Online Condition Monitoring of Battery Systems

232 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 29, NO. 1, MARCH 2014

Online Condition Monitoring of Battery SystemsWith a Nonlinear Estimator

Gunyaz Ablay, Member, IEEE

AbstractThe performance of batteries as uninterruptablepower sources in any industry cannot be taken for granted. The fail-ures in battery systems of safety-related electric systems can leadto performance deterioration, costly replacement, and, more im-portantly, serious hazards. The possible failures in battery systemsare currently determined through periodic maintenance activities.However, it is desirable to be able to detect the underlying degra-dation and to predict the level of unsatisfactory performance byan online real-time monitoring system to prevent unexpected fail-ures through early fault diagnosis. Such an online fault diagnosismethod can also contribute to better maintenance and optimal bat-tery replacement programs. A robust nonlinear estimator-basedonline condition monitoring method is proposed to determine thestate of health of the battery systems online in industry. Real-worldexperimental data of a modern battery system are used to assess theefficiency of the proposed approach in the existence of parameteruncertainties.

Index TermsBattery management, battery modeling, condi-tion monitoring, fault diagnosis.

I. INTRODUCTION

THE increasing needs for high energy, power, life-cycle,FUEL economy, wide-range operating temperature, andenvironmentally acceptable batteries in electric and hybrid elec-tric systems are the driving forces for rapid growth of batterytechnologies. While there are many battery types, some bat-teries are more preferable to others in certain industries. Forexample, Ni-MH batteries are dominant battery technology forhybrid electric vehicle applications by having the best overallperformance in the wide-range requirements set by automobilecompanies [1]. The nuclear plants benefit from lead-acid batter-ies for their wide range of electrical systems as battery-backedsupplies (UPSs) to ensure continuity of function during outagesor interruptions [2], [3]. Fig. 1 shows a general working princi-ple of the battery systems in various industries. The dc load ispowered from battery chargers (rectifiers) during normal oper-ation, and it is automatically powered from station batteries incase of loss of normal power to the battery chargers.

Reliability of the battery system is significant for any indus-try due to the safety-related usage aim of the batteries. There

Manuscript received July 5, 2013; revised September 23, 2013 and October21, 2013; accepted November 14, 2013. Date of publication December 3, 2013;date of current version February 14, 2014. Paper no. TEC-00379-2013.

The author is with the Department of Electrical-Electronics Engineering,Abdullah Gul University, 38039 Kayseri, Turkey (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TEC.2013.2291812

Fig. 1. General working principle of battery systems.

are many factors that cause failures in battery systems, includ-ing design errors, battery component failures, overloading of dcbusses, flaking of cell plates, and aging-related failures [3], [4].For these reasons, monitoring and maintenance activities arenecessary for battery systems. Many industries (e.g., nuclearpower plants) perform periodic maintenance (monthly, quar-terly, and yearly) and battery parameter testing (capacity andinternal ohmic tests) for battery systems within the mainte-nance program. The functionality and reliability of batteries canbe enhanced with online fault diagnosis and health monitoring.The diagnostic algorithm can monitor the battery system for anypossible faults and malfunctions. A battery monitoring systemis specifically necessary for sealed batteries, e.g., valve regu-lated lead-acid and lithium-ion batteries, since it is not possibleto directly measure their internal parameters, i.e., internal cellresistances. It helps in detecting deviations of the battery perfor-mance from its normal behavior and also isolates the possiblecauses for the faults. In practice, output signals (measurements)of the system under consideration are often directly evaluatedand compared with a given threshold [5]. However, such anapproach is insufficient in critical processes due to capabilityto react only after a relatively large change in the measuredvariable [6], [7]. If the system is modeled, and the differencebetween the measurement and its estimation (residual) is ob-tained, then it is theoretically possible to detect every fault withresidual generation [8], [9]. The measurements of rechargeablebatteries are current and voltage at the poles of the batteries andthe battery temperature, which are enough to model the batterysystem for fault diagnosis and health monitoring in order to pre-vent serious damage and failures and to have better maintenanceactivities. In the literature, most of the fault diagnosis and healthmonitoring studies are provided for lithium-ion batteries due totheir usage in wide-range applications. The approaches includeextended Kalman filter, autoregressive moving average model,and fuzzy logic, which are summarized in [10], model-basedstate-of-charge (SOC) estimation [11], model-based fault diag-nosis algorithm [12], and parabolic regression algorithm [13].However, the robustness and efficiency of the above estima-tion approaches are questionable due to parameter uncertainties,simplifications, and linearization in the models.

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ABLAY: ONLINE CONDITION MONITORING OF BATTERY SYSTEMS WITH A NONLINEAR ESTIMATOR 233

In this study, a robust nonlinear estimator-based online con-dition monitoring methodology is proposed for robust fault di-agnosis in battery systems in the presence of parameter uncer-tainties that make the previous studies questionable. In reality,the periodic maintenance activities are the only way to deter-mine health of a battery in industries, e.g., nuclear power plants.With the usage of the proposed online condition monitoringapproach, unexpected failures can be prevented by early faultdetection, and optimization in the replacement programs andbetter maintenance activities can be obtained efficiently.

The organization of the paper is as follows. Section II de-scribes the characterization and modeling of battery systems.Section III describes the design, synthesis, and analysis of onlinecondition monitoring strategy. The assessments and conclusionsare given in Sections IV and V, respectively.

II. BATTERY SYSTEMSThere have been significant developments in battery tech-

nologies that offer excellent advantages, including flexible cellsizes from 30 mAh to 250 Ah, safe operation at high voltage(+320 V), high volumetric energy and power, maintenance-freedesigns, excellent thermal properties, environmentally accept-able and recyclable materials, and simple and inexpensive charg-ing and electronic control circuits [1], [14]. The lithium-ion andespecially nickelmetal hydride (Ni-MH) batteries are the cur-rent batteries that can provide the above advantages. However,the common use of these new rechargeable battery systems inUPSs and industry requires further studies and new technicalstandards.

The electrochemistry of rechargeable batteries is based oncharge-discharge mechanism between positive and negativeelectrodes. The electricity generation processes in a battery cellare chemical reactions that either consume or release electronsas the electrode reaction proceeds to completion. Such reac-tion, depending on battery electrode and electrolyte materialsand mechanisms that affect battery terminal voltage, is similarto all types of batteries. Battery terminal voltage changes withthe electrolyte concentration and there are resistive drops inelectrodes with current flow [15].

To extend the life of a battery system, charge and thermalmanagements play important roles and any problem relatedto overcharge, overdischarge, or control system must be di-agnosed with an online condition monitoring system. For de-velopments of online real-time battery monitoring systems, thelarge-scale storage batteries have been commonly modeled inthree ways: equivalent circuit battery models [16][19], electro-chemical battery models [20][23], and correlation-based mod-els [24]. Since electrochemical and experimental models are notwell suited to demonstrate battery dynamics accurately [25], theequivalent circuit battery model that is based on current-voltagerelations of the batteries is considered in this study.

The battery system consists of two main subsystems: batterypackage and temperature controller. Considering battery (load)current as an input, and battery voltage and temperature as out-puts, the battery model consists of three submodels: electrical,

Fig. 2. Battery Thevenin equivalent model.

TABLE IEXPERIMENTAL BATTERY PARAMETERS

thermal, and SOC models. Each of these submodels is describedbelow.

A. Electrical ModelThe voltage (capacity) in the battery cells is represented by

a voltage source, the electrochemical delay of the battery dueto shifting ion concentrations and plate current densities is de-scribed by a capacitorresistor model, and the internal resis-tance of the battery due to electrolyte diffusion is modeled bya resistor [26], [27]. The most commonly used battery mod-els are ideal model, linear model, and Thevenin equivalentmodel [16], [28], [29]. The Thevenin equivalent model withvarying parameters due to temperature and SOC variations rep-resents batteries with higher accuracy, as experimentally shownin many studies [30], and thus, it is considered in this study. Thismodel is made of electrical values of the open-circuit voltage(Eo), internal resistance (R), capacitance (Co), and the over-voltage resistance (Ro) [16]. The Thevenin equivalent model ofa battery is depicted in Fig. 2.

From Fig. 2, the dynamic electric equations of the circuit canbe obtained by applying Kirchhoffs rules as

dVcdt

= 1RoCo

Vc +1Co

I

V = Eo RI Vc(1)

where I (in Amperes) is the current at the input, Vc (in Volts) isthe capacitance voltage and V (in Volts) is the output voltage.All the parameters of (1) are functions of battery temperature (Tin C) and SOC (denoted by S), and can be different in chargeand discharge phases. The battery parameters are determinedusing experimental battery charge and discharge data for a Ni-MH battery system, and given in Table I. The meanings ofthe parameters described by other parameters in Table I areexplained in Section II-C. The data used in this study wereacquired as part of the activities of the Center for AutomotiveResearch at the Ohio State University. A general structure ofthe battery test system is illustrated in Fig. 3. The test system


Fig. 3. Battery test system.

Fig. 4. Battery electrical model validation using voltage measurements atroom temperature.

Fig. 5. Nominal current discharge characteristics for different types ofbatteries.

is appropriate for modeling any battery systems. With the useof this battery test system, the accuracy of the battery electricalmodel is tested and showed in Fig. 4. As seen from Fig. 4, thebattery model has a good level of accuracy.

To represent a particular battery type, the parameters of theelectrical model can be changed depending on its dischargecharacteristics as illustrated in Fig. 5. It can be seen from thefigure that the exponential voltage drop sections of the batteriescan have more or less wide areas depending on the battery type.The parameters gathered from the discharge characteristics areusually assumed to be the same for charging when the electricalmodel parameters are determined.

B. SOC ModelSOC provides information about remaining useful energy

and the remaining usable time of the battery. Many systemsare sensitive to overcharge and too high or too low SOC canresult in irreversible damage in the battery. It can be difficultto measure the SOC in the battery systems depending on thetype and application of the battery. There have been a num-

ber of different modeling approaches in the literature includingdischarge test, ampere hour counting, linear model, impedancespectroscopy, internal resistance, Kalman filter, and open-circuitvoltage model [10], [31][33]. One of the most acceptable SOCcalculation methods is the ampere hour counting (current inte-gration) method [10], [31] defined by

S = S0 1Cn

t

0I(t)dt (2)

where I (in Amperes) is the battery (load) current, Cn (inAmpere-hours) is the nominal capacity, and the initial SOCis given by S0 . This approach requires dynamic measurementof the battery current. It is applicable to all battery systems, easyto calculate and accurate with good current measurements.

Practically, the operating range of batteries with respect toSOC is confined with specific numbers. For example, a Ni-MHbattery has an operating range around 4080% with respect toSOC. Hence, this method implies that the charging operation iscontrolled.

C. Thermal ModelIn many systems, it is critical to achieve performance and ex-

tended life of batteries through thermal management. Recharge-able batteries are designed to work in room temperature (25 C),but a battery cannot be held at a certain temperature due todaily and seasonal temperature changes. It is well known thatlow temperatures slow up the chemical reactions in any bat-tery, resulting in reduced performance; however, from the otherextreme high temperatures destroy batteries. According to theArrhenius equation [34], for every 10 C increase in batterytemperature, battery life is halved due to faster positive gridcorrosion. Suitable modeling for predicting thermal behaviorof battery systems in applications can help to improve batterydesign and development process. Therefore, thermal models forbatteries have been developed based on thermal energy balanceof batteries, and they are coupled with electrochemical or elec-tric models [21], [22]. Based on the electric model and thermalenergy balance of a battery, a simple thermal model can be builtas

dT

dt=

R + Romc

I2 hAmc

(T T) (3)

where mc (in J/C) is the effective heat capacity per cell, hA (inJ/C) is the effective heat transfer per cell, and T (in C) is thebulk temperature. The effective heat transfer capacity per cell isgiven in terms of temperature controller (fan) settings by

hA = h0A0 (1 + 0.5fs) (4)

where h0A0 (in J/C) is given in Table I for natural convection,and the controller setting fs depends on the temperature. In thisstudy, the following temperature controller settings will be used:

{fs = 0 off mode, fs = 1 if T 30Cfs = 2 if T 35 oC fs = 3 if T 40C.

(5)


Fig. 6. Fault diagnosis scheme for the battery system.

III. ONLINE CONDITION MONITORING IN BATTERY SYSTEMSThe model of battery systems is complicated due to the feed-

back loop and the state-depended and time-varying parameters.The equivalent electrical model parameters of batteries are func-tions of temperature and SOC, which make fault detection dif-ficult. Moreover, the temperature feedback controller can maskthe temperature sensor faults so that the detection problem canpose some additional challenges. A model-based online condi-tion monitoring scheme for the battery systems is illustrated inFig. 6. The residual generator is composed of a nonlinear esti-mator, and the residual evaluation subsystem is used to providefault information by comparing the residuals with their nom-inal values. The residual generator and evaluation algorithmsare designed below to detect and isolate possible system faultsonline.

A. Robust Nonlinear Estimator for Residual GenerationA robust nonlinear estimator-based approach is considered to

generate residuals in this study. The main advantages of this ap-proach are robustness and high precision state estimation in thepresence of parameter variations. These features of the nonlin-ear estimator can enhance detection of internal battery problemsthrough detection of internal cell resistance variations. Based onthe system model given in (1)(5), a nonlinear estimator can bedesigned as

dT

dt=

R + Romc

I2 hAmc

(T T) + 1sign(T T )dVcdt

= 1RoCo

Vc +1Co

I

V = Eo RI VchA = h0A0(1 + 0.5fs)

(6)

where (T , Vc , V ) are the estimates of (T, Vc , V ), the observergain 1 is a constant to be selected, and the sign() function isthe unit vector defined by

sign(e) = e/ |e| (7)

where eT is the error state defined by eT = T T . The nonlin-ear estimator gain 1 must be selected large enough to bring theestimation errors to zero as explained in the following section.

B. Dynamical Analysis of the Residual GeneratorBy considering dynamic equations (1) and (3), the state space

form of the battery model can be written as[dVc/dt

dT/dt

]

=[k1 0

0 k2

] [Vc

T

]

+[

b1

b2I

]

I +[

0

k2

]

T

(8)where k1 = 1/RoCo, k2 = hA/mc, b1 = 1/Co , and b2 =(R + Ro)/mc. Since I and T are bounded, i.e., sup |I(t)| > |T |, im-plying that the slow state variable T (t) determines the dynamicbehavior of the battery system under bounded input values. It isclear from (8) that the dynamics of Vc and T are almost com-pletely independent of each other (uncoupled). Temperature Tis a directly measurable state, but capacitance voltage Vc is anindirectly measurable state through battery voltage V as givenin (1). For these reasons, the error dynamics of the estimatorcan be analyzed separately.

To analyze the stability of the nonlinear estimator (6), firstwe can consider the temperature estimation error eT = T T .The dynamic of the temperature estimation error is

eT = k2eT + (b2 b2)I2 1sign(eT ). (9)A candidate Lyapunov function [35], [36] can be selected as

W = e2T /2; then, its time derivative is

eT eT = eT ((b2 b2)I2 1sign(eT )) k2e2T (|(b2 b2)I2 | 1) |eT | k2e2T . (10)

Here, the observer gain 1 is selected large enough to satisfy1 >

(b2 b2)I2

. Hence, the derivative of the Lyapunov func-

tion turns out to be negative definite, eT eT < 0, which indicateserror convergence to zero.

Finally, the dynamic of capacitance voltage estimation erroreVc = Vc Vc can be written as

eVc = k1Vc + b1I + k1 Vc b1I= k1eVc . (11)

It is clear form (11) that eVc is going to approach to zerowith increasing time since k1 > 0. As a result, the estimationerrors on the temperature and capacitance voltage decay to zero,i.e. eT 0, eVc 0, with some time by choosing the observergain 1 sufficiently large.

IV. RESIDUAL EVALUATION

The battery system has three measurements: voltage, tem-perature as outputs, and a load current input. By using thesemeasurements, it is possible to detect and isolate single faults intemperature and voltage sensors, and internal resistance devia-tions. In addition, a failure in the temperature controller can bedetected.


Fig. 7. Probability density estimation for voltage residual (normalized).

The residuals can be acquired with the usage of estimationerror states:

{rT eT = T TrV eV = V V

(12)

where rT and rV are residuals for temperature and voltagemeasurements, respectively.

The generated residuals can be evaluated based on somethreshold selections. There will always be a tradeoff betweenthe avoidance of false alarms and the detection of small faults inthe existence of noise and modeling errors. Practically, a faultcan be detected only if it causes the residual evaluation functionto surpass a threshold [8]

|ri(t)| Ri (13)where ri(t) is the function of the ith residual and Ri is theselected threshold for ith residual function.

A systematic threshold selection may be based on the statisti-cal evaluation of the residuals under the absence of the fault sinceresiduals can be degraded by the measurement noise or distur-bance. The thresholds for each residual can be calculated fromthe mean and standard deviation of the corresponding residualsunder nonfaulty cases. For example, probability density estima-tions of the voltage residual under nonfaulty and faulty casesare illustrated in Fig. 7, which shows different mean and stan-dard deviation values for nonfaulty and faulty cases. An optimalthreshold value can be the intersection of the probability densityfunctions of nonfaulty and faulty residual signals (see Fig. 7).However, in such a case, the overlapped regions result in eitherfalse alarms or missed detections. Therefore, more conservativethreshold values must be selected to avoid false alarms. To avoidfalse alarms, thresholds for residuals rV and rT can be selectedas RV = V + 4V and RT = T + 4T , similar to the She-whart control chart [37], where T and V are the means, andT and V are the standard deviations of related residuals underfault-free cases.

A residual evaluation chart is given in Table II, which showsthat single faults can be detected and isolated. The temperaturesensor fault and unexpected internal resistance change may notbe isolated with the given logic because both affect the sameresiduals.

TABLE IIFAULT DIAGNOSIS CHART

Fig. 8. Flow diagram of the proposed fault diagnosis approach.

A flow diagram of the proposed fault diagnosis approach isillustrated in Fig. 8. This dynamic method is an online real-timeapproach, so measurements must be obtained continuously forearly fault detections.

V. NUMERICAL RESULTS

The implementation of the online condition monitoring ap-proach for the battery systems are performed with MAT-LAB/Simulink programs by using the experimental current mea-surements of the Ni-MH battery system. The nonlinear estimatorgain is selected as 1 = 2 (note that since the nonlinear estimatoris robust, this gain should not be selected very large in order tohave high sensitivity to faults). Initial conditions for estimatorare taken as To = 19 C and Vco = 0. For threshold calculations,the mean and standard deviation of voltage and temperatureresiduals, by considering their root mean square (rms) values,are found as V = 0.44, V = 0.65, T = 0.0004, and T =0.0004. The rms functions of the residuals are used in the resid-ual evaluations. For the estimator, the sat() function definedbelow is used instead of the sign() function in order to easenumerical calculations via continuous approximation.

sat(e) ={

e/ |e| , |e| > 1e, |e| 1. (14)

Fig. 9 displays the load current and the SOC estimation foran initial value 60% and under normal operating conditions.While the SOC is a difficult parameter to predict in the batterymanagement system, the current integral method is commonlyused to estimate SOC and provides information about remaininguseful energy and the remaining usable time of the battery.

Different faults on measurements and battery parameters areconsidered for fault diagnosis as given in Table II. Several incip-ient type faults are injected into the battery system for diagnosissince the detection of incipient faults is most difficult. Fig. 10 il-lustrates a voltage sensor fault and its detection using the voltageresidual rV . It is obvious from the figure that once an incipi-ent voltage sensor fault occurs, it is detected and isolated viaresidual surpassing the threshold RV .


Fig. 9. SOC estimation from the load current. (a) Load current. (b) SOCestimation.

Fig. 10. Voltage sensor fault and its monitoring. (a) Time response of voltage.(b) Residual rv . (c) Residual rT .

In Fig. 11, it is assumed that the temperature controller failedat the time t = 3000 s. This failure is detected by temperatureresidual rT . The figure shows that the controller failure immedi-ately affects the temperature residual so that the residual exceedsthe threshold RT .

An incipient temperature sensor fault that is injected into thebattery system is depicted in Fig. 12. The temperature and volt-age residuals immediately exceed their threshold values to indi-cate the existence of temperature sensor fault. We can observefrom figures that the nonlinear estimator exhibits robustnesscharacteristics, which is important for healthy online conditionmonitoring. It should be noted that rV may not exceed its thresh-old for small temperature sensor fault values unless the thresholdis decreased, but then there will be some false alarms.

Fig. 11. Control (fan) failure and its detection. (a) Control signal [unitless,see (5)]. (b) Residual rv . (c) Residual rT .

Fig. 12. Temperature sensor fault and its detection. (a) Time response oftemperature. (b) Residual rv . (c) Residual rT .

An unexpected deviation in the internal resistance of the bat-tery is shown in Fig. 13. A small and drift-like deviation in theresistance results in alarms in voltage and temperature residualsby exceeding thresholds. The internal resistance of battery pro-vides knowledge about several problems, including grid growth,sulfation, dry out, and corrosion. Hence, the diagnosis of inter-nal resistance fault is an important aspect of the methodologyin terms of its good performance and efficiency.


Fig. 13. Internal resistance deviation and its detection. (a) Time response ofinternal resistance. (b) Residual rv . (c) Residual rT .

VI. CONCLUSIONThis paper proposed a nonlinear estimator-based online con-

dition monitoring system for battery systems used in the in-dustry. The study set out to determine the possibility of onlinebattery health monitoring system based on battery modeling anddetection of internal battery problems. This research has shownthat the nonlinear estimator-based approach provides a robustand efficient fault diagnosis for internal faults through detectionof internal cell resistance deviations, measurement faults, andtemperature controller failure in the battery system. The resultsof this study indicate that the proposed online real-time healthmonitoring approach can provide early fault detection, extendeduseful life, better maintenance, and optimized replacement tim-ing for battery systems.

ACKNOWLEDGMENT

The author gratefully would like to thank Prof. G. Rizzoni,the Director of the Center for Automotive Research, Ohio StateUniversity, for his valuable guidance and contributions.

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Authors photograph and biography not available at the time of publication.

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Online Condition Monitoring of Battery Systems

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