Enhanced Identification of Battery Model for Real Time Battery Management

300 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY, VOL. 2, NO. 3, JULY 2011

Enhanced Identification of Battery Models forReal-Time Battery Management

Mark Sitterly, Student Member, IEEE, Le Yi Wang, Senior Member, IEEE, G. George Yin, Fellow, IEEE, andCaisheng Wang, Senior Member, IEEE

Abstract—Renewable energy generation, vehicle electrification,and smart grids rely critically on energy storage devices for en-hancement of operations, reliability, and efficiency. Battery sys-tems consist of many battery cells, which have different character-istics even when they are new, and change with time and operatingconditions due to a variety of factors such as aging, operationalconditions, and chemical property variations. Their effective man-agement requires high fidelity models. This paper aims to developidentification algorithms that capture individualized characteris-tics of each battery cell and produce updatedmodels in real time. Itis shown that typical batterymodelsmay not be identifiable, uniquebattery model features require modified input/output expressions,and standard least-squares methods will encounter identificationbias. This paper devises modified model structures and identifica-tion algorithms to resolve these issues. System identifiability, algo-rithm convergence, identification bias, and bias correction mecha-nisms are rigorously established. A typical battery model structureis used to illustrate utilities of the methods.

Index Terms—Battery management system, battery model, biascorrection, convergence, identifiability, parameter estimation,system identification.

I. INTRODUCTION

R ENEWABLE energy generation, vehicle electrification,and smart grids rely critically on energy storage devices

for enhancement of operations, reliability, and efficiency. Alarge-scale battery system consists of hundreds, even thou-sands, of battery cells, which have different characteristicseven when they are new, and change with time and operatingconditions due to a variety of factors such as aging, operationalconditions, and chemical property variations. State of charge,battery health, remaining life, charge and discharge resistance

Manuscript received September 10, 2010; accepted February 06, 2011. Dateof publication February 17, 2011; date of current version June 22, 2011. Thework of L. Y. Wang was supported in part by the National Science Foundationunder DMS-0624849, and in part by the Air Force Office of Scientific Researchunder FA9550-10-1-0210. The work of G. G. Yin was supported in part by theNational Science Foundation under DMS-0907753, and in part by the Air ForceOffice of Scientific Research under FA9550-10-1-0210. The work of C. Wangwas supported by the National Science Foundation under ECS-0823865.M. Sitterly, L. Y. Wang are with the Department of Electrical and Com-

puter Engineering, Wayne State University, Detroit, MI 48202 USA (e-mail:[email protected]; [email protected]).G. G. Yin is with the Department of Mathematics, Wayne State University,

Detroit, MI 48202 USA (e-mail: [email protected]).C. Wang is with the Division of Engineering Technology and the Department

of Electrical and Computer Engineering, Wayne State University, Detroit, MI48202 USA (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TSTE.2011.2116813

and capacitance demonstrate nonlinear and time-varying dy-namics [4], [5], [8], [12], [18], [24]. Consequently, for enhancedbattery management, reliable system diagnosis, and improvedpower efficiency, it is necessary to capture battery cell modelsin real time [18]. This paper aims to develop a real-time au-tomated battery characterizer that will capture individualizedcharacteristics of each battery cell and produce updated modelsin real time. The core of such a system is advanced systemidentification techniques [15], [27], [28], [29] that providefast tracking capability to update each battery cell’s individualmodel when it is plugged into the battery system and to trackbattery aging and health conditions during operation.The main ideas of such identification methods include:

1) using load changes to “stimulate” or “excite” the internalbehavior of the cell; 2) using measured voltage and current datato estimate model parameters such that the model-producedvoltage and current trajectories match those from the actualbattery cell; 3) employing recursive algorithms to accomplishautomated model generation and real-time operation so thatnew measurement data are immediately used to update themodel.To facilitate discussions on the key issues and challenges

in real-time battery model identification, we employ, as atypical model structure, the resistance–capacitance batterymodel, which is part of ADVISOR, developed at NationalRenewable Energy Laboratory (NREL) [12]. The parametersof the components are functions of the state of charge (SOC)and cell temperature. In addition, the resistance values differwhen the battery is in “charge” mode or “discharge” mode.Typically the parameters of the model and their dependence onthe SOC and temperatures are experimentally established. Inthis work, we will use system identification methods to identifythem in real time, without laboratory testing facilities. Whenidentification can capture the circuit model parameters fasterthan a battery’s charge/discharge operations, one may employthe “frozen time” concept and view the model parameters astheir linearized values at a given operating condition. As such,identification of the system can concentrate on time-varyingbut linearized models.The goal of system identification is to identify system pa-

rameters on the basis of observations on the measured inputsand outputs. Continuing our recent work on battery models[22], [23], in this paper, we will use adaptive filtering algo-rithms to derive convergent algorithms. System identifiability,algorithm convergence, identification bias, and bias correctionmechanisms are rigorously established. The paper is organizedas follows. Section II introduces battery model structures.

1949-3029/$26.00 © 2011 IEEE

SITTERLY et al.: ENHANCED IDENTIFICATION OF BATTERY MODELS FOR REAL-TIME BATTERY MANAGEMENT 301

Fig. 1. Battery model.

Although our methodology is generic, it is helpful to usea typical model structure to reveal key issues and discusstheir resolutions. System identifiability is first discussed inSection III. It is shown that physically meaningful models maynot be real-time identifiable. Modifications of model structuresto facilitate system identification are studied, leading to amodified regression expression for system identification. Thesection further explores the issue of identification bias correc-tion. It is revealed that due to noise corruption in observationdata and inherent correlation in the regressors, the standardleast-squares (LS) algorithms will encounter identificationbias, implying that parameter estimates will have an inherenterror even when data sizes become very large. Bias correctionmeasures are introduced to overcome this drawback. Strongconvergence of the modified algorithms is established. Forcomputational efficiency, recursive algorithms are derived. Themethodologies of this paper are then evaluated and illustratedby using simulation studies in Section IV. Both standard LSalgorithms and modified algorithms are illustrated for theirutilities. Finally, our findings and potential applications arediscussed in Section V.

II. BATTERY MODEL STRUCTURES

The methodologies developed in this paper can be appliedto different battery models. We choose a well-developed andvalidated model structure to facilitate discussions of essentialissues, including identification algorithms, identifiability, biascorrection, noise correlation, and convergence analysis. We em-ploy the resistance–capacitance battery model which is part ofADVISOR, developed at NREL [3], [12] (see Fig. 1).The model contains two capacitors ( and ) and three

resistors ( , , and ). The capacitor models themain storage capacity of the battery. The capacitor cap-tures the fast charge–discharge aspect of the battery and ismuch smaller than . The parameters of the componentsare functions of the SOC and cell temperature ( ). In ad-dition, the resistance depends on also if the battery is in“charge” or “discharge” mode. These will be expressed as

whenneeded. To describe the model details, we define the followingsymbols:

terminal voltage (V);

terminal current (A);

voltage of the capacitor (V);

current through the capacitor (A);

Fig. 2. Battery thermal model.

voltage of the capacitor (V);

current through the capacitor (A);

air temperature (degree Celsius);

cell temperature (degree Celsius);

conducting heat transfer rate (W);

heat transfer rate generated by the battery cell (W);

air conditioning forced heat transfer rate (W);

SOC;

SOC ;

SOC ;

It was given in [12] that the overall state of charge is aweighted combination of the states of charge on and

(1)

where . In the NREL/Saft model, and. and will be related to the voltages

on and .The thermal model is a lumped first-order linear dynamics,

shown in Fig. 2

where is the equivalent thermal resistance ( ) andis the equivalent heat capacitance ( ).In [3] and [12], the parameters of the model and their depen-

dence on the SOC and temperatures are experimentally estab-lished. In this work, wewill use system identificationmethods toidentify them in real time, without laboratory testing facilities.The states of charge of and are closely related to their

voltages and . The relationship andcan be experimentally established. In the normal oper-

ating ranges of and , they can be well approximated by linearfunctions [12].From , model parameters become

functions of the state variables and the mode

(2)


The battery model is derived from the following basicequations:

These lead to

and

With state variables ; inputs (current load), (airtemperature), (battery cell generated heat flow rate), and(convective heat flow rate due to cooling air); operating mode; and outputs (terminal voltage), (state of charge), and ;the state space model is

(3)

Remark 1: By (2), the model parameters depend on the state.Consequently, the system is highly nonlinear. Within the inputs,is measured and fed back as an input to the model. is a dis-turbance but is measured with some measurement noise. Sinceis not modeled in detail, it will be considered as an unmea-

sured disturbance to the battery system. is controlled (bythe cooling system). The cooling system dynamics are not con-sidered in this model. As a result, we will view as a con-trol input. The outputs and are measured with measurementnoise. is not measured.Denote the state vector by , input vector

, and output vector . The state spacemodel (3) may be written in an abstract form, for methodologyand algorithm development, as

(4)

This is a nonlinear system in an affine form. Since is a controlvariable taking only two possible values, the system (4) is ahybrid system.

For simulation studies, we will use the NREL/Saft model[10]–[12]. The model structure is given in Fig. 1. Nominalvalues of the parameters at temperature 20 C are

(5)

Although dependence of these parameters on and can bederived from experimental data, in this paper we employ systemidentification methods to capture real-time parameter values.

III. IDENTIFICATION OF BATTERY MODELS

Although system parameters in the battery model (3) canbe established by using experimental data from laboratorytesting, for real-time operation under a battery managementsystem (BMS), the parameters must be derived using real-timeoperational data. This is due to several factors: 1) New batterieshave different characteristics even for the same model, due tomanufacturing variations. 2) Battery features depend on manyfactors that cannot be totally captured in model details. 3) Bat-teries experience significant aging effects. Consequently, it isnot only desirable, but in fact imperative that model parametersbe obtained individually in real time.

A. Identifiability of Battery Models

We first derive the transfer function for the battery modelshown in Fig. 1. Using for the capacitors and derivingthe transfer function in the -domain, we obtain

(6)

where. For

example, under kF, kF, mm m , we have

(7)

The input–output model (6) contains four coefficients. How-ever, the internal circuit model in Fig. 1 contains five parame-ters. In other words, there will be one redundant parameter in themodel. As a result, the circuit model is not input–output identi-fiable when only the terminal voltage and current are measured.Due to its physical meanings, the pair represents a

much faster branch than the branch. Consequently, itis a sensible choice to let , reducing the battery systeminto a four-parameter circuit model. We show now that this sim-plification results in a direct inverse mapping from the transferfunction parameters to the circuit parameters.When , (6) is reduced to

(8)


where , , ,, . The inverse mapping of the parameters

can be derived as

(9)

This defines a mapping fromto . As a result, simplified circuit model (8)is always identifiable.

B. Regression Structure for System Identification

Although the battery model’s physical input is the load (cur-rent ), since the model contains an integrator, for system iden-tification the input/output setting needs to be modified.Suppose that the signal sampling interval in a BMS is . Let

the sampled values be , , etc. To derive asampled expression to identify parameters in (9), we note that

(10)

where . Using the forward approximation, wehave . Equation (10) is mapped to

(11)

where , ,, . For the data

from (7) and second, we have

(12)

Define . can be de-rived as a mapping from

Consequently, we have a mapping to the circuit parameters

(13)

The discrete-time system (11) leads to the regression expres-sion of the new input/output relationship

(14)

where the regressor is . Itshould be pointed out that in practical applications, the measure-ments on the current and voltage are subject to noises. Asa result, is measured as and as .Consequently,

where . In other words,noises enter the regressor also. This is a more complicatedproblem of errors-in-variable identification.

C. Identification Algorithms

For algorithm implementation, only and can be used.From the observation equation

and the mapping , we would like to derive identifica-tion algorithms to track time-varying parameters.Assumption 1: Suppose that the measurement on is

subject to measurement noise and the voltage mea-surement is subject to measurement noise . The jointvector sequence is stationary and ergodic [in thesense of convergence with probability one (w.p.1)] such that

, , and that bothand are ergodic. That is,

Note that we do not need the sequences and tobe independent. A sufficient condition to ensure the ergodicityin the above assumption is that the underlying sequence is astationary -mixing sequence, which is a sequence whose re-mote past and distant future are asymptotically independent.The well-known results [13, p. 488] then yield that and

are strongly ergodic.It is noted that for time-varying systems, identification of

system parameters can only be performed on the basis ofmost recent data, such as a finite-time moving window orexponentially decaying window. Hence, suppose the data on

and are collected in a finite-time window . Let, the largest integer below . When ,

, and convergence analysis in this case should be inter-preted as asymptotic accuracy of identification when samplingintervals become small.


Let

......

......

...

Then, . From, the observation equation becomes. When is nonsingular, w.p.1, the standard

LS estimate is

(15)

We should demonstrate that due to signal correlation, this al-gorithmwill introduce identification bias, namely, parameter es-timates will converge to values away from the true value.

D. Identification Bias and Correction

Under Assumption 1, since and are deterministic, as, with probability one,

which imply

for some matrices . , , and . As a result,w.p.1. On the other hand, the true parameter satis-

fies . Consequently, we have the following theorem.Theorem 1: Assume that Assumption 1 holds and that

exists. Then the least-squares estimate (15) is asymptoticallybiased in that

Proof: This follows from

This completes the proof.

Identification bias can be corrected if and are known.The algorithm (15) is modified to

(16)

It follows from Theorem 1 that this modified has a desiredconvergence property. If and are unknown, we can usestatistical methods to estimate them. Then in the bias correctionalgorithm (16), in place of the true and , we may use theirestimates.Theorem 2: Under the assumptions of Theorem 1, the esti-

mates in (16) satisfy

Proof: By the strong law of large numbers, as

E. Recursive Algorithms for Bias Corrected LS Algorithms

We now introduce a recursive algorithm for (16).Theorem 3: The estimates in (16) can be updated recur-

sively as

Proof: From (16),

Let . Since, we have

By the matrix inversion lemma

(17)


Moreover,

Define

By (17)

It follows that

Finally,

IV. SIMULATION STUDIES

Although we use a specific battery model structure in thispaper, the main methodologies introduced in this paper aregeneric and can be applied to different battery models. Inthis section, we first illustrate the utility of bias correctionalgorithms by using some models of various structures andcomplexity. Then the specific circuit model is used for moredetailed evaluations.

A. Illustrative Examples on Identification Bias Correction

We now illustrate effectiveness of the bias correction mech-anisms described in Section III.Example 1: This example involves a finite impulse response

(FIR) system of order 2 and one step delay:. The true parameter is . The input

and the corresponding output are shown in the top plot ofFig. 3. Suppose that the input is corrupted by an independentand identically distributed (i.i.d.) Gaussian noise of mean zero

Fig. 3. Comparison of identification algorithms with and without bias correc-tion for a second-order FIR system with a delay.

Fig. 4. Comparison of identification algorithms with and without bias correc-tion for a third-order ARX system.

and variance 0.01, and the output is subject to an i.i.d. Gaussianmeasurement noise of mean zero and variance 0.16. Input andoutput noises are independent. In this example, and

, where is the 2 2 identity matrix. Without di-rect noise correction, identification errors demonstrate a persis-tent bias of norm 0.6373 (averaged Euclidean norm), with theexit estimate . With direct bias correc-tion, such a bias is substantially reduced to an error norm 0.0156and the exit estimate . These are shownin the bottom plot of Fig. 3.Example 2: This example involves an auto-regression with

external input (ARX) system

The true parameter is . Theinput and the corresponding output are shown in the topplot of Fig. 4. The input is corrupted by an i.i.d. Gaussian noiseof mean zero and variance 0.04, and the output is subject to an


Fig. 5. Battery model in Simulink.

i.i.d. Gaussian measurement noise of mean zero and variance0.01. Input and output noises are independent. In this example,

and

Under a data window of size , without direct noisecorrection, identification errors demonstrate a persistent bias ofnorm 0.1778, with the exit estimate

With direct bias correction, such a bias is reduced to an errornorm 0.0061 and the exit estimate

These are shown in the bottom plot of Fig. 4.

B. Identification of Circuit Models for Battery Systems

The circuit model of the nominal parameter values (5) is sim-ulated in a Simulink model shown in Fig. 5.The Simulink model generated the current and voltage pro-

files shown in Fig. 6, which will be used for parameter esti-mation. It should be emphasized here that to enhance identi-fication quality, a very small random dither has been added tothe load (current). This is indicated in the Simulink model by arandom signal generator, and reflected in the signal profiles withnoise-like signals. No measurement noises are added in the pro-files at this point.The true system parameter in the modified regression struc-

ture (11) is

The estimated system by using the LS (or equivalently RLS)algorithms produced the parameter estimation for

Fig. 6. Current and voltage profiles of the battery.

Due to added dithers, the estimates are highly accurate, evenwith a very small data window of size 50.Although the estimation is of high fidelity in this case, es-

timation quality deteriorates substantially when measurementnoises are introduced. When a very small measurement noise, aGaussian noise of mean 0 and variance 0.00001, is added to thevoltage measurements, parameter estimation loses its accuracy,shown in Fig. 7. The identification algorithms are then modifiedto include bias correction. Fig. 8 demonstrates substantially im-proved identification accuracy after bias correction.

V. CONCLUDING REMARKS

This paper has introduced identification methods for real-time battery model updates. The methods capture time-varyingmodel parameters which can then be used for real-time control,optimization, diagnosis, and management. Due to some uniquefeatures in battery model structures, battery model identifica-tion encounters some challenging issues, such as identifiability,


Fig. 7. Parameter estimation errors increase when voltage measurements areslightly noise corrupted.

Fig. 8. Parameter estimation becomes more accurate when bias correction al-gorithms are implemented.

bias, and convergence. Modified identification algorithms areintroduced to resolve these issues. Applications of the methodsare demonstrated in some typical models in this paper. Muchbroader utilities are currently under investigation in different as-pects of battery management systems. Also, discussions of thispaper are limited to a single battery cell. Extensions to a batterypack consisting of a network of battery cells remain an open andcritically important scenario for investigation.

REFERENCES

[1] A. Benveniste, M. Metivier, and P. Priouret, Adaptive Algorithms andStochastic Approximations. Berlin: Springer-Verlag, 1990.

[2] K. Astrom and B. Wittenmark, Adaptive Controls, 2nd ed. Mineola,NY: Dover, 2008, pp. 42–52.

[3] Advanced Vehicle Simulator (ADVISOR) ver. 3.2 [Online]. Available:http://www.ctts.nrel.gov/analysis

[4] C. Barbier, H. Meyer, B. Nogarede, and S. Bensaoud, “A battery stateof charge indicator for electric vehicle,” in Proc. Int. Conf. Institutionof Mechanical Engineers, Automotive Electronics, London, U.K., May17–19, 1994, pp. 29–34.

[5] E. Barsoukov, J. Kim, C. Yoon, and H. Lee, “Universal battery param-eterization to yield a non-linear equivalent circuit valid for battery sim-ulation at arbitrary load,” J. Power Sour., vol. 83, no. 1/2, pp. 61–70,1999.

[6] H. Chan and D. Sutanto, “A new battery model for use with batteryenergy storage systems and electric vehicle power systems,” in Proc.2000 IEEE Power Engineering Society Winter Meeting, Singapore,Jan. 23–27, 2000, pp. 470–475.

[7] H.-F. Chen and G. Yin, “Asymptotic properties of sign algorithms foradaptive filtering,” IEEE Trans. Automatic Control, vol. 48, no. 9, pp.1545–1556, Sep. 2003.

[8] R. Giglioli, P. Pelacchi, M. Raugi, and G. Zini, “A state of charge ob-server for lead-acid batteries,” Energia Elettrica, vol. 65, no. 1, pp.27–33, 1988.

[9] W. B. Gu and C. Y. Wang, “Thermal-electrochemical modeling of bat-tery systems,” J. Electrochem. Soc., vol. 147, no. 8, pp. 2910–2922,2000.

[10] V. Johnson, A. Pesaran, and T. Sack, “Temperature-dependent batterymodels for high-power lithium-ion batteries,” in Proc. 17th ElectricVehicle Symp., Montreal, Canada, Oct. 2000.

[11] V. Johnson, M. Zolot, and A. Pesaran, “Development and validationof a temperature-dependent resistance/capacitance battery model forADVISOR,” in Proc. 18th Electric Vehicle Symp., Berlin, Germany,Oct. 2001.

[12] V. H. Johnson, “Battery performance models In ADVISOR,” J. PowerSources, vol. 110, pp. 321–329, 2001.

[13] S. Karlin and H. M. Taylor, A First Course in Stochastic Processes,2nd ed. New York: Academic, 1975.

[14] H. J. Kushner and G. Yin, Stochastic Approximation and RecursiveAlgorithms and Applications, 2nd ed. New York: Springer-Verlag,2003.

[15] L. Ljung, System Identification: Theory for the User. EnglewoodCliffs, NJ: Prentice-Hall, 1987.

[16] S. Piller, M. Perrin, and A. Jossen, “Methods for state-of-charge deter-mination and their applications,” J. Power Sour., vol. 96, pp. 113–120,2001.

[17] G. Plett, “Extended Kalman filtering for battery management systemsof LiPB-based HEV battery packs. Part 1. Background,” J. PowerSour., vol. 134, no. 2, pp. 252–261, 2004.

[18] G. Plett, “Extended Kalman filtering for battery management systemsof LiPB-based HEV battery packs. Part 2,” Modeling and Identifica-tion, J. Power Sour., vol. 134, no. 2, pp. 262–276, 2004.

[19] G. Plett, “Extended Kalman filtering for battery management systemsof LiPB-based HEV battery packs. Part 3. State and parameter estima-tion,” J. Power Sour., vol. 134, no. 2, pp. 277–292, 2004.

[20] S. Rodrigues, N. Munichandraiah, and A. Shukla, “A review ofstate-of-charge indication of batteries by means of ac impedancemeasurements,” J. Power Sour., vol. 87, no. 1/2, pp. 12–20, 2000.

[21] A. Salkind, C. Fennie, P. Singh, T. Atwater, and D. Reisner,“Determination of state-of-charge and state-of-health of batteriesby fuzzy logic methodology,” J. Power Sour., vol. 80, no. 1/2, pp.293–300, 1999.

[22] M. Sitterly and L. Y. Wang, “Identification of battery models for en-hanced battery management,” in Proc. Clean Technology Conf. Expo2010, Anaheim, CA, Jun. 21–24, 2010.

[23] M. Sitterly, L. Y. Wang, and G. Yin, “Enhanced identification algo-rithms for battery models under noisy measurements,” in Proc. SAEPower Systems Conf., Ft. Worth, TX, Nov. 2–4, 2010.

[24] K. Takano, K. Nozaki, Y. Saito, A. Negishi, K. Kato, and Y.Yamaguchi, “Simulation study of electrical dynamic characteristicsof lithium-ion battery,” J. Power Sour., vol. 90, no. 2, pp. 214–223,2000.

[25] Battery Modeling for HEV Simulation by ThermoAnalytics Inc.[Online]. Available: http://www.thermoanalytics.com/support/publi-cations/batterymodelsdoc.html

[26] E. Wan and A. Nelson, , S. Haykin, Ed., “Dual extended Kalman filtermethods,” in Kalman Filtering and Neural Networks. New York:Wiley/Interscience, 2001, pp. 123–174.


[27] L. Y. Wang, “Persistent identification of time varying systems,” IEEETrans. Automatic Control, vol. 42, no. 1, pp. 66–82, Jan. 1997.

[28] L. Y. Wang, J. F. Zhang, and G. Yin, “System identification usingbinary sensors,” IEEE Trans. Automat. Control, vol. 48, no. 11, pp.1892–1907, Nov. 2003.

[29] L. Y. Wang, G. Yin, J.-F. Zhang, and Y. Zhao, System IdentificationWith Quantized Observations. Boston,MA: Birkhäuser, 2010, ISBN:978-0-8176-4955-5.

[30] G. Yin, “Stochastic approximation: Theory and applications,” inHandbook of Stochastic Analysis and Applications, D. Kannan andV. Lakshmikantham, Eds. New York: Marcel Dekker, 2002, pp.577–624.

Mark Sitterly (S’02) received the B.S. and M.S. de-grees in electrical engineering fromWayne State Uni-versity, Detroit, MI, in 2000 and 2005, respectively.He is currently a Graduate Teaching Assistant andPh.D. student at Wayne State University, Detroit, MI.He also serves in the U.S. Air Force with the

Michigan Air National Guard as a Bioenviron-mental Engineer. He previously worked at EatonCorporation in Southfield, MI, as a Senior ElectricalEngineer.

Le Yi Wang (S’85–M’89–SM’01) received thePh.D. degree in electrical engineering from McGillUniversity, Montreal, Canada, in 1990.Since 1990, he has been with Wayne State Univer-

sity, Detroit, MI, where he is currently a Professorin the Department of Electrical and Computer En-gineering. His research interests are in the areas ofcomplexity and information, system identification,robust control, optimization, time-varyingsystems, adaptive systems, hybrid and nonlinearsystems, information processing and learning, as

well as medical, automotive, communications, power systems, and computerapplications of control methodologies. He was a keynote speaker in severalinternational conferences. He serves on the IFAC Technical Committee onModeling, Identification and Signal Processing. He was an Associate Editor ofthe IEEE TRANSACTIONS ON AUTOMATIC CONTROL and several other journals,

and currently is an Associate Editor of the Journal of System Sciences andComplexity and Journal of Control Theory and Applications.

G. George Yin (S’87–M’87–SM’96–F’02) receivedthe B.S. degree inmathematics from the University ofDelaware in 1983, the M.S. degree in electrical engi-neering, and the Ph.D. degree in applied mathematicsfrom Brown University in 1987.He joined the Department of Mathematics, Wayne

State University in 1987, and became a Professorin 1996. His research interests include stochasticsystems, applied stochastic processes and applica-tions, stochastic recursive algorithms, identification,signal processing, and control and optimization. He

severed on the IFAC Technical Committee on Modeling, Identification andSignal Processing, and many conference program committees; he was theeditor of SIAM Activity Group on Control and Systems Theory Newsletters,Cochair of the 1996 AMS-SIAM Summer Seminar in Applied Mathematicsand the 2003 AMS-IMS-SIAM Summer Research Conference: Mathematicsof Finance, Co-organizer of the 2005 IMA Workshop on Wireless Commu-nications and the 2006 IMA PI conference. He is Cochair of 2011 SIAMControl Conference, Program Director of SIAM Activity Group on Controland Systems Theory, is an associate editor of Automatica and SIAM Journal onControl and Optimization, and is on the editorial board of a number of otherjournals. He was an Associate Editor of IEEE TRANSACTIONS ON AUTOMATICCONTROL 1994–1998.

Caisheng Wang (S’02–M’06–SM’08) received theB.S. and M.S. degrees from Chongqing University,China in 1994 and 1997, respectively, and the Ph.D.degree from Montana State University, Bozeman, in2006, all in electrical engineering.From August 1997 to May 2002, he worked as

an electrical engineer in Zhejiang Electric PowerTest and Research Institute, Hangzhou, China.Since August 2006, he has been a Faulty Memberat the Division of Engineering Technology and theDepartment of Electrical and Computer Engineering

at Wayne State University. His current research interests include modelingand control of power systems and electrical machines, energy storage devices,alternative/hybrid energy power generation systems, and fault diagnosis andon-line monitoring of electric apparatus.

Enhanced Identification of Battery Model for Real Time Battery Management

Documents

Transcript of Enhanced Identification of Battery Model for Real Time Battery Management