见解是什么意思>小学二年级数学口算题Modeling of lithium ion cells—A simple equivalent-circuit model approach
Bor Yann Liaw a,*,Ganesan Nagasubramanian b ,Rudolph G.Jungst c ,Daniel H.Doughty b
高二英语作文a
Electrochemical Power Systems Laboratory,Hawaii Natural Energy Institute,SOEST,University of Hawaii at Manoa,1680East-West Road,POST 109,Honolulu,HI 96822,USA b
Lithium Battery R and D Department,Sandia National Laboratories,Albuquerque,NM 87185,USA c
Long-Life Power Sources Department,Sandia National Laboratories,Albuquerque,NM 87185,USA
realityshowAbstract
We prent an equivalent-circuit-bad battery model,capable of simulating charge and discharge behavior of lithium-ion batteries (LiB).The model,although simple in concept,can simulate complex discharge behavior with high fidelity,as validated by experimental results.D 2004Elvier B.V .All rights rerved.
Keywords:Equivalent circuit model;Lithium-ion battery;Computer modeling and simulation
1.Introduction
参加英语Equivalent-circuit-bad battery modeling is gaining popularity becau this simple modeling technique can be ud to successfully simulate battery performance for various chemistries,including valve-regulated lead-acid (VRLA)[1,2],nickel metal hydride (Ni-MH)[3],and LiB [4].This approach reduces the need to understand detailed mechanisms and only requires a few parameters,which are easily obtainable from experiments,to reach high-fidelity predictions.Unlike first-principle-bad modeling,this approach simplifies mathematical and numerical treatments to minimize or even avoid complicated and intensive computation requirements,so results can be quickly obtained.
Conventionally,electrochemical impedance spectro-scopy (EIS)has been ud to study transport and interfacial reaction kinetics in an electrochemical system.Analys of complex impedance data rely on a framework that employs equivalent circuit diagrams to emulate the behavior of a ries of elements in circuitry that reprents
the electrochemical system.Using the same framework,we can deploy a circuit of electrical elements in a proper configuration,bad on our physical understanding of the cell configuration and chemistry,to construct an equivalent circuit model (ECM)to simulate cell performance and behavior.
An ECM may compri three major parts:a static part reprenting the thermodynamic properties of the battery chemistry,such as the nominal capacity and open-circuit voltage (OCV)as a function of state-of-charge (SOC);a dynamic part that reprents the kinetic aspects of the cell internal impedance behavior;and a source or load to complete the circuit for charge or discharge regimes;thus,allowing us to mimic the battery behavior and simulate its performance characteristics.As an example in Fig.1,Yang and Liaw [5]show that,using a transmission-line ECM suggested by Barsoukov et al.[4],they were able to simulate the impedance respon of an inrtion electrode in a LiB cell by imposing the condition of a small voltage perturbation on the cell over a range of frequencies in MATLAB.
Our current interest is to u a more simplified model,with proper initial and boundary conditions,to simulate battery performance under dynamic charge or discharge conditions,and eventually,to predict life.The chemistry
0167-2738/$-e front matter D 2004Elvier B.V .All rights rerved.doi:10.1016/j.ssi.2004.09.049
*Corresponding author.Tel.:+18089562339;fax:+18089562336.E-mail address:bliaw@hawaii.edu (B.Y .Liaw).
Solid State Ionics 175(2004)835
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ud in this work is currently under investigation by the U.S.Department of Energy (USDOE)Advanced Technol-ogy Development (ATD)program [6]for hybrid electric vehicle (HEV)applications.
2.Model description
A schematic of the model that we ud for the remaining part of this paper is shown in Fig.2,which rembles that ud by Verbrugge and Conell [3]for Ni-MH cells.The unique feature we adopted in the model is the paration of (1)all Ohmic resistant components lumping into R 1,and (2)faradic non-linear components into the R 2C circuit.We favored this model over the transmission-line model
shown in Fig.1due to its simplicity in describing behavior of an electrochemical system and the success we enjoyed in modeling a variety of chemistries.To develop this model for LiB,we first needed to incorporate the SOC-dependent OCV and resistance values (R 1and R 2)into the model.Fig.3shows the SOC-dependent values of the Li
B chemistry ud in this work.The OCV values were obtained by discharging a fully charged cell at the C/25rate,as reported in Ref.[7].
The resistance values were estimated from experimen-tal data.A typical Nyquist plot of a cell is shown in Fig.4,where the ac impedance spectra at 60%and 100%SOC are illustrated.R 1was taken from the Nyquist plot,as shown in the figure,and assumed constant in the entire SOC range.This assumption is valid,since (1)we do not expect that the Ohmic resistance changes noticeably with SOC,and (2)the R 1values at the two SOCs in the figure do coincide with each other at the real axis on the Nyquist plot.The SOC-dependent R c (the cell total resistance R 1+R 2)values could be estimated from the difference in the voltage of the discharge curves deter-mined at C/25and C/1rates,of which the experimental data are shown in Fig.5.In the actual simulations,the R c values were assumed to be a combination of two parategoodbye my lover
functions,R c o and R c s
,as shown in Fig.3,to adequately approximate the resistance change with SOC.The values of R 2were obtained from subtracting R 1from R c .The capacitance,C ,values can be calculated from the characteristic frequency,f c2=1/R 2C ,of the micircle in the Nyquist plot that reprents R 2C .
In this work,we will show how the cell voltage can be simulated from the ECM.Under a constant-current con-dition,Verbrugge and Conell [3]have derived the time-dependent cell voltage as V t ðÞ¼
Q 0ðÞC
e Àt =R 2C
þV o ÀIR 1ÀIR 21Àe Àt =R 2C
;where I ¼constant ðÞ
ð1Þ
where Q (0)is the nominal capacity,and V o is the nominal SOC-dependent cell OCV.For any given time step,we estimate the charge pasd,thus,deriving the SOC value at the end of the step.We u Eq.(1)to calculate the cell voltage change at various rates.Thus,a simulated voltage versus SOC (or t
ime)discharge curve for a specific rate can be obtained.Fig.5shows a ries of discharge curves at various rates,from C/25to 10C,simulated from the
ECM.
Fig.1.(Left)A transmission-line equivalent circuit model describing the behavior of an inrtion electrode in a lithium-ion battery under a small voltage perturbation,as propod by Barsoukov et al.[4].(Right)Simulated impedance spectra at different SOC for a Sony 18650cell [5]
.
Fig.2.The equivalent circuit model ud in this work to simulate LiB
performance for Gen 2cells.
B.Y.Liaw et al./Solid State Ionics 175(2004)835–839
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The ability to simulate cell voltage under charge or discharge regimes is quite uful for battery rearch.For example,by imposing a suitable cut-off condition,we then calculate the amount of charge put in and relead from the cell to yield the rate capacity,as well as charge efficiency.Furthermore,if the aging effects and degrada-tion rates in the cell impedance are known,we can then perform simulations using various temperature and power conditions impod on the cell to simulate the life performance.Other voltage or current versus time relationships,similar to that of Eq.(1),under different operating conditions can be derived accordingly for model-ing other cell behaviors.
3.Experimental
The test cells (so called b Gen 2Q cells)were received from Quallion (Sylmar,CA)as part of the USDOE ATD program efforts,and Sandia National Laboratories was commissioned to evaluate the cell performance to develop accelerated life tests.More detailed cell chemistry,config-uration,test protocol;procedure,test result,and cell’s Arrhenius behavior from thermal aging can be found in Refs.[6–10]and will not be repeated here.This chemistry in a nominal 18650cell consists of MAG-10graphite-negative electrode,LiNi 0.8Co 0.15Al 0.05O 2-positive electrode,and 1.2M LiPF 6in ethyl carbonate/ethyl methyl carbonate
(3:7
Fig.3.The SOC-dependent OCV and resistance values for the total cell resistance (R c and the two independent contributions R c o and R c s
小学生国庆节演讲稿),R 1,and R 2of the Gen 2chemistry in the
model.
Fig.4.A Nyquist plot showing the cell impedance change with frequency (0.01to 10,000Hz)and SOC in the Gen 2cells.
B.Y.Liaw et al./Solid State Ionics 175(2004)835–839837cubs
wt.%ratio).The discharge curves at C/25and C/1and the complex impedance data of the Gen 2cells generated in the tests were ud in the development of the ECM and for validation.
4.Results and discussion
Barsoukov et al.[4]and Yang and Liaw [5]have previously shown that complex impedance respons of Sony 18650cells could be simulated from a transmission-line model,as illustrated in Fig.1.Fig.1illustrates a uful approach to simulate impedance respon from the cell bad on a transmission-line ECM.The synthesis of the Nyquist plot is significant for validation,since experimen-tal data can be obtained from tests.The synthesis and validation with test results can assist us to enhance the understanding of the underpinning process related to aging and degradation.For example,we can hypothesize how the impedance would change with aging condition and synthesize the complex impedance respon.By comparing with the test results,we can verify if such a hypothesis is correct or not.Through validation,the conformity with actual test results can then be ud to simulate other cell performance characteristics.A greater conformity with other test results,such as power fade or capacity fade,can corroborate our quest for a better understanding of the degradation process to achieve a better life prediction.Fig.3shows the OCV and resistance values determined from the experimental data as a function of SOC,which were ud in the ECM de
scribed in Fig.2for the Gen 2cells.Fig.4displays a typical Nyquist plot measured from
one of the Gen 2cells and the assignment of a few critical parameters such as the resistance values and the character-istic frequency ud in the simulation.Fig.5shows a ries of discharge curves of voltage versus SOC simulated at various rates for the Gen 2cells.The simulation curves show a high degree of fidelity,as compared with experimental data collected at C/25and C/1.In the simple ECM we ud,we usually combine Ohmic-like contact resistance,including the electronic resistance of the leads,taps,and current collectors to the cell,into the rial resistance component R 1.For other non-linear,faradic behavior,including any mi-conducting path in the circuitry,and charge transfer or redox-related properties,we combine them into R 2.This simple treatment ems to work successfully so far.
In our current model,the behavior of R c with SOC is quite intriguing,since it ems to be compod of at least two independent contributions.The contribution dominating in the higher SOC region ems to follow a power law,R c o =0.021–0.02(1-SOC)6,while the other,becoming signifi-cant below 15%SOC,exhibits an exponential relationship,R c s =0.58[exp(À35*SOC)].The emerging of the two contributions greatly impacts the shape of the discharge curves,thus,it is good for validation of the system.The origins of the contributions and their physical meanings are not clear at this mome
nt.Additional efforts to investigate the impacts of the contributions to the cell performance,such as capacity and power fade,cycle and calendar life,are under way and will be reported elwhere.
In all,the ECM approach shows simplicity,flexibility,and yet high fidelity in simulating battery performance characteristics,as illustrated in the accurate prediction
of
Fig.5.Simulated discharge curves of cell voltage versus SOC at various rates and compared with experimental data collected at C/25and C/1rates for the Gen 2cells.
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cell discharge behavior as shown in Fig.5.With a t of carefully determined experimental data,such as OCV and resistance values as a function of SOC,we can construct an ECM with high fidelity to emulate cell performance and predict its characteristics via computer simulation.
5.Conclusion
A simple equivalent circuit model(ECM)can be ud to express complicated lithium-ion battery performance via computer simulation,showing a high degree of agreement with the experimental data.Cell impedance respon and discharge behavior can be simulated with this simple ECM approach.The validity of using this type of simple ECM approach exhibits great potential for battery rearch and development.
Acknowledgements
Sandia is a multi-program laboratory operated by Sandia Corporation,a Lockheed Martin Company,for the United States Department of Energy under Contract DE-AC04-94AL85000.The authors would like to thank Herbert L. Ca for conducting battery testing and data reduction.BYL would also like to thank Sandia for providing support for his sabbatical leave at Sandia.Dr.X.G.Yang contributed to some of the earlier work prented in Fig.1. References
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