INTELEC95 1995 IEEE

Some aspects of battery impedance characteristics

J.M. Hawkins† & L.O.Barling

Telstra Research LaboratoriesBOX 249 Rosebank MDC

Clayton, Victoria, 3169Australia

Abstract

Impedance and conductance techniques have beenadvocated in the determination of the condition oflead-acid batteries in service. The usefulness of these"ohmic" techniques lies in an understanding of thebounds and domain of the measurement. This paperreports the frequency response and batteryimpedance behaviour generally observed for a rangeof commercially available batteries. The genericbehaviour of batteries typically used intelecommunications networks is demonstrated. Theeffect of temperature and residual capacity on theimpedance spectra are also reported.

Introduction

In recent years there has been considerable activity anddebate regarding the use of internal "resistance"characteristics as a battery condition measurement [1-9].The interest reflects the desire for simple electronicmeans to replace discharge testing as a practicaldetermination of residual battery capacity, particularlygiven the increased usage of valve-regulated lead-acid(VRLA) batteries. The available techniques, whichinclude AC impedance and conductance methods andmomentary "DC" loading, all involve controlled currentor voltage perturbations to determine a representation ofthe internal "ohmic" condition of the battery.

Internal battery "resistance" has been proposed as ameans to track battery life, [1,4,6] but greater interestlies in reported claims of specific correlation betweencell impedance or conductance with battery capacity[2,3,5]. More recent reports indicate that the currentlyavailable single-frequency "internal ohmicdetermination" techniques can not, in general, provideunequivocal absolute battery capacity information [6,7].However, the techniques have been shown to havesome merit as a comparative tool, and thus are useful indetecting early trends in rogue cells and componentswith poor conduction integrity. In this sense, batteryimpedance, conductance or resistance measurementsare now currently best viewed as an aid in assessmentof battery "state-of-health" [7,8,9].

† e-mail address :j.hawkins@trl.oz.au

Telstra is cautiously incorporating simple impedancemeasurements into various battery and power systemmaintenance routines [9].

Advocacy of merit of any one determination methodover the other is both of interest and a source ofconfusion to the end-user. For AC techniques, theselection of measurement frequency appears empiricalin origin, drawn from very limited determinations of thefrequency response of specific types of batteries.Furthermore, the published literature on fundamentalimpedance characteristics of lead-acid batteries is notunequivocal [10-13]. Electrochemical impedancespectroscopy has been used in studies of electrode andplate behaviour during charging and discharging, butthere has been only limited application to the near-equilibrium condition for lead-acid batteries on floatduty. The ohmic response of the battery depends on themeasurement frequency and the "state" of the batteryand has been reported to be affected, to varying degrees,by many fundamental cell characteristics, including celldesign [3,12], temperature [12,14], and capacity [3,14].

An understanding of the behaviour of lead-acid batterieson float is of paramount importance for stand-byapplications. The frequency response of lead-acidbatteries is important in determining the relative meritsof various AC perturbation techniques currently used toprobe the "state-of-health" of lead-acid batteries onstandby duty. This Paper reports on the frequencyresponse and the general impedance behaviour of arange of different types of lead-acid cells.

Experimental

The AC impedance behaviour of lead-acid batteriesreported in this work was measured over eight decadesof frequency (10-3 - 105 Hz) by two-electrodepotentiostatic techniques similar to those previouslydescribed [3,10-13]. A known and controlled, small ACvoltage amplitude is applied to the steady-state batterycondition, and the resultant AC current measured. Thecomplex impedance behaviour of the battery is thendetermined directly from the in-phase and quadraturephase components of the applied AC perturbationvoltage and the measured current. The equipment usedin this work is shown in Figure 1. The battery understudy was connected to a standard commercial

INTELEC95 1995 IEEE

potentiostat (E&EG PAR Model 273), and a lock-inamplifier (Hewlett-Packard Model 5208), both of whichare connected to a controlling computer (IBM-compatible PC).

Computer control

Potentiostat

Lock- in amp

Wide Band Current Amp

v

Battery/cellunder test

Figure 1: Experimental set-up used to study and measure theAC impedance behaviour of lead-acid batteries.

A specifically designed wide-band current amplifier wasused to overcome current limitations of the potentiostat.Commercially available control and measurementsoftware (E&EG PAR Electrochem ImpedanceSoftware Vr 2.92) was used. Single sine-waveexcitation was used over the frequency range ofapproximately 10 Hz - 100 kHz. For the frequencyrange of approximately 5 mHz - 100 Hz, the frequencyresponse was determined by multi-sine (white noise)excitation followed by Fourier Transform (FT) analysis.Voltage amplitudes in the range 1-5 mV were typicallyused, depending on the size of the battery. Using thisequipment, impedance spectra could be recorded forboth steady-state open circuit and float conditions.Lower limit of reproducible impedance determination inthe potentiostatic mode on a test resistance wasapproximately ± 50 µΩ. Galvanostatic determination ofimpedance behaviour at fixed frequencies using amodified commerical battery impedance meter [9] wasused to better than 10 µΩ resolution.

For batteries subjected to changed equilibriumconditions, spectra were measured after 2-4 hours resttimes as per previously reported wait times [12,13].Generally, the reported spectra were measured at roomtemperature (21°C ±1°C). Temperature effects of theimpedance behaviour were studied using computercontrolled environment chambers with temperaturecontrol to better than 0.1°C. Controlled discharge andcharge were performed on an automated battery testfacility [15].

Results and Discussion

Electrochemical interpretation and modelling of theimpedance behaviour is outside the scope of this paper.Spectra are presented in Bode plot format.

A wide range of batteries of different batterytechnologies and capacities have been studied in thework. As expected, the absolute value of the impedancedepends on both the battery technology and the capacity.Figure 2 illustrates the general frequency response ofbattery impedance for three different types of batterytechnologies.

-4

-3

-2

-1

-3 -2 -1 0 1 2 3 4 5log (frequency (Hz))

log IZI(in m Ω)

-1

2

3

(a)1 - 6V 100Ah AGM VRLA

2 - 2V 250 Ah Gell VRLA

3 - 2V 500Ah Vented

-90

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-30

0

30

60

90

-3 -2 -1 0 1 2 3 4 5

log (frequency (Hz))

Phase θ(in degrees) (b)

1

2 3

Figure 2: Bode magnitude (a) and phase (b) plots of thetypical open-circuit impedance spectra for three different typesof nominally charged lead-acid batteries.

The frequency response of the impedance behaviour isclearly generic for the three basic types of batterytechnology. The magnitude plot can be characterised asa "skewed parabola" with the impedance increasing forhigher and low frequencies and a relatively broadminimum occuring across the mid-frequency region.From the phasing information, lead acid batteries arepredominantly inductive for higher frequencies ( ƒ > ≈ 1kHz, θ > ≈ +10°), generally increasingly capacitive forlower frequencies (f <≈ 10 Hz, θ < ≈ −10°) and mainlyresistive over mid-frequencies (≈ 10 Hz < ƒ < ≈ 1kHz, θ ≈ 0). The impedance response in the capacitivereactance region was found to be relatively sensitive tobattery condition and experimental techniques, andreproducibility is not as high as for either the resistive orinductive regions. The reproducibility of repeatedexperiments on the same battery was typically 2%-5%.

The inductive reactance is similar in both impedancemagntitude and phase behaviour for all three batteries,

INTELEC95 1995 IEEE

and thus supports previously reported assumptions thatthis results primarly from the metallic lead componentryof the conduction path [2,4,6]. The general behaviour isconsistent with previously noted impedancecharacteristics of some types of lead-acid batteries [2,6],although "generic" similarity over a wide range offrequency has not hitherto been reported.

For all batteries studied, the minimum impedance occursin the resistive region. The impedance determined whenthe phase angle, θ, is zero, is termed the ohmicresistance, and is denoted |Z|θ=0. Table 1 compares theohmic resistance for a number of different types ofbatteries used in the Telstra network. The ohmicresistance is similar for batteries of similar capacity andconstructin technology, although there is somefrequency dependence. The phase information suggeststhat frequency of the ohmic resistance is lowered as thenominal capacity of the battery increases. This is animportant observation in that there does not appear to beone unique measurement frequency optimised for alltypes of lead-acid batteries. In practical terms thismeans that some single frequency impedance andconductance meters may be more suitable for use with aparticular type of lead-acid battery.

Battery type|Z| @ selected

frequencies, (Hz)(mΩ)

|Z|θ=0(mΩ)

ƒ @|Z|θ=0(Hz)

10 100 1 k

AGM 6V, 6 Ah 32.3 16.4 13.6 13.4 1580AGM 6V, 10 Ah 17.1 8.3 6.9 7.0 800AGM 2V, 25 Ah 2.9 1.8 3.4 1.8 100AGM 6V, 100 Ah 2.1 1.6 1.7 1.5 210AGM 6V, 105 Ah 2.5 1.8 3.4 1.8 100AGM 6V, 110 Ah 2.8 1.7 1.8 1.6 300AGM 2V, 250 Ah 2.6 1.7 2.7 1.7 100AGM 2V, 400 AhGell 6V, 8 AhGell 2V, 250 Ah 1.0 0.7 1.0 0.7 100Vented 6V, 50 Ah 3.6 2.8 3.1 2.8 160Vented 2V, 225 Ah 0.9 0.7 0.9 0.7 100Vented 2V, 560 Ah 0.6 0.5 0.8 0.4 400

Table 1 : Some characteristic values obtained from thebattery impedance spectra.

Effect of the charged condition

The state of charge of the battery is observed to affectboth the phase and magnitude information in the batteryspectrum. Figure 3 illustrates the typical impedancebehaviour of a VRLA battery subjected to differentcharge and float conditions. There are clearly twodistinct spectra in the capacitive reactance region. Onehas an easily discernible higher impedance at lowfrequency than the other. This high impedanceresponseis only observed after the fully charged and float

condition is attained. That is, a lower impedance isobserved for a battery charged with nominal capacity

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0

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log (frequency (Hz))

log IZI(in m Ω)

Nominal C10 Capacity re-charge

Fully charged & floated

44hrs on O/C after float

5 Days on O/C after float

Figure 3: Bode magnitude spectra of impedance response toa AGM VRLA battery subject to float charging.

replacement but not subjected to a period of floatovercharge. Furthermore, the high impedance spectralresponse is not significantly affected by measurementunder float polarisation or time on float charge. Thehigh impedance behaviour only very slowly decreaseswith time on open circuit. There are no discernabledifferences in impedance response for frequencieshigher than about 10 Hz for any of these conditions.

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0

-3 -2 -1 0 1 2 3 4 5

log (frequency (Hz))

log IZI(in m Ω)

Fully charged & floated

0.2% C10 Capacity removed

1% C10 Capacity removed

10% C10 Capacity removed

(a)

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0

30

60

90

-3 -2 -1 0 1 2 3 4 5

log (frequency (Hz))

Phase θ(in degrees)

Fully charged & floated0.2% C10 Capacity removed1% C10 Capacity removed10% C10 Capacity removed

(b)

Figure 4: Comparison of impedance behaviour of a AGMVRLA battery in the float condition with those after minorcapacity depletion.

INTELEC95 1995 IEEE

Figure 4a compares the impedance behaviour of afloated battery with the open-circuit impedance spectraof the same battery after minor capacity removal. Avery small capacity depletion (by discharge) results inthe immediate collapse of the high impedance spectrumto the condition seen when the battery is not subjected toovercharge. The phase spectra is similarly interesting.Figure 4b shows that the higher impedance region overlow frequencies corresponds to a very large increase inthe capacitive reactance of a floated cells compared tothe non-floated battery. That is, under float conditionsthe battery is passivated (increase in absoluteimpedance). Again, the high capacitive reactance isonly observed once the battery has attained floatconditions. Any capacity removal results in a collapseof the capacitive phase behaviour and resembles that ofFigure 2b. The cell thus becomes predomiantlyresistive over these same low frequencies. Neither thephase nor the magnitude of the impedance issignificantly affected for frequencies above about 100Hz, and there is no measurable affect in the ohmicresistance of the battery as a function of float or veryminor capacity depletion. This phenomen appears to begeneric and has been observed, to a similar extent in allthe VRLA batteries and to a lesser extent in all thevented batteries studied in this work. For vented cellsthe effect appears to be linked to the extent of gassingcharge used. Profound impedance changes at 0.1 Hzand 0.01 Hz during advanced charging and overcharging have been reported in plate behaviour studiesof model AGM VRLA cells [12].

In practical terms, the observed increase in impedance atlow frequencies for the fully charged or float conditionof the all batteries may itself form the basis of a simpleon-line determination of "correctly" floating cells withina battery string. The results also indicate that "ohmic"determinations at lower frequencies may be influencedby the increased capacitive contribution arising fromfully charge cells. This may contribute to the some ofthe reported diversity between correlation of cellimpedance or conduction determinations and measuredcell capacity [7,8].

Effect of capacity

Battery impedance spectra were observed to change as afunction of residual battery capacity. Figure 5 showsthe typical open-circuit impedance behaviour for AGMVRLA battery subjected to various known amounts ofcapacity removal. Clearly evident from Figure 5a is theunilateral increase in absolute impedance over mid-frequencies as capacity is removed from the battery.Figure 5b illustrates that there is no general correlationbetween phase and residual capacity. After significantcapacity removal, the phase spectrum collapses and thebattery becomes predominantly resistive for frequenciesas low as 0.01 Hz. The behaviour illustrated by Figure5 is again found to be generic, although the range of

-2.5

-1.5

-0.5

-3 -2 -1 0 1 2 3 4 5

log(frequency (Hz))

log IZI(in mΩ)

Fully Charged (not floated)75%50%25%Fully Discharged

(a)

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0

30

60

90

-3 -2 -1 0 1 2 3 4 5

log (frequency (Hz))

Phase θ(in degrees)

Fully Charged (not floated)75%50%25%Fully Discharged

(b)

Figure: 5: Typical open-circuit impedance spectra as afunction of nominal residual capacity.

impedance change depends on both battery capacity andbattery technology. In general, vented cells exhibitsmaller relative impedance changes than AGM or gelledVRLA cells. This indicates increased discrimination isneeded to track the impedance with changes in capacityin vented batteries. In practical terms, the increase inbattery impedance with removed capacity is the basis ofsingle-frequency impedance and conductancemeasurements. The typical correlation of the impedancechanges as a function of residual capacity for a numberof single frequencies in the resistive region is shown inFigure 6.

An approximately linear relationship between thelogarithm of the impedance and nominal residualcapacity is observed from the discharge state toobserved to about 80% capacity. Over this range, theimpedance decreases with increase in the residualcapacity. Between 80%-100% capacity, however, theimpedance behaviour becomes non-linear, and theimpedance increases as the battery approaches fullycharge. The data is more resolved for the VRLAbattery. Figure 6 also demonstrates that the most linearrelationship between the logarithm of the impedance andresidual capacity is not necessarily at the frequency ofthe lowest impedance, and the gradient of therelationship is not necessarily the same for each"chosen" single frequency. Further, the frequency ofohmic resistance is observed to increase as the batteryresidual battery capacity decreases. These resultsindicate that an "optimum" measurement frequency

INTELEC95 1995 IEEE

-3.0

-2.8

-2.6

-2.4

-2.2

-2.0

-1.8

0 10 20 30 40 50 60 70 80 90 100

% Nominal C Capacity

log lZl(in m Ω)

1.1Hz9.69Hz100Hz400Hz

(a)

10

-2.7

-2.6

-2.5

-2.4

-2.3

-2.2

0 20 40 60 80 100% Nominal C Capacity

Log IZI(in m Ω)

10Hz

150Hz

630Hz

(b)

10

Figure 6 : Variation in battery impedance as a function ofresidual capacity determined for a number of singlefrequencies for (a) 6V, 110 Ah AGM VRLA monoblock and(b) 2V, 225Ah flooded cells.

might need to be established for a particular battery.There appears to be a general correlation betweenresidual capacity and impedance for all types of lead-acid battery.However, useful capacity prediction mayrequire specific frequency selection and "calibration" ofthe impedance-capacity relationship for specificbatteries. Furthermore, dimensioning for service use,and end-of-service life criteria is usually based on 80%of the nominal battery capacity rating. The capacity-impedance behaviour observed in this work diminishesthe claimed usefulness of single frequency impedancedeterminations as a fuel gauge for standby batteries.

Effect of Temperature

The effect of temperature on the impedance spectrumwas studied for a variety of lead-acid batteries. Figure 7illustrates the typical impedance response of a 2V, 250Ah (C10) gelled VRLA cell over the temperature rangeof 25°C - 75°C. The cell was fully charged at 25°C, butnot float charged during the higher temperaturedeterminations. The characteristic float conditionimpedance appears to collapse for the highertemperatures. Over the entire mesurement frequencyrange, the impedance appears to be relativelyinsensisitve to the ambient temperature. This generalbehaviour was observed for both AGM and vented cells.Smaller capacity AGM batteries have been observed toexhibit a relatively larger, and less

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log(frequency (Hz))

log IZI(in m Ω)

25 deg C45 deg C55 deg C65 deg C

(a)

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0

30

60

90

-3 -2 -1 0 1 2 3 4 5

log(frequency (Hz))

Phase θ(in degrees)

25 deg C 45 deg C

55 deg C 65 deg C

(b)

(b)

Figure 7 : Typical temperature effect on the impedancereponse of a gelled VRLA battery.

reproducible, temperature effect at low frequencies [12].However, for the mid range frequencies commonly usedin commercial impedance measuring equipment, theimpedance behaviour appears to be largely insensitive totemperature. Table 2 compares the change inimpedance at various frequencies for differenttemperatures for a selection of batteries used in theTelstra network. The gelled battery shows the greatestsensitivity to temperature over the frequency range 1 Hz- 1 kHz, although in absolute terms, the impedance isnot significantly affected by temperature for any of thebatteries.

Battery Freq Temperature (oC)type (Hz) 25 35 45 55 65 756V 10 2.1 2.2 2.1 1.9 1.8 2.8

110 Ah 100 1.5 1.5 1.5 1.4 1.4 1.3AGM 1000 1.7 1.9 1.8 1.7 1.7 1.62V 10 0.9 0.9 0.9 0.9 0.8 0.8

225 Ah 100 0.8 0.8 0.8 0.7 0.7 0.7vented 1000 0.9 1.2 1.1 1.1 1.0 1.1

2V 10 0.3 0.3 0.3 0.3 0.3400 Ah 100 0.2 0.2 0.2 0.2 0.2AGM 1000 0.5 0.5 0.5 0.5 0.52V 10 0.9 0.8 0.7 0.7 0.6 0.6

250 Ah 100 0.7 0.7 0.6 0.6 0.5 0.5gelled 1000 1.0 0.9 0.9 0.9 0.9 0.8

Table 2 : Absolute impedance values (in mΩ) as a functionof frequency and ambient battery temperature for fourbatteries types.

INTELEC95 1995 IEEE

Figure 8 plots the ohmic resistance as a function ofbattery temperature for the batteries in Table 2. A smalltrend to lower impedance at higher temperatures isevident. However, over the 50°C range, the measuredimpedance for any of the frequencies in the "resistive"region changes less than approximately 10% in absoluteterms. This is a level similar to the previously reportedtemperature sensitivity of conductance measurements ofVRLA batteries [14].

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

15 25 35 45 55 65 75Temperature (°C)

Ohmic Resistance

(mΩ)

2V, 225Ah Flooded 6V,100Ah AGM

2V,400Ah AGM 2V,250Ah Gelled

Figure 8: Variation in ohmic resistance as a function ofambient temperature for four different lead-acid batteries

Conclusions

The general AC impedance characteristics over a widefrequency range for a number of different types of lead-acid batteries has been studied. Generally similarbehaviour is observed and all batteries exhibitpredominantly resistive behaviour between 10 Hz and1kHz. The impedance is found to affected by the stateof charge of the battery. The impedance in the resistiveregion of the impedance characteristics does not exhibitany significant variation with temperature between 25°Cand 75°C. The impedance behaviour at low frequenciescan be used to discern the fully charged and floatcondition, and thus may be meritorious for in-servicestandby batteries.

Acknowledgments

The Authors would like to acknowledge the contributionto this work from Mr R. Hand and Dr L. Moore. Thepermission of the Director of Research, Telstra ResearchLaboratories, to publish this work is also acknowledged.

References

[1] S. DeBardelaben, "Determining the end ofbattery life", in Proc. Conf. INTELEC 86, 1986,pp 365-368.

[2] F.J. Vaccaro and P. Casson, "Internal Resistance:Harbinger of capacity loss in starved electrolytesealed lead-acid batteries", in Proc. Conf.INTELEC 87, 1987, pp 128-131.

[3] R.T. Barton, and P.J. Mitchell, J. Power Sources27, (1989), 287.

[4] G. Markle, "AC Impedance testing for valve-regulated cells", in Proc. Conf. INTELEC 92,1992, pp 212-217

[5] M.J Hlavac, D.O. Feder, T.G. Croda and K.S.Champlin, "Field and laboratory studies to assessthe state of health of valve-regulated lead-acidbatteries", in Proc Conf. INTELEC 93, 1993, pp218-233.

[6] M. Yamanaka, K. Ikuta and T. Matsui, "A lifeindicator of stationary type sealed lead-acidbattery" in Proc Conf. INTELEC 91, 1991, pp202-208.

[7] S.S. Misra, T.M. Noveske, L.S. Holden and S.L.Mraz, "Use of AC impedance/conductance andDC resistance for determining the reliability ofVRLA battery systems", in Proc. Conf.INTELEC 93, 1993, pp 384-391.

[8] R. Heron, A. McFadden and J.Dunn, "Evaluationof conductance and Impedance Testing on VRLABatteries for the Sentor Operating Companies",in Proc. Conf. INTELEC 94, 1994, pp 270-281.

[9] J.M. Hawkins, "Some field experience withbattery impedance measurement as a usefulmaintenance tool", in Proc. Conf. INTELEC 94,1994, pp 263-269.

[10] M.A. Bari, and A.K. Jonscher, J. ElectrochemSoc., 133 (5), (1986), 863.

[11] M. Keddam, Z. Stoynov, and H. Takenouti, J.Appl. Electrochem, 7 (1977), 539.

[12] P.R. Roberge, E. Halliop, G. Verville and J.Smit, J. Power Sources, 32 (1990), 261.

[13] J. Jindra, M. Musilova, and J. Mrha, J. PowerSources, 37 (1992), 403.

[14] G. Markle, "Variables that influence results ofimpedance testing for valve-regulated cells", inProc. Conf. INTELEC 93, 1993, pp 444-447.

[15] J.M. Hawkins, J. Power Sources, 35, (1991),417.