Second-order RC Equivalent Circuit Research Articles

Estimation of Lithium-Ion Battery SOC Based on IFFRLS-IMMUKF

The state of charge (SOC) is a characteristic parameter that indicates the remaining capacity of electric vehicle batteries. It plays a significant role in determining driving range, ensuring operational safety, and extending the service life of battery energy storage systems. Accurate SOC estimation can ensure the safety and reliability of vehicles. To tackle the challenge of precise SOC estimation in complex environments, this study introduces an improved forgetting factor recursive least squares (IFFRLS) method, which integrates the Golden Jackal optimization (GJO) algorithm with the traditional FFRLS method. This integration is grounded in the formulation of a lithium battery state equation derived from a second-order RC equivalent circuit model. Additionally, the research utilizes the interactive multiple model unscented Kalman filter (IMMUKF) algorithm for SOC estimation, with experimental validation conducted under various conditions, including hybrid pulse power characterization (HPPC), urban dynamometer driving schedule (UDDS), and real underwater scenarios. The experimental results demonstrate that the SOC estimation method of lithium batteries based on IFFRLS-IMMUKF exhibits high accuracy and a favorable temperature applicability range.

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

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

Study on Second-order RC Model Charge State Estimation Method for Lithium Battery Based on EKF Algorithm

In order to improve the estimation accuracy of the state of charge (SOC) of lithium-ion batteries, this paper proposes a SOC estimation method based on the second-order RC equivalent circuit model and the extended Kalman filter (EKF) algorithm. Firstly, the second-order RC equivalent circuit model is selected as the research object in this paper, and the parameters of the second-order RC model are identified by combining the hybrid pulse charging and discharging test and the 1stopt software, and then the extended Kalman filtering algorithm is applied under the MATLAB environment to estimate the SOC based on the second-order RC equivalent circuit model. The simulation results show that the adopted estimation method can accurately track the SOC trend of the battery compared with the actual state-of-charge (SOC) reference value. Through experimental analysis, the estimation results of the EKF algorithm combined with the second-order RC equivalent circuit model have a small error with the actual value, and the estimation accuracy is high and ideal.

Enhanced Second-Order RC Equivalent Circuit Model with Hybrid Offline–Online Parameter Identification for Accurate SoC Estimation in Electric Vehicles under Varying Temperature Conditions

Accurate estimation of State-of-Charge (SoC) is essential for ensuring the safe and efficient operation of electric vehicles (EVs). Currently, second-order RC equivalent circuit models do not account for the influence of battery charging and discharging states on battery parameters. Additionally, offline parameter identification becomes inaccurate as the battery ages. Online identification requires real-time parameter updates during the SoC estimation process, which increases the computational complexity and reduces the computational efficiency of real vehicle Battery Management System (BMS) chips. To address these issues, this paper proposes a SoC estimation method that combines online and offline identification based on an optimized second-order RC equivalent circuit model, which distinguishes it from existing methods in the field. On the basis of the traditional second-order RC model, the Ohmic resistance (R0), polarization resistance (R1), polarization capacitance (C1), diffusion resistance (R2), and diffusion capacitance (C2) during the charging and discharging processes are discussed separately. R0, which does not change frequently, is identified offline, while R1, R2, C1, and C2, which dynamically change with time and current, are identified online. To thoroughly verify the feasibility of the proposed method, we construct an SoC estimation test bench, which allows us to adjust the battery’s surface temperature in real time using a temperature control chamber. Experimental validation under Federal Urban Driving Schedule (FUDS) (−10 °C to 45 °C, 80% battery capacity) and Dynamic Stress Test (DST) (−10 °C to 45 °C, 8% battery capacity) conditions demonstrate that our method improves SoC estimation accuracy by 16.28% under FUDS and 28.2% under DST compared to the improved GRU-based transfer learning method, while maintaining system SoC estimation efficiency.

Lithium battery state of charge estimation based on improved variable forgetting factor recursive least squares method and adaptive Kalman filter joint algorithm

As one of the core functions of the battery management system, battery state of charge (SOC) estimation is crucial to battery life and safety. As the traditional recursive least squares method cannot adapt well to complex variable current conditions, this paper proposes a SOC estimation method that combines the improved variable forgetting factor recursive least squares (IVFFRLS) and the adaptive extended Kalman filter (AEKF). First, IVFFRLS removes the rounding operation of the original algorithm to improve the sensitivity to errors and uses a genetic algorithm to optimize the upper and lower bounds of the variable forgetting factor and the sensitivity coefficient to improve the accuracy of the VFFRLS algorithm. Meanwhile, AEKF introduces a noise covariance adaptive update link based on the covariance matching method to correct the system's process noise Q and measurement noise R in real time to improve the SOC estimation accuracy. Based on the second-order RC equivalent circuit model, the method proposed in this paper has good accuracy and robustness under four different working conditions. The experimental results show that compared with traditional methods, the proposed IVFFRLS-AEKF algorithm has higher SOC estimation accuracy and better robustness.

A hybrid model for state of charge estimation of lithium-ion batteries utilizing improved adaptive extended Kalman filter and long short-term memory neural network

With lithium-ion batteries being utilized in all aspects of life, accurately estimating the state of charge (SOC) of a battery has become a key issue in battery management systems. In this paper, an improved hybrid model based on adaptive extended Kalman filter (AEKF) and improved long short-term memory (ILSTM) neural network is proposed. The proposed model is based on a second-order RC equivalent circuit model, and the dynamic forgetting factor recursive least squares (DFFRLS) and AEKF algorithms are utilized to obtain the initial SOC estimates. And the estimation error in the AEKF algorithm due to neglecting the higher order terms of the Taylor expansion equations is compensated by the improvement of the LSTM network. The results under different working conditions indicate that the SOC estimation of the hybrid model has good convergence and high system robustness. The maximum error (MAX) of this algorithm is less than 2.3 %, especially the root mean square error (RMSE) and mean absolute error (MAE) are less than 0.84 % and 0.65 %, respectively.

A Li-Ion Battery State of Charge Estimation Strategy Based on the Suboptimal Multiple Fading Factor Extended Kalman Filter Algorithm

The state of charge (SOC) is an important indicator for evaluating a battery management system (BMS), which is crucial for the reliability, performance, and life management of a battery. In this paper, the characteristics of a Li-ion battery are deeply studied to explore the charge/discharge curve under different environments. Meanwhile, a second-order RC equivalent circuit model is constructed. The function identification of the EMF and SOC is performed based on the least squares method. The model estimation error is verified by simulation to be less than 0.05 V. Based on the Suboptimal Multiple Fading Factor Extended Kalman Filter (SMFEKF) algorithm, the SOC under constant current and UDDS conditions are estimated. Matlab/simulink simulations illustrate that the estimated accuracy of the proposed algorithm is improved by 79.36% compared with the EKF algorithm. Finally, the validity of the algorithm is verified jointly with the BMS. The results show that the estimation error is within 4% in both constant current condition as well as UDDS conditions, and it can still be predicted quickly and accurately under the uncertainty in the initial value of the SOC.

Lithium-ion point-of-care ultrasound battery joint state of charge estimation

With recent advances in ultrasound technology, including accessibility and portability, point-of-care ultrasound systems (POCUS) are becoming ubiquitous in urban and rural health services. The efficient use of POCUS battery power is necessary due to the limited access to electricity in rural locations. Accurate estimation of the state-of-charge (SOC) of the onboard lithium-ion battery is crucial in ensuring the safe, efficient, and reliable operation of the battery management system (BMS). This research suggests a novel approach for striking a reasonable balance between the POCUS battery management systems computation time and SOC estimate accuracy. Given that the lithium-ion battery is a non-linear and time-varying system, it is modelled by a second-order RC equivalent circuit model (2-RC ECM). Real-time parametric identification is carried out using the method of recursive least squares with respect to an adaptive forgetting factor (AFFRLS). The joint SOC evaluation technique, ordering the results of real-time identification and the Extended Kalman Filter (EKF) recommended for estimating battery SOC at temperatures between 0 and 45 °C. Simulations were carried out using experimental data from the DST (Dynamic Stress Test), incremental current and, the Federal Urban Driving Program (FUDS) of the CALCE research group to evaluate the proposed approach. Based on the monitoring of dynamic changes in model parameters and the computational complexity of existing algorithms, the results reveal that the joint AFFRLS-EKF estimation proposed for the SOC strategy achieves good accuracy, high adaptability and rapid convergence of SOC estimation.

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

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

Combing dynamic parameter identification and singular value decomposition adaptive unscented Kalman filter for predictive state of charge of lithium-ion batteries

The development of a secure battery management system (BMS) for electric vehicles depends heavily on the correct assessment of the online state-of-charge (SOC) of Li-ion batteries. The ternary lithium battery is used as the research object in this paper, and a second-order RC equivalent circuit model is developed to characterize the dynamic operating characteristics of the battery. In order to solve the problem that the adaptive unscented Kalman filter (AUKF) algorithm is easy to fail SOC estimation because the error covariance matrix is not positively definite due to the incomplete accuracy of the equivalent circuit model, a corresponding solution is proposed. Considering the poor real-time battery SOC estimate caused by the battery model’s fixed parameters, therefore we propose the Variable Forgetting Factor Recursive Least Squares (VFFRLS) algorithm for joint estimation of Li-battery SOC and the Singular Value Decomposition-AUKF (SVD-AUKF) algorithm. The SVD-AUKF algorithm can accurately estimate the SOC of the battery when the error covariance is negative. The algorithm can be adaptively adjusted in both the parameter identification and SOC estimation stages, which can effectively solve the problem of poor estimation accuracy caused by fixed parameters. According to experiments, under two separate dynamic operating situations, the joint estimation algorithm’s error is less than 2%, and its stability has also been greatly enhanced. At the same time, when the initial SOC value is set incorrectly, the convergence time of the algorithm proposed in this paper can reach within 2.1 seconds for BBDST and DST conditions, which can be well adapted to complex working conditions.

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.

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.

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 and error analysis of lithium-ion batteries for electric vehicles using Kalman filter and deep neural network

The lithium-ion battery has a great significance in meeting the growing demand for Electric Vehicles (EVs) due to its higher energy density, longer life cycle, and notable nominal voltage and capacity. One crucial parameter for lithium-ion batteries is the State of Charge (SOC), which represents the available capacity and ensures that the system operates in a secure and reliable mode for EVs. SOC plays a significant role in the Battery Management System (BMS). This research aims to propose an Equivalent Circuit Model (ECM) based on Kalman filtering method and a data-driven technique, Deep Feed-Forward Neural Network (DFNN), for accurate SOC estimation of Electric Vehicle Battery (EVB). Initially, lithium-ion battery parameters are identified using a second-order RC (2-RC) Equivalent Circuit Model (ECM). Subsequently, battery modeling is performed, and various operating conditions such as terminal voltage, load current, and temperature are measured to obtain initial values for the filtering method used in SOC estimation. These operating conditions are crucial for ensuring safe and efficient charging and discharging of lithium-ion batteries. Based on the identified ECM parameters, SOC estimation error and bound error are then minimized using Kalman Filter (KF), Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF) techniques. These filtering methods are employed to accurately estimate the SOC of the battery. The results demonstrate that the proposed model based on KF and EKF algorithms estimates SOC bound error within 2.5 % - –2 % and estimation error <1.5 % - –0.7 %. On the other hand, the UKF estimates a SOC bound error of 1.5 % and an estimation error of 0.5 %, proving the algorithm's efficiency and reliability. Particularly, this estimation error rejects measurement noise and parametric uncertainties for lithium-ion batteries to drive EVs with efficacy using UKF. Hence, the UKF algorithm estimated SOC has low estimation error, ensuring more accurate results. Finally, data-driven, DFNN method is implemented for accuracy enhancement of SOC estimation with trained 20 iterations and epochs data. Using this method, the SOC estimation accuracy is satisfactory with only 0.04 % Root Mean Squared Error (RMSE). The validation results indicate that the model-based filtering method is an effective method for SOC estimation to be applicable. In contrast, in a novel data-driven approach, SOC estimation accuracy is improved by approximately 0.46 %.

An Improved Comprehensive Learning - Particle Swarm Optimization - Extended Kalman Filtering Method for the Online High-Precision State of Charge and Model Parameter Co-Estimation of Lithium-Ion Batteries

The precise assessment of the state of charge (SOC) of lithium-ion batteries (LIBs) is critical in battery management systems. This work offers a comprehensive learning particle swarm optimization (CLPSO) and extended Kalman filter (EKF) technique to forecast the SOC of LIBs in order to obtain an accurate SOC estimate for power batteries. Firstly, to address the challenge of identifying various parameters of the battery model, the bilinear transformation technique is employed to determine the parameters of the second-order RC equivalent circuit model. Secondly, to improve the fitness values for the conventional PSO algorithm, which is prone to entering local optimality, a learning strategy () is added to the particle velocity update method. The optimized PSO and EKF algorithms are integrated to perform online prediction of the SOC of LIBs. The experimental results demonstrate that under the conditions of the Beijing Bus Dynamic Stress Test (BBDST), Dynamic Stress Test (DST), and Hybrid Pulse Power Characterization Test (HPPC), the parameter identification inaccuracy of CLPSO is restricted to 1%. After multi-metric evaluation, the maximum error and mean absolute error of the CLPSO-EKF algorithm in SOC estimation are 0.32% and 0.0652%, respectively, demonstrating a higher robustness and accuracy advantage over other versions.

Research on Multi-Time Scale SOP Estimation of Lithium–Ion Battery Based on H∞ Filter

Battery state of power (SOP) estimation is an important parameter index for electric vehicles to improve battery utilization efficiency and maximize battery safety. Most of the current studies on the SOP estimation of lithium–ion batteries consider only a single constraint and rarely pay attention to the estimation of battery state on different time scales, which can reduce the accuracy of SOP estimation and even cause safety problems. In view of this, this paper proposes a multi-time scale and multi-constraint SOP estimation method for lithium–ion batteries based on H∞ filtering. Firstly, a second-order RC equivalent circuit model is established with a ternary lithium–ion monolithic battery as the research object, and parameter identification is performed by using the recursive least squares method with a forgetting factor. Secondly, the H∞ filtering algorithm is applied to estimate the state of charge (SOC), and then the joint multi-time scale multi-constrained SOC-SOP estimation is performed. Finally, the joint estimation algorithm is validated under UDDS conditions. The mean absolute value relative error (MARE) of SOC estimation is 1.17%, and the MARE of SOP estimation at different time scales is less than 1.6%. The results indicate the high accuracy and strong robustness of the joint estimation method.

Parameter Identification Model and Capacity Analysis of Retired Power Battery

The accuracy and connection mode of the equivalent model of retired power battery cells will affect the size of the combined capacity. To this end, this article analyzes series-parallel combination capacity of retired power batteries. First, because an accurate single equivalent circuit model of retired power batteries is necessary for the capacity analysis of the combination, the forgetting factor recursive least squares (FFRLS) algorithm is used to identify the parameters of the model, and the second-order RC equivalent circuit is selected as the single equivalent circuit model of retired power battery. Then the equivalent circuit model is used as the basis, respectively constructing first-parallel-before-series and first-series-before-parallel power battery combination, and fully and unequally arranged the retired power batteries under the two assemblies. Finally, the capacity and distribution characteristics of the two combinations under different arrangements are verified by simulation. The results show that no matter how the arrangement is changed, the maximum capacity of the first-parallel-before-series retired power battery combination is always better than the first-series-before-parallel combination, and the distribution position of the single retired battery in both combinations under the maximum combination capacity is obtained.

Study on SOC Estimation of Li-ion Battery Based on the Comparison of UKF Algorithm and AUKF Algorithm

In this study, a state of charge (SOC) estimate technique for lithium-ion batteries is presented using an adaptive traceless Kalman filter (AUKF). First, the battery’s second-order RC equivalent circuit model is created, and its parameters are identified. Next, in contrast to the traceless Kalman filter (UKF) algorithm, which ignores the time-varying characteristics of the system noise when estimating the lithium-ion battery’s state of charge, the AUKF-based SOC estimation method is formed from the perspective of adaptive noise adjustment (SOC). The results of testing the AUKF algorithm in real-world settings demonstrate that it has great estimate accuracy and stability and that its estimation outcomes outperform those of the UKF method.

State of Charge Estimation for Power Battery Base on Improved Particle Filter

In this paper, an improved particle filter (Improved Particle Swarm Optimized Particle Filter, IPSO-PF) algorithm is proposed to estimate the state of charge (SOC) of lithium-ion batteries. It solves the problem of inaccurate posterior estimation due to particle degradation. The algorithm divides the particle population into three parts and designs different updating methods to realize self-variation and mutual learning of particles, which effectively promotes global development and avoids falling into local optimum. Firstly, a second-order RC equivalent circuit model is established. Secondly, the model parameters are identified by the particle swarm optimization algorithm. Finally, the proposed algorithm is verified under four different driving conditions. The results show that the root mean square error (RMSE) of the proposed algorithm is within 0.4% under different driving conditions, and the maximum error (ME) is less than 1%, showing good generalization. Compared with the EKF, PF, and PSO-PF algorithms, the IPSO-PF algorithm significantly improves the estimation accuracy of SOC, which verifies the superiority of the proposed algorithm.

State of Charge Estimation of Lithium-Ion Batteries Based on an Improved Sage-Husa Extended Kalman Filter Algorithm

An improved Sage-Husa extended Kalman filter (SHEKF) algorithm is intended to improve the accuracy and stability of SOC prediction. In this paper, two different exponential weighting algorithms are used to adaptively select the forgetting factor for adaptive noise estimation. Moreover, the OCV-SOC curve is obtained using a 7-segment linear fitting method before the algorithms estimate the SOC. In addition, by combining this improved method with a third-order RC equivalent circuit model in the dynamic stress test (DST) case the convergence time is reduced by 0.15 s compared to the second-order RC equivalent circuit model. Following that, four different types of comparison experiments are carried out by comparing the improved algorithm to EKF and other SHEKF algorithms.The estimation accuracy under DST conditions of 0 °C, 25 °C and 45 °C is approximately 0.5%, 2.2% and 1.3% improvement compared to the EKF algorithm.