State Of Charge Estimation Algorithm Research Articles

A novel adaptive unscented kalman filter algorithm for SOC estimation to reduce the sensitivity of attenuation coefficient

A new exponential adaptive strong tracking unscented Kalman filtering algorithm (ASTRUKF) is proposed to address the issues of slow tracking speed, untimely response of model parameter changes, and inaccurate noise statistical characteristics when estimating the State of Charge (SOC) of batteries at different temperatures, in order to reduce the sensitivity of attenuation coefficients. This algorithm improves upon the traditional method of calculating attenuation factor by incorporating the correlation between current and past residuals. It dynamically updates the Kalman gain and contribution rate using an exponential model, which increases the impact of current data. This algorithm also ensures the stability of the noise covariance matrix by stabilizing the attenuation factor within a fixed range. The contribution rate is utilized to estimate the statistical characteristics of detection noise, however it may exhibit bias. The ASTRUKF method exhibits a maximum estimation error of 10−8 at 0 °C and 10−12 at 15 and 25 °C. This value is well below the levels of the UKF and EKF algorithms. The ASTRUKF algorithm outperforms the UKF and EKF algorithms in terms of prediction accuracy at different temperatures. The ASTRUKF method is well-suited for estimating SOC and has excellent adaptability to temperature variations.

An improved electrochemical equivalent circuit model and precise state-of-charge estimation comparative study for lithium-rich manganese-based battery

State-of-charge (SOC) serves as a crucial metric for lithium-ion batteries. A precise battery model is an essential factor influencing the accuracy of SOC estimation. Notably, lithium-rich manganese-based (LRMB) layered oxide batteries exhibit distinct voltage characteristics that differentiate them from other battery types. Experimental findings reveal that traditional equivalent circuit models (ECMs) are not well-suited for capturing the behavior of LRMB batteries. To address the aforementioned problem and its attendant phenomenon of large SOC estimation error, in this paper, we proposed an improved electrochemical equivalent circuit model (IEECM) for LRMB batteries that concurrently enhances accuracy and mitigates error. The proposed model comprehensively accounts for the long-term diffusion process of lithium ions within the solid phase, thereby offering a more precise representation of the battery's behavior. The results indicate that under different operating conditions, the RMSE of voltage error remains below 31.3 mV. Notably, under UDDS conditions, the MAE and RMSE are merely 15.1 mV and 20.6 mV, respectively. To further validate its effectiveness, we utilize three common SOC estimation algorithms under various operation conditions. Experimental results show that the RMSEs of SOC estimation based on the proposed model under different algorithms are lower than 2.21 %, which is better than ECMs. Consistently, our findings indicate that this model is particularly well-suited for LRMB batteries, leading to a notable enhancement in SOC estimation accuracy.

Multi-Cell-to-Multi-Cell active equalization method based on k-means clustering and battery pack SOC estimation

In this paper, a MC2MC (Multi-Cell-to-Multi-Cell) battery pack active equalization scheme based on reconfigurable circuits and Buck-Boost converters is proposed and validated for the problem of inconsistent single cell power in battery packs. This scheme can simultaneously equalize multiple non-adjacent cells in a single equalization process, improving the equalization time efficiency. Then, based on the relationship between duty cycle and voltage difference, the MC2MC battery pack active equalization control strategy based on adaptive duty cycle is designed. In addition, a k-means based clustering algorithm is used to cluster and reorganize batteries with different charges, and the SOC (State of charge) estimation algorithm of the battery pack is improved and introduced into the equalization control among multiple batteries. Finally, AC2AC (Any-Cell-to-any -Cell), MC2MC, and MC2MC simulations considering the SOC estimation of the battery pack are validated and analyzed for the unbalanced battery packs under MATLAB/Simulink environment, respectively. On the basis of verifying the accuracy of the simulation process, the effectiveness of the MC2MC equalization control method considering the SOC estimation of the battery pack is verified through the comparative analysis of four aspects, namely, equalization time, computational workload, resultant variance, and energy efficiency.

An improved Cauchy robust correction-sage Husa extended Kalman filtering algorithm for high-precision SOC estimation of Lithium-ion batteries in new energy vehicles

The accurate estimation of battery State of Charge (SOC) is a key technology in the research of electric vehicle battery management systems. In order to solve the problem of inaccurate noise estimation in nonlinear systems, an improved Cauchy robust correction-Sage Husa extended Kalman filtering (CRC-SHEKF) algorithm is proposed for high-precision SOC estimation of lithium-ion batteries in new energy vehicles. Considering the polarization effect of the battery, the FFRLS algorithm is used for online parameter identification of the Dual Polarization model. Using robust data correction methods, the Cauchy robust function is simplified for real-time correction of the covariance matrix Q of system state noise and the covariance matrix R of the observed noise in the filtering process and combined with SHEKF for SOC estimation. The experimental results show that under different temperature conditions and complex working conditions, the proposed CRC-SHEKF algorithm has the minimum mean absolute error (MAE), root mean square error (RMSE), and maximum error (MAX). Under the condition of the Beijing bus dynamic stress test (BBDST) at 15 °C, the MAE, RMSE, and MAX of the CRC-SHEKF algorithm are 0.392 %, 0.716 %, and 0.945 %, with the computing time of only 4.839 s. The algorithm proposed in this article has high accuracy and robustness, and has practical application value, providing a reference for the application of lithium battery condition monitoring.

Battery multi-time scale fractional-order modeling method for state of charge estimation adaptive to full parameters updating

The fractional-order theory has been successfully applied to battery modeling and state of charge (SOC) estimation thanks to the rapid development of smart energy storage and electric vehicles. The fractional-order model (FOM) has high nonlinearity, which makes it difficult to identify the parameters of the FOM, especially the online identification of the order. Aiming at the problem of parameter identification and SOC estimation of the FOM of battery, a multi-time scale fractional-order modeling method is proposed in this paper. Then, a multi-time scale parameter identification strategy based on feature separation is proposed, and two sub-filters are used to complete the online identification of parameters. Finally, a fractional-order multi-innovation unscented Kalman filtering (FO-MI-UKF) algorithm is proposed for SOC estimation to utilize the value of historical information better. Under dynamic stress test (DST) and Beijing bus dynamic stress test conditions (BBDST), compared with the single-time scale parameter identification algorithm and the single-innovation SOC estimation algorithm, the root mean square error of the estimation results is reduced by 13.3 % and 8.7 %, respectively. The experimental results verify the effectiveness of the modeling method and provide a new idea for fractional-order modeling.

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.

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 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.

State of charge estimation for Lithium-Ion battery cell considering the influence of aging parameters and operating temperature

This article presents a state of charge (SoC) estimation for Lithium-Ion batteries (LiB) based on first-order equivalent circuit model (ECM) that takes into account the aging parameters and operating temperature of the cell. First, the first-order ECM of the cell is proposed considering parameters of the aging process including state of health (SoH) solid electrolyte interphase (SEI) layer resistance, and charge transfer resistance. The parameters of this equivalent circuit model are established for a new cell at different operating temperatures. The model's physical parameters are identified based on experimental data from specific discharge/charge scenarios. Based on the ECM proposed, the SoC estimation algorithm for battery cells using the principle of Sigma Point Kalman Filter (SPKF) filter is applied. The use of the SPKF filter allows for consideration of the non-linearity of the relationship between open circuit voltage and SoC in the model. The parameters describing the cell aging process used in ECM permit representation more accurate of the dynamics of the cell change during operation. The estimated SoC for aged cells corresponding to different SoH values shows that the amount of SoC increase during constant-current charging, full-charging time, and average SoC increase rate during charging depend strongly the aging of the cell. SoC estimation results considering SoH will achieve higher accuracy, especially for cells used in practical applications.

Hydrostatic pressure adaptive dual-polarized model for state of charge estimation of lithium-ion batteries

Pressure-tolerated lithium-ion batteries have been used in autonomous underwater vehicle (AUV), due to their ability to withstand pressure directly and save structural parts that protect itself. As an important component of the battery, state of charge (SOC) is critical for evaluating the reliable operation of AUV batteries. The influence of hydrostatic pressure is not considered in typical SOC estimation process, which leads to a large deviation of terminal voltage estimation, and finally the accurate estimation of SOC cannot be realized. In this paper, a dual-polarized equivalent circuit model dependent on hydrostatic pressure is established, which fully considers the influence of pressure on the internal characteristic parameters of the battery. The characteristic parameters in the equivalent circuit model are measured at hydrostatic pressure and identified by forgetting factor recursive least squares (FFRLS). Compared with the blank model without considering hydrostatic pressure, the proposed model can capture voltage and SOC, which can contribute to the estimation accuracy of terminal voltage in a wide pressure range. The typical algorithms of unscented Kalman filter (UKF), cubature Kalman filter (CKF) and adaptive cubature Kalman filter (ACKF) are used to estimate the SOC based on the two models (OCV-SOC-Pressure and OCV-SOC) at different hydrostatic pressures. The results show that the accuracy of the SOC estimation algorithm under different hydrostatic pressure environments is improved, which is attributed to the compensation correction of the original OCV-SOC model. The root mean square error (RMSE) value of the ACKF algorithm based on the hydrostatic pressure adaptive multivariate regression model is 0.94 %, which significantly improves the SOC estimation effectiveness of the OCV-SOC model without considering the pressure factor (RMSE is 7.36 %) at the hydrostatic pressure of 60 MPa. At the preset different SOC initial values, the three algorithms based on the hydrostatic pressure adaptive multivariate regression model can achieve fast convergence, and ACKF shows the best environmental adaptability.

VLSI design and FPGA implementation of state-of-charge and state-of-health estimation for electric vehicle battery management systems

State of charge (SOC) and state of health (SOH) estimation is an important function in electric-vehicle (EV) battery-management systems (BMSs). SOC and SOH are the principal parameters for judging a battery’s state and critical for ensuring its safety and performance. In a conventional EV BMS, SOC and SOH estimation is performed on the master. However, owing to the increasing number of battery cells and computational cost of estimation algorithms, hardware-oriented processing for each single-battery module on the slave is being researched to reduce the master’s burden. Accordingly, this paper describes the hardware-optimized algorithm, VLSI design, and field-programmable gate array (FPGA) implementation verification results of an application-specific integrated circuit in a slave module to estimate SOC and SOH for multiple cells. We introduce an SOC and SOH estimation algorithm with 70% complexity reduction within a 2% error margin based on each cell’s voltage, current, and temperature and design a hardware block and logic circuit to implement the algorithm. An FPGA was utilized to verify the designed logic circuit, revealing a performance time of 0.65μs at 100 MHz. Finally, an FPGA testbed connected to a real battery and analog-front-end board was built to check the real-time performance through a graphical user interface.

Optimized EKF algorithm using TSO-BP neural network for lithium battery state of charge estimation

The BP neural network can effectively improve the accuracy of state of charge (SOC) estimation by the EKF algorithm. However, the BP neural network is strongly influenced by the initial weights and thresholds, which limits its application in the SOC estimation. To improve the current defects of the BP neural network for better application to the SOC estimation, this paper proposes a method to improve the performance of the EKF algorithm for SOC estimation by optimizing the BP neural network using the tuna swarm optimization (TSO) algorithm. Based on the constructed first-order RC battery model, the optimized BP neural network was trained offline and used to compensate the SOC estimation error of the EKF algorithm online. The superiority of the proposed algorithm for SOC applications was demonstrated by simulation experiments under both dynamic stress test (DST) and Beijing dynamic stress test (BJDST) operating conditions. In addition, comparative experiments with existing hybrid algorithms were conducted. The simulation results show that compared with the EKF algorithm and the traditional BP-EKF algorithm, the proposed algorithm has better estimation accuracy and convergence for SOC and can track the SOC variation well. Compared with the conventional BP-EKF algorithm, the RMSE and MAE values of the proposed algorithm decreased respectively by 35.7 % and 37 % under DST, and respectively by 38.4 % and 43.3 % under BJDST. Besides, the proposed algorithm has better performance than other hybrid algorithms.

SOC Estimation Methods for Lithium-Ion Batteries without Current Monitoring

State of charge (SOC) estimation is an important part of a battery management system (BMS). As for small portable devices powered by lithium-ion batteries, no current sensor will be configured in BMS, which presents a challenge to traditional current-based SOC estimation algorithms. In this work, an electrochemical model is developed for lithium batteries, and three methods, including the incremental seeking method, dichotomous method, and extended Kalman filter algorithm (EKF), are separately developed to establish the framework of current and SOC estimation simultaneously. The results show that the EKF algorithm performs better than the other two methods in terms of estimation accuracy and convergence speed. In addition, the estimation error of the EKF algorithm is within ±2%, which demonstrates its feasibility.

An Improved Multi-Timescale AEKF–AUKF Joint Algorithm for State-of-Charge Estimation of Lithium-Ion Batteries

State-of-charge (SoC) estimation is one of the core functions of battery energy management systems. An accurate SoC estimation can guarantee the safe and reliable operation of the batteries system. In order to overcome the practical problems of low accuracy, noise uncertainty, poor robustness, and adaptability in parameter identification and SoC estimation of lithium-ion batteries, this paper proposes a joint estimation method based on the adaptive extended Kalman filter (AEKF) algorithm and the adaptive unscented Kalman filter (AUKF) algorithm in multiple time scales for 18,650 ternary lithium-ion batteries. Based on the slowly varying characteristics of lithium-ion batteries’ parameters and the quickly varying characteristics of the SoC parameter, firstly, the AEKF algorithm was used to online identify the parameters of the model of batteries with a macroscopic time scale. Secondly, the identified parameters were applied to the AUKF algorithm for SoC estimation of lithium-ion batteries with a microscopic time scale. Finally, the comparative simulation experiments were implemented, and the experimental results show the proposed joint algorithm has higher accuracy, adaptivity, robustness, and self-correction capability compared with the conventional algorithm.

Comparison and Analysis of SOC Estimation Based on First-Order and Second-Order Thevenin Battery Models Based on EKF

The accurate modeling and estimation of state-of-charge (SOC) of lithium-ion batteries are of great significance for their utilization efficiency, service life extension and battery management system (BMS) design. This paper aims to provide understanding and guidance for understanding and guidance on different battery models and their parameter selection by comparing and analyzing the performance differences of Extended Kalman Filter (EKF) algorithm based on the first-order Thevenin battery model and the second-order Thevenin battery model. The Battery module in Matlab/Simulink is used to simulate the HPPC (HybridPulse Power Characterization) test of real batteries, and the model is parameterically identified. By establishing Thevenin battery models of different orders and applying the EKF algorithm for SOC estimation, the differences in accuracy, robustness and computational complexity of the two models are compared and analyzed, and experimental verification is carried out under different working conditions.

A comprehensive study on state-of-charge and state-of-health estimation of sodium-ion batteries

Nowadays, sodium-ion batteries (SIBs) are becoming another kind of potential energy storage batteries in the energy storage systems (ESS) with their unique advantages compared with the lithium-ion batteries. The accurate estimation of key battery states, especially state-of-charge (SOC) and state-of-health (SOH), ensures the safe and reliable operation of the ESS. In this paper, complete experimental tests on a commercial SIB are performed, and different SOC and SOH estimation methods of the SIB are compared comprehensively, which provides a basis for the selection of state estimation methods for the SIB. For SOC estimation, the battery is modeled with the third-order equivalent circuit model based on the electrochemical impedance spectra test results, and model parameters are identified by the particle swarm optimization algorithm. Moreover, three real-time model-based estimation algorithms, extended kalman filter, unscented kalman filter, and particle filter are adopted to estimate the SOC of the SIB. For SOH estimation, three health indicators that are strongly correlated with SOH are extracted. Furthermore, three lightweight data-driven estimation algorithms, multiple linear regression, ridge regression, and support vector regression are employed to estimate the SOH of the SIB. Through comprehensive comparison, experimental results indicate that unscented kalman filter and ridge regression are the most suitable algorithms for SOC and SOH estimation of the SIB respectively. Specifically, the mean absolute error (MAE) and root mean squared error (RMSE) of the SOC estimation are lower than 1.2% and 1.6% respectively. Both MAE and RMSE of the SOH estimation are lower than 0.06%. In addition, some unique characteristics of SIBs are found.

Mitigation of state of charge estimation error due to noisy current input measurement

The key indicator to assess the performance of a battery management system is the state of charge (SoC). Although various SoC estimation algorithms have been developed to increase the estimation accuracy, the effect of the current input measurement error on the SoC estimation has not been adequately considered in these algorithms. The majority of SoC estimation algorithms are based on noiseless current measurement models in the literature. More realistic battery models must include the current measurement modelled with the bias noise and the white noise. We present a novel method for mitigating noise in current input measurements to reduce the SoC estimation error. The proposed algorithm is validated by computer simulations and battery experiments. The results show that the proposed method reduces the maximum SoC estimation error from around 11.3% to 0.56% in computer simulations and it is reduced from 1.74% to 1.17% in the battery experiment.

Coestimation of SOC and Three-Dimensional SOT for Lithium-Ion Batteries Based on Distributed Spatial–Temporal Online Correction

Energy storage system based on batteries is a key to achieve green industrial economy and the online estimation of its status is critical for the battery management system. Therefore, this paper proposed a distributed spatial-temporal online correction algorithm for state of charge (SOC) -three-dimensional state of temperature (SOT) co-estimation of battery. Firstly, the internal resistance is identified, and state of charge SOC are estimated based on the adaptive Kalman filter. Then, to improve the fidelity of electrical status estimation under the dynamic operation condition, the SOC estimation is coupled with an online restoration algorithm of distributed temperature. An improved fractal growth process is used to achieve the self-organization and convergence during the restoration of three-dimensional temperature distribution. Finally, to validate the fidelity of online co-estimation algorithm for electrical and thermal parameters, dynamic current profiles are used. The co-estimation method raises the fidelity of SOC estimation by 1.5% at most, compared with the SOC estimation algorithm without the SOT estimation. It also keeps the mean relative error of SOT estimation within 8%. Additionally, the robustness of the spatial-temporal online correction method with dual adaptive Kalman filters is validated. The result shows that the co-estimation algorithm still has a good converge performance with disturbance added.

State of charge estimation of lithium-ion battery based on extended Kalman filter algorithm

Due to excellent power and energy density, low self-discharge and long life, lithium-ion battery plays an important role in many fields. Directed against the complexity of above noises and the strong sensitivity of the common Kalman filter algorithm to noises, the state of charge estimation of lithium-ion battery based on extended Kalman filter algorithm is investigated in this paper. Based on the second-order resistor-capacitance equivalent circuit model, the battery model parameters are identified using the MATLAB/Simulink software. A battery parameter test platform is built to test the charge-discharge efficiency, open-circuit voltage and state of charge relationship curve, internal resistance and capacitance of the individual battery are tested. The simulation and experimental results of terminal voltage for lithium-ion battery is compared to verify the effectiveness of this method. In addition, the general applicability of state of charge estimation algorithm for the battery pack is explored. The ampere-hour integral method combined with the battery modeling is used to estimate the state of charge of lithium-ion battery. The comparison of extended Kalman filter algorithm between experimental results and simulation estimated results is obtained to verify the accuracy. The extended Kalman filter algorithm proposed in this study not only establishes the theoretical basis for the condition monitoring but also provides the safe guarantee for the engineering application of lithium-ion battery.