Condition monitoring of electrolytic capacitor in power electronic circuits using input current

Afroz M. Imam*, Thomas G. Habetler, Ronald G. Harley, Deepak M. DivanDept. of Electrical and Computer Engineering

Georgia Institute of TechnologyAtlanta, Ga-30332

Abstract---Electrolytic capacitors are responsible for frequentbreakdowns of static converters. To set a predictive maintenance,adaptive filter modeling based method is presented using LMSalgorithm. Signature of changes in capacitance and ESR willreflect in capacitor ripple voltage because of aging; and thesechanges are monitored using this adaptive filter modeling topredict the future status of the capacitor using only the inputcurrent of the system.

I. INTRODUCTION

Power electronic circuits are used in variety ofapplications ranging from small power supplies in computersto more specialized applications such as; satellite, airplane,medical equipments and different war-machines. In all ofthese applications, static converters are an essential subsystemwhose failure leads to the imminent and total stoppage of theequipment. Electrolytic capacitor is commonly used in all ofthese equipments as smoothening element of the convertersbecause it has high capacitance for its size and low price.Since failure of single element may lead to collapse of theentire system. So we need to develop some kind of mechanismwhich will alert the operator in advance for predictivemaintenance before failure. Most of the breakdowns in powersupplies are attributed to the electrolytic capacitors Figure 1[1]. Thus, a study of changes in the electrical waveformsresulting from worn out capacitors is necessary to evolvepredictive maintenance scheme for the converter in real-time.

The purpose of this paper is to show that capacitor ripplevoltage can be used to predict the failure of electrolyticcapacitor. Experimental data is processed to model the systemusing and adaptive filter model to estimate the capacitor ripplevoltage using only the input current signal of the system. Thecommon failure modes of electrolytic capacitors are due to thechemical reactions between electrodes and electrolytes. Thisleads to changes in effective series resistance (ESR),capacitance and leakage resistance of the electrolytic capacitorwhich in tum results in changes in capacitor ripple voltage andcapacitor current. In literature, some research has beenreported for condition monitoring of an electrolytic capacitorsbut they are complex and difficult to implement in practice[2], [3], [4]. In our proposed work, we use a much simpler,generalized and efficient method to predict the behavior of thecapacitor and predict the future status of the capacitor and thetotal useful life left in the capacitor. We believe that theproposed technique can be applied with any other powerprocessing topology.

07803-9124-1/05/$20.00 ©2005 IEEE

80%

70%

60%60%

l!:! 50%.2~ 40%"t-o

';Ie. 30%

20%

10%

0%Electrolytic Semiconductor hductive DiodesCapacitor Switch Element

Figure 1. Distribution of failure for each power component.

II. CONSTRUCTION AND FAILURE MECHANISM

A standard electrolytic capacitor consists of positive andnegative electrodes placed in a conducting electrolyte solution,generally a paper saturated in an electrolytic solution. Thisassembly is sealed into a can with the foils connected toterminal leads, (Figures 2 and 3). The dielectric material is anoxide that is formed by the "anodic polarization" of a "suitablemetal" immersed in a "suitable electrolyte" [6]-[8]. The term"suitable metal" generally refers to aluminum or tantalum,although niobium, zirconium, hafnium, silicon, bismuth,tungsten, and antimony, along with some other metals may beuseful in electrolytic capacitors [5]. These metals are knownas "valve metals." Nearly all metals are unstable at roomtemperature in contact with oxygen at atmospheric pressure,and they tend to form an oxide layer on the surface. The namevalve metal stems from the fact that the oxide layer tends toact as a rectifier, hence, a ''valve'' to the flow of current. Thereare several theories as to the nature of exactly why the oxideacts to rectify, discussed in Young [5]. The electrolyte isordinarily the limiting factor for lifetime and workingtemperature range in electrolytic capacitors due to itstemperature dependence [6]. Finding an electrolyte that hasstable temperature dependence and does not react with themetal of the electrode is not a trivial task. Electrochemicalreactions at the electrodes may form gases, which may causethe capacitor to rupture or explode. Some electrolyticcapacitors have a "blowout" provision, a plug built into the

container that will rupture easily to vent these gases andprevent catastrophic case rupture. In the long run ageingprocess accelerates the temperature rise because of ripplecurrents, resulting evaporation of the electrolyte. When theelectrolyte volume is reduced, the etch tunnels are not fullyfilled with electrolyte. A decrease in the effective surface areaof the electrode causes the capacitance to decrease. At thesame time, the ESR increases since the electrolytic resistanceincreases because of drying up of the electrolyte [5], [6], and[7]. Figure 9 shows that the value of ESR increases withaging. Voltage rating of an electrolytic capacitor is limited bythe oxide thickness on electrodes of the capacitor. Aluminumsurface of the capacitor is etched to increase the effectivesurface area of the capacitor.

,..----- negativechargeconnection

positivechargeconnection

dielectric

metal plate

aluminum

plasticinsulation

placed in an oven at around 115°C for accelerated aging. Thesampling rate for data acquisition is 20kSaiSc and 10,000points are captured at every 15 minutes for an efficient use ofmemory using National Instrument data acquisition system.The amplitude of the capacitor ripple voltage and the capacitorcurrent changes because of variation in capacitor parameters.An equivalent circuit for a typical electrolytic capacitor isshown in Figure 3.

CRI

+vrnL~ +VOIt

C In

.vrnJ~

.... Ql

lCv~JLGateV

Figure 4. Basic boost-converter.

Figure 2. Schematic diagram of an electrolytic capacitor.Ch1 5.OYCh3 5.OY

Ch2 100mV M4O.01JS 12.SMSJs 8O.om~

A Ch1 /' O.OY

Figure 3. Equivalent-circuit of an electrolytic capacitor.

III. EXPERIMENTAL SETUP

An open-loop basic boost converter with constant load,Figure 4, is used to carry out the experiment on the aging ofthe electrolytic capacitor. A 100 volt, 85°C, 1000JlFelectrolytic capacitor by Panasonic is used for this experiment.The switching frequency is held constant around 5 kHz with aduty cycle of 0.6. Capacitor voltage, switching-signal, andcapacitor current are shown in Figure 5. The capacitor is

07803-9124-1/05/$20.00 ©2005 IEEE

Figure 5. Capacitor voltage, switching-signal,and capacitor current.

IV. THEORY

A. Modeling

Figure 6 depicts the block diagram of an adaptive filter.The aim is to estimate the parameters of the model W(z), for aplant, G(z). On the basis of some priori knowledge of theplant, G(z) , a transfer function W(z) , with certain number ofadjustable parameters is selected first. The parameters of W(z)are then chosen through an adaptive filtering algorithm suchthat the difference between the plant output d(n) , and theadaptive filter output y(n), is minimized. In our application, apower converter is used as a plant which is being modeledusing the digital filter W(z).

x(n)-----~-~~ G(z)

N-I

yen) =I w;(n)x(n-i).;==0

(1)

andx(n) = [x(n) x(n-1) ... x(n-N+ l)]T, (4)

(3)

(8)

(6)

°0.:----'10'--0-------l20-0-----.l30-0-----.l..40-0--5-l..00-~600

Time in hours

1 I I 1 I

0.9 - - - -1- - - - J - - - - .!-- - - - - 1- - - - -I - - - -1 1 I 1 I

0.8 - - - _1- J 1 1 I _

1 1 1 1 I

~ 0.7 - - - ~ - - - - ~ - - - - - -: - - - -

'0 1 lin and Va I I~ 0.6 ,. - - -8 I I I 1 1

c 0.5 - - - -1- - - - -+ - - - - +- - - - -1- - - - ---I - - - -

~ I 1 1 1 1

~ 0.4 - - - -: - - - - ~ - - - - ~ - - - -:- - - - -: - - - -

8 0.3 - - - _1- --.! _ Vinland Va 1 I~ T --- T T~

0.2 - - - - - - - - ~ - - - - ~ - - - -:- - - - ~ - - - -

I I I 1 1

0.1 - - - -1- - - - -+ - - - - +- - - - - 1- - - - -l - - - -

1 1 1 I I

Figure 7. Time average correlation-coefficient plot over time

w(n+1) == w(n) - J1Ve2(n)

The filter output is,y(n) = wTx(n). (5)

The conventional LMS algorithm is a stochasticimplementation of the steepest descent algorithm. It replacesthe cost function ~ == E[e2(n)] by its instantaneous coarseestimate ~ ~ [e2(n)] in steepest-descent recursion. Hence weobtain the tap-weight vector update as,

The tap weights Worn), wj(n), ...... , wN-l(n) are selected so thatthe difference (error),

e(n) =d(n)- yen), (2)

is minimized in some sense. It may be noted that the filter tapweights are function of time index, n, since they arecontinuously being adapted so that any variations in thesignal's statistics could be tracked. The LMS algorithmchanges the filter tap weights so that ern) is minimized in themean-square sense. The filter input and tap-weight vectors aredefined, respectively, by the column vectors,

where J1 is the algorithm step-size parameter and V is thegradient operator defined as the column vector

[a a a ]T

v:= Owo

Owl ... OwN-l · (7)

It can be noted that the ith element of the gradient vectorVe2(n) is

oe2(n) := 2e(n) oe(n) .

Ow; Ow;

Afn)

W(z)

Figure 6. Structure of adaptive filter model.

B. Correlation

In any system, signals are correlated with varying degreeof values. In order to estimate an output signal, it is desired tohave signals with strong correlation as input signal foradaptation of tap-weights of the adaptive filter model. Thehigher the correlation coefficients between input and outputsignals the better will be the estimation of output signal.Hence it is very important to understand the physical systemand choose the appropriate signals as input. In the proposedwork, we observe that there exists strong correlation betweeninput current, iim and capacitor ripple voltage, Vo; and alsobetween input voltage, Vin, and vo, though relatively smaller.

It is possible to estimate capacitor ripple voltage, vo, withthe help of input quantities of boost converter either Vin or iin;or both. Figure 7 shows the time-average plot for correlation­coefficients between converter input quantities and capacitorripple voltage. As it can be observed from Figure 7 there isstronger correlation between iin and Vo compared withcorrelation between Vin and Vo. In our application, we usedonly input current, iin, to model the system in order to monitorthe status of the electrolytic capacitor. Results are discussed inlater part of this paper.

D. Derivation ofthe LMS Algorithm

Figure 8, depicts an N-tap transversal adaptive filter. Thefilter input, x(n), desired output, d(n), and the filter output,

C. Wiener Adaptivefilter theory

According to the Wiener filter theory, which comes fromthe stochastic framework, the optimum coefficients of a linearfilter are obtained by minimization of its mean-square-error(MSE). Least-mean-square (LMS) algorithm is the most basicand widely used algorithm in various adaptive filteringapplications, uses the instantaneous value of the square of theerror signal as an estimate of the MSE. It turns out that thisvery rough estimate of the MSE, when used with a small step­size parameter in searching for the optimum coefficients of theWiener filter, leads to a very simple and yet reliable adaptivealgorithm [9].

07803-9124-1/05/$20.00 ©2005 IEEE

Figure 8.Adaptive filter model.

after 480 hours of aging HP impedance analyzer. Theseparameters are listed in Table I.

400030002000

t (hours)

1000

100

50

O-t------,-----,------r--------I

o

350 ---,---------------------,

300

250

~ 200

~ 150w

(9)Be2 (n) .--= -2e(n)x(n-z).

Bwi

Substituting for y(n) from (1), we get,

Using (7) and (9) we obtain,Figure 9. Effect of aging on capacitor ESR.

V. RESULTS AND DISCUSSION

As explained in section II, the best signature for the statusof the electrolytic capacitor in a power electronic circuit canbe determined by monitoring the value of effective seriesresistance (ESR) of the electrolytic capacitor, directly orindirectly. Value of capacitor ESR increases with aging of thecapacitor as shown in Figure 9. Capacitor ripple voltageamplitude is directly related to the value of capacitor ESR.Capacitor ripple voltage increases with increase in thecapacitor ESR value. Hence health of the capacitor can bemonitored by monitoring capacitor ripple voltage. Thisconcept is discussed in later part of this section. Equivalentparameters of the capacitor are measured at the beginning and

This is referred to as LMS recursion. It suggests a simpleprocedure for recursive adaptation of the filter coefficientsafter the arrival of every new input sample, x(n) , and itscorresponding desired output sample, d(n). Equations (1, 2and 11), specify the three steps required to complete eachiteration of the LMS algorithm. Equation (1) is referred to asfiltering. It is performed to obtain the filter output. Equation(2) is used to calculate the estimation error. Equation (11) isthe tap-weight adaptation recursion. LMS algorithm is verysimple to implement as adaptive filtering scheme. Itsimplementation requires 2N+1 multiplications (Nmultiplications for calculating the output y(n), one to obtain(2/1 )xe(n) and N for the scalar-by-vector multiplication(2/1e(n)) x x(n)) and 2N additions, where N is the order of thefilter. In our modeling we used N= 10 as filter order.

TABLE IEFFECT OF AGING

(14)

(15)

(16)

(13)

Aging Duration C ESR(hours) (J.lF) (mn)o(New) 997.63 82.46

480 852.24 161.83

w9(n)

Estimated output,y(n) = wT(n)x(n)

Actual output of the system, d(n) = vo(n)

Error signal, ern) = d(n) - y(n)

wo(n)

wl(n)Tap-weights, w(n) =

An FIR filter with order lOis used to model the DCIDCboost-converter in order to estimate output side boostcapacitor ripple voltage, Va' using input current. Adaptive filtertap-weights are estimated using the LMS algorithm with astep-size of /1=0.005. Input ripple current iin, is used as inputsignal, x(n), and capacitor ripple voltage, Va' is used as outputsignal, d(n) , to determine tap-weights of adaptive filter byrecursive adaptation. Around 2000 data files are used to traintap-weights recursively. Each of these data files contains10000 points; hence in total 2000x 10000=20x 106 data pointsare used for this adaptation. We can write the LMS algorithmin mathematical form for this application as,

iin (n)

iin (n -1)Input, x(n) = (12)

(10)

(11 )w(n) = w(n)+2/1e(n)x(n)

Ve2(n) = -2e(n)x(n)

Substituting this result in (6), we get,

07803-9124-1/05/$20.00 ©2005 IEEE

30 -

-20 -

I____ ---l __ 1 __ L __ 1 I _

1

1 1 I 1 1 1- I - - I - - "I - - 1- - - - - -I - - I - -1 I 1 1 1 I I I 1

-30 - - 1- - -I - - I - - T - - I - - I - -1- - -I - - I - -

1 I 1 I 1 1 1 1 1-40 - - 1- - -I - - ---1 + - - t- - - I- - - 1- - -I - - --t - -

I I I I I 1 I I I

-50 '-----------'-_------'--_---'-_--'-_--L-_.......L-_~_---L--_-'-----------'

300 320 340 360 380 400 420 440 460 480 500

Time in hours

I I I I 1 1 I I 1

40 - - 1- - -I - - -4 - - 4- - - .L- - - l- - -1- - -I - - -4 - -1 I 1 I 1 1 I I I

__I __ ---l __ 1 __ L __ 1 1 I __ -.l _ ~

I I 1 1 I 1 I I

20 - - - - -: - - ~ - - +- - ~ - - :- - -:- - -: - -1 I I I 1 1 1 I'* 10 --:---:--~--T--~--~ -1---1--

~ 0 ~IU1\ij\~IVlltlgW -10

180

120

100 '----------'_------"-_------'--_-----'---_-----"---_--'--_-"--_--L-_--'----------'

300 320 340 360 380 400 420 440 460 480 500

Time in hours

Fundamental component of estimated Vo ripple over time220 r--------,------,------,--,---,-----,----,----.----,----------,

50,--------,.-------,-----,--,------,---,----,----.-------r-----.Percentage error variation over time

120

II1

200 - - - - -I - -

Fundamental component of actual Vo ripple over time

200

180 -

220,.--------,------,------,--,---,-----,----,----.----,----------,

140 -

100 '-----------'-_------'--_---'-_--'-_--L-_.......L-_~_---L--_-'-----------'

300 320 340 360 380 400 420 440 460 480 500

Time in hours

Figure 13. Evolution of fundamental component of estimatedcapacitor ripple voltage.

>.s 160o>

>.s 160o>

Figure 12. Evolution of fundamental component of actual capacitorripple voltage.

10000

10000

8000

8000

1 1__I ---l _

I I

I I- -I - - - - - -I - - - - -

I I- -I - - - - - ---j - - - - -

I I- _1- _

I

I- -I - - - - - - - - - - -

I 1

- -I - - - - - ---j - - - -

I 1__I ---l _

1 I1 I

- -1- I

I I-I

1

---- 1 -

II

--------1-----

I-----1-----

I II _I _

1 I

1 I- -I - - -I - - - - -

I I- -I - - - - - ---1 - - - -

1 1

__I ---l __

I I

I I- -I - - - - - -I - - -

I I

4000 6000Frequency (Hz)

4000 6000Frequency (Hz)

2000

2000

I 1- - - - _1- 1 _

I I

I~----I---

1

20

1

- - - - _1- _I

1

- - - - - 1- - - - - - - - -

1 1

- - - - -1- - - - - -1- -

I I___ 1 __ -

I

I----------1---

1

- - - - -1- - -

I

- - _1- __I

40 -----------:--I

- - -I-

I

60

40

I- - - - -1- - - - -

I 1

- - - - - 1- 1 _1 1

1

----1---

1 1

- - - - -I~ - - - - -1- - -

1 1

60 -----1------1---I 1

1

- - - -1- - - -

1

140

160

180

140

200,.----------,--------,--------,------,--------------,

180

160

120

l100

80

120

l100

80

FFT plot for actual capacitor ripple voltage

Figure 11. FFT plot for estimated capacitor ripple voltage.

200,----------,---------,--------r--------,---------,FFT plot for estimated capacitor ripple voltage

Figure 10. FFT plot for actual capacitor ripple voltage.

An enlarged portion of the fundamental component ofactual and estimated capacitor ripple voltage is shown inFigure 15; and it can be seen that actual and estimatedfundamental components are tracking very well.

Weight update, w(n+1) = w(n) + 2pe(n)x(n) (17)

Figure 10 and 11 shows the FFT plots for actual andestimated capacitor ripple voltage. It can be observed thatadaptive filter modeling is able to estimate the fundamentalcomponent at 5 kHz accurately with only a small error.Evolution of fundamental component of actual and estimatedcapacitor ripple voltage is shown in Figure 12 and 13, and thecorresponding percentage error plot is shown in Figure 14.

Figure 14. Percentage error variation over time.

07803-9124-1/05/$20.00 ©2005 IEEE

600500200 300 400lime in hours

100

120

I 1

I 1

160 - - - - 1- - - - - - - - - - - - - - - _.~

I X: 479.8I Y: 160.91 I150 - - - - 1- - - - - - - - - - - - - - - - - - -I - - - -

1 1

I I I I I- - - 1- - - - - 1- - - - -I - - - - -I - - - - --1 - - -

I I I 1 1

I I I I 1_ _ _ 1 1 1 I .J _

1 1 1 1 1

1 1 1 1 I

I 1 1 1 I- - - 1- - - - -1- - - - -1- - - - -I - - - - -I - - - -

I I I 1 I

I I I 1 1110 - - - - 1- - - - - - - -I - - - - -I - - - - -j - - - -

1 I 1 I

1 I 1 I

140

~-130

lime average fundamental component of estimated Vo ripple170,-------,--------,------.----,-------,-----,

315310295 300 305lime in hours

290

II

190 - - - -1- - -:k::/-.I--':-=-==-;=:~===¥_~__=__=j

·1If I

180 1- - - 1- - -

II'

170 -...- - - 1- - - - - I-

I 1

l160 - - - -:- - - - -:- -I I

150 - - - -:- - - - -:- - - -1 1

140 ----:-- --:----I I

130 - :- - - - -: - - - -1 I

200,----------,-------,--------.---------,-----,--------,

Figure 15. Enlarged portion of actual and estimated fundamentalcomponent of capacitor ripple voltage.

Figure 17. Time-average evolution of fundamental component ofestimated capacitor ripple voltage.

VI. CONCLUSION

The effect of changes in ESR (effective series resistance)and capacitance value of the electrolytic capacitor is reflectedin the capacitor ripple-voltage. The capacitor ripple voltagechanges because of change in ESR and capacitance value.Capacitor ripple voltage is estimated by using only converterinput current using adaptive filter modeling. Using FFT ofestimated capacitor ripple-voltage along with time-averagetechnique we can predict the life ofthe capacitor.

It can be easily observed using equation (20), we cangreatly reduce the amount of memory required in actualimplementation of this algorithm. Figures 16 and 17 are mostimportant results obtained after processing experimental datausing FFT and time-average technique. As we can observefrom plots in Figure 16 and 17; and comparing it withcapacitor parameter values given in Table I. There is a directrelation between change is capacitor parameter and time­average value of capacitor ripple voltage. As it can be seen thetime-average plot is monotonic in nature and it is possible toset some kind of threshold point on this plot in order to predictfuture status of the capacitor.

I I I

I I I

160 - - - - 1- - - - - - - - - - - 1 - ~-I.~~_-_1 I X: 479.8I I Y: 161.7

I I I150 - - - - - - - - - - - - - - - - -I - - - - -I - - - -

I II I 1 I I

- - - - 1- - - - -1- - - -1- - - - -I - - - - - - - -

I I I 1 I1 I I I 1

____ 1 1 1 I -.J _

1 I I I I

I I I I I

120 - - - -:- - - - -: - - - - - - - -: - - - ~ - - - -1 I 1 I

1 1 1 1 1

110 - - - - 1- - - - -1- - - - -I - - - - -I - - - -j - - - -

1 I I I 11 1 1 I 1

140

~-130

lime average fundamental component of actual Vo ripple170r___-~--_,___-----r------.----r___-----,

Where v(n) and V(n) represents instantaneous and time­average value of the fundamental component of actual andestimated capacitor ripple voltage at any given time nrespectively. Figure 16 and 17 are time average plots forfundamental component of actual and estimated capacitorripple voltage using equation (18). It helps in plottingsmoothened out plots and it is much easier now to estimate thecurrent and future condition of the capacitor.

Figure 16. Time-average evolution of fundamental component ofactual capacitor ripple voltage.

By using equation (18) in (19), it can be again written as,

V(n) = v(n)+(n-l)V(n-l) (20)

n

Further, equation (18) can be written as,n-l

v(n) + Lv(k)V(n) = k=l (19)

n

100 200 300 400lime in hours

500 600

REFERENCES

[1]. Military Handbook 217 F, "Reliability prediction of electronicequipment," Revision F, Dec. 1991, Notice 1, 10 July 1992, Notice 2,Feb. 28, 1995.

[2]. A. Lahyani, P. Venet, G. Grellet, and P. Vierge, "Failure Prediction ofElectrolytic Capacitors During Operation of a Switchmode PowerSupply," IEEE Trans. Power Electronics, Vol. 13, No.6, Nov. 1998.

[3]. K. Harada, A. Katsuki, and M. Fujiwara, "Use of ESR forDeterioration Diagnosis of Electrolytic Capacitors," IEEE Trans.Power Electronics, vol. 8, no. 4, pp. 355-361,1993.

[4]. M. L. Gasperi, "Life prediction model for aluminum electrolyticcapacitors," in IEEE lAS Conf Proc., 1996, pp. 1347-1351.

[5]. L. Young, Anodic Oxide Films. London, UK: Academic Press, 1961.[6]. 1. B. Birks and 1. Hart, Progress in Dielectrics, Volume 5. NewYork,

NY: Academic Press, 1963.[7]. T. L. Brown and H. E. Lemay, Chemistry: The Central Science.

Englewood Cliffs, NJ: Prentice-Hall, 1981.

07803-9124-1/05/$20.00 ©2005 IEEE

[8]. B. G. Streetman, Solid State Electronic Devices. Englewood Cliffs,NJ: Prentice-Hall, 1980.

[9]. B. Farhang-Boroujeny, AdaptiveFilters. John Wiley & Sons Ltd,England, 2003.