aging estimation method for lead-acid battery

264 IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 26, NO. 1, MARCH 2011

Aging Estimation Method for Lead-Acid BatteryYu-Hua Sun, Member, IEEE, Hurng-Liahng Jou, Member, IEEE, and Jinn-Chang Wu, Member, IEEE

Abstract—In this paper, an aging estimation method is pro-posed for the lead-acid batteries serially connected in a string.This method can prevent the potential battery failure and guar-antee the battery availability, and it can serve as an indicator foraging or degradation of the lead-acid battery. The salient featureof the proposed method is that aging of the individual battery isestimated automatically at the end of each discharge cycle by onlymeasuring individual battery voltage in a string of batteries, so thatno complicated measurement is required. To verify the proposedaging estimation method, aging experiments for lead-acid batter-ies are developed. The experimental results show that the proposedaging estimation method provides the expected results.

Index Terms—Aging, discharge, lead-acid battery.

I. INTRODUCTION

L EAD-ACID battery converts the chemical energy con-tained in its active materials into electrical energy by

means of an electrochemical reaction. The major aging pro-cesses in lead-acid batteries are anodic corrosion, positive ac-tive mass degradation, irreversible formation of lead sulfate inthe active mass, short-circuits, and loss of water [1]. Batteryis widely used as a backup power for interruption-free criticalloads, such as computer and telecommunication equipment [2],[3]. Recently, the battery has been used in the battery energystorage system (BESS) as the energy buffer scheme for the pur-pose of attenuating the effects of unsteady input power fromwind farms [4]. Although, the state of charge (SOC) [5]–[7], re-serve life [8], and residual capacity of the lead-acid battery waswidely used to determine the status of the battery, but the healthcondition of lead-acid battery will evidently affect the reliabilityof critical loads. The state of health (SOH) indicates the abilityof the battery to perform well both in charge and discharge, andit can be adapted to supply the aging or degradation informationof battery to the users.

The SOH is addressed in this paper. If the SOH can be esti-mated accurately, the users will know the aging or degradationof the battery and whether the battery should be replaced ornot. There were several methods have been developed for mon-itoring SOH of batteries [9]–[24] and these methods can bemainly categorized into capacity, coup de fouet, and impedancemethods.

Manuscript received September 22, 2008; revised March 15, 2009 and July29, 2009. Date of publication December 10, 2010; date of current versionFebruary 18, 2011. Paper no. TEC-00396-2008.

Y.-H. Sun and H.-L. Jou are with the Department of Electrical Engineering,National Kaohsiung University of Applied Sciences, Kaohsiung 80782, Taiwan(e-mail: [email protected]; [email protected]).

J.-C. Wu is with the Department of Microelectronic Engineering, NationalKaohsiung Marine University, Kaohsiung 80782, Taiwan (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.2010.2040478

The capacity method is the most popular for indicating theSOH [10]. In this type of method, the life of battery is defined tobe stopped, when the capacity of battery is decreased to approx-imately 80% of the initial capacity for general battery [11] and60% of the initial capacity for small-capacity battery [12]. TheSOH diagnosis using the capacity is the ratio between the nom-inal capacities of the present time to that of the initial time [13].The capacity method is based on counting discharging Coulombto determine the SOH of a battery. However, the discharging ef-ficiency and the precision of the current measurement must beconsidered carefully to improve the accuracy [14]. The Coulombcounter is an open loop capacity estimator. Errors caused by thecurrent detector are accumulated by the estimator. Besides, theCoulomb counter does not consider the changes of the battery’scapacity as the battery ages. For many SOC levels, this esti-mation carries an average error of ±15% [15]. Therefore, thecapacity method used in determining the SOH of a battery isimprecise and must be further improved.

The “coup de fouet” is a phenomenon particular to lead-acid battery, which occurs at the beginning of the dischargeprocess [16]. The “coup de fouet” can be ascribed to a crys-tallization overvoltage, which is the energy gap needed for theformation of PbSO4 nuclei on the plates from the Pb2+ super-saturated electrolyte during the first instants of discharge [17].Aging of lead-acid batteries may be caused by various processes,such as grid corrosion, sulfation, and the change in pore struc-ture causing decrease in active surface area and increase in localresistance. As a result of these changes, the deliverable capacitydecreases and the “coup de fouet” voltage is lowered [18]. Thecoup de fouet method involves measuring the trough voltage(low-voltage point) in the “coup de fouet” region and determin-ing the SOH of a battery [17]. However, the coup de fouet phe-nomenon only occurs in batteries that are completely charged,i.e., there are no lead sulfate nuclei on the positive electrode. Ithas also been found that the coup de fouet only appears at thepositive electrode, but not at the negative electrode [16]. There-fore, the coup de fouet method cannot be used to determine theSOH of a battery in all conditions.

The impedance and the resistance of a valve-regulated lead-acid (VRLA) battery increase with the battery age and the ca-pacity lost. Various impedance meters have been claimed tobe capable of measure accurately the SOH of batteries [18].The fuzzy logic data analysis can also be incorporated with theimpedance measurement to effectively estimate the SOH of thebattery [19], [20]. Although, the trend of the internal impedancecan be used to determine the SOH of a battery, the measurementrequires more accurate and expensive apparatus due to this theimpedance of a battery is less than tenths of milliohms. More-over, the parasitic inductance of the cables, current collectors,and grids of the plates will result in the substantial errors inthe imaginary part of the measured battery’s impedance [21].

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SUN et al.: AGING ESTIMATION METHOD FOR LEAD-ACID BATTERY 265

Besides, the measurement of internal impedance will also inter-fere with the excessive ripple of discharging current and radi-ation noise [22]. This means that the accurate measurement ofthe internal impedance of battery is very difficult. Hence, thetrend of the internal impedance used to determine the SOH of abattery is hard to implement in practical applications.

Some other methods, which involve measuring the voltage,temperature, capacity, or internal impedance of a battery havebeen developed to estimate the SOH of battery accurately [23],[24]. However, these methods are more complex.

Approximate entropy (ApEn) is a robust regularity statisticsuitable for practical amounts of data [25]. The ApEn has poten-tial application to time-series data from heart rate, respiration,and blood pressure. It also appears to be applicable to clinicalendocrinology and to distinguish abnormal hormonal secretionpatterns [26]. It is a new mathematical approach, which can beused to quantify the irregularity of signals. Signals containingregular patterns (e.g., sinusoidal signals) have small ApEn val-ues, whereas those with irregular behavior (e.g., random noise)show high ApEn values. The ApEn has been widely used toquantify the subtle difference in regularity of signals. Greaterirregularity of a signal will produce a larger ApEn value [27],and then it can be detected easily. Hence, it can be used todetermine the SOH of a battery.

In this paper, an aging estimation method is proposed to esti-mate the aging or degradation of individual lead-acid batteriesserially connected in a string. This method can prevent the po-tential battery failure and guarantee the battery availability. Thesalient feature of the proposed method is that the aging or degra-dation of the individual battery is estimated automatically at theend of each discharge cycle by only measuring the individualbattery voltage in a string of batteries, and it does not involveany complicated measurement procedures. Aging experimentsof lead-acid battery are developed to verify the proposed agingestimation method.

II. PROPOSED AGING ESTIMATION METHOD

The proposed aging estimation method is based on the ApEn.ApEn was developed for processing a complex system with adata sequence [28] and has been applied to classify ventriculartachycardia and fibrillation [29], [30]. ApEn can reveal the vari-ation of a data sequence. The algorithm for computing ApEn(r,m, N ) has been published [28]. For a data sequence x(n) =x(1), x(2), x(3), . . . , x(N ), where N is the total number ofdata points to calculate ApEn(r, m, N ), a run length m and atolerance window r must be specified to compute ApEn(r, m,N ). In order to use fewer data points to measure the changein a complex system, the parameter m used in this paper is2 [28]. Normally, tolerance window r is 0.2 times the standarddeviation (r = 0.2 × SD) of the original data [28]. SD can berepresented as follows:

SD =

√√√√ 1N − 1

N∑n=1

[x(n) − 1

N

N∑n=1

x(n)

]2

. (1)

ApEn algorithm [28], [31] can be summarized as follows:

1) Form m-vectors, X(1) to X(N – m + 1) are defined by

X(i) = [x(i), x(i + 1), . . . , x(i + m − 1)]

i = 1 to N − m + 1 (2)

X(j) = [x(j), x(j + 1), . . . , x(j + m − 1)]

j = 1 to N − m + 1. (3)

2) Defining the distance d[X(i), X(j)] between vectors X(i)and X(j) as the maximum absolute difference betweentheir respective scalar components. Then, it can be writtenas follows:

d[X(i),X(j)] = max[|x(i + k) − x(j + k)|],k = 0 to m − 1. (4)

3) Defining Cmr (i), and it is represented as follows:

Cmr (i) =

V m (i)N − m + 1

(5)

where V m (i) = number of d[X(i),X(j)] � r, and i isfrom 1 to N – m + 1.Taking the natural logarithm of each Cm

r and averagingover i, and it can be written as follows:

φm (r) =1

N − m + 1

N −m+1∑i=1

ln(Cmr (i)). (6)

4) Increasing the dimension to m + 1 and repeating steps (1)to (4).

5) The ApEn value for a finite data length of N can be calcu-lated as follows:

ApEn(m, r,N) = φm (r) − φm+1(r). (7)

In some applications, many batteries are serially connected ina string to provide a desired battery voltage. Because the perfor-mance of individual battery in a battery string is not the same,some batteries will be overdischarge in a long string [32] beforethe discharge process is stopped at the end of discharge volt-age. For a lead-acid battery, the overdischarge often causes thecapacity loss, active material shedding, and an extremely pooracceptance of charging current [33]. An aging or degradationbattery will cause the other batteries in the same string to supplymore energy so as to decrease the discharge time. In addition,the voltage of aging or degradation battery may discharge belowthe specified end discharge voltage (overdischarge).

Because the end discharge voltage of an aging or degradationbattery is smaller than the average end discharge voltage inthe same string and all the batteries in the same string willaffect each other during charge/discharge processes, the enddischarge voltage will be different in the different dischargeprocess. Hence, the aging or degradation of a battery cannotexactly indicate by only using the end discharge voltage ofindividual battery. Since ApEn can reveal the variation of a datasequence, the calculated value of ApEn using a data sequenceof the discharge voltage for an aging or degradation battery islarger.

Hence, ApEn can be used in the proposed aging estimationmethod to indicate the aging or degradation battery in a string


Fig. 1. Flow chart of the proposed method for estimating aging or degradationof a battery.

Fig. 2. Experimental system for a string of batteries.

of batteries. If the calculated ApEn value is over a preset value,this battery can be diagnosed as an aging or degradation battery.

Fig. 1 shows the flowchart of the proposed aging estimationmethod for a string of batteries. First, the data of battery voltageduring the discharge process is obtained from the measuringdevices. Then, the ApEn value is calculated by using the data ofthe discharge voltage. The calculated value of ApEn is recorded.Finally, the value of ApEn is converted into an aging index.

III. EXPERIMENTAL SYSTEM

The accelerated aging experiment is developed [34] to shortenthe experimental period of batteries. The critical loads in moststandby use batteries are the constant resistor or constant power.Figs. 2–4 show the experimental system. The experimental sys-

Fig. 3. Picture of experimental system.

Fig. 4. Picture of thermostat of experimental system.

tem includes a thermostat, several electromagnetic contactor(M.C.) switches, and a battery measure system (BMS). The bat-tery set acts as the energy storage device for the UPS. The M.C.switched is used to connect or disconnect the load. BMS is usedto measure the voltages and currents of battery set, and then,sends the measured signals to the personal computer. The con-ditions for accelerated battery aging experiment are defined asfollows.

1) Four independent strings of batteries are used in the ex-periments, and each string of batteries is consisted ofeight 7-Ah 12-V VRLA battery units connected in series.Each battery unit consists of six cells connected in seriesinternally.

2) The ambient temperature was kept at 55 ◦C by thethermostat.

3) Sampled data was retrieved every 6 s when the battery wascharged/discharged.

4) The final discharge voltage for each string of batteries was76.8 V.

5) The discharge load for each battery string is a halogenlamp (120 V 500 W × 3).


Fig. 5. ΔV of discharge voltage between each sample time at the 22nd cycle.

Fig. 6. Values of ApEn × 100 of the discharge voltage for the batteries S1B2and S1B4 in the string 1 at the 22nd discharge cycle under the value of r within0.1 × SD–0.5 × SD.

In order to collect more experimental data, four strings ofbatteries were used simultaneously in the aging experiment.Because the value of ApEn was calculated by a data sequenceof the discharge voltage for individual battery, the proposedaging estimation method is also suitable for a single battery.

The experiment stops as the capacity of each battery stringdecreased to 60% of the initial capacity. Each battery capacity inthe string may be large or small than 60% of the initial capacity,which depends on the degradation of battery.

IV. EXPERIMENTAL RESULTS

The best and two worsen batteries in the same string areselected in the following analyses.

While the recommended values of r is applied for a widevariety of signals, in certain cases r values will lead to an in-correct assessment of the complexity of a given signal [35]. Ingeneral, r is essentially a filter, where the type of filter dependson the choice of r. For example, a large r can be thought of asan all-pass filter, since the number of self-matches will be large,whereas a small r can lead to a low-pass filter like behavior,since it will lead to few self-matches and detailed informationmay be lost [35].

For example, the difference discharge voltage value betweenthe sample time of the battery S1B2 (string 1, no. 2) and S1B4(string 1, no. 4) at the 22nd cycle are shown in Fig. 5. Except

Fig. 7. Values of ApEn × 100 of the discharge voltage for the batteries S1B2and S1B4 in the string 1 at the 22nd discharge cycle under the value of r within0.01–0.4.

the beginning of battery discharge process caused by the coupde fouet, the variation of difference voltage (ΔV ) of batteryS1B2 is below 0.05 V. The curve variation of ΔV for batteryS1B4 is changed abruptly at the end of discharge section. Itshows the battery S1B4 is aged. As seen in Fig. 6, when thevalue of r within 0.1 × SD–0.5 × SD, the values of ApEn ×100 of the battery S1B2 (string 1, no. 2) and S1B4 (string 1, no.4) at the 22nd cycle were approximated to be 43 and 35. Thismeans that the value of r within 0.1 × SD–0.5 × SD cannotclearly distinguish the aging battery from the normal battery.Hence, r = 0.2 × SD [28] is not suitable for the applicationsfor determining the SOH of lead-acid battery. Fig. 7 shows thevalues of ApEn × 100 of battery S1B2 and S1B4 at the 22ndcycle when the value of r is a constant value within 0.01–0.4.It can be found that the values of ApEn × 100 of the batteryS1B2 (string 1, no. 2) and S1B4 (string 1, no. 4) is very closeif a larger value of r is used. The smaller value of r is, thehigher sensitivity of ApEn will be. However, the ApEn will bedisturbed by the normal change of battery voltage between thesample duration if the value of r is too small. Hence, the valueof r is suggested to be a constant value 0.05 in the applicationsfor determining the SOH of lead-acid battery.

The recommended r value of 0.2 × SD [28] is not suitableand r is defined as a constant value of 0.05 in this paper. Thetotal measured experimental data during a discharge period are342 points at the first cycle of the string 1. A huge computingresource will be used for calculating ApEn, while the parameterN is large. On the contrary, the calculated results of ApEn maybe inaccurate for the small parameter N [36]. The parameter Nused in the following experiments is 5. Hence, the parameters r,m, and N of ApEn used in the following experiments are 0.05,2, and 5, respectively.

Fig. 8 shows the difference between the end discharge voltageof three batteries and the average end discharge voltage in thestring 1. As seen in Fig. 8, the best battery S1B2 (string 1, no.2), and two worsen batteries S1B4 (string 1, no. 4) and S1B8(string 1, no. 8) are used in the following analyses. As seen inFig. 8, the end discharge voltage of the worsen battery S1B4 isthe lowest. Fig. 9 shows the ApEn value of the discharge voltagefor the batteries in string 1. In order to verify the ApEn valuecan be used to estimate the aging of the lead-acid battery, the


Fig. 8. Difference between the end discharge voltage of three batteries andthe average end discharge voltage in the string 1.

Fig. 9. ApEn value of the discharge voltage for the batteries in the string 1.

Fig. 10. Capacity for the batteries in the string 1.

capacity of each battery in a string was calculated according tothe IEEE standards (IEEE 1188) time capacity determinationfor VRLA [11]. The battery capacity based on IEEE 1188 isdefined as follows:

C =[

tAtS × KT

]× 100 (8)

where C is the percent capacity at 25 ◦C, tA is the actual timeof test to specified terminal or cell/unit voltage, tS is the ratedtime to specified terminal or cell/unit voltage, and KT is thecorrection factor. Fig. 10 shows the capacity curves for thebatteries in the string 1.

The end discharge voltage of battery S1B4 shown in Fig. 8deviates from the average end discharge voltage of string 1 atthe 16th cycle, and the ApEn value × 100 for the battery S1B4shown in Fig. 9 is simultaneously increased. The battery S1B4is overdischarge evidently after 16th cycle. The ApEn value ×100 for the battery S1B4 is over 4.5 after 16th cycle, and the




capacity is less than 60% after 23rd cycle. As seen in Fig. 8,the voltage of battery S1B2 is the largest in this string, and itsApEn value × 100 is ranged from 0.51 to 2.89.

As the aforementioned description, the ApEn value × 100 ofan aging or degradation battery is larger than that of a healthbattery, so that the ApEn value × 100 can be converted into anaging or degradation index to indicate the aging or degradationstatus of a battery. The ApEn value × 100 used to alarm can beset by the users. The ApEn value × 100 is set to be 4.5 in thispaper. Hence, an alarm signal should be sent to users when thevalue of ApEn exceeds 4.5.

Figs. 11–13 show the experimental and analyzed results ofstring 2. The batteries of S2B1, S2B2, and S2B6 are used in thefollowing analyses. As seen in Fig. 11, the difference betweenthe end discharge voltage of the battery S2B1 and the averageend discharge voltage of the string 2 is undulated evidently, andthe voltage difference between the end discharge voltage of thebattery S2B6 and the average end discharge voltage of the string




2 has the fall trend monotonously. If the diagnosis of an aging ordegradation battery only uses the difference voltage between theend discharge voltage and the average end discharge voltage ofthe same string, the battery S2B1 may be diagnosed to be agingat the 10th cycle. However, the capacity of S2B1 is still morethan 80% at the 10th cycle. This result implies that the voltagedifference between the end discharge voltage and the averageend discharge voltage of the same string cannot exactly indicatethe aging or degradation of the battery. As seen in Figs. 12 and13, the ApEn value × 100 of S2B1 is still smaller than 4.5before 22nd cycle, and its capacity is 77.6% at the 22nd cycle.Hence, the proposed method can avoid this false diagnosis. Thecapacity of batteries S2B6 and S2B1are less than 60% after 31stand 34th cycle, respectively, and the ApEn value × 100 of themare higher than 4.5 before their capacity is less than 60%. Thisverifies that the ApEn value × 100 can be used as the agingor degradation index to prevent the potential battery failure andguarantee the battery availability.

Figs. 14–16 show the analyzed results of string 3. The batter-ies of S3B3, S3B4, and S3B8 are used in the following analyses.Figs. 17–19 show the analyses results of string 4. The batteriesof S4B4, S4B7, and S4B8 are used to analyze. As seen in thesefigures, the analyzed results of these batteries are similar to theanalyzed results of the string 1. Hence, the proposed ApEn-based aging estimation method can effectively estimate agingor degradation batteries in the same string.

From aforementioned experimental results, the ApEn-basedaging estimation method can convert the detected battery voltageinto its ApEn value. Since the ApEn value of aged battery in theaforementioned experimental results is enlarged significantly





and different from that of normal battery, then the ApEn-basedaging estimation method can estimate aging or degradation oflead-acid batteries. Hence, it verifies that the ApEn-based agingestimation method can accurately and effectively estimate theaging or degradation of lead-acid batteries.


TABLE ICOMPARED RESULTS OF AGING ESTIMATION METHODS

In comparison with the capacity of battery at each dischargecycle in the aforementioned experimental results, it can be foundthat the capacity of battery is less than 60% when ApEn × 100value of the battery is more than 4.5. Hence, it verifies that theproposed ApEn-based aging estimation method can accuratelyand effectively estimate the aging or degradation of lead-acidbatteries.

The accuracy of capacity method is affected by 1) the pre-cision of current measurement; 2) the calculation of chargingand discharging power; 3) the discharging efficiency; and 4)aging. Moreover, a battery string contains several batteries andthe end of discharge is determined by the string voltage (notthe individual battery voltage). The end discharge voltages ofbatteries in the same string are not equal. Hence, the calculatedcapacity of the individual battery cannot represent its actual ca-pacity. For example, if the end discharge voltage of a batteryin the battery string is higher than the standard value for theend of discharge voltage, it means that the battery is not dis-charged completely and the calculated capacity will be smallerthan its actual capacity. Hence, the estimation of SOH for theindividual capacity in a battery string is not accurate by usingthe capacity method. The accurate measurement of dischargingcurrent and accurate calculation of power capacity is omittedin the proposed aging estimation method. Hence, the complex-ity of the proposed is simplified as compared with the capacitymethod.

Although, the coup de fouet method also uses only the de-tected voltage in determining the SOH of a battery, but it canonly detect the degradation at the positive electrode of a batteryunder full charge. Besides, the variation of coup de fouet voltageis different in the different battery. Hence, the accuracy of coupde fouet method is limited. Because the variation of coup defouet voltage is small and the coup de fouet region is short, thehigh-resolution voltage detector and fast sampled measurementare required. This results in the complexity of the measurementof battery voltage in comparison with the proposed method.

Since the impedance of a battery is very small (only several ortenths milliohms), the measurement circuit is very complicatedand difficult to measure such small impedance of the battery.Consequently, the accuracy of the impedance method for SOHestimation is restricted due to the measurement accuracy oftiny impedance is difficult. Besides, the impedance at differentfrequencies represents different characteristics. This results in

the complexity of the measurement of battery impedance incomparison with the proposed method.

Table I shows the compared results of the proposed ApEnmethod and other aging estimation methods.

V. CONCLUSION

Although several methods, such as capacity method, coup defouet method, and impedance method, have been developed toestimate the SOH of a battery, these methods still have somerespective problems. This paper proposes a novel aging or degra-dation estimation method based on ApEn for the lead-acid bat-tery. In this method, ApEn is used to estimate and indicate theaging or degradation of the lead-acid batteries serially connectedin a string. The salient feature of the proposed method is thataging or degradation of a battery is estimated automatically atthe end of each discharge cycle by only measuring individualbattery voltage connected in a string, and it does not require anycomplicated measurement techniques. The experimental resultsshow that the proposed method can effectively estimate agingor degradation batteries in a string of batteries.

ACKNOWLEDGMENT

The authors would like to thank to ABLEREX CorporationLtd. for the financial and technical support in this paper.

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Yu-Hua Sun (M’08) was born in Taiwan in 1961.He received the M.S.E.E and Ph.D. degrees fromNational Kaohsiung University of Applied Sciences,Kaohsiung, Taiwan, in 2006 and 2010, respectively.

His research interests include battery modelingtechnology, and power-electronics applications.

Hurng-Liahng Jou (M’99) was born in TaiwanR.O.C. in 1959. He received the B.S.E.E. degree fromChung Yuan University, Jonglih, Taiwan, in 1982, andthe M.S.E.E and Ph.D.E.E. degrees from NationalCheng Kung University, Tainan, Taiwan, in 1984 and1991, respectively.

He is currently a Professor in the Department ofElectrical Engineering of National Kaohsiung Uni-versity of Applied Sciences, Kaohsiung, Taiwan. Hismajor interests are power electronics applications andpower quality improvement technique.

Jinn-Chang Wu (M’07) was born in Tainan, Tai-wan in 1968. He graduated from National Kaohsi-ung Institute of Technology, Kaohsiung, Taiwan in1988, and received the M.S.E.E. and Ph.D.E.E. de-grees from National Cheng Kung University, Tainan,Taiwan in 1992 and 2000, respectively.

Currently, he is an Associate Professor at the De-partment of Microelectronics Engineering, NationalKaohsiung Marine University. His research interestsare in power-electronics applications.

aging estimation method for lead-acid battery

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