State Of Charge Estimation Research Articles

Towards fast embedded moving horizon state-of-charge estimation for lithium-ion batteries

For state-of-charge (SOC) estimation with high precision, moving horizon estimation (MHE) has recently emerged as a competitive alternative to various Kalman filters or observers due to its significantly improved accuracy and robustness. However, MHE demands considerably higher computational complexity, preventing its deployment on a low-cost embedded microcontroller. To address this challenge, we propose a fast moving horizon SOC estimation algorithm to retain the benefits of MHE at a vastly reduced computational cost. In particular, we consider joint SOC and parameter estimation for an SOC-dependent equivalent circuit model subject to model mismatch. The proposed fast joint MHE (jMHE) algorithm performs a fixed number of Gauss–Newton (GN) iterations to approximate the fully converged solution. At each iteration, the GN Hessian matrix is factorized by exploiting its block tridiagonal structure to construct computationally efficient forward–backward recursions. To further speed up computations, another fast jMHE algorithm wtih an Event-Triggered Relinearization strategy (jMHE-ETR) is proposed to avoid refactorizing the GN Hessian matrix at each iteration. Using experimental datasets under different operating conditions, it is verified on both laptop and Raspberry Pi microcontroller that compared to the conventional optimal MHE solved with an off-the-shelf solver, the proposed fast jMHE and jMHE-ETR algorithms both have a slight loss of performance (still significantly better than extended Kalman filtering) while reducing its computational cost by an order of magnitude.

State-of-charge estimation of lithium-ion battery based on second order resistor-capacitance circuit-PSO-TCN model

Accurate state-of-charge (SOC) estimation of lithium-ion battery is directly related to the reliability, performance, and safety of the battery. In this work, the second order resistor-capacitance (RC) circuit is equivalent to the battery model and the particle swarm optimization (PSO) algorithm is employed for achieving accurate identification of the parameters of circuit model under dynamic stress test (DST) conditions. Furthermore, the values of open circuit voltage (OCV) obtained from the identification results are input into the temporal convolutional network instead of the terminal voltages, and then the SOC of the Li-ion battery is estimated by directly learning the mapping relationship of OCV-SOC curves, which further improves the estimation accuracy and robustness of the proposed method. Finally, the SOC estimation is validated with the public dataset of LiFePO4 batteries under all driving conditions at different temperature and compared with the individual TCN method. Results show that the SOC estimation of the second order resistor-capacitance circuit-PSO-TCN model is optimal with a root mean square error (RMSE) and maximum error (MAXE) less than 1.8% and 7.65%, respectively.

Intelligent Renewable Energy Source Allocation Scheme for Internet of Things Enabled PHEVs Systems

Plug-in hybrid electric vehicles (PHEVs) have received a lot of interest because of their ability to cut fuel usage by using electricity from the grid as an alternative energy source. PHEVs differ from typical hybrid electric vehicles (HEVs) in terms of increased battery capacity, the availability of plug-in recharging, and improved battery state of charge (SOC) management systems. Efficient energy consumption and excellent performance are critical issues for hybrid powertrains. The estimation of SOC in PHEVs is a difficult NP-hard problem that is frequently tackled utilising metaheuristic techniques. In this paper, we offer an enhanced dingo optimisation with deep learning-based prediction (EDOA-DLP) model specifically tailored for PHEVs. The EDOA-DLP model includes an efficient SOC estimate algorithm for real-time energy management. The EDOA-DLP technique's performance has been thoroughly proven through considerable experimentation in a variety of circumstances. The results show that the proposed EDOA-DLP method beats other current methods in terms of predicting SOC accurately and reaching the targeted goals for PHEVs. Overall, this research presents a unique EDOA-DLP SOC prediction approach for PHEVs, with promising results in terms of energy management and performance optimisation. The experimental results highlight the EDOA-DLP model's improved performance. Overall, this research presents a unique EDOA-DLP SOC prediction approach for PHEVs, with promising results in terms of energy management and performance optimisation. The experimental results illustrate the EDOA-DLP model's improved performance when compared to competing methodologies, highlighting its potential to improve the efficiency and efficacy of PHEV systems.

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.

Equivalent circuit modeling and state-of-charge estimation of lithium titanate battery under low ambient pressure

The low ambient pressure during the flight of aircraft has a significant impact on the performance and safety of the onboard power battery. In order to ensure the safe operation of the battery system, it is very important to accurately estimate and manage the state-of-charge (SOC) of the battery. In this work, the equivalent circuit modeling (ECM) of lithium titanate battery (LTB) is studied in detail, and the influence of analog circuit model parameters in low ambient pressures is discussed for the first time. The forgetting factor recursive least square algorithm is introduced to accurately identify the ECM parameters of the LTB under different pressures online. The particle swarm optimization algorithm is innovatively proposed to optimize the covariance matrix of the Kalman filter algorithm. The verification shows that the root mean square error of the ECM of LTB under different ambient pressures is less than 0.025. In the SOC estimation process, the noise covariance matrixes of the extended Kalman filter and the unscented Kalman filter are optimized by the particle swarm algorithm. The optimized SOC estimation absolute error is less than 3 %, especially at 96 kPa and 30 kPa, where the absolute error is less than 2 %.

Co-estimation of maximum available capacity and state-of-charge for lithium-ion batteries in multi-operating mode with temperature and degradation state adaptivity

Accurate state of charge (SOC) estimation is critical for battery management systems (BMS). A new SOC estimation framework is developed, containing four modules: battery modeling, parameter identification, SOC estimation, and capacity estimation. It mainly makes three improvements to improve the adaptability. In the parameter identification module, an improved forgetting factor parameters identification method is proposed to obtain model parameters with high precision. For SOC estimation, considering the impact of noise on SOC estimation, an adaptive square root unscented Kalman filter is proposed, which can solve the divergence issue caused by inappropriate noise matrix iteration. Moreover, a weighted recursive least squares algorithm is developed to estimate the maximum available capacity and feed the result back into the SOC estimation module to improve the estimation accuracy. The experimental results show that the proposed framework can obtain high-precision SOC estimation results under different temperatures and aging conditions.

A Novel Redacted Extended Kalman Filter and Fuzzy Logic-Based Technique for Measurement of State-of-Charge of Lithium-Ion Battery

Abstract This paper presents a novel technique based on an adaptive approach of redacted extended Kalman filter (REKF) assimilating fuzzy logic features for measuring the state-of-charge (SoC) of lithium-ion batteries. Accurately determining SoC is crucial for maximizing battery capacity and performance. However, existing extended Kalman filtering algorithms suffer from issues such as inadequate noise resistance and noise sensitivity, as well as difficulties in selecting the forgetting factor. The aforementioned REKF technique addresses these challenges adequately for accurate measurement of SoC. The proposed method involves establishing a Thevenin equivalent circuit model and using the recursive least squares with forgetting factor (RLSFF) to identify model parameters. Furthermore, an evaluation factor is established, and to adaptively adjust the value of the forgetting factor, fuzzy control is utilized, which enhances the extended Kalman filtering algorithm with noise adaptive algorithm features to estimate the SoC accurately. This modified algorithm considers the identification results from the parameter estimation step and executes them circularly to achieve precise SoC estimation. Results demonstrate that the proposed method has excellent robustness and estimation accuracy compared to other filtering algorithms, even under variable working conditions, including a wide range of state-of-health (SOH) and temperature. The proposed method is expected to enhance the performance of battery management systems for various applications.

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.

State of charge estimation of lithium-titanate battery based on multi-model extended Kalman filter considering temperature and current rate

To tackle the issue of accurately estimating the state of charge (SOC) of lithium-titanate (Li-Ti) batteries in complex vehicle applications, a multi-model extended Kalman filter (MM-EKF) algorithm considering the effects of temperature and current rate is proposed. Based on the operational characteristics of Li-Ti batteries in the context of electric vehicle applications, second-order RC equivalent circuit models (ECMs) are established to account for the temperature and current rate influences. Model parameters are identified using an adaptive recursive least squares method with a forgetting factor based on experimental data. Subsequently, a SOC estimation method based on the MM-EKF algorithm for Li-Ti batteries is proposed and its effectiveness is validated under different ambient temperatures. Experimental results demonstrate that the MM-EKF algorithm, which considers the effects of temperature and current rate, can accurately estimate the SOC of Li-Ti batteries. The maximum estimation error is within 5 % at different ambient temperatures, and the algorithm can quickly eliminate initial SOC errors. Consequently, it fulfills the requirements for SOC estimation of hybrid tracked vehicles in intricate operating conditions.

Lithium-Ion Battery State of Charge Estimation With Adaptability to Changing Conditions

Accurate state of charge (SOC) estimation provides critical information to ensure the safe operation of lithium-ion batteries (LIBs). With the evolution of artificial intelligence, the model-free deep learning-based SOC estimation has made extraordinary progress. However, collecting sufficient data to train an accurate SOC estimator of batteries' whole lifecycle is costly, and generalizing the estimator to different operating conditions is challenging. To this end, aiming to enhance the generalization ability of data-driven SOC estimators, this paper proposes a novel SOC estimation framework based on adversarial transfer learning (TL), which transfers a well-trained SOC estimator with fewer data demands to fit different conditions. Specifically, a source SOC estimator is trained under a specific condition to learn the basic characteristics of the battery, which is defined as the source domain. Target domains correspond to measured data of the battery under different conditions. An adversarial TL-based training framework is developed to extract the domain invariants of the source and target domains, which is guided by minimizing the distribution discrepancies. The effectiveness of the proposed method is demonstrated through the use of two LIBs datasets. The successful generalization to multiple operating conditions and aging health states demonstrates the estimation accuracy, robustness, and good generalization.

Differential current in constant-voltage charging mode: A novel tool for state-of-health and state-of-charge estimation of lithium-ion batteries

Compared with extensive discussions on constant current (CC) charging for lithium-ion batteries, the probe into constant voltage (CV) charging is currently insufficient. Analogous to the differential analysis of the voltage curve in CC charging, this paper introduces the differential current curve (dQ/dI curve) in CV charging and uses it as the feature to identify battery states. The differential curve is qualitatively interpreted with an equivalent circuit model, and the relationship between the dQ/dI value and the battery states is fitted with the Gaussian process regression (GPR) model. With a total of 4836 sets of CV charging data, an excellent state of health (SOH) estimation with a mean absolute error (MAE) of 0.18 % can be achieved by using the first 190 data points of the dQ/dI curve as the model input. For state of charge (SOC) estimation, a brand-new experimental work is introduced by adjusting the cutoff voltage of the previous CC charging to generate a benchmark database illustrating the relation between the SOC value at the initial CV charging and the subsequent current curve. Through GPR, the SOC prediction MAE is reduced to about 0.88 %, which confirms that the dQ/dI curve is a promising candidate for battery state estimation.

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.

The Elastic Net Regularized Extreme Learning Machine for State of Charge Estimation

The state of charge (SOC) is a crucial component of battery management, and the reliability of its assessment is crucial for predicting battery life. In this paper, an elastic net regularized extreme learning machine is developed for SOC estimation. Unlike traditional neural networks, the extreme learning machine does not require updating all the weights/parameters of the network to obtain accurate SOC estimates, thus, it has a simpler structure. In addition, the elastic net regularization combining the L1 regularization and L2 regularization, can better describe the relationship between current, voltage and SOC. The simulation results show the effectiveness of the proposed method.

Hybrid energy-temperature method (HETM): A low-cost apparatus and reliable method for estimating the thermal capacity of solid–liquid phase change material for heat storage system

Estimating the total thermal capacity for phase change material (PCM) as heat storage material is extremely important to set the proper operational parameter of the latent storage tank (LST) unit. However, estimating the total thermal capacity for solid–liquid PCM is relatively complex due to temperature-dependent properties for each phase. Thus, predicting the state of charge (SoC) indicator for the LST unit is technically complex. The common approach is taken by estimating the heat of fusion during the melting process and monitoring the working fluid temperature, which makes the SoC estimation less accurate. The present project proposes a reliable method with an affordable apparatus to estimate the total thermal capacity simultaneously based on the temperature of low-temperature PCM. Moreover, sensible heating during phase transition is also estimated precisely based on the energy balance at a given temperature. The developed apparatus employs widely available components at an affordable cost which is possible for further customization. Validation and characterization are done comprehensibly by comparing the measurement from differential scanning calorimetry and previous studies. The results indicate a suitable estimation for estimating the solid–liquid heat capacity, including partial heat capacity and latent heat of fusion.

Estimation of Battery State of Charge Based on Electrochemical Impedance Spectroscopy and Machine Learning

With the increasing application of lithium-ion batteries in energy storage (ES) and electric vehicles (EV), the operation state and the safety early warning are particularly important. Due to the complexity of lithium-ion batteries, predicting the state of charge (SOC) of batteries is still a great challenge. In this paper, an electrochemical impedance spectroscopy (EIS) based on the SOC estimation method was proposed. The EIS of different SOC under 25℃ was measured, and the variation characteristics of EIS were summarized from the aspects of amplitude and phase by using the full band information. Finally, the linear system and BP neural network model were constructed by selecting the characteristic parameters at a specific frequency. The results demonstrate that the prediction effect of the BP neural network is better, and the error is found to be less than 3%.

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.

A novel integrated SOC–SOH estimation framework for whole-life-cycle lithium-ion batteries

Accurate estimating the state of health (SOH) and state of charge (SOC) is crucial for ensuring the reliable and safe operation of lithium-ion batteries. Traditional methods for the joint estimation of SOC and SOH typically rely on separate models, resulting in a decoupling of their relationship. Moreover, the current convolutional and recurrent-based deep models overlook the inherent connection between local features and global temporal features. These limitations not only hinder the extraction of combined feature information relevant to SOC and SOH during the charging process, but also increase computational complexity and diminish estimation accuracy. To solve these problems, this study proposes a novel SOC–SOH Estimation Framework (SSEF). The framework achieves parameter sharing by segmented training, effectively accounting for the intrinsic coupling between SOC and SOH. This enables a unified joint estimation of the two variables, leading to a substantial enhancement in efficiency. Additionally, a novel charging encoder that alternates between Temporal Convolutional Network and Bidirectional Gated Recurrent Unit is designed. It captures local temporal information and long-term dependencies related to SOC and SOH during charging. SSEF enables precise SOC and SOH estimation for whole-life-cycle lithium-ion batteries, enhancing accuracy and efficiency compared to prevalent methods.