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.

A novel order-reduced thermal-coupling electrochemical model for lithium-ion batteries

Although the single-particle model enhanced with electrolyte dynamics(SPMe)is simplified from the pseudo-twodimensional(P2D)electrochemical model for lithium-ion batteries,it is difficult to solve the partial differential equations of solid–liquid phases in real-time applications.Moreover,working temperatures have a heavy impact on the battery behavior.Hence,a thermal-coupling SPMe is constructed.Herein,a lumped thermal model is established to estimate battery temperatures.The order of the SPMe model is reduced by using both transfer functions and truncation techniques and merged with Arrhenius equations for thermal effects.The polarization voltage drop is then modified through the use of test data because its original model is unreliable theoretically.Finally,the coupling-model parameters are extracted using genetic algorithms.Experimental results demonstrate that the proposed model produces average errors of about 42 mV under 15 constant current conditions and 15 mV under nine dynamic conditions,respectively.This new electrochemicalthermal coupling model is reliable and expected to be used for onboard applications.

Electrothermal Model Based Remaining Charging Time Prediction of Lithium-Ion Batteries against Wide Temperature Range

Battery remaining charging time(RCT)prediction can facilitate charging management and alleviate mileage anxiety for electric vehicles(EVs).Also,it is of great significance to improve EV users’experience.However,the RCT for a lithiumion battery pack in EVs changes with temperature and other battery parameters.This study proposes an electrothermal model-based method to accurately predict battery RCT.Firstly,a characteristic battery cell is adopted to represent the battery pack,thus an equivalent circuit model(ECM)of the characteristic battery cell is established to describe the electrical behaviors of a battery pack.Secondly,an equivalent thermal model(ETM)of the battery pack is developed by considering the influence of ambient temperature,thermal management,and battery connectors in the battery pack to calculate the temperature which is then fed back to the ECM to realize electrothermal coupling.Finally,the RCT prediction method is proposed based on the electrothermal model and validated in the wide temperature range from-20℃to 45℃.The experimental results show that the prediction error of the RCT in the whole temperature range is less than 1.5%.

Aging Characteristics of Lithium-Ion Battery Under Fast Charging Based on Electrochemical-thermalmechanical Coupling Model

The aging characteristics of lithium-ion battery(LIB)under fast charging is investigated based on an electrochemical-thermal-mechanical(ETM)coupling model.Firstly,the ETM coupling model is established by COMSOL Multiphysics.Subsequently,a long cycle test was conducted to explore the aging characteristics of LIB.Specifically,the effects of charging(C)rate and cycle number on battery aging are analyzed in terms of nonuniform distribution of solid electrolyte interface(SEI),SEI formation,thermal stability and stress characteristics.The results indicate that the increases in C rate and cycling led to an increase in the degree of nonuniform distribution of SEI,and thus a consequent increase in the capacity loss due to the SEI formation.Meanwhile,the increases in C rate and cycle number also led to an increase in the heat generation and a decrease in the heat dissipation rate of the battery,respectively,which result in a decrease in the thermal stability of the electrode materials.In addition,the von Mises stress of the positive electrode material is higher than that of the negative electrode material as the cycling proceeds,with the positive electrode material exhibiting tensile deformation and the negative electrode material exhibiting compressive deformation.The available lithium ion concentration of the positive electrode is lower than that of the negative electrode,proving that the tensile-type fracture occurring in the positive material under long cycling dominated the capacity loss process.The aforementioned studies are helpful for researchers to further explore the aging behavior of LIB under fast charging and take corresponding preventive measures.

Design and management of lithium-ion batteries:A perspective from modeling,simulation,and optimization

Although the lithium-ion batteries(LIBs) have been increasingly applied in consumer electronics, electric vehicles,and smart grid, they still face great challenges from the continuously improving requirements of energy density, power density, service life, and safety. To solve these issues, various studies have been conducted surrounding the battery design and management methods in recent decades. In the hope of providing some inspirations to the research in this field, the state of the art of design and management methods for LIBs are reviewed here from the perspective of process systems engineering. First, different types of battery models are summarized extensively, including electrical model and multi-physics coupled model, and the parameter identification methods are introduced correspondingly. Next, the model based battery design methods are reviewed briefly on three different scales, namely, electrode scale, cell scale, and pack scale. Then, the battery model based battery management methods, especially the state estimation methods with different model types are thoroughly compared. The key science and technology challenges for the development of battery systems engineering are clarified finally.

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.

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.

Physics-informed neural network approach for heat generation rate estimation of lithium-ion battery under various driving conditions

Accurate insight into the heat generation rate(HGR) of lithium-ion batteries(LIBs) is one of key issues for battery management systems to formulate thermal safety warning strategies in advance.For this reason,this paper proposes a novel physics-informed neural network(PINN) approach for HGR estimation of LIBs under various driving conditions.Specifically,a single particle model with thermodynamics(SPMT) is first constructed for extracting the critical physical knowledge related with battery HGR.Subsequently,the surface concentrations of positive and negative electrodes in battery SPMT model are integrated into the bidirectional long short-term memory(BiLSTM) networks as physical information.And combined with other feature variables,a novel PINN approach to achieve HGR estimation of LIBs with higher accuracy is constituted.Additionally,some critical hyperparameters of BiLSTM used in PINN approach are determined through Bayesian optimization algorithm(BOA) and the results of BOA-based BiLSTM are compared with other traditional BiLSTM/LSTM networks.Eventually,combined with the HGR data generated from the validated virtual battery,it is proved that the proposed approach can well predict the battery HGR under the dynamic stress test(DST) and worldwide light vehicles test procedure(WLTP),the mean absolute error under DST is 0.542 kW/m^(3),and the root mean square error under WLTP is1.428 kW/m^(3)at 25℃.Lastly,the investigation results of this paper also show a new perspective in the application of the PINN approach in battery HGR estimation.

Towards a business model for second-life batteries: Barriers,opportunities, uncertainties, and technologies

Electric vehicles(EVs) and the recent pandemic outbreak give cities a new trend to primarily private and shared mobility with low noise and less air pollution.Crucial factors for the widespread of EVs are the electrical charging infrastructure,driving range,and the reduction of the cost of battery packets.For this reason,there is a massive effort from manufacturers,governments,and the scientific community to reduce battery costs and boost sustainable electrical production and distribution.Battery reuse is an alternative to reduce batteries’ costs and environmental impacts.Second-life batteries can be used in a wide variety of secondary applications.Second-life batteries can be connected with off-grid or on-grid photovoltaic and wind systems,vehicle charging stations,forklifts,and frequency control.The present work aims to analyze the main challenges imposed on the reuse of batteries,the leading technologies for their reuse,and the different types of batteries in terms of their feasibility for second-life use.The main novelty of this work is the discussion about the barriers,opportunities,uncertainties,and technologies for the second life market.Here we summarize the present state of the art in reusing lithium-ion batteries discussing technical and economic feasibility,environmental impacts,and perspectives.The results show five business models that have been proposed in the literature,three types of markets for trading second-life batteries,and the main opportunities and barriers for each actor in the battery supply chain.

Robust state of charge estimation of lithium-ion battery via mixture kernel mean p-power error loss LSTM with heap-based-optimizer

The state of charge(SOC)estimation of lithium-ion battery is an important function in the battery management system(BMS)of electric vehicles.The long short term memory(LSTM)model can be employed for SOC estimation,which is capable of estimating the future changing states of a nonlinear system.Since the BMS usually works under complicated operating conditions,i.e the real measurement data used for model training may be corrupted by non-Gaussian noise,and thus the performance of the original LSTM with the mean square error(MSE)loss may deteriorate.Therefore,a novel LSTM with mixture kernel mean p-power error(MKMPE)loss,called MKMPE-LSTM,is developed by using the MKMPE loss to replace the MSE as the learning criterion in LSTM framework,which can achieve robust SOC estimation under the measurement data contaminated with non-Gaussian noises(or outliers)because of the MKMPE containing the p-order moments of the error distribution.In addition,a meta-heuristic algorithm,called heap-based-optimizer(HBO),is employed to optimize the hyper-parameters(mainly including learning rate,number of hidden layer neuron and value of p in MKMPE)of the proposed MKMPE-LSTM model to further improve its flexibility and generalization performance,and a novel hybrid model(HBO-MKMPE-LSTM)is established for SOC estimation under non-Gaussian noise cases.Finally,several tests are performed under various cases through a benchmark to evaluate the performance of the proposed HBO-MKMPE-LSTM model,and the results demonstrate that the proposed hybrid method can provide a good robustness and accuracy under different non-Gaussian measurement noises,and the SOC estimation results in terms of mean square error(MSE),root MSE(RMSE),mean absolute relative error(MARE),and determination coefficient R2are less than 0.05%,3%,3%,and above 99.8%at 25℃,respectively.

A Comparative Study on Open Circuit Voltage Models for Lithium-ion Batteries

The current research of state of charge(SoC) online estimation of lithium-ion battery(LiB) in electric vehicles(EVs)mainly focuses on adopting or improving of battery models and estimation filters. However, little attention has been paid to the accuracy of various open circuit voltage(OCV) models for correcting the SoC with aid of the ampere-hour counting method. This paper presents a comprehensive comparison study on eighteen OCV models which cover the majority of models used in literature. The low-current OCV tests are conducted on the typical commercial LiFePO/graphite(LFP) and LiNiMnCoO/graphite(NMC) cells to obtain the experimental OCV-SoC curves at different ambient temperature and aging stages. With selected OCV and SoC points from experimental OCV-SoC curves, the parameters of each OCV model are determined by curve fitting toolbox of MATLAB 2013. Then the fitting OCV-SoC curves based on diversified OCV models are also obtained. The indicator of root-mean-square error(RMSE) between the experimental data and fitted data is selected to evaluate the adaptabilities of these OCV models for their main features, advantages,and limitations. The sensitivities of OCV models to ambient temperatures, aging stages, numbers of data points,and SoC regions are studied for both NMC and LFP cells. Furthermore, the influences of these models on SoC estimation are discussed. Through a comprehensive comparison and analysis on OCV models, some recommendations in selecting OCV models for both NMC and LFP cells are given.

Physics-based battery SOC estimation methods:Recent advances and future perspectives

The reliable prediction of state of charge(SOC)is one of the vital functions of advanced battery management system(BMS),which has great significance towards safe operation of electric vehicles.By far,the empirical model-based and data-driven-based SOC estimation methods of lithium-ion batteries have been comprehensively discussed and reviewed in various literatures.However,few reviews involving SOC estimation focused on electrochemical mechanism,which gives physical explanations to SOC and becomes most attractive candidate for advanced BMS.For this reason,this paper comprehensively surveys on physics-based SOC algorithms applied in advanced BMS.First,the research progresses of physical SOC estimation methods for lithium-ion batteries are thoroughly discussed and corresponding evaluation criteria are carefully elaborated.Second,future perspectives of the current researches on physics-based battery SOC estimation are presented.The insights stated in this paper are expected to catalyze the development and application of the physics-based advanced BMS algorithms.

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.

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.

A hierarchical enhanced data-driven battery pack capacity estimation framework for real-world operating conditions with fewer labeled data

Battery pack capacity estimation under real-world operating conditions is important for battery performance optimization and health management,contributing to the reliability and longevity of batterypowered systems.However,complex operating conditions,coupling cell-to-cell inconsistency,and limited labeled data pose great challenges to accurate and robust battery pack capacity estimation.To address these issues,this paper proposes a hierarchical data-driven framework aimed at enhancing the training of machine learning models with fewer labeled data.Unlike traditional data-driven methods that lack interpretability,the hierarchical data-driven framework unveils the“mechanism”of the black box inside the data-driven framework by splitting the final estimation target into cell-level and pack-level intermediate targets.A generalized feature matrix is devised without requiring all cell voltages,significantly reducing the computational cost and memory resources.The generated intermediate target labels and the corresponding features are hierarchically employed to enhance the training of two machine learning models,effectively alleviating the difficulty of learning the relationship from all features due to fewer labeled data and addressing the dilemma of requiring extensive labeled data for accurate estimation.Using only 10%of degradation data,the proposed framework outperforms the state-of-the-art battery pack capacity estimation methods,achieving mean absolute percentage errors of 0.608%,0.601%,and 1.128%for three battery packs whose degradation load profiles represent real-world operating conditions.Its high accuracy,adaptability,and robustness indicate the potential in different application scenarios,which is promising for reducing laborious and expensive aging experiments at the pack level and facilitating the development of battery technology.

Improved Multiple Feature-electrochemical Thermal Coupling Modeling of Lithium-ion Batteries at Low-temperature with Real-time Coefficient Correction

Monitoring various internal parameters plays a core role in ensuring the safety of lithium-ion batteries in power supply applications.It also influences the sustainability effect and online state of charge prediction.An improved multiple feature-electrochemical thermal coupling modeling method is proposed considering low-temperature performance degradation for the complete characteristic expression of multi-dimensional information.This is to obtain the parameter influence mechanism with a multi-variable coupling relationship.An optimized decoupled deviation strategy is constructed for accurate state of charge prediction with real-time correction of time-varying current and temperature effects.The innovative decoupling method is combined with the functional relationships of state of charge and open-circuit voltage to capture energy management ef-fectively.Then,an adaptive equivalent-prediction model is constructed using the state-space equation and iterative feedback correction,making the proposed model adaptive to fractional calculation.The maximum state of charge estimation errors of the proposed method are 4.57% and 0.223% under the Beijing bus dynamic stress test and dynamic stress test conditions,respectively.The improved multiple feature-electrochemical thermal coupling modeling realizes the effective correction of the current and temperature variations with noise influencing coefficient,and provides an efficient state of charge prediction method adaptive to complex conditions.

Digital twin modeling method for lithium-ion batteries based on data-mechanism fusion driving

Lithium-ion batteries have been rapidly developed as clean energy sources in many industrial fields,such as new energy vehicles and energy storage.The core issues hindering their further promotion and application are reliability and safety.A digital twin model that maps onto the physical entity of the battery with high simulation accuracy helps to monitor internal states and improve battery safety.This work focuses on developing a digital twin model via a mechanism-data-driven parameter updating algorithm to increase the simulation accuracy of the internal and external characteristics of the full-time domain battery under complex working conditions.An electrochemical model is first developed with the consideration of how electrode particle size impacts battery characteristics.By adding the descriptions of temperature distribution and particle-level stress,a multi-particle size electrochemical-thermal-mechanical coupling model is established.Then,considering the different electrical and thermal effect among individual cells,a model for the battery pack is constructed.A digital twin model construction method is finally developed and verified with battery operating data.

Modeling of LiFePO4 battery open circuit voltage hysteresis based on recursive discrete Preisach model

This paper focuses on the modeling of LiFePO4 battery open circuit voltage （OCV） hysteresis. There exists obvious hysteresis in LiFePO4 battery OCV, which makes it complicated to model the LiFePO4 battery. In this paper, the recursive discrete Preisach model （RDPM） is applied to the modeling of LiFePO4 battery OCV hysteresis. The theory of RDPM is illustrated in detail and the RDPM on LiFePO4 battery OCV hysteresis modeling is verified in experiment. The robust of RDPM under different working conditions are also demonstrated in simulation and experiment. The simulation and experimental results show that the proposed method can significantly improve the accuracy of LiFePO4 battery OCV hysteresis modeling when the battery OCV characteristic changes, which conduces to the online state estimation of LiFePO4 battery.

Thermal Modeling of Cylindrical LiFePO₄Batteries

Thermal management of Li-ion batteries is important because of the high energy content and the risk of rapid temperature development in the high current range. Reliable and safe operation of these batteries is seriously endangered by high temperatures. It is important to have a simple but accurate model to evaluate the thermal behavior of batteries under a variety of operating conditions and be able to predict the internal temperature as well. To achieve this goal, a radial-axial model is developed to investigate the evolution of the temperature distribution in cylindrical Li-ion cells. Experimental data on LiFePO4 cylindrical Li-ion batteries are used to determine the overpotentials and to estimate the State-of-Charge-dependent entropies from the previously developed adaptive thermal model [1]. The heat evolution is assumed to be uniform inside the battery. Heat exchange from the battery surfaces with the ambient is non-uniform, i.e. depends on the temperature of a particular point at the surface of the cell. Furthermore, the model was adapted for implementation in battery management systems. It is shown that the model can accurately predict the temperature distribution inside the cell in a wide range of operating conditions. Good agreement with the measured temperature development has been achieved. Decreasing the heat conductivity coefficient during cell manufacturing and increasing the heat transfer coefficient during battery operation suppresses the temperature evolution. This modified model can be used for the scale-up of large size batteries and battery packs.

Modeling of a Lithium-Ion Capacitor and Its Charging and Discharging Circuit in a Model-Based Design

For several years now, electric vehicles (EVs) have been expected to become widely available in the micro-mobility field. However, the insufficiency of such vehicles’ battery-charging and discharging performance has limited their practical use. A hybrid energy storage system, which comprises a capacitor and battery, is a promising solution to this problem;however, to apply model-based designs, which are indispensable to embedded systems, such as the electronic control units used in EVs, a simple and accurate capacitor model is required. Within this framework, a lithium-ion capacitor (LIC) model is proposed, and its charging and discharging performances are evaluated against an actual LIC. The model corresponds accurately to the actual LIC, and the results indicate that the proposed LIC model will work well when used with Model-Based Design (MBD).