Accurate State Of Charge Estimation Research Articles

State of Charge Estimation of Lithium-ion Battery Based on Improved Recurrent Neural Network

Aiming at the problem of gradient disappearance and gradient explosion in the recurrent neural network (RNN) algorithm in the battery estimation model, this paper proposes a state of charge (SOC) estimation model developed using an independent recurrent neural network (IndRNN). Firstly, the Thevenin equivalent model of the battery is established, and the parameters of the equivalent model are identified through experiments. Then, the Relu activation function is introduced into the RNN to separate the neurons in each layer. Finally, the model was trained on various experimental data sets collected from the lithium iron phosphate battery experimental platform under different discharge conditions. Without any prior knowledge about the battery interior, the proposed battery model successfully characterizes the non-linear behavior of the battery. The results show that under different discharge conditions, IndRNN is better than RNN in terms of maximum error, the mean error, and the root mean square error (RMSE), which greatly improves the accuracy of SOC estimation.

Parameters identification of Thevenin model for lithium-ion batteries using self-adaptive Particle Swarm Optimization Differential Evolution algorithm to estimate state of charge

State of charge (SOC) estimation is a significant task for lithium-ion batteries. However, the accuracy of SOC estimation is closely related to parameters of battery and system non-linearity. To identify the parameters of lithium-ion battery better, this proposed a self-adaptive particle swarm optimization differential evolution (SaPSODE) algorithm. First, to describe the dynamic behaviors of battery, we presented a first-order RC equivalent circuit model (ECM). Second, to calculate open-circuit voltage (OCV) versus time during the dynamic test procedure, an optimizing objective function was built to minimize errors between the true and optimized terminal voltages. Further, control parameters of F and Cr were also self-adapted according to previous successful records. Third, by using OCV-SOC mapping curves, this work obtained estimated SOC curve which was compared with true SOC curve. Comprehensive experimental results demonstrated effectiveness of the proposed framework and methodology, compared with several highly-cited DE variants.

Accurate and reliable state of charge estimation of lithium ion batteries using time-delayed recurrent neural networks through the identification of overexcited neurons

Various neural network models have been adopted for lithium ion battery state of charge (SOC) estimation with good accuracy. However, problems for battery states estimation from neural networks were usually not reported, which is mainly due to the lack of effective solutions other than a trial and error training process. This paper firstly proposes time-delayed recurrent neural network for lithium ion battery modeling and SOC estimation. Both exceptional performances and unexpected overfitting or poor performances are reported with in-depth analysis of the root cause. With explicit formulation of the network, each hidden neuron’s output is examined. It is discovered that overexcited neurons could be the root cause for unexpected poor performances of the neural network. Without overexcited neurons, expectational SOC estimation accuracy is consistently obtained with estimation error being less than 1% for lithium ion magnesium phosphate (LiFeMgPO4) batteries considering a fair comparison in literature.

A joint moving horizon strategy for state-of-charge estimation of lithium-ion batteries under combined measurement uncertainty

Measurement uncertainty is a common problem for state of charge (SOC) estimation of lithium-ion batteries in real applications. In this paper, to mitigate the negative effect of unseen measurement uncertainty, a joint moving horizon estimation (joint-MHE) approach is proposed. First, the equivalent circuit model (ECM) is constructed for battery modeling. Then, on the basis of ECM, the augmented state space model is formulated, in which the bias current is treated as an additional state and the measurement noises are summarized in covariance matrices. Finally, by integrating joint-MHE strategy with augmented model, the SOC estimation under measurement uncertainty condition is implemented. The effectiveness of proposed method is conducted under three uncertainty issues, including current bias, combined current uncertainty, and combined current and voltage uncertainty, and compared to the conventional MHE and the joint-extended Kalman filter (EKF) thoroughly. The results demonstrate that the joint strategy is an effective way to suppress the uncertainties in measurements. Furthermore, although two joint methods both can reduce the negative effect of unseen measurement uncertainty, the joint-MHE could provide better convergence speed and SOC estimation accuracy, and is much less sensitive to different uncertainty sources. Under the combined measurement uncertainty, the RMSE by joint-EKF is 5.32% during the whole applied DST range, while that by joint-MHE is only 1.46%. It thus indicates that the joint-MHE is a potential promising approach to tackle the measurement uncertainty problem, which would greatly assist in improving the feasibility of ECM-based SOC estimation approach in commercial BMS.

Research on the State of Charge of Lithium-Ion Battery Based on the Fractional Order Model

Accurate estimation of the state of charge (SOC) of lithium batteries is paramount to ensuring consistent battery pack operation. To improve SOC estimation accuracy and suppress colored noise in the system, a fractional order model based on an unscented Kalman filter and an H-infinity filter (FOUHIF) estimation algorithm was proposed. Firstly, the discrete state equation of a lithium battery was derived, as per the theory of fractional calculus. Then, the HPPC experiment and the PSO algorithm were used to identify the internal parameters of the second order RC and fractional order models, respectively. As discovered during working tests, the parameters identified via the fractional order model proved to be more accurate. Furthermore, the feasibility of using the FOUHIF algorithm was evaluated under the conditions of NEDC and UDDS, with obvious colored noise. Compared with the fractional order unscented Kalman filter (FOUKF) and integer order unscented Kalman filter (UKF) algorithms, the FOUHIF algorithm showed significant improvement in both the accuracy and robustness of the estimation, with maximum errors of 1.86% and 1.61% under the two working conditions, and a terminal voltage prediction error of no more than 5.29 mV.

Deep learning approach towards accurate state of charge estimation for lithium-ion batteries using self-supervised transformer model

Accurate state of charge (SOC) estimation of lithium-ion (Li-ion) batteries is crucial in prolonging cell lifespan and ensuring its safe operation for electric vehicle applications. In this article, we propose the deep learning-based transformer model trained with self-supervised learning (SSL) for end-to-end SOC estimation without the requirements of feature engineering or adaptive filtering. We demonstrate that with the SSL framework, the proposed deep learning transformer model achieves the lowest root-mean-square-error (RMSE) of 0.90% and a mean-absolute-error (MAE) of 0.44% at constant ambient temperature, and RMSE of 1.19% and a MAE of 0.7% at varying ambient temperature. With SSL, the proposed model can be trained with as few as 5 epochs using only 20% of the total training data and still achieves less than 1.9% RMSE on the test data. Finally, we also demonstrate that the learning weights during the SSL training can be transferred to a new Li-ion cell with different chemistry and still achieve on-par performance compared to the models trained from scratch on the new cell.

State of charge estimation of Lithium-ion batteries based on the probabilistic fusion of two kinds of cubature Kalman filters

The accurate simulation of batteries’ dynamic characteristics is important for improving the State of Charge (SoC) estimation performance. However, an equivalent circuit model of batteries tends to have changing simulation accuracy of the battery’s dynamic characteristics during SoC estimation. Although the adaptive high-degree cubature Kalman filter (AHCKF) has a more accurate estimation of the dynamic characteristics simulated by the battery model than the adaptive cubature Kalman filter (ACKF) does, AHCKF may have lower estimation accuracy of the battery’s real dynamic characteristics. Therefore, AHCKF does not always outperform ACKF at each time step during SoC estimation.To improve SoC estimation accuracy, this paper proposes an estimation method based on the probabilistic fusion of ACKF and AHCKF. Furthermore, the impact of the filters’ initial weights on the accuracy of the fusion method is analyzed. Under the dynamic stress test, when ACKF’s initial weight is 0.5, the mean absolute error and the root mean square error of SoC estimation based on the proposed method decrease by 22.35% and 6.36% compared with ACKF, respectively, as well as 7.04% and 4.63% compared with AHCKF, respectively. The result shows that the proposed method can improve the accuracy of SoC estimation when the filters’ initial weights are appropriately set.

Modified dual extended Kalman filters for SOC estimation and online parameter identification of lithium-ion battery via modified gray wolf optimizer

In order to achieve accurate state of charge (SOC) estimation of Lithium-Ion Battery, A method that dual Extended Kalman filters (DEKF) optimized by PSO-based Gray Wolf optimizer (MGWO) is proposed. A second-order equivalent circuit model with two resistor-capacitor branches is applied. The battery parameters are determined by battery test. Dual Extended Kalman filters are divided into state filter and parameter filter. Parameter filter is applied to adjust battery parameters online, state filter is applied to SOC estimation. Meanwhile, MGWO is applied to optimize the noise covariance matrix to improve the state estimation accuracy of SOC which reduces the linearization error from EKF. The results shows that the accuracy of algorithm is improved by adding online parameter identification and the optimization of the noise covariance matrix, meanwhile, the proposed method can adapt to the initial error well.

Online Parameters and State of Charge Co-estimation of Lithium-Ion Battery in Varying Temperature Using Joint Extended Kalman Filter

This paper compares the mode based lithium-ion battery state of charge (SOC) estimations using offline and online parameters under varying temperature. An innovative offline identification method based on genetic algorithm (GA) is used for off-line identification of battery model parameters. The common extended Kalman filter (EKF) and the joint extended Kalman filter (JEKF) are implemented as the algorithms to implement SOC estimation with offline and online parameters. The SOC estimations by JEKF using online parameters and by EKF using offline parameters from mismatched temperature are compared. The results are as follows. When battery temperature is inaccurate, the inaccurate temperature can result in inaccurate offline parameters parameters, which will further increase the SOC estimation errors by EKF using offline parameters. In contrast, SOC estimation accuracy by JEKF are still accurate when no temperature information is provided, because the parameters are online updated by JEKF.

A Novel Fading Memory Recursive Least Square Method (FMLS) for Accurate State of Charge Estimation of Lithium-ion Batteries Combined with Improved Second Order PNGV Modeling

A Novel Fading Memory Recursive Least Square Method (FMLS) for Accurate State of Charge Estimation of Lithium-ion Batteries Combined with Improved Second Order PNGV Modeling

Consensus-Based Stochastic Control for Model-Free Cell Balancing

Balancing the state of charge (SOC) of the cells improves both the capacity and the health of the battery. State of the art cell balancing algorithms assume highly accurate SOC estimation which can only be achieved using model-based control solutions. Unfortunately, electrochemical models of batteries are complicated and are still not reliable enough. We propose a simple consensus-based cell balancing algorithm that does not assume any knowledge of the electrochemical model of the battery. Instead, our algorithm only uses SOC estimates from online measurements to make sequential balancing decisions. Using martingale techniques, we prove that our algorithm equalizes the SOC of all cells with probability 1 even with very noisy SOC estimates under a general non-i.i.d. noise model. We then analyze the convergence time of our algorithm as a function of the problem parameters. We also prove performance guarantees for the more challenging case where balancing is done while the battery is charging or discharging. Finally, we present simulations that support our theoretical claims and show the reliability of our algorithm. Our model-free cell balancing is easy to implement and therefore is a major step towards making active cell balancing practical.

Online SOC Estimation Based on Simplified Electrochemical Model for Lithium-Ion Batteries Considering Current Bias

State of Charge (SOC) is essential for a smart Battery Management System (BMS). Traditional SOC estimation methods of lithium-ion batteries are usually conducted using battery equivalent circuit models (ECMs) and the impact of current sensor bias on SOC estimation is rarely considered. For this reason, this paper proposes an online SOC estimation based on a simplified electrochemical model (EM) for lithium-ion batteries considering sensor bias. In EM-based SOC estimation structure, the errors from the current sensor bias are addressed by proportional–integral observer. Then, the accuracy of the proposed EM-based SOC estimation is validated under different operating conditions. The results indicate that the proposed method has good performance and high accuracy in SOC estimation for lithium-ion batteries, which facilitates the on-board application in advanced BMS.

A Battery SOC Estimation Method Based on AFFRLS-EKF

The lithium-ion battery is the key power source of a hybrid vehicle. Accurate real-time state of charge (SOC) acquisition is the basis of the safe operation of vehicles. In actual conditions, the lithium-ion battery is a complex dynamic system, and it is tough to model it accurately, which leads to the estimation deviation of the battery SOC. Recursive least squares (RLS) algorithm with fixed forgetting factor is widely used in parameter identification, but it lacks sufficient robustness and accuracy when battery charge and discharge conditions change suddenly. In this paper, we proposed an adaptive forgetting factor regression least-squares–extended Kalman filter (AFFRLS–EKF) SOC estimation strategy by designing the forgetting factor of least squares algorithm to improve the accuracy of SOC estimation under the change of battery charge and discharge conditions. The simulation results show that the SOC estimation strategy of the AFFRLS–EKF based on accurate modeling can effectively improve the estimation accuracy of SOC.

Online Parameters Identification and State of Charge Estimation for Lithium-Ion Battery Using Adaptive Cubature Kalman Filter

The state of charge (SOC) of a lithium-ion battery plays a key role in ensuring the charge and discharge energy control strategy, and SOC estimation is the core part of the battery management system for safe and efficient driving of electric vehicles. In this paper, a model-based SOC estimation strategy based on the Adaptive Cubature Kalman filter (ACKF) is studied for lithium-ion batteries. In the present study, the dual polarization (DP) model is employed for SOC estimation and the vector forgetting factor recursive least squares (VRLS) method is utilized for model parameter online identification. The ACKF is then designed to estimate the battery’s SOC. Finally, the Urban Dynamometer Driving Schedule and Dynamic Stress Test are utilized to evaluate the performance of the proposed method by comparing with results obtained using the extended Kalman filter (EKF) and the cubature Kalman filter (CKF) algorithms. The simulation and experimental results show that the proposed ACKF algorithm combined with VRLS-based model identification is a promising SOC estimation approach. The proposed algorithm is found to provide more accurate SOC estimation with satisfying stability than the extended EKF and CKF algorithms.

SOC estimation for lithium‐ion batteries based on a novel model

Lithium-ion batteries (LIBs) are widely used in electric vehicles because of their high energy density and less pollution. As an important parameter of the battery management system, accurate estimation of the state of charge (SOC) of the battery can ensure the energy distribution and safe use of the battery. This paper obtains better estimation accuracy from four aspects. First, the battery model is established via Thevenin equivalent circuit model, and the parameters are identified by the forgetting factor recursive least squares. Second, the influence of dual extended Kalman filter on SOC estimation is analysed, a novel algorithm-based improved dual Kalman filter is proposed. Besides, to reduce the influence of the system noise on the estimation results, an adaptive intelligent algorithm is applied to promote the accuracy of SOC estimation. Finally, compared with the estimated SOC results of the traditional algorithm, the experimental results show the effectiveness of the algorithm.

More intelligent and robust estimation of battery state-of-charge with an improved regularized extreme learning machine

State-of-charge (SOC) is the key parameter for battery management, and the accurate estimation of SOC is pretty important for the safe and stable operation of lithium batteries. This paper investigates a regularized extreme learning machine trained with the spectral Fletcher–Reeves algorithm and tuned with the beetle antennae search algorithm (BAS-SFR-RELM) for intelligent and robust SOC estimation. In the experiment section, the urban dynamometer driving schedule (UDDS) profile and the Los Angeles 92 (LA92) profile are performed on a battery test platform for data collection. In the simulation section, the root mean squared error (RMSE) and the mean absolute error (MAE) are adopted to evaluate the performance of the model. Compared with the linear regression (LR), the back propagation (BP) network, the multi-layer perceptron (MLP), and the long short-term memory (LSTM) network, the BAS-SFR-RELM method can efficiently obtain the optimal regularization coefficient to effectively prevent overfitting with faster convergence speed. Increasing the number of hidden neurons in the BAS-SFR-RELM appropriately can improve the SOC estimation precision. Implementing the BAS-SFR-RELM with the noise-added data set gives high robustness for SOC estimation

An improved coulomb counting method based on dual open‐circuit voltage and real‐time evaluation of battery dischargeable capacity considering temperature and battery aging

Coulomb Counting (CC) method plays an important role in the state of charge (SOC) estimation theory of lithium-ion batteries, and a lot of improvement and optimization strategies are based on it. With the increasing demand for precise management of lithium-ion battery systems, the performance of the traditional CC method is no longer suitable for more complex working conditions. First, the battery aging, extreme temperature, and high-rate discharging were considered as the main influencing factors which limit the SOC estimation accuracy of the CC method, and the performance degradation mechanism of the traditional CC method under the influence of the above factors are experimentally analyzed, especially the change of battery total dischargeable capacity after aging, and the change rules of key parameters in the CC equation are analyzed. Then the initial SOC and the total dischargeable capacity of the CC method are modified and estimated respectively to realize the accurate estimation of SOC under complex working conditions, especially the accurate SOC estimation during the whole life cycle of lithium-ion batteries. The experimental results show that the improved CC method can effectively deal with complex working conditions, and the comprehensive estimation accuracy of SOC is within 3.6%.

Parameter and State of Charge Estimation Simultaneously for Lithium‐Ion Battery Based on Improved Open Circuit Voltage Estimation Method

Herein, the improved open‐circuit voltage (OCV) estimation method is developed and applied to estimate the model parameters and state of charge (SOC) for lithium‐ion batteries simultaneously. First, the OCV and SOC mapping relationship with temperature dependence is explored with the help of the low‐current OCV test and the improved OCV estimation method is proposed for all test temperatures. Afterward, the dual adaptive extended Kalman filter (DAEKF) based on the residual sequence is utilized to identify the model parameters and estimate the SOC simultaneously. Finally, the proposed approach is verified with 50% initial SOC error and compared with the residual sequence‐based DEKF method at different temperatures under the Federal Urban Driving Schedule (FUDS) test. The results of this study indicate that the proposed DAEKF based on the proposed improving OCV estimation method and residual sequence could achieve higher SOC estimation accuracy with good robustness at all test temperatures.

New Artificial Intelligence Technology Applied in Automobile Lithium Battery Manufacturing

In order to improve the estimation accuracy of the state of charge (SOC) of electric vehicle power batteries, this paper is based on artificial intelligence technology for lithium-ion battery model and parameter identification algorithm, adaptive unscented Kalman filter algorithm and SOC estimation based on battery model fusion Algorithm for research. The simulation results show that the SOC error estimated by the artificial intelligence adaptive Kalman filter method is less than 2.4%, which effectively reduces the impact of unknown interference noise on the battery management system when the electric vehicle is driving. The SOC estimation accuracy is higher than that of the extended Kalman method, and has good robustness.

State estimation based on least square support vector

As one of the important parameters of battery management system (BMS), accurate estimation of the state of charge (SOC) of lithium-ion battery (LIB) can ensure the safety of electric vehicles and improve the utilization rate of batteries. A new SOC estimation algorithm based LSSVM is applied. The battery parameters, including current and voltage, which are used as the inputs to estimate SOC. To promote the accuracy of SOC estimation, the SOC estimated at the previous time is taken as the feedback vector to estimate the SOC at the current time. The experimental results show that the proposed model can improve the estimation accuracy of SOC.