A study on equivalent circuit model of lead-acid battery for electric vehicles

A 100Ah@42V lead-acid battery package for electric vehicles are used for study. 1he hybrid pulse test is applied to the battery package to acquire enough data, by which the partnership for a new generation of vehicles （PNGV） equivalent circuit model parameters are identified by the least square method. Then, the PNGV model is verified under two conditions, i.e., the composite pulse excitation and the constant-current respectively. The corresponding maximum relative errors of output voltage are less than 3 % and 3.5 %. Results show that the present PNGV equivalent circuit model and verification method is effective, which can satisfy requirement of simulation of power system of electric vehicles.

Simulation of second-order RC equivalent circuit model of lithium battery based on variable resistance and capacitance

With the rise of the electric vehicle industry,as the power source of electric vehicles,lithium battery has become a research hotspot.The state of charge(SOC)estimation and modelling of lithium battery are studied in this paper.The ampere-hour(Ah)integration method based on external characteristics is analyzed,and the open-circuit voltage(OCV)method is studied.The two methods are combined to estimate SOC.Considering the accuracy and complexity of the model,the second-order RC equivalent circuit model of lithium battery is selected.Pulse discharge and exponential fitting of lithium battery are used to obtain corresponding parameters.The simulation is carried out by using fixed resistance capacitance and variable resistance capacitor respectively.The accuracy of variable resistance and capacitance model is 2.9%,which verifies the validity of the proposed model.

Extreme Learning Machine-Based Thermal Model for Lithium-Ion Batteries of Electric Vehicles under External Short Circuit

External short circuit(ESC)of lithium-ion batteries is one of the common and severe electrical failures in electric vehicles.In this study,a novel thermal modelis developed to capture the temperature behavior of batteries under ESC conditions.Experiments were systematically performed under different battery initial state of charge and ambient temperatures.Based on the experimental results,we employed an extreme learming machine(ELM)-based thermal(ELMT)model to depict battery temperature behavior under ESC,where a lumped-state thermal model was used to replace the activation function of conventional ELMs.To demonstrate the effectiveness of the proposed model,wecompared the ELMT model with a multi-lumped-state thermal(MLT)model parameterized by thegenetic algorithm using the experimental data from various sets of battery cells.It is shown that the ELMT model can achieve higher computa-tional efficiency than the MLT model and better fitting and prediction accuracy,where the average root mean squared error(RMSE)of the fitting is 0.65℃ for the ELMT model and 3.95℃ for the MLT model,and the RMES of the prediction under new data set is 3.97℃ for the ELMT model and 6.11℃ for the MLT model.

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.

An adaptive fuel cell hybrid vehicle propulsion sizing model

As we enter the age of electrochemical propulsion,there is an increasing tendency to discuss the viability or otherwise of different electrochemical propulsion systems in zero-sum terms.These discussions are often grounded in a specific use case;however,given the need to electrify the wider transport sector it is evident that we must consider systems in a holistic fashion.When designed adequately,the hybridisation of power sources within automotive applications has been demonstrated to positively impact fuel cell efficiency,durability,and cost,while having potential benefits for the safety of vehicles.In this paper,the impact of the fuel cell to battery hybridisation degree is explored through the key design parameter of system mass.Different fuel cell electric hybrid vehicle(FCHEV)scenarios of various hydridisation degrees,including light-duty vehicles(LDVs),Class 8 heavy goods vehicles(HGVs),and buses are modelled to enable the appropriate sizing of the proton exchange membrane(PEMFC)stack and lithium-ion battery(LiB)pack and additional balance of plant.The operating conditions of the modelled PEMFC stack and battery pack are then varied under a range of relevant drive cycles to identify the relative performance of the systems.By extending the model further and incorporating a feedback loop,we are able to remove the need to include estimated vehicle masses a priori enabling improving the speed and accuracy of the model as an analysis tool for vehicle mass and performance estimation.

A Nonlinear Observer Approach of SOC Estimation Based on Hysteresis Model for Lithium-ion Battery

In this paper, a state of charge U+0028 SOC U+0029 estimation approach for lithium-ion battery based on equivalent circuit model and the input-to-state stability U+0028 ISS U+0029 theory has been proposed. According to the electrochemical performance of lithiumion battery, the equivalent circuit model with two RC networks is established, which includes hysteresis characteristic in inner electrochemical response process. The nonlinear relation between open circuit voltage U+0028 OCV U+0029 and SOC is obtained from a rapid test. Exponential fitting method is used to identify the parameters of the model. A novel state observer based on ISS theory is designed for lithium-ion battery SOC estimation. The designed observer is tested on AMESim and Simulink co-simulation. The simulation results show that the proposed method has a high SOC estimation accuracy with an error of about 2 percent. © 2017 Chinese Association of Automation.

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 model-based driving cycle test procedure of electric vehicle batteries

The battery test methods are the key issues to investigate the energy-storage characteristics and dynamic characteristics of electric vehicle(EV) batteries.In this paper,the research advances of existing battery test methods as well as driving cycles are reviewed.An electric vehicle model that consists of EV dynamics model,battery model and electric motor model is built.The dynamic characteristics of the battery in frequency domain are analyzed.Based on the EV model and the frequency domain characteristics of the battery,a driving cycle test procedure of EV battery is proposed.The battery test procedure is able to reflect the real-world characteristics of EV batteries,and can be used as a universal EV battery test method.

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.

Online Identification of Lithium-ion Battery Model Parameters with Initial Value Uncertainty and Measurement Noise

Online parameter identification is essential for the accuracy of the battery equivalent circuit model(ECM).The traditional recursive least squares(RLS)method is easily biased with the noise disturbances from sensors,which degrades the modeling accuracy in practice.Meanwhile,the recursive total least squares(RTLS)method can deal with the noise interferences,but the parameter slowly converges to the reference with initial value uncertainty.To alleviate the above issues,this paper proposes a co-estimation framework utilizing the advantages of RLS and RTLS for a higher parameter identification performance of the battery ECM.RLS converges quickly by updating the parameters along the gradient of the cost function.RTLS is applied to attenuate the noise effect once the parameters have converged.Both simulation and experimental results prove that the proposed method has good accuracy,a fast convergence rate,and also robustness against noise corruption.

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.

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).

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%.

An improved state-of-charge estimation method for sodium-ion battery based on combined correction of voltage and internal resistance

ABSTRACT The accurate state-of-charge(SOC)estimation of sodium-ion batteries is the basis for their efficient application.In this paper,a new SOC estimation method suitable for sodium-ion batteries and their application conditions is proposed,which considers the combination of open circuit voltage(OCV)and internal resistance correction.First,the optimal order of equivalent circuit model is analyzed and selected,and the monotonic and stable mapping relationships between OCV and SOC,as well as between ohmic internal resistance and SOC are determined.Then,a joint estimation algorithm for battery model parameters and SOC is estab-lished,and a joint SOC correction strategy based on OCV and ohmic internal resistance is established.The test results show that OCV correction is reliable when polarization is small,that the ohmic internal resistance correction is reliable when the current fluctuation is large,and that the maximum absolute error of SOC estimation of the proposed method is not more than 2.6%.

Cycle life prediction and match detection in retired electric vehicle batteries

The lifespan models of commercial 18650-type lithium ion batteries （nominal capacity of 1150 mA-h） were presented. The lifespan was extrapolated based on this model. The results indicate that the relationship of capacity retention and cycle number can be expressed by Gaussian function. The selecting function and optimal precision were verified through actual match detection and a range of alternating current impedance testing. The cycle life model with high precision （〉99%） is beneficial to shortening the orediction time and cutting the prediction cost.

基于Modelica的电动汽车电池建模与仿真

为了实时仿真电动汽车电池组的动态性能,应用Modelica多领域建模语言建立描述电池组的PNGV等效电路模型。通过电池的动态充放电性能实验标定电池组模型的电阻、电容等参数,并利用Dymola多领域仿真软件进行性能参数求解。将该电池模型应用在电动汽车整车的仿真分析中,实验结果表明,该模型准确度高,能实时地仿真电动汽车的动力性能。该电池组建模方法实现简单且便于扩展,可以为电动汽车的产品设计、系统性能分析提供有效的解决办法。

Performance Study of the MPC based on BPNN Prediction Model in Thermal Management System of Battery Electric Vehicles

In this paper,a model predictive control(MPC)based on back propagation neural network(BPNN)prediction model was proposed for compressor speed control of air conditioning system(ACS)and battery thermal management system(BTMS)coupling system of battery electric vehicle(BEV).In order to solve the problem of high cooling energy consumption and inferior thermal comfort in the cabin of the battery electric vehicle thermal management system(BEVTMS)during summer time,this paper combines the respective superiorities of artificial neural network(ANN)predictive modeling and MPC,and creatively combines the two methods and uses them in the control of BEVTMS.Firstly,based on ANN and heat transfer theory,BPNN prediction model,ACS and BTMS coupling system were established and verified.Secondly,a mathematical method of MPC was established to control the speed of the compressor.Then,the state parameters of the coupled system were predicted using a BPNN prediction model,and the predicted values were passed to the MPC,thus achieving accurate control of the compressor speed using the MPC.Finally,the effects of PID control and MPC based on BPNN prediction model on thermal comfort of cabin and compressor energy consumption at different ambient temperatures were compared in simulation under New European Driving Cycle(NEDC)conditions.The results showed for the constructed BPNN prediction model predicted and tested values of the selected parameters the mean squared error(MSE)ranged from 2.498%to 8.969%,mean absolute percentage error(MAPE)ranged from 4.197%to 8.986%,and mean absolute error(MAE)ranged from 3.202%to 8.476%.At ambient temperatures of 25℃,35℃ and 45℃,the MPC based on the BPNN prediction model reduced the cumulative discomfort time in the cabin by 100 s,39 s and 19 s,respectively,compared with the PID control.Under three NEDC conditions,the energy consumption is reduced by 1.82%,2.35%and 3.48%,respectively.When the ambient temperature was 35℃,the MPC based on BPNN prediction model can make the ACS and BTMS coupling system have better thermal comfort,and the energy saving effect of the compressor was more obvious with the temperature.

Machine learning modeling for fuel cell-battery hybrid power system dynamics in a Toyota Mirai 2 vehicle under various drive cycles

Electrification is considered essential for the decarbonization of mobility sector, and understanding and modeling the complex behavior of modern fuel cell-battery electric-electric hybrid power systems is challenging, especially for product development and diagnostics requiring quick turnaround and fast computation. In this study, a novel modeling approach is developed, utilizing supervised machine learning algorithms, to replicate the dynamic characteristics of the fuel cell-battery hybrid power system in a 2021 Toyota Mirai 2nd generation (Mirai 2) vehicle under various drive cycles. The entire data for this study is collected by instrumenting the Mirai vehicle with in-house data acquisition devices and tapping into the Mirai controller area network bus during chassis dynamometer tests. A multi-input - multi-output, feed-forward artificial neural network architecture is designed to predict not only the fuel cell attributes, such as average minimum cell voltage, coolant and cathode air outlet temperatures, but also the battery hybrid system attributes, including lithium-ion battery pack voltage and temperature with the help of 15 system operating parameters. Over 21,0000 data points on various drive cycles having combinations of transient and near steady-state driving conditions are collected, out of which around 15,000 points are used for training the network and 6,000 for the evaluation of the model performance. Various data filtration techniques and neural network calibration processes are explored to condition the data and understand the impact on model performance. The calibrated neural network accurately predicts the hybrid power system dynamics with an R-squared value greater than 0.98, demonstrating the potential of machine learning algorithms for system development and diagnostics.

A Comparative Study of Fractional Order Models on State of Charge Estimation for Lithium Ion Batteries

State of charge(SOC)estimation for lithium ion batteries plays a critical role in battery management systems for electric vehicles.Battery fractional order models(FOMs)which come from frequency-domain modelling have provided a distinct insight into SOC estimation.In this article,we compare five state-of-the-art FOMs in terms of SOC estimation.To this end,firstly,characterisation tests on lithium ion batteries are conducted,and the experimental results are used to identify FOM parameters.Parameter identification results show that increasing the complexity of FOMs cannot always improve accuracy.The model R(RQ)W shows superior identification accuracy than the other four FOMs.Secondly,the SOC estimation based on a fractional order unscented Kalman filter is conducted to compare model accuracy and computational burden under different profiles,memory lengths,ambient temperatures,cells and voltage/current drifts.The evaluation results reveal that the SOC estimation accuracy does not necessarily positively correlate to the complexity of FOMs.Although more complex models can have better robustness against temperature variation,R(RQ),the simplest FOM,can overall provide satisfactory accuracy.Validation results on different cells demonstrate the generalisation ability of FOMs,and R(RQ)outperforms other models.Moreover,R(RQ)shows better robustness against truncation error and can maintain high accuracy even under the occurrence of current or voltage sensor drift.