Accurate State Of Charge Estimation Research Articles

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

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

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

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

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

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

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

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

Transductive Transfer Learning-Assisted Hybrid Deep Learning Model for Accurate State of Charge Estimation of Li-Ion Batteries in Electric Vehicles

Transductive Transfer Learning-Assisted Hybrid Deep Learning Model for Accurate State of Charge Estimation of Li-Ion Batteries in Electric Vehicles

Maximum capacity and state of health estimation based on equivalent circuit model for degraded battery

In real-time systems, state of health (SOH) and maximum capacity need to be updated regularly as battery degrades with time. Incorrect estimation of SOH or maximum capacity leads to inaccurate state of charge (SOC) estimation, especially for degraded batteries. Maximum capacity or SOH is usually obtained by constant-current discharging test, which is impractical in real-time battery management system (BMS). Therefore, it is meaningful to find an adaptive method to estimate SOH or maximum capacity in real-time BMS instead of discharging test. This paper proposes a two-step approach to estimate SOC and SOH. In the first step, SOC and battery electrical parameters (such as resistance, capacitor, etc.) are estimated simultaneously with fixed maximum capacity by using (dual) extended Kalman filter model. In the second step, the maximum capacity of degraded battery is estimated based on estimated electrical parameters using (dual) unscented Kalman filter, which rending estimated SOH. The above two step could be deployed on real-time applications to improve the accuracy of SOC estimation even when battery degrades.

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.

State of charge estimation for lithium-ion batteries based on battery model and data-driven fusion method

The voltage plateau phase of LiFeO4 (LFP) batteries presents a formidable challenge when estimating the state of charge (SOC). Although numerous data-driven methods have been developed to address this issue, they often depend heavily on high-quality training data. Furthermore, these methods are typically regarded as “black-box” models, lacking interpretability. To overcome these challenges, a novel approach that integrates both model-based and data-driven techniques for battery SOC estimation is proposed in this paper. The proposed method is grounded in the battery model and complemented by the data-driven model, thus enhancing interpretability by incorporating domain knowledge. To reduce computational complexity, the Rint model is used for rough SOC estimation, with the eXtreme Gradient Boosting model (XGBoost) used for residual learning. The parameters of the battery model serve as input features for the XGBoost model. The effectiveness of the proposed method is empirically validated under different dynamic testing profiles. Experimental results demonstrate that integration battery domain knowledge into data-driven approaches not only enhances method interpretability but also significantly improves the SOC estimation accuracy for LFP batteries. Moreover, it exhibits robustness and exceptional generalization performance under unseen dynamic conditions, yielding root mean square errors of less than 1 % and maximum errors of less than 2 %.

Research on battery state of charge estimation based on variable window adaptive extended Kalman filter

Battery state of charge (SOC) estimation is one of the indispensable functions in the battery management system. Among them, the Kalman filter series of algorithms are widely used in the battery SOC estimation process. The adaptive extended Kalman filter uses the difference between the measured voltage and the estimated voltage (error innovation) as the innovative covariance matrix update noise in battery SOC estimation. However, the general adaptive Kalman filter does not consider the error innovation in the estimation process. The change. This will lead to inaccurate battery SOC estimation. In order to solve this problem, we proposes a variable window Kalman filter algorithm that takes into account the changes in the error innovation sequence. The algorithm updates the innovation covariance matrix according to the change of error innovation to improve the accuracy of SOC estimation. The results show that compared with the extended Kalman filter and the fixed window Kalman filter, its calculation efficiency is also improved while its accuracy is improved. Finally, its accuracy is verified under different initial parameters, and the study shows that the algorithm proposed in this article is robust.

State of charge estimation for lithium-ion battery based on improved online parameters identification and adaptive square root unscented Kalman filter

Accurate state of charge estimation is crucial for the safe and efficient operation of lithium-ion batteries. The Kalman filtering algorithm has been widely used in state-of-charge (SOC) estimation. To solve the problem of filter divergence and sensitivity to noise, the joint SOC estimation method is proposed to achieve accurate and robust estimation of SOC, which is composed of improved variable forgetting factor recursive least square (VFFRLS) and adaptive square root unscented Kalman filter (ASRUKF). The improved VFFRLS method uses the mean square value of the multi-step voltage residual instead of the traditional one-step voltage residual to correct the forgetting factor, and the ASRUKF improves the accuracy and stability of estimation by introducing the square root method and the adaptive method. Estimations under three typical working conditions are quantitatively studied, the experimental results show that the proposed method has good accuracy and stability. The maximum mean absolute error (MAE) is 0.0061, and the corresponding root mean square error (RMSE) is 0.0090. Furthermore, the experimental verification after adding offset errors to measured data shows that the proposed method can still track the reference SOC with satisfactory accuracy in the range of voltage offset error less than ±0.5 % and current offset error less than ±3 %, both for the constant offset error and the random error, and the SOC error is less than 2.5 %.

An Extended Kalman Filter Design for State-of-Charge Estimation Based on Variational Approach

State of charge (SOC) is a very important variable for using batteries safely and reliably. To improve the accuracy of SOC estimation, a novel variational extended Kalman filter (EKF) technique based on least square error method is herein provided by establishing a second-order equivalent circuit model for the battery. It was found that when SOC decreased, resistance polarization occurred in the electrochemical model, and the parameters in the equivalent RC model varied. To decrease the modeling error in the equivalent circuit model, the system parameters were identified online depending on the SOC’s estimated result. Through the SOC-estimation process, the variation theorem was introduced, which enabled the system parameters to track the real situations based on the output measured. The experiment results reveal the comparison of the SOC-estimation results of the variational EKF algorithm, the traditional EKF algorithm, the recursive least square (RLS) EKF algorithm, and the forgotten factor recursive least square (FFRLS) EKF algorithm based on different indices, including the mean square error (MSE) and the mean absolute error (MAE). The variational EKF algorithm provided in this paper has higher estimation accuracy and robustness than the traditional EKF, which verifies the superiority and effectiveness of the proposed method.

Dual time-scale state-coupled co-estimation of state of charge, state of health and remaining useful life for lithium-ion batteries via Deep Inter and Intra-Cycle Attention Network

The reliable and safe battery operations demand accurate estimation of battery states in the battery management system (BMS). Due to the complex electrochemical process, it is challenging to directly measure SOH and RUL of batteries for online applications. Moreover, the battery aging can strongly influence SOC estimation. The paper proposes a SOC, SOH, and RUL co-estimation method based on Deep Inter and Intra-Cycle Attention Network (DIICAN). From BMS data, the dual time-scale inter-cycle and intra-cycle features are automatically extracted with neural networks. The state degradation attention (SDA) unit is employed to recognize the state evolution pattern and evaluate battery degradation degree based on inter-cycle features. In addition, the extracted inter-cycle and intra-cycle features are simultaneously coupled for the SOC estimation to calibrate the capacity degradation. The mean absolute error (MAE) and root mean square error (RMSE) of the state of health (SOH) estimation are 0.30% and 0.43%, respectively. For the remaining useful life (RUL) estimation, the MAE is 178.5, and the RMSE is 230.3. With state coupling, the MAE of the state of charge (SOC) estimation decreases from 2.36% to 1.00%, and the RMSE decreases from 3.27% to 1.36% over the entire lifespan. In summary, the proposed method can not only accurately co-estimate SOH and RUL, but improve SOC estimation accuracy over the entire battery life.

A wide dynamic range diamond quantum sensor as an electric vehicle battery monitor.

To demonstrate the application capability of the diamond quantum sensor as an electric vehicle (EV) battery monitor, we (i) investigated the measurable current in a real car noise level and (ii) compared the linearity with conventional sensors. Consequently, (i) we could measure a 20 mA current pulse even under an external magnetic field of 80 µT, which is larger than that of 50 µT around the EV battery module in a real car during driving. The 20 mA pulse measurement corresponds to the EV battery state of charge estimation accuracy of 0.2% in the standard driving pattern, which is smaller than the present level of 10%. (ii) The linearity degradation seen in the Hall sensor near the upper limit of the measurement range was not seen in the diamond sensor. Although the Hall sensor and the shunt resistor showed linearity degradation in the current range of several tens of amperes or less, the degradation was smaller for the diamond sensor. The transverse magnetic field effect in the diamond sensor on the linearity was estimated to be less than 0.01% for a several-degree misalignment of the sensor surface to the magnetic field direction and under a 340 A current. This article is part of the Theo Murphy meeting issue 'Diamond for quantum applications'.

Establishment of a Lithium-Ion Battery Model Considering Environmental Temperature for Battery State of Charge Estimation

Accurate estimation of the state-of-charge (SOC) is essential to prevent overcharging and over-discharging of lithium-ion batteries. However, traditional SOC estimation methods exhibit significant errors under large temperature variations due to the strong temperature dependence of battery characteristics. To enhance the accuracy of SOC estimation, this study proposes a second-order RC equivalent circuit model with temperature correction. By considering the influence of temperature on model parameters, the model’s accuracy is improved by adjusting the estimated parameters. A polynomial coefficient data table for model parameters is established to expedite the computation time of the SOC estimation process. Finally, the temperature-corrected model is combined with an Adaptive Extended Kalman Filter (AEKF) algorithm for SOC estimation. The results of the Dynamic Stress Test (DST) condition experiments show that the temperature correction model can improve the accuracy of SOC estimation under different temperature conditions. It has a more lower SOC estimation error than the model without temperature correction.

Multi-Measurement Kalman-Filtering-Based Neural Network Estimator for SOC of Lithium Batteries

State of charge (SOC) refers to the remaining capacity of the battery, which cannot be measured directly. A multi-measurement Kalman filter which is composed of two sub Kalman filters is constructed to improve the estimation accuracy of SOC. The two sub filters share the same state function but have different measurements, namely the terminal voltage and the SOC estimation from neural network, respectively. Based on minimizing the trace of error covariance, an optimal weighted matrix is computed to fuse the estimates of the two sub filters. The training dataset of neural network is collected from mixed discharging cycles experiment and corresponding charging process. By comparing the results with model-based methods, such as H-infinity filter, unscented Kalman filter, data-driven methods, like neural networks and hybrid method, the multi-measurement Kalman filter is verified by both the root mean square error and mean absolute error that are less than 2% in different drive cycles.

Soc Estimation of Li-ion Battery Based on Adaptive CKF Algorithm

A second-or der RC equivalent circuit model was established to improve the estimation accuracy of state of charge (SOC) of power Li-ion batteries, and the model parameters were identified by the recursive least square method with forgetting factor (FFRLS). On this basis, an adaptive cubature kalman filter (ACKF) algorithm was proposed to adaptively modify the process noise covariance matrix and the measurement noise covariance matrix to improve the SOC estimation accuracy. Finally, the SOC estimation algorithm was verified by MATLAB simulations. The results show that compared with UKF and CKF algorithms, the proposed algorithm has higher estimation accuracy and robustness, and can meet the application requirements.

State of Charge Estimation of Lithium-Ion Battery Based on Back Propagation Neural Network and AdaBoost Algorithm

The accurate estimation of the state of charge (SOC) of lithium-ion batteries is critical in battery energy storage systems. This paper introduces a novel approach, the AdaBoost–BPNN model, to overcome the limitations of traditional data-driven estimation methods, such as a low estimation accuracy and poor generalization ability. The proposed model employs a back propagation neural network (BPNN) for the preliminary estimation. Subsequently, an AdaBoost–BPNN model is developed as a strong learner using the AdaBoost integration algorithm. Each BPNN sub-model serves as a weak learner within the AdaBoost framework. The final output of the strong learner is obtained by combining the individual outputs from the weak learners using weighting factors. This adaptive adjustment of weighting factors enhances the accuracy of SOC estimation. The proposed SOC estimation algorithm is evaluated and validated through experimental analysis. Throughout the paper, theoretical analysis is conducted, and the proposed AdaBoost–BPNN model is validated and verified using experimental results. The results demonstrate that the AdaBoost–BPNN model outperforms traditional methods in accurately estimating SOC under various conditions, including constant current-constant voltage (CCCV) charging, dynamical stress testing (DST), US06, a federal urban driving schedule (FUDS), and pulse discharge conditions.

Dynamic ultrasonic response modeling and accurate state of charge estimation for lithium ion batteries under various load profiles and temperatures

Accurate estimation of the State of Charge (SoC) plays a vital role in ensuring the efficient and safe operation of lithium iron phosphate (LFP) batteries. However, the flat open circuit voltage (OCV) curve of the LFP battery implies a low sensitivity to SoC, which results in large SoC estimation errors in the presence of noisy terminal voltage measurements. To address this challenge, an SoC estimation methodology utilizing an ultrasonic reflection response model is proposed, which is the first methodology regarding highly accurate and robust ultrasonic model-based SoC estimation under dynamic load profiles. Since ultrasound waves enable non-destructive acquisition of battery internal physical property changes directly associated with SoC, the ultrasonic battery near-surface reflection feature is extracted and demonstrated to exhibit a highly linear correlation with and higher sensitivity to SoC. We pioneeringly construct an empirical differential ultrasonic model to describe how the ultrasonic feature depends on the SoC and dynamic current. The advantage of such an ultrasonic model is demonstrated by theoretical and experimental results of an Adaptive Extend Kalman Filter (AEKF) and an Adaptive H-infinity Filter (AHIF) under various dynamic load profiles and temperatures. The Root Mean Square Error (RMSE) for ultrasonic model-based SoC estimation remains at approximately 1% across all tests, reducing by 36.7% compared to the voltage model, which shows its great potential in accurate SoC estimation.

An extended Kalman-Bucy filter for state of charge estimation of 2-RC network modelled Li-ion battery

Li-ion batteries have increased dramatically in the automobile industry over the past few decades. Lithium-ion batteries are viewed more favourably due to their high energy density, specific energy, etc. Optimising the performance of lithium-ion batteries requires accurate modelling and estimation of the state of charge (SOC). This article introduces an efficient second-order resistor-capacitor (2RC) network battery model and an optimised extended Kalman-Bucy filter (EKBF) as the most effective way to model a battery and estimate its state of charge (SOC). The operating parameters of a lithium-ion battery are measured with the least-squares curve fitting method. At a temperature of 20 °C, the proposed method for estimating SOC has a mean absolute error (MAE) of 0.72 % and a root mean square error (RMSR) of 0.71 %. In addition, the operational characteristics of the proposed EKBF were validated by simulating its operation at temperatures ranging from 0 °C to 40 °C. Under all conditions, the proposed method maintained an average error rate of 0.40%. The output of the proposed topology was validated using OPAL-RT (OP5700) hardware-in-the-loop real-time simulator. Consequently, the proposed method is preferable for accurate and dependable SOC estimation in real-time battery management system (BMS) applications.

SOC estimation of lithium battery based on the combination of electrical parameters and FBG non-electrical parameters and using NGO-BP model

Accurately estimating of the state of charge (SOC) of lithium batteries is of great significance for improving the service life and utilization efficiency of lithium batteries. In this paper, fiber Bragg grating (FBG) sensors are used to capture the offset of the FBG central wavelength caused by strain and temperature during the charging and discharging process of lithium batteries, and the current state of charge of lithium batteries is obtained through the combination of electrical parameters and FBG non-electrical parameters.A battery monitoring experimental system was established, and the comparison of wavelength offset collected by PDMS packaged FBG and bare FBG during the charging and discharging process of lithium batteries was discussed. The prediction results were compared by temperature compensating the central wavelength offset collected during the charging and discharging of lithium batteries, then introduced BP neural network and optimized NGO- BP neural network regression models for training to compare the prediction effects, the results of which point to the fact that in terms of regression model performance and improvement of FBG non-electrical parameters on model performance, the various indicators predicted by NGO-BP are stronger than those predicted by BP. After adding FBG non-electrical parameters, both the BP regression model and the NGO-BP regression model showed remarkable improvement in RMSE, MAE, and R2 compared to the purely electrical parameters, and the best prediction method for the NGO-BP non-purely electrical parameters, with RMSE of 0.0201 and MAE of 0.0154, which decreased by 77.94% and 73.12% respectively compared to the BP pure electrical parameter prediction method, and R2 of 0.9988, which increased by 5.88%, thus the joint accurate estimation of lithium battery SOC by electrical measurement characteristics and FBG non-electrical parameters is basically realized, which brings values for the design and development of battery management system.