on cross-domain transfer learning with feedback mechanism

When the deep learning model is applied to estimate battery state of charge (SOC), the information inside the training set cannot be leveraged thoroughly, which would cause poor SOC estimation accuracy and robustness on the testing set. To solve the problem, this paper proposes an adaptive convolutional neural network-gated recurrent unit with Kalman filter and feedback mechanism (Fb-Ada-CNN-GRU-KF) for SOC estimation considering distribution difference of data segments inside the training set through transfer learning and extracting the spatial information through convolutional layer. Furthermore, the feedback mechanism provides the model more information to learn to correct the systematic error, and the KF in the proposed model works as a post data processor to obtain a steady and smooth SOC estimation results. Experimental and comparison results show that the proposed model for SOC estimation outperforms the existing deep learning methods in terms of the accuracy, generalization and stability.

A novel M-1 structured Bidirectional Long Short Term Memory-Rauch Tung Striebel Smoothing algorithm for the joint estimation State of Charge and multi-constrained sustained peak power of lithium-ion batteries

The estimation of State of Charge (SoC) and State of Power (SoP) of lithium-ion batteries is an important part of battery management system. For the purpose of obtaining high-precision SoC and SoP estimation results, this paper proposes a novel M-1 structured Bidirectional Long Short Term Memory-Rauch Tung Striebel Smoothing (BiLSTM-RTSS) algorithm, which can effectively fit current, voltage, temperature and SoC by using the improved sliding window M-1 technique. The RTSS algorithm is applied to update the SoC estimation of the BiLSTM to facilitate the accuracy and speed of SoC estimation. Subsequently, to better estimate the SoP with duration of 30 s, 2 min, and 4 min, three key constraints including SoC estimation results, second-order RC model and battery limits, are simultaneously used in SoP estimation. According to experiment, the mean absolute error of SoC is 0.602, 0.619 and 0.548, 0.469 respectively, under the conditions of HPPC and BBDST. When the duration is 30s, the peak charging and discharging currents up to 170 A and 380 A. In addition, the estimation trends of sustained peak power and peak current are in the same direction. The experimental results verify the rapidity and reliability of the proposed algorithm for SoC and SoP.

Lithium-ion battery electro-thermal modelling and internal states co-estimation for electric vehicles

Battery modelling, temperature monitoring and accurate estimation of capacity and state of charge (SOC) are fundamental functions of the battery management system (BMS) for ensuring the safety and reliability of lithium-ion batteries (LIBs). Most studies focus on estimating one or two of these states while ignoring the influence of temperature and ageing on the battery’s performance. Neglecting the coupling effects between the battery capacity, SOC and temperature will hinder the accuracy of their estimates. This study uses an enhanced electrothermal battery model (EETM) to build a co-estimation scheme of the battery capacity, SOC, core and surface temperature. Regular updates of the battery capacity help track the battery’s health and enhance the precision of the SOC estimation results. The model monitors the battery core and surface temperature inside a 1s3p 18650 battery pack to prevent thermal runaway. The battery model and the co-estimation system is validated using COMSOL Multiphysics® simulation software. Results show that real-time updates of the battery operating temperatures, capacity, and SOC yielded good results and improved the estimators’ accuracy. Using the urban dynamometer driving schedule (UDDS) test, the proposed approach was able to reduce the estimation errors to ±9 mV for the battery model output voltage, 0.5% for the SOC and 0.5 K for the core temperature.

Stable and Accurate Estimation of SOC Using eXogenous Kalman Filter for Lithium-Ion Batteries

The state of charge (SOC) for a lithium-ion battery is a key index closely related to battery performance and safety with respect to the power supply system of electric vehicles. The Kalman filter (KF) or extended KF (EKF) is normally employed to estimate SOC in association with the relatively simple and fast second-order resistor-capacitor (RC) equivalent circuit model for SOC estimations. To improve the stability of SOC estimation, a two-stage method is developed by combining the second-order RC equivalent circuit model and the eXogenous Kalman filter (XKF) to estimate the SOC of a lithium-ion battery. First, approximate SOC estimation values are observed with relatively poor accuracy by a stable observer without considering parameter uncertainty. Second, the poor accuracy SOC results are further fed into XKF to obtain relative stable and accurate SOC estimation values. Experiments demonstrate that the SOC estimation results of the present method are superior to those of the commonly used EKF method. It is expected that the present two-stage XKF method will be useful for the stable and accurate estimation of SOC in the power supply system of electric vehicles.

State of Charge Estimation of Li-Ion Battery Based on Adaptive Sliding Mode Observer.

As the main power source of new energy electric vehicles, the accurate estimation of State of Charge (SOC) of Li-ion batteries is of great significance for accurately estimating the vehicle’s driving range, prolonging the battery life, and ensuring the maximum efficiency of the whole battery pack. In this paper, the ternary Li-ion battery is taken as the research object, and the Dual Polarization (DP) equivalent circuit model with temperature-varying parameters is established. The parameters of the Li-ion battery model at ambient temperature are identified by the forgetting factor least square method. Based on the state space equation of power battery SOC, an adaptive Sliding Mode Observer is used to study the estimation of the State of Charge of the power battery. The SOC estimation results are fully verified at low temperature (0 °C), normal temperature (25 °C), and high temperature (50 °C). The simulation results of the Urban Dynamometer Driving Schedule (UDDS) show that the SOC error estimated at low temperature and high temperature is within 2%, and the SOC error estimated at normal temperature is less than 1%, The algorithm has the advantages of accurate estimation, fast convergence, and strong robustness.

Lithium-ion battery state-of-charge estimation based on a dual extended Kalman filter and BPNN correction

It is challenging for a battery management system to estimate the State-Of-Charge (SOC) of batteries. A novel model-based method, using a Dual Extended Kalman Filtering algorithm (DEKF) and Back Propagation Neural Network (BPNN), is proposed to estimate and correct lithium-ion batteries. The results of acceptable SOC estimation are achieved using the DEKF to estimate the battery SOC and simultaneously update model parameters online, while the SOC estimation error is in real-time predicted by the trained BPNN. To further reduce the SOC estimation error, the SOC estimated by the DEKF is corrected by adding the predicted estimation error. The SOC estimation results between the original DEKF and BPNN-based updated DEKF methods under the Federal Urban Driving Schedule (FUDS), the Dynamic Stress Test (DST), the Beijing Dynamic Stress Test (BJDST) and the US06 Highway Driving Schedule are compared. Experimental results show that the SOC error reduces considerably after correcting the estimated SOC. The corrected SOC Root-Mean Square Errors (RMSEs) decrease by an average of seven times compared with the case of no correction. The constant current discharge test verifies the generality and robustness of the proposed method. The modification to the SOC estimation results using ordinary EKF under the above four sophisticated dynamic tests verifies the effectiveness of the proposed method.

Elaborated EECM parameter identification reflecting adaptive weight for achieving a high‐accuracy SOC estimator

AbstractIn this paper, a combined method is proposed to improve the accuracy of an electrical equivalent circuit model (EECM) and state‐of‐charge (SOC) estimation in situations where a lithium‐ion battery is frequently charged and discharged. To calculate the terminal voltage in the dynamic region, where charging and discharging are frequently repeated at 0.1 s intervals, a specific region is determined and historical weight is selected, based on the amount of charge in that region, to reflect the model parameters. The historical weights are applied to the charging and discharging parameters to improve the estimated performance of the EECM in estimating the terminal voltage of the battery. Also, the improved EECM is applied to the extended Kalman filter to improve the performance of SOC estimation. A 21,700 cylindrical lithium nickel manganese cobalt oxide‐type battery was used for verification, and the parameters required for modeling were extracted through experiments that were conducted to determine electrical characteristics. This paper compared two models not considering the history of charging or discharging characteristics with a model considering history to verify the accuracy of voltage and SOC estimation results. The result shows that the voltage and SOC estimation errors of the proposed combined method are the lowest in the three cases.

SOC estimation of Li-ion battery using convolutional neural network with U-Net architecture

State-of-charge (SOC) is critical to the safe operation and energy management of electric vehicles. Data-driven SOC estimation algorithms all require a period of data to ensure convergence of the estimation results and cannot accurately estimate the SOC values near the starting point. We propose a SOC estimation method based on the U-Net architecture that can handle variable-length input data and output equal-length SOC estimation results, including accurate SOC of the starting point. Symmetric padding convolutional layer was proposed to address the boundary effect of Convolutional Neural Networks (CNN) and improve the accuracy of SOC estimation at the edges. We also propose a total variation loss function, which improves the stability of the estimation only by optimizing the loss function without increasing the model complexity, and significantly reduces the maximum error. The model was trained using dynamic drive cycle data at five constant temperatures, and the model has high accuracy at both constant and variable temperature conditions. The proposed method can estimate the SOC at constant temperatures with mean absolute error (MAE) within 1.1% and root-mean-square error (RMSE) within 1.4%. This method also can estimate SOC at varying temperatures with MAE within 1.5% and RMSE within 1.8% under different driving conditions.

Battery state-of-charge estimation amid dynamic usage with physics-informed deep learning

Accurate estimation of state of charge (SOC) constitutes the basis to enable the reliable operations of lithium-ion batteries. The recent development in deep learning provides an emerging solution to SOC estimation. However, the limited training and testing profiles and the ignorance of battery working principles jeopardise the performance of deep learning-based methods. In this study, we propose to incorporate two kinds of domain knowledge into the deep learning-based methods. First, voltage and current sequences are decoupled into open circuit voltage (OCV), ohmic response and polarisation voltage to augment the input of deep neural networks (DNNs). Second, as conventional DNNs ignore the time-dependency in SOC estimation results, we propose a combination framework to adaptively fuse the SOC estimation results from the DNN and short-term Ampere-hour predictions. The proposed method is validated on a large dataset which is collected by conducting the tests on eight batteries at various real-world driving profiles and is compared with a basic long short-term memory DNN based on the input of only voltage and current. The results show that the proposed method can sharply reduce the SOC estimation root mean square error and maximum absolute error by 30.89% and 64.88%, respectively, with only slightly increased computational cost. Further validations under different temperatures and the applications of the proposed method to other DNNs also demonstrate its effectiveness. These results highlight the potential to boost the performance of DNNs by making effective use of battery domain knowledge.

Design of a Non-Linear Observer for SOC of Lithium-Ion Battery Based on Neural Network

This paper presents a method for use in estimating the state of charge (SOC) of lithium-ion batteries which is based on an electrochemical impedance equivalent circuit model with a controlled source. Considering that the open-circuit voltage of a battery varies with the SOC, an equivalent circuit model with a controlled source is proposed which the voltage source and current source interact with each other. On this basis, the radial basis function (RBF) neural network is adopted to estimate the uncertainty in the battery model online, and a non-linear observer based on the radial basis function of the RBF neural network is designed to estimate the SOC of batteries. It is proved that the SOC estimation error is ultimately bounded by Lyapunov stability analysis, and the error bound can be arbitrarily small. The high accuracy and validity of the non-linear observer based on the RBF neural network in SOC estimation are verified with experimental simulation results. The SOC estimation results of the extended Kalman filter (EKF) are compared with the proposed method. It improves convergence speed and accuracy.

State-of-charge estimation using data fusion for vanadium redox flow battery

Accurate estimation of the state of charge (SOC) is important for preventing overcharge and overdischarge of vanadium redox flow batteries (VRFBs). In this paper, we propose a data-fusion (DF) method to improve the accuracy of SOC estimation for VRFBs by combining two different SOC estimation results. First, the extended Kalman filter (EKF) and adaptive extended Kalman filter (AEKF) were used to estimate the SOC according to the equivalent circuit model (ECM) of the VRFB. Thereafter, the SOC estimation results of the EKF and AEKF were utilized separately as the basic estimation of the DF method to obtain two different DF results, which can be explicitly divided into DF-EKF and DF-AEKF. The ECM parameters were extracted using the recursive least squares (RLS) algorithm in real time. Subsequently, an experiment involving a hybrid pulse discharge was conducted to validate the proposed method. Here, the root-mean-square error (RMSE) and mean absolute error (MAE) are used as statistical methods for outcome evaluation. Compared with the RMSE and MAE (0.0012, 0.0010, and 0.0010 and 0.0009) of the EKF and AEKF, the RMSE and MAE of the DF-EKF decreased by 33.3%, 20%, and 36.3% and 22.2% to 0.0008 and 0.0007, respectively. The same downward trend also occurs in DF-AEKF. The RMSE of the results of DF-AEKF decreased by 33.3% and 20% to 0.0008, and the MAE decreased by 45.5% and 33.3% to 0.0006, respectively. The results show that the proposed DF method exhibited a high fidelity and accuracy in estimating the SOC of the VRFB.

A Novel State of Charge Estimation for Energy Storage Systems Based on the Joint NARX Network and Filter Algorithm

Lithium-ion batteries have the advantage of high energy density, low self-discharge rate, and long cycle life, and are currently the most widely used energy storage carriers. Accurate state of charge (SOC) estimation is essential to ensure the lithium-ion battery's safe and reliable operation. In order to improve the accuracy of estimation, this paper creatively applies the extended Kalman filter (EKF) to the improved nonlinear autoregressive algorithm with an exogenous neural network (NARXNN), forming a NARX-EKF neural network model for SOC prediction of the lithium-ion battery for the first time. This method avoids complicated equivalent modeling and parameter identification, rather directly maps the measured voltage, current, and temperature to the SOC. The data set is obtained by simulating the driving cycle load of the lithium-ion battery under different working conditions, and the network is tested under cyclic working conditions, dynamic working conditions, different temperature conditions, and different aging cycles. The SOC estimation results of the NARX-EKF model are evaluated from three aspects: mean absolute error (MAE), root mean square error (RMSE), and SOC error. Under cyclic conditions, the RMSE and MAE of NARXNN are only 1.4% and 1.3%, which is only 50% of other neural networks. In the dynamic working condition test, the maximum error of NARXNN optimized by EKF is reduced by about 50%, and the RMSE and MAE of the model are only 20% of other neural networks. When the ambient temperature changes, the RMSE and MAE of the model under low-temperature conditions were 1.2% and 0.9% respectively. The RMSE and MAE of the model under high-temperature conditions were 0.6% and 0.5% respectively. In addition, the NARX-EKF network can well solve the impact of different aging degrees of lithium-ion batteries on SOC estimation. When the battery health status is only 70%, the RMSE and MAE of the model were only 2.7% and 2.5% respectively. The results show that the NARX-EKF model has high accuracy, robustness, and good application prospects.

State of Charge Estimation of Lithium-Ion Battery Based on Improved Adaptive Unscented Kalman Filter

State of charge (SOC) of the lithium-ion battery is an important parameter of the battery management system (BMS), which plays an important role in the safe operation of electric vehicles. When existing unknown or inaccurate noise statistics of the system, the traditional unscented Kalman filter (UKF) may fail to estimate SOC due to the non-positive error covariance of the state vector, and the SOC estimation accuracy is not high. Therefore, an improved adaptive unscented Kalman filter (IAUKF) algorithm is proposed to solve this problem. The IAUKF is composed of the improved unscented Kalman filter (IUKF) that is able to suppress the non-positive definiteness of error covariance and Sage–Husa adaptive filter. The IAUKF can improve the SOC estimation stability and can improve the SOC estimation accuracy by estimating and correcting the system noise statistics adaptively. The IAUKF is verified under the federal urban driving schedule test, and the SOC estimation results are compared with IUKF and UKF. The experimental results show that the IAUKF has higher estimation accuracy and stability, which verifies the effectiveness of the proposed method.

State of Charge Estimation for Li-Ion Batteries Based on an Unscented H-Infinity Filter

The state of charge (SOC) of lithium-ion batteries reflects their remaining capacity. Accurate estimation of SOC helps battery safety and is beneficial to the efficient management of batteries. The charging and discharging processes of lithium-Ion batteries are very complicated, and it is difficult to obtain accurate SOC estimation results. Therefore, it is important to study improved algorithms for SOC estimation for this nonlinear non-Gaussian battery system. In this paper, we propose an unscented H-infinity filter (UHF) based SOC estimation method, which combines the advantages of both the unscented Kalman filter (UKF) and the H-infinity filter (HF). The UKF propagates the sigma points through the nonlinear system and does not need the first-order linear approximation of the system equation, while the HF can suppress the non-Gaussian noise in the system to the greatest extent. The proposed UHF based SOC estimation algorithm is verified and evaluated in the battery management system, and further optimized in practical problems. Experimental results show that the proposed UHF based algorithm can perform accurate SOC estimation for lithium-ion batteries, and is superior to the UKF based SOC estimation.

State of Charge Estimation for Lithium-Ion Power Battery Based on H-Infinity Filter Algorithm

To accurately estimate the state of charge (SOC) of lithium-ion power batteries in the event of errors in the battery model or unknown external noise, an SOC estimation method based on the H-infinity filter (HIF) algorithm is proposed in this paper. Firstly, a fractional-order battery model based on a dual polarization equivalent circuit model is established. Then, the parameters of the fractional-order battery model are identified by the hybrid particle swarm optimization (HPSO) algorithm, based on a genetic crossover factor. Finally, the accuracy of the SOC estimation results of the lithium-ion batteries, using the HIF algorithm and extended Kalman filter (EKF) algorithm, are verified and compared under three conditions: uncertain measurement accuracy, uncertain SOC initial value, and uncertain application conditions. The simulation results show that the SOC estimation method based on HIF can ensure that the SOC estimation error value fluctuates within ±0.02 in any case, and is slightly affected by environmental and other factors. It provides a way to improve the accuracy of SOC estimation in a battery management system.