An iterative computation method for interpreting and extending an analytical battery model

Battery models are of great importance to develop portable computing systems,for whether the design of low power hardware architecture or the design of battery-aware scheduling policies.In this paper,we present a physically justified iterative computing method to illustrate the discharge,recovery and charge process of Li/Li-ion batteries.The discharge and recovery processes correspond well to an existing accurate analytical battery model:R-V-W's analytical model,and thus interpret this model algorithmically.Our method can also extend R-V-W's model easily to accommodate the charge process.The work will help the system designers to grasp the characteristics of R-V-W's battery model and also,enable to predict the battery behavior in the charge process in a uniform way as the discharge process and the recovery process.Experiments are performed to show the ac-curacy of the extended model by comparing the predicted charge times with those derived from the DUALFOIL simulations.Various profiles with different combinations of battery modes were tested.The experimental results show that the extended battery model preserves high accuracy in predicting the charge behavior.

Online battery model parameters identification approach based on bias-compensated forgetting factor recursive least squares

Accuracy of a lithium-ion battery model is pivotal in faithfully representing actual state of battery,thereby influencing safety of entire electric vehicles.Precise estimation of battery model parameters using key measured signals is essential.However,measured signals inevitably carry random noise due to complex real-world operating environments and sensor errors,potentially diminishing model estimation accuracy.Addressing the challenge of accuracy reduction caused by noise,this paper introduces a Bias-Compensated Forgetting Factor Recursive Least Squares(BCFFRLS)method.Initially,a variational error model is crafted to estimate the average weighted variance of random noise.Subsequently,an augmentation matrix is devised to calculate the bias term using augmented and extended parameter vectors,compensating for bias in the parameter estimates.To assess the proposed method's effectiveness in improving parameter identification accuracy,lithium-ion battery experiments were conducted in three test conditions—Urban Dynamometer Driving Schedule(UDDS),Dynamic Stress Test(DST),and Hybrid Pulse Power Characterization(HPPC).The proposed method,alongside two contrasting methods—the offline identification method and Forgetting Factor Recursive Least Squares(FFRLS)—was employed for battery model parameter identification.Comparative analysis reveals substantial improvements,with the mean absolute error reduced by 25%,28%,and 15%,and the root mean square error reduced by 25.1%,42.7%,and 15.9%in UDDS,HPPC,and DST operating conditions,respectively,when compared to the FFRLS method.

Online model identification of lithium-ion battery for electric vehicles

In order to characterize the voltage behavior of a lithium-ion battery for on-board electric vehicle battery management and control applications,a battery model with a moderate complexity was established.The battery open circuit voltage (OCV) as a function of state of charge (SOC) was depicted by the Nernst equation.An equivalent circuit network was adopted to describe the polarization effect of the lithium-ion battery.A linear identifiable formulation of the battery model was derived by discretizing the frequent-domain description of the battery model.The recursive least square algorithm with forgetting was applied to implement the on-line parameter calibration.The validation results show that the on-line calibrated model can accurately predict the dynamic voltage behavior of the lithium-ion battery.The maximum and mean relative errors are 1.666% and 0.01%,respectively,in a hybrid pulse test,while 1.933% and 0.062%,respectively,in a transient power test.The on-line parameter calibration method thereby can ensure that the model possesses an acceptable robustness to varied battery loading profiles.

SOC distribution-based modeling for lithium-ion battery for electric vehicles using numerical optimization

In order to simulate electrical characteristics of a lithium-ion battery used in electric vehicles in a good manner,a three-layer battery model is established.The charge of the lithium-ion battery is assumed to distribute among the three layers and their interaction is used to depict hysteresis and relaxation effect observed in the lithium-ion battery.The model parameters are calibrated and optimized through a numerically nonlinear least squares algorithm in Simulink Parameter Estimation Toolbox for an experimental data set sampled in a hybrid pulse test of the battery.Evaluation results showed that the established model is able to provide an acceptable accuracy in estimating the State of Charge of the lithium-ion battery in an open-loop fashion for a sufficiently long time and to describe the battery voltage behavior more accurately than a commonly used battery model.The battery modeling accuracy can thereby satisfy the requirement for practical electric vehicle applications.

Modeling the dynamic behavior of a lithium-ion battery for electric vehicles using numerical optimization

In order to simulate the dynamical behavior of a lithium ion traction battery used in elec tric vehicles, an equivalent circuit based battery model was established. The methodology in the guide document of the ADVISOR software was used to determine the initial parameters of the model as a function of state of charge （ SoC ） over an experimental data set of the battery. A numerically nonlinear least squares algorithm in SIMULINK design optimization toolbox was applied to further op timize the model parameters. Validation results showed that the battery model could well describe the dynamic behavior of the lithinm ion battery in two different battery loading situations.

Failure Prediction Modeling of Lithium Ion Battery toward Distributed Parameter Estimation

Lithium ion battery has typical character of distributed parameter system, and can be described precisely by partial differential equations and multi-physics theory because lithium ion battery is a complicated electrochemical energy storage system. A novel failure prediction modeling method of lithium ion battery based on distributed parameter estimation and single particle model is proposed in this work. Lithium ion concentration in the anode of lithium ion battery is an unmeasurable distributed variable. Failure prediction system can estimate lithium ion concentration online, track the failure residual which is the difference between the estimated value and the ideal value. The precaution signal will be triggered when the failure residual is beyond the predefined failure precaution threshold, and the failure countdown prediction module will be activated. The remaining time of the severe failure threshold can be estimated by the failure countdown prediction module according to the changing rate of the failure residual. A simulation example verifies that lithium ion concentration in the anode of lithium ion battery can be estimated exactly and effectively by the failure prediction model. The precaution signal can be triggered reliably, and the remaining time of the severe failure can be forecasted accurately by the failure countdown prediction module.

An analytical model for predicting battery lifetime

We used an analytical high-level battery model to estimate the battery lifetime for a given load.The experimental results show that this model to predict battery lifetime under variable loads is more appropriate than that under constant loads.

Characterization and identification towards dynamic-based electrical modeling of lithium-ion batteries

Lithium-ion batteries are widely recognized as a crucial enabling technology for the advancement of electric vehicles and energy storage systems in the grid.The design of battery state estimation and control algorithms in battery management systems is usually based on battery models,which interpret crucial battery dynamics through the utilization of mathematical functions.Therefore,the investigation of battery dynamics with the purpose of battery system identification has garnered considerable attention in the realm of battery research.Characterization methods in terms of linear and nonlinear response of lithium-ion batteries have emerged as a prominent area of study in this field.This review has undertaken an analysis and discussion of characterization methods,with a particular focus on the motivation of battery system identification.Specifically,this work encompasses the incorporation of frequency domain nonlinear characterization methods and dynamics-based battery electrical models.The aim of this study is to establish a connection between the characterization and identification of battery systems for researchers and engineers specialized in the field of batteries,with the intention of promoting the advancement of efficient battery technology for real-world applications.

Letter to the Editor Re “Fractional Modeling and SOC Estimation of Lithium-ion Battery”

A Recent paper by Ma et al.,claims to estimate the state of charge of Lithium-ion batteries with a fractionalorder impedance model including a Warburg and a constant phase element(CPE)with a maximum error of 0.5%[1].The proposed equivalent circuit model from[1]is reproduced in Fig.1.

Application of Digital Twin in Smart Battery Management Systems

Lithium-ion batteries have always been a focus of research on new energy vehicles,however,their internal reactions are complex,and problems such as battery aging and safety have not been fully understood.In view of the research and preliminary application of the digital twin in complex systems such as aerospace,we will have the opportunity to use the digital twin to solve the bottleneck of current battery research.Firstly,this paper arranges the development history,basic concepts and key technologies of the digital twin,and summarizes current research methods and challenges in battery modeling,state estimation,remaining useful life prediction,battery safety and control.Furthermore,based on digital twin we describe the solutions for battery digital modeling,real-time state estimation,dynamic charging control,dynamic thermal management,and dynamic equalization control in the intelligent battery management system.We also give development opportunities for digital twin in the battery field.Finally we summarize the development trends and challenges of smart battery management.

Review of lithium-ion battery state of charge estimation

The technology deployed for lithium-ion battery state of charge(SOC)estimation is an important part of the design of electric vehicle battery management systems.Accurate SOC estimation can forestall excessive charging and discharging of lithium-ion batteries,thereby improving discharge efficiency and extending cycle life.In this study,the key lithium-ion battery SOC estimation technologies are summarized.First,the research status of lithium-ion battery modeling is introduced.Second,the main technologies and difficulties in model parameter identification for lithium-ion batteries are discussed.Third,the development status and advantages and disadvantages of SOC estimation methods are summarized.Finally,the current research problems and prospects for development trends are summarized.

Identification of dynamic model parameters for lithium-ion batteries used in hybrid electric vehicles

An electrical equivalent circuit model for lithium-ion batteries used for hybrid electric vehicles （HEV） is presented. The model has two RC networks characterizing battery activation and concentration polarization process. The parameters of the model are identified using combined experimental and extended Kalman filter （EKF） recursive methods. The open-circuit voltage and ohmic resistance of the battery are directly measured and calculated from experimental measurements, respectively. The rest of the coupled dynamic parameters, i.e. the RC network parameters, are estimated using the EKF method. Experimental and simulation results are presented to demonstrate the efficacy of the proposed circuit model and parameter identification techniques for simulating battery dynamics.

Battery Charger for Electric Vehicles based on a Wireless Power Transmission

In this paper,the case of a battery charger for electric vehicles based on a wireless power transmission is addressed.The specificity of every stage of the overall system is presented.Based on calculated and measured results,relevant capacitive compensations of the transformer and models are suggested and discussed in order to best match the operating mode and aiming at simplifying as much as possible the control and the electronics of the charger.

State of Health Estimation of LiFePO_(4) Batteries for Battery Management Systems

When considering the mechanism of the batteries,the capacity reduction at storage(when not in use)and cycling(during use)and increase of internal resistance is because of degradation in the chemical composition inside the batteries.To optimize battery usage,a battery management system(BMS)is used to estimate possible aging effects while different load profiles are requested from the grid.This is specifically seen in a case when the vehicle is connected to the net(online through BMS).During this process,the BMS chooses the optimized load profiles based on the least aging effects on the battery pack.The major focus of this paper is to design an algorithm/model for lithium iron phosphate(LiFePO4)batteries.The model of the batteries is based on the accelerated aging test data(data from the beginning of life till the end of life).The objective is to develop an algorithm based on the actual battery trend during the whole life of the battery.By the analysis of the test data,the complete trend of the battery aging and the factors on which the aging is depending on is identified,the aging model can then be recalibrated to avoid any differences in the production process during cell manufacturing.The validation of the model was carried out at the end by utilizing different driving profiles at different C-rates and different ambient temperatures.A Linear and non-linear model-based approach is used based on statistical data.The parameterization was carried out by dividing the data into small chunks and estimating the parameters for the individual chunks.Self-adaptive characteristic map using a lookup table was also used.The nonlinear model was chosen as the best candidate among all other approaches for longer validation of 8-month data with real driving data set.

Dynamic Cell Modeling for Accurate SOC Estimation in Autonomous Electric Vehicles

This paper presents findings on dynamic cell modeling for state-of-charge (SOC) estimation in an autonomous electric vehicle (AEV). The studied cells are Lithium-Ion Polymer-based with a nominal capacity of around 8 Ah, optimized for power-needy applications. The AEV operates in a harsh environment with rate requirements up to ±25C and highly dynamic rate profiles, unlike portable-electronic applications with constant power output and fractional C rates. SOC estimation methods effective in portable electronics may not suffice for the AEV. Accurate SOC estimation necessitates a precise cell model. The proposed SOC estimation method utilizes a detailed Kalman-filtering approach. The cell model must include SOC as a state in the model state vector. Multiple cell models are presented, starting with a simple one employing “Coulomb counting” as the state equation and Shepherd’s rule as the output equation, lacking prediction of cell relaxation dynamics. An improved model incorporates filter states to account for relaxation and other dynamics in closed-circuit cell voltage, yielding better performance. The best overall results are achieved with a method combining nonlinear autoregressive filtering and dynamic radial basis function networks. The paper includes lab test results comparing physical cells with model predictions. The most accurate models obtained have an RMS estimation error lower than the quantization noise floor expected in the battery-management-system design. Importantly, these models enable precise SOC estimation, allowing the vehicle controller to utilize the battery pack’s full operating range without overcharging or undercharging concerns.

CIM Model Extension for Intelligent DAS of Smart Power Grid in Korea

The CIM （common information model） is an abstract information model that can be used to model an electrical network and various equipments used on the network. By using a common model, utilities and vendors can reduce their integration costs, which should allow more resources to be applied toward increased functionality for managing and optimizing the electrical system. As a part of smart grid, the SPG （smart power grid） was built on Jeju Island. The SPG consists of IDAS （intelligent distribution automation system）, substation automation system, intelligent transmission system, and active telemetrics system. To integrate these systems which have different operating systems and platforms CIM standard was used. But IDAS has many functions and advanced algorithms not defined in CIM. In this paper, the authors introduce how to develop and extend the CIM model for managing the IDAS.

Modeling and SOC estimation of lithium iron phosphate battery considering capacity loss

Modeling and state of charge(SOC)estimation of Lithium cells are crucial techniques of the lithium battery management system.The modeling is extremely complicated as the operating status of lithium battery is affected by temperature,current,cycle number,discharge depth and other factors.This paper studies the modeling of lithium iron phosphate battery based on the Thevenin’s equivalent circuit and a method to identify the open circuit voltage,resistance and capacitance in the model is proposed.To improve the accuracy of the lithium battery model,a capacity estimation algorithm considering the capacity loss during the battery’s life cycle.In addition,this paper solves the SOC estimation issue of the lithium battery caused by the uncertain noise using the extended Kalman filtering(EKF)algorithm.A simulation model of actual lithium batteries is designed in Matlab/Simulink and the simulation results verify the accuracy of the model under different operating modes.

Data-Based Interpretable Modeling for Property Forecasting and Sensitivity Analysis of Li-ion Battery Electrode

Lithium-ion batteries have become one of the most promising technologies for speeding up clean automotive applications,where electrode plays a pivotal role in determining battery performance.Due to the strongly-coupled and highly complex processes to produce battery electrode,it is imperative to develop an effective solution that can predict the properties of battery electrode and perform reliable sensitivity analysis on the key features and parameters during the production process.This paper proposes a novel tree boosting model-based framework to analyze and predict how the battery electrode properties vary with respect to parameters during the early production stage.Three data-based interpretable models including AdaBoost,LPBoost,and TotalBoost are presented and compared.Four key parameters including three slurry feature variables and one coating process parameter are analyzed to quantify their effects on both mass loading and porosity of battery electrode.The results demonstrate that the proposed tree model-based framework is capable of providing efficient quantitative analysis on the importance and correlation of the related parameters and producing satisfying early-stage prediction of battery electrode properties.These can benefit a deep understanding of battery electrodes and facilitate to optimizing battery electrode design for automotive applications.

Theoretical model of lithium iron phosphate power battery under high-rate discharging for electromagnetic launch

Due to the large error of the traditional battery theoretical model during large-rate discharge for electromagnetic launch,the Shepherd derivative model considering the factors of the pulse cycle condition,temperature,and life is proposed by the Naval University of Engineering.The discharge rate of traditional lithium-ion batteries does not exceed 10C,while that for electromagnetic launch reaches 60C.The continuous pulse cycle condition of ultra-large discharging rate causes many unique electrochemical reactions inside the cells.The traditional model cannot accurately describe the discharge characteristics of the battery.The accurate battery theoretical model is an important basis for system efficiency calculation,precise discharge control,and remaining capacity prediction.To this purpose,an experimental platform for electromagnetic launch is built,and discharge characteristics of the battery under different rate,temperature,and life decay are measured.Through the experimental test and analysis,the reason that the traditional model cannot accurately characterize the large-rate discharge process is analyzed.And a novel battery theoretical model is designed with the help of genetic algorithm,which is integrated with the electromagnetic launch topology.Numerical simulation is compared with the experimental results,which verifies the modeling accuracy for the large-rate discharge.On this basis,a variety of discharge conditions are applied to test the applicability of the model,resulting in better results.Finally,with the continuous cycle-pulse condition in the electromagnetic launch system,the stability and accuracy of the model are confirmed.

Visualizing surface-enriched Li storage with a nanopore-array model battery

The coupling of model batteries and surface-sensitive techniques provides an indispensable platform for interrogating the vital surface/interface processes in battery systems.Here,we report a sandwich-format nanopore-array model battery using an ultrathin graphite electrode and an anodized aluminum oxide(AAO)film.The porous framework of AAO regulates the contact pattern of the electrolyte with the graphite electrode from the inner side,while minimizing contamination on the outer surface.This model battery facilitates repetitive charge-discharge processes,where the graphite electrode is reversibly intercalated and deintercalated,and also allows for the in-situ characterizations of ion intercalation in the graphite electrode.The ion distribution profiles indicate that the intercalating Li ions accumulate in both the inner and outer surface regions of graphite,generating a high capacity of~455 mAh·g^(-1)(theory:372 mAh·g^(-1)).The surface enrichment presented herein provides new insights towards the mechanistic understanding of batteries and the rational design strategies.