zaengl spectroscopy theory

8/13/2019 Zaengl Spectroscopy Theory

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Dielectric Spectroscopy in Timeand Frequency Domain for HVPower Equipment, Part I:Theoretical Considerations

Key Words:Dielectrics, polarization effects, dielectric response function, dielectric measurements

in time and/or frequency domain.

Today, the catchword in utility companies is condi-tion-based or predictive testing and maintenance,or even life management, as opposed totime-based or preventive maintenance only. The reasonsfor this evolution are well known: In North America, forinstance, their roots canbe found in therestructuring andde-regulation of the electric utility industry. Here in Eu-rope, it was the adoption of the Single Market Direc-tive which became the norm in February 1999, whereas

it was still theexception many years before [1]. The mainissue of this de-regulation of the electricity market, nowsubdivided into independentpower producers, transmis-sion companies, system operators and distribution com-panies, is to encourage competition while stillmaintaining basic public policy and service objectives.

All partners within this new scheme are thus forced tocut costs in maintenance and operation without endan-gering a steady supply of electricity to demanding cus-tomers. Costs can be reduced, first of all, by a transitionfrom time-based maintenance (TBM) to condition basedmaintenance (CBM), if the actual conditions of the ex-pensive high voltage components within the electricpower transmission systems are reliably known. The ap-plication of unscheduled maintenance, a philosophybased on a reactive mode of operation, will not reducecosts. Unscheduled maintenance means that repairs andmaintenance will be made only when the equipment, e.g.a transformer or cable, breaks down. But this generallycauses a downtime of theelectricity supply, so that break-downs become much more costly than planned mainte-nance. A CBM based on reliable diagnostic tools shouldthus be applied today.

Thedriving force forthedevelopment andapplicationof improved diagnostic methods is the steadily increasingage of expensive HV components. In many parts of theworld, the majority of large power transformers were in-stalled in the 1960s and 70s. Also, cable technologychanged at this time, and the first generations of PE orXLPE cablesarestill prone to breakdowns. All these factsare very well known.

It is not the aim of this article to discuss the full com-plexity of all the existing diagnostic techniques that havebeen successfully applied to different HV components tosupport CBM. Most of the dangerousbreakdowns, how-ever,arecausedbythe aging effects of HV insulation sys-temsused within these components, and there is still alack of appropriate tools to diagnose such systemsnon-destructively and reliably in the field. New methodshave been published in the last decade and even before,

September/October 2003 Vol. 19, No. 5 0883-7554/03/$17.002003IEEE 5

F E A T U R E A R T I C L E

Walter S. ZaenglSwiss Federal Institute of Technology (ETH), Zurich,

Switzerland

Most dangerous breakdowns arecaused by the aging effects of HVinsulation systems used within [HV]

components, and there is still a lack ofappropriate tools to diagnose suchsystems non-destructively and reliablyin the field.


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for which reliable diagnostics are claimed. Some of thesemethods are based on changes of the dielectricpropertiesof the insulation. Dielectric properties are dependent onmany factors, e.g. on frequency or time, on temperatureand chemical composition of an individual dielectric, oron the structure of an insulation system composed of dif-ferent dielectrics. In electric power engineering, most ofthese factors, e.g. dielectric dissipation or power factor,

areconsidered during standardized tests for many powerapparatus, but the frequency of the test voltage is, in gen-eral, only the power frequency for which the equipmentis designed. The power factor at a single frequency is,however, sometimes insufficient to qualify even strongchanges in the dielectric properties in complex systems.

A critical review of publications related to alternativediagnostic methods that are based on different dielectricresponse methods, as well as discussions with users ofsuch methods, disclose a lack of knowledge of the funda-mentals of such alternative methods. Part I of this articleintroducesthe fundamentals of dielectricspectroscopyinthe time, as well as in the frequency, domain, and pro-

vides a short overview of more recently applied methodswhich areable to quantify dielectric properties in the lab-oratory as well as in the field. This contribution will ex-tend the short introduction into dielectric responsemeasurements recently published in EIby Barry H.Ward in his feature article on power transformers [2].Part II will describe some specific applications of dielec-tric spectroscopy for HV power equipment, and it willshow why some interpretations of the methods will notcomply with assumed expectations.

Background of Dielectric ResponseEvery kind of insulation material consists, at an atomic

level, of negative and positive charges balancing eachother on the microscopic as well as on more macroscopicscales(ifnounipolarchargewasdepositedwithinthema-terial before by well known charging effects). Macro-scopically, some localized bipolar space charge may bepresent,buteventhen,anoverallchargeneutralityexists.

As soon as a material is exposed to an electric field(generated by a voltage across electrodes embedded inthe insulation), the positive and negative charges becomeoriented thus forming different kinds ofdipoleseven onatomic scales. A local charge imbalance is thus inducedwithin the neutral species (atoms or molecules) as the

centers of gravity for theequal amounts of positive andnegative charges,q, become separated by a small dis-tance d, thus creatinga dipole with a dipole moment, p =qd,which is related to the local or microscopic elec-tric fieldE actingin close vicinity to the species. Thus, thedipole moment can also be written asp = E, where isthepolarizabilityof the species or material under con-sideration. Note thatp, dandEare vectors not markedhere. As the distancedwill be different for different spe-cies as well as their number of dipoles per unit volume,

their polarizability is also different. Due to chemical in-teractions between dissimilar atoms forming molecules,many molecules will have a stable distance dbetween thecharge centers, thus forming permanent dipoles, whichare usually randomly oriented and distributed within thematerial,aslongasnoexternalfieldisapplied.(Notethatany kind of permanent polarization, for example, inelectretsor ferroelectrics,is not considered here). The

macroscopic effect of the polarizability of individual spe-cies can be given in a general relationbetweenthe macro-scopicpolarizationP andthenumberof polarizedspeciesper unit volume of the material. These relationships arewell known, but not treated here.

But let us now briefly recall the main mechanisms thatproduce macroscopic polarization P:

Electronic Polarizationis effective in every atom ormolecule as the center of gravity of the electrons sur-rounding the positive atomic cores will be displaced bytheelectric fieldE. This effect is extremelyfast and thuseffective up to optical frequencies.

Ionic (oratomic/molecular)Polarization referstoma-terial containing molecules forming ions that are notseparatedbylowelectricfieldsorlowworkingtempera-tures. Apart from electronic polarization induced insuch moleculesby anelectric field,elasticdisplacementsof charges (nuclei and electrons) will also occur; i.e.these types ofmoleculesarepolarsubstances,whichcanbe polarized up to infra-red frequencies.

Dipolar (ororientational)Polarization referstomate-rials containing molecules withpermanentdipole mo-ments with orientations statistically distributed due tothe action of thermal energy. Under the influence ofE,thedipoles will beorientedonly partially, soagain,a lin-eardependencyofP andE exists. Ionic and dipolar po-larization are still quite fast effects and may follow acfrequencies up to MHz or GHz.

Interfacial Polarizationis predominantly effectivein insulating materials composed of different dielec-tric materials,suchase.g. oil impregnated paper/cellu-lose. The mismatch of the product of permittivitytimes resistivity for the different dielectrics causes,under the influence of an electric field, movable posi-tive andnegative charges to becomedepositedon the(micro- or macro-) interfaces of the different materi-als,alsoformingsomekindsofdipoles.Thisphenom-

ena is oftenvery slowand in general active in thepower frequency range and below. Trapping andhopping of charge carriersbetweenlocal-

ized charge sites may occur also creating polarization.This is also a slow, butstrongly temperature dependent,processfound mostly insolids,forexample incable ma-terials (PE etc.). For more details the reader may eitherrefer to one of the standard text books, e.g. [3], or tosome more generalized reflections on this subject, e.g.[4][7].

6 IEEE Electrical Insulation Magazine


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In summary, the dielectric polarization is the result ofarelative shift of positive andnegative charges in a mate-rial.During all of these processes, the electric field isnot

able to force the charges to escape from the material,which would cause inherentelectric conduction.

Measurement methods to perform dielectric spectros-copy (Dielectric Response Methods) are based on funda-mental interactions between well known electric

quantities: Usually, HV insulation materials (also calleddielectrics) are isotropic and usually homogeneous, atleast at macroscopic scales. Then, the vectors of the mac-roscopic polarization Pand the electric field Eare ofequal direction and related by

P= 0E. (1)

Here, is the electricsusceptibilityof the material, adimensionless, pure number which is zero for ideal vac-uum. Thus, the susceptibility accounts for all kinds ofpolarization processes within a dielectric. 0 is thepermittivity of free space or vacuum (8.85419 10-12

[As/Vm]), a number with units relating the unit for elec-tric field [V/m] to that of electric displacement [As/m2].This already provides a hint that all polarization pro-cesses will induce electric charges at the electrodes, assoon as a voltage is applied.

From eq. (1), it follows that the polarization Pwillchangeor vanish if thefieldE ischangedorsettozero.Inany dielectric ( > 0), a reduction inEwill thus lead to adepolarization(orrelaxation) process, which will followwith somedelay or retardationto the reduction ofE. Di-electric properties thus becomedynamicevents that canbe quantified in the time- as well as in the frequencydomain.

Dielectric Response/Spectroscopyin Time Domain (TD)

In a vacuum-insulatedelectrode arrangement, the vec-torofelectricdisplacement(ordielectricfluxdensity orelectrical induction) Dis exactly proportional to theelectric field vectorE,

D= 0E (2)

or, if the electric field is generated by a time-varying volt-age,

D(t)= 0E(t). (2a)

Here, 0is again the permittivity of vacuum. The ori-ginofD andE isusuallyprovidedbyavoltagesourcecon-nected to the electrodes under consideration. No timedelay will exist between both magnitudes, if the timescales consideredstillproduce electrostatic field condi-tions. Note, however, thatDrepresents the positive andnegative electric charges perunit area induced at theelec-trode surface, and that these charges are the origin

sources and sinksof all electric field lines. Fortime-varying fields,E(t), the so calleddisplacement cur-rent must be supplied by the voltage source to maintainthe area charge density at the electrodes. This current isgoverned by dQ/dt, where Q is the total electric chargedeposited on each of the electrodes.

If the vacuum is now replaced by any kind ofisotropicdielectric material, the electric displacementDof eq. (2)

increases by its inherent (macroscopic) polarizationPasdefined in eq. (1):

D(t) =0E(t) +P(t) = 0(1 + )E(t). (3)

Thesignificanceof this equation is first of allrelated tothe fact that it separates the two kinds of charge induc-tion. (Asboth vectors,P andD,arestillinparalleltoE forisotropicmaterials, we will from now on in this articleavoid theuse of bold letters to denote vectors). Of no mi-nor importance is the fact that the time dependency of

P(t)willnolongerbethesameasthatofE(t),asthediffer-

entpolarizationprocesseshave different time delayswithrespect to the appearance ofE. This delay is obviouslycaused by the time-dependent behavior of the susceptibil-ity = (t).

This time delay may best be understood in the follow-ing way: Let us assume that a step-like electric field ofmagnitudeE0 isappliedtothedielectricatanytimet0 andthat this field remains constant fortt0. The dielectriccan then be characterized by its time dependent suscepti-bility (t) as well as by its specific polarizationP(t)asa re-sponse in the time domain, i.e. the formation andevolutionof thedifferentkinds of polarizationprocesses,which develop within extremely short times (as e.g. elec-

tronic polarization) as well as in longer (e.g. dipolar po-larization) or even much longer (e.g. interfacialpolarization) time spans. Fortt0, the magnitude of thesusceptibility or polarization is zero.

Figure 1 shows the development of polarization pro-cesses in the time domain, which, according to eq. (1),can be expressed as

P(t)/E0= 0 (t) 1(t). (4)

Here (t) as well asP(t) represent step response func-tions. The factor 1(t) is used to indicate the unit step for

the electric fieldE0. In Figure 1 the first part of this func-tion issimplifiedby an ideal step to account for the veryfast polarization processes, an instantaneous polariza-tion,P(t = t0) =P, which includes not only electronicbutalsootherveryfastpolarizationprocesses.(Theindex ofPis thus related to the frequency domain). Thisstep, at least for large HV power equipment, can be re-corded neither in the time- nor in an equivalent fre-quency domain. As all polarization processes are finite inmagnitude and will settle at long times, the polarizationfinally becomes static,P(t ) =PS.

September/October 2003 Vol. 19, No. 5 7


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According to Figure 1, the step response of this some-what simplified polarization can be written as

P(t)=P+ (PSP)g(t t0), (5)

whereg(t)is a dimensionless, monotonously increasingfunction. Therefore, eq. (4) may also be written as

P(t)= 0[ + ( S )g(t t0)]E0 (5a)or, if therelativepermittivity, = 1 + , is introduced:

P(t)= 0[( 1) + ( S )g(t t0)]E0. (5b)

As known from general circuit theory, it is now possi-ble to computeany othertime dependent polarization

P(t) forany othertime dependent excitationE(t) of a testobject, as the special solutions for the step excitation arealready known. This can be done by the use ofDuhamels Integralor convolution in the time domain.For the quantities in eq. (5a), the result is:

P t E t f t E dt

( ) ( ) ( ) ( ) ,= + 0 0

(6)

where f(t) is the so called dielectric response function:

f(t) = ( S )g(t)/t = ( S )g(t)/t. (7)

f(t) defined by eq. (7) is obviously amonotonously de-creasingfunction and inherent to the dielectric being in-vestigated.

The polarization P(t) produces themainpart of thepolarization (or absorption, or charging) current inatest

object if theelectric field,E(t),issuddenly applied. So far,we have not yet considered any pure dc conductivity

0, which represents the movement of the free charges inthe dielectric and which is not involved in polarization.

As already postulated by Maxwell in 1891 [8], the fieldE(t) generates a total current densityj(t), which can be

written as a sum of conduction, vacuum and polarizationdisplacement currents, i.e.:

j t E t D t

t

E t E t

t

P t

t

( ) ( ) ( )

( ) ( ) ( )

= +

= + +

0

0 0(8)

and with eq. (6) forE(t) = const.

j t E t t f t E t( ) ( ) [ ( ) ( )] ( )= + + 0 0 (8a)

with = 1 + .Equation (8a) and eq. (9) are afirst basis for the mea-

surement of the dielectric response function f(t)or forcharacterizing dielectric materialswith the time-domain(TD) method [5]. To do so, a step dc charging voltageof magnitude UC, which must be constant and free of rip-ple, is suddenly applied to the test object which has beenpreviously carefully discharged. Then the polarization(or absorption, or charging) current i

pol

(t)through thetest object can be recorded according to

i t C U t f tpol c( ) ( ) ( )= + +

0

0

0

(9)

whereC0is the geometric capacitance of the test object,and (t)is thedelta functionarising from thesuddenlyap-plied step voltage att=t0.

(NOTE:Thedimension off(t) is 1/s and its magnitudeis tied toC0, the geometric capacitance, which may ei-ther be the vacuum capacitance of the electrode systembetween which the dielectric is sandwiched, or the high

frequency capacitance of the dielectric at time t0 atwhich the current measurement was started.)

The transition from eq. (8a) to (9) is easy to perform.The charging current contains three terms: The first oneis related to the intrinsic conductivity of the test objectand is independent of any polarization process, the lastonerepresents all theactivate polarizationprocesses dur-ing the voltage application and the middle part with thedelta function cannot be recorded in practice due to thelarge dynamic range of current amplitudes inherent withthe very fast polarization processes.

A polarization current measurement can usually bestopped if the current becomes either stable due to thedcterm or becomes very low. If the test object is nowshort-circuited att = tc, thedepolarization (or discharg-ing, de-sorption) current idepolcan be measured, see Fig-ure 2. According to the superposition principlethesuddenreductionofthevoltageUC tozeroisregardedasanegative voltage step at time t = tc-and neglecting the sec-ond term in eq.(9) which is again a very short currentpulsewe get fort (t0+ TC):

i t C U f t f t T depol C C( ) [ ( ) ( )].= +0 (10)


Figu re 1. Polari zat ion of a diel ect ric exposed to a st ep field of mag -

nitude E0at t = t0.


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Tc is thetime duration when thestep voltage was applied.This current is of opposite polarity. The second term inthis equation can only be neglected if the chargingperiodTc was long enough to complete all polarization pro-cesses. The depolarization current then becomes directlyproportional to the dielectric response functionf(t), asthedcconductivity 0 ofthedielectricisnotinvolved,butcan easily be calculated from the difference between the

polarization and depolarization currents. Equation (10)is thus asecond basis for the measurement of the dielec-tric response functionf(t)or forcharacterizing dielectricmaterialsin the time-domain (TD). Note, however, thatinsufficientcharging periodsTcwill not force the secondtermtobecomezero,i.e.thereisamemoryeffectinthedielectric dueto polarizationphenomenawhich have notbeen completed due to the insufficient charging periodTc. (This effect is demonstrated later in Figure 5). In Fig-ure 2, the sharp current peaks associated with the deltafunctions (t) in eqs. (9) and (10) are not included for ob-vious reasons.

In practice, the polarization and depolarization cur-

rents are conveniently measured with a two electrodetechnique as illustrated in Figure 3. The two resistors ofthis circuit represent small protection resistances, whichwill not influence the recorded currents. If the test objectcontains an insulation system, which can be subdividedinto different sub-systems, the polarization and depolar-ization currents can then be defined by theselectedelec-trode arrangement and conveniently be sensed at virtualground potential. The complex insulation system ofpower transformer test samples embedded in guard ringelectrodes are typical examples for such an application.

Performing Time Domain (TD)Measurements

Combined polarization and depolarization currentmeasurements covering some decades in TD are indi-catedintheliteratureasPDCmeasurements.Aslongasboth kinds of currents are measured during time periodsstartingatnotlessthanabout0.1to1saftertheswitchingevents (t0 and tc respectively in Figure 2), and if measure-ment periods up to hours are made, the measurementscaneasilybeperformedbymeansofstandardequipment.

As too high electric fields within dielectric materials maycause non-linear effects, thedc power supply indicated inFigure 3 need only be designed for voltages up to about1000 V. However, the power supply must be free of sig-nificant ripple and provide a constant and very stablevoltage about 1 ms after each switching event. Switchingevents can be performed by means of relays or electron-ics.Electrometersshouldbeabletorecordcurrentsdownto some pA or less.

Figure 4 shows typical results for such a PDC mea-surement procedure, carried out on oil-impregnatedpressboard samples with different moisture content(m.c.) in the pressboard (Type T IV of Weidmann Elec-

trical Technology, Switzerland). The test cellwasa cylin-drical glass vessel in which the electrode arrangement(parallel plate electrodes with a guard ring on theground electrode, diameter of guarded section 113mm)was placed. The currents were monitored between theguarded electrode and ground. The pressboard samples(circular disks of 160 mm diameter and 2 mm thick)were carefully dried under vacuum (


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that stable polarization currents could be reached onlyforthehighermoisturecontent after about 200,000s,i.e.about 56hours.The slowand moreor lesscontinuousde-cayof thedepolarization currents confirms that themate-rial is highly dispersive, i.e. that quite a large distributionof relaxation effects (interfacial polarizationdue to thetissue structure of the pressboard) exists. Representationof such results on log-log-scale is paramount due to the

large dynamic range of the quantities.Accordingto eq. (10) it can be assumed that all fourde-polarization currents of Figure 4 represent the more orless perfect dielectric response functions f(t) of thepressboard samples with different moisture contents, asthe charging timeTCwas very long. But this may not betrue, as even for this very longchargingperiod not all po-larization processes may not have been completed. Thiseffect is well known and is called the memory effect,whichcanalsobeexplainedbytheequivalentcircuit,Fig-ure9,discussedlater.Thiseffectcanclearlybeseenbytheexperimental results shown in Figure 5 for the very drysample from Figure 4 (m.c. 0.2 %). Between each mea-

surement, the sample was carefully discharged for a longtime, so that every new measurement cycle started withthe same virgin conditions. This can be easily recognizedby the polarization currents, which follow the samecurve. The depolarization currents, however, becomesmaller and smaller for every reduction in the chargingtime. A ruleof thumb for the measurements is that the di-electric response functionsf(t) or the depolarization cur-

rent become quite accurate if the charging time is about 5to 10 times longer than the depolarization current isquantified.

Measurements of depolarization currents on oil-im-pregnated Kraft paper for limited time durations (0.01 to0.10 s) were performed nearly fifty ago, see [10]. Themagnitudes of the currents and the slopes of their decaywere dependent on the moisture content, which variedbetween 0.5to 7.5%. Such transient measurementsweremade with an oscilloscope.

The example in Figure 4 as well as the measurementspublished in [10] demonstrate the complexity of the timedependence of the polarization (charging) and depolar-

ization (discharging) currents of a typical power trans-former dielectric. Dependencies of this kind are quitedifferent from the time-domain behavior for several sol-ids discussed in Jonschers publications [5]-[7]. Never-theless, certain time spans may be simulated by idealizedresponses [11]; but quite long periods as measured andquantified here should always take the specific responsefunction for the investigated material into account.

Dielectric Response/Spectroscopyin Frequency Domain (FD)

An analytical transition from time to frequency do-

maincanbemadeusingtheLaplace-orFouriertransformby rewriting eqs. (6) and (8). Anidealstep response forthe total current density of a dielectric response function

f(t), considering also instantaneous polarizationprocesses are assumed:

j t E t dE t

dt

d

dtf t E d

t

( ) ( ) ( )

( ) ( )= + + 0 0 00 (11)

with

j(t)j(p);E(t)E(p);E(t)p E(p);f(t)F(p);

and considering the convolution of the last term in thisequation we get, withpbeing the Laplace Operator:

j p E p pE p pF p E p( ) ( ) ( ) ( ) ( ).= + + 0 0 0 (12)

Aspis thecomplex frequencyi , we can reduce theequation to

j E i I F( ) ( ( ( )[ )].= + +0 0 (13)


Figu re 4. Polarization and depolari zat ion cur rent s of unaged

oil-impregnated pressboard samples with different moisture con-tent (m.c.).

Figu re 5. Pola rization and depola rization cur rents of a drypres sboard sample as a function o f charging duration TC.


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ThusF( )is the Fourier Transform of the dielectric re-sponse functionf(t) or thecomplexsusceptibility :

( ) ( ) ( ) ( )

( )exp( ) .

= =

=

F i

f t i t dt0 (14)

Note that the frequency scale is now 0 . Combin-ing eqs. (13) and (14) shows the total current density:

j i E( ) { ( ) [ ( )]} ( ). = + + + 0 0 01 (15)

The main part of this current has its origin in the com-plex electric displacementD( )which is proportional tothe complex dielectric permittivity, (), with therelation:

D E( ) ( ) ( ) = 0 (16)

where:

( ) ( ) ( ) ( ( )) ( ).= = + i i1 (17)

Actual measurements of this dielectric response in thefrequency domain are difficult to perform, if the fre-quency range becomes very large. Usually and at least inelectric power engineering, only a single C - tan mea-surement is made, i.e., at power frequency. Sophisticatedlaboratory instruments can cover, however, even manydecades in frequency [12]. Note, that according to eq.(15) such instrumentscannot distinguishbetween thecurrent contributionof thepuredc conductivity 0 and

that of the dielectric loss (). This means that the mea-sured relative dielectric permittivity~ ( ) r is differentfrom the relative permittivity () defined in eqs. (16)and (17). Then the measured relative dielectricpermittivity~ ( ) r isdefinedfromthefollowingrelation:

j i Er( ) ~ ( ) ( ). = 0 (18)

Therefore:

~ ( ) ( ) ( )

( ) [ ( ) / ]

=

r r ri

i

=

+

= + 0 0

1 ( ) [ ( ) / ] +i 0 0 (19)

and the dielectric dissipation factor,tan ( ),

tan ( ) ( )

( )

( ) /

( )

=

=

+

r

r r

0 0

(20)

The realpartof eq. (19) represents the capacitance ofatest object, whereas the imaginary part represents thelosses.Both quantities depend on frequency. Often, thisfact is not appreciated, if a C - tan measurement is

made at only one frequency. As aging effects will changethese quantities in quite different and specific frequencyranges, new diagnostic tools will monitor and detect thiseffect.

Equation (14) disclosed the coherency between thetime and frequency domains. Thus it is obvious that thecomplex susceptibility () and its real and imaginaryparts canbe converted to the dielectric response function

f(t)and vice versa [13]. Both domains extend from zeroto infinity, but in practice for every conversion, only themeasurement results will be available. Possible conver-sion procedures arenotdiscussedhere in detail, but someinformation is provided at the end of this article.

Finally, it should be noted that all dielectric quantitiesaremore or less dependenton temperature.Anycompar-ison or measurement of these quantities must take thisinto account.

Performing Frequency Domain (FD)Measurements

Typical results of FD measurements are shown inFigures 6 and 7. The example is taken from recently per-formed investigations [9] and carried out on the sameoil-impregnatedpressboard samples with different mois-ture content (m.c.) as used for the PDC measurements inFigure 4.

A special dielectric spectrometer manufactured byDielectric Instrumentation [12] was applied enablingmeasurements over an extremely wide frequency rangefor these small samples (3.16 10-4 Hz to 10 kHz). Byapplying good EM shielding of the instrumentation andthe test cells, a test voltage of only 3 V was sufficient toperform the measurements. In Figures 6 and 7 the actual

testfrequenciescanbeidentifiedaspointsonthecurves.FD measurements always need a pair of magnitudes

for each individual frequency, see eq. (19). Insteadof dis-playing the results by the real and imaginary parts of thecomplex magnitudesforpermittivity or susceptibility, thefrequencydependenceofcapacitanceanddissipationfac-tor are shown in both figures. Figure 6 displays the realpartofthecapacitanceC = C0 andFigure7thedissipa-tionfactor tan (eq. 20). Theresults confirm that them.c.of the pressboard affects the low and very low frequencyresults much more pronounced than that at power fre-quency only. Figure 7 also shows that power and higherfrequencies may not identify moisture contents with reli-ability. The increase inC (Figure 6) is obviously mainlycausedby theconductivityof water andthus by increasedinterfacial polarization inside the pressboard.Please notethat the vacuumcapacitance C0 of the test cell, which canbecomputed fromthedimensions of thiscell, isonly44.3pF. Increased interfacial polarization also produces theincrease in dissipation factor, mainly in the low and verylow frequency range.

Measurements in the frequency domain need voltagesources of variable frequencies and, for applications re-



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lated to HV power equipment, output voltages up to atleast some hundreds of volts.Such measurementsbecomequite lengthy if very low frequencies are considered. Atleast two cycles of an ac voltage are necessary to quantifythe amplitudes and phase shift between voltage and cur-rents. Therefore, up to more than 2000 seconds is neces-sarytogetasinglevalueforaC - tan measurement ata frequency of 1 mHz.

Alternative MeasurementTechniques Related toDielectric Response/Spectroscopy

Measuringchangesof itsoriginaldielectric response inthe timeand frequency domains are not the onlymeans ofdetectingaging or the destructive decomposition of insu-lation materials and/or complete insulation systems.There are also many other methods to detect deteriora-tion, e.g. changes in chemical, mechanical or optical be-havior. As far as typical power transformer insulation isconcerned, for which a combination of oil gaps andoil-impregnated pressboard is used, examples of such

methods are thedetermination of the DP (degree ofpoly-merization) for quantifying decomposition and thus me-chanical strength of cellulose, oil parameter analysisincluding DGA (dissolved gas in oil) or HPLC (high per-formance liquid chromatography)for identifyingdecom-position products dueto high temperatures (hot spots) orpartial discharges, or Karl Fischer tests for detectingmoisture inoil and paper orpressboard. A survey of theseand similar techniques related to insulation monitoringcanbefoundin [2] togetherwithsomehintstodielectricmonitoring, to which this article is exclusivelyaddressed.

Before we go into an overview of alternative measure-ment techniques as applied to HV power equipment, thefollowing must be mentioned:

Dielectric response techniques are global methods, i.e.eachtestobjectistreatedasablackboxaccessibleonlyby its electric terminals. Therefore, only global changesof the insulation can be identified but not localized de-

fects. Partial discharge (PD) measurements for instancecan be applied to find such localized defects [2].

Inherent to all dielectric response measurements in ei-therof thetwo domains is their off-line character, i.e.equipment in operation must be removed from serviceto perform the measurement.

As dielectric response measurements should be per-formedonequipmentinstalledonsiteinthefield,and

as the measurement instruments used are usually quitesensitive to electromagnetic disturbances, the electro-magnetic compatibility of such instruments must beguaranteed. Therefore, the test voltage levels of theinstruments cannot be too low.

Alternative Time Domain Techniques

A) The Common Return Voltage TechniqueOneof theoldestmethods to qualify dielectric proper-

ties (permittivity and losses) of anomalous dielectricswas, and still is, to perform asingleReturn or RecoveryVoltage measurement. The expression anomalous was

earlier used to define a dielectric whose after-effects -also an earlier expression to identify polarizationand de-polarization currents and effects - could not have beenexpressed by a single number for capacitance and resis-tance, see e.g. [14]-[15]. The measurement principle isshown in Figure 8. Similar to Figure 3, a dc voltage ofknown amplitudeUCis applied to the test object (whichwaspreviously completely discharged) duringan intervalt1=TC, which should be so long that at its end the af-ter-effects produced by the application of the potentialUChave dispersed completely [15].

After a short, but often not well defined short-circuit-ing period, a return or recovery voltage,UR(t), can

then be measured across the test object, if the input im-pedance of the voltmeter used is very high. (Note: Thecondition of a very high input impedance, even one cen-turyago,waseasytofulfillbyusingelectrostaticvoltme-ters; which is why the effects of relaxation orresidual charge could be detected). The origin andsource of the recovery voltages are the depolarizationcurrents, idepol(t), as defined in eq. (10), i.e. the still activerelaxation processes inside the dielectric material whichdid not relax during the short-circuit period. Early mea-surements confirmed [15] that the magnitudes andshapes of the recovery voltages, UR(t), are strongly de-pendent on the amplitudeU

Cof the voltage and its dura-

tiont1, as well as on the duration of the short-circuit orgrounding period, (t2-t1), see Figure 8. If, therefore, anyquantitative results of this technique have to be judged,all three factors have to be taken into account, i.e. theyshould be well quantified.

All these effects and the results gained from the ReturnVoltage Technique can be easiest explained if we repre-sent the behavior of a dielectric by anequivalent circuit,shown in Figure 9. This circuit can be traced back toMaxwell [8] and is thus sometimes called the Maxwell


Figu re 6. Real par t of the c omplex capaci tance of the p ressboa rd

sample s, Fi gure 4.


9/15

model [16], [27]. A simplebackground exists forthis general equivalent circuit: As already shown,for slow polarization processes the depolariza-tion currents and thus the dielectric responsefunctionsf(t) are monotonically decreasing, seeFigure 4. Such dependencies can always be simu-lated by a superposition or a sum of exponentialfunctions as shown in [9], [17] and elsewhere.

This sum can be modeled most easilyby aparallelconnectionofseries RiCi elements, together with ahigh frequency capacitanceC=C0accord-ing to eq. (9), which can be determined by con-ventional methods, and the insulation resistance

R0(representing 0in eq. (9)) of the test object.This resistance,R0, can either be taken from amore or less final value of the polarization/charg-ingcurrent,oritcanbecalculatedfromanalreadyknown dc conductivity, 0, of the dielectric andthe geometry of the test sample.

If this circuit, according to Figure 9, is suddenlycharged with a dc voltage sourceUCduring 0tt1,the

individual polarizationcurrents including the constantcurrent throughR0will flow into the circuit, charging in-stantaneouslyCand, with some delay, the capacitorsCiof theRiCi-elements according to their time constants(themagnitudeandnumberofwhichdependsonthesim-ulation procedure applied). Depending on how long (t1)the object is charged, the different polarization processesas represented by theRiCi-elements becomeeither fullyoronly partlyactivated. A very short grounding periodfrom t1 < t t2 will only dischargeC,butifthisperiodislarger, the slower polarization processes with large timeconstants will also start to relax. As soon as the short cir-

cuit is opened for t > t2, the recovery voltage UR(t) can bemeasured under open circuit conditions, as the polariza-tion processes (orRC elements), some of which were par-tially relaxed during the short circuit period, will partlydischarge intoCandR0. The magnitude of the returnvoltage which is thus always proportional toUC, is de-pendent on the charging timet1= TCand grounding pe-riod, (t2-t1). The initial slope of the return voltage (SRinFigure 8) is proportional to the activedepolarization cur-rent at time instant t2 and thus proportional to theintensity of the polarization process at this very specificinstant.

The proportionality of the magnitudes of the returnvoltages toUCis self-evident, but the other dependenciesaremore sophisticated. An example of thedependence ofthe shape of the return voltage on the grounding period,Td=(t2-t1), is shown in Figure 10. The results were cal-culated from the measured depolarization current of thetest sample, Figure 4 with an m.c. 2.5 %, and its specificequivalent circuit, Figure 9, for which the insulation re-sistance is not too large. A chargingduration of 100 s wasassumed to demonstrate the effect that, even for ground-ingperiodsofashighas10000s,areturnvoltagewillstill

exist, the magnitude of which, however, become verysmall and could no longer be measured in practice. Thecalculation assumes ideal conditions for the measure-ment of the returnvoltage slopes. Thepronounced decayof the voltages after its peak values is due to the magni-tude of the insulation resistance,R0, in Figure 9.

One advantage of the return voltage measurement isthe fact that only one terminal of the test object is neces-sary to connect the charging voltage to the test object andto perform the return voltage measurement, assumingthe second terminal is at ground potential. If, however,the testobject is a combination of individual sub-systems,it is aconsiderable disadvantagenot to be able to sensesuch individual sub-systems. Another advantage is theself-calibrating effect of this method: The magnitude ofthe return voltages is always more or less related to thegeometric or high frequency capacitanceCof the test


Figu re 7. Dis sipation fac tor tan of the pressboard sample s,

Figu re 4.

Figure 8. Principle of a Retur n Volt age mea surement. Charging

with UC dur ing 0 t t1, grounding per iod from t1 < t t2, for t > t2,the recovery voltage is measured at open circuit conditions.


10/15

objectsee Figure 8which can also be used to qualifythe magnitude of the polarization processes.

Even in the 1950s, some specialized return voltagemeasurement instruments for the detection of moisturein the insulation of transformer and for controlling thetransformer drying process after batch production be-came obviouslyattractive. As a result, special instrumentswere developed in France, UK, and Russia. It is notknown if such instruments are still in use, but further in-formation can be found in [10], [19]-[20].

(NOTE:R0may also be approximately evaluated byapplying a voltage response measuring method [18]

not discussed in this paper. This method is based on theReturn Voltage Technique, but at the end of the chargingperiod of between 10 to 1000 s duration, the test sampleis disconnected from the dc source and a slowly decayingdischarge voltage curve is measured. It is claimed thatthenegative slope of this curve is directly proportional tothe conductivity of the test object. However, this state-ment is not completely accurate as the decay of this volt-age is also somewhat influenced by depolarizationprocesses. In [18], no quantitative instructions are pro-vided about the duration of this open circuit period,which will be followed by a shorter short-circuit period

of 1 to 100 s before the normal return voltage UR(t) andits initial slope are measured.)

B) Measurements of Polarization Spectraby Means of a Return Voltage Meter

About a decade ago, a particular return voltage mea-surement techniquefor theon-site assessment of the bulkdielectric properties for power transformers appeared.This method, now called RVM-technique, was origi-nally proposed in [21] and in succeeding papers (e.g. in[22]-[23]). It became very attractive, as it was, and still is,claimed that the moisture content in the pressboard of atransformers composite insulation system canbe quanti-fied by analyzing a polarization spectrum evaluatedfrom the measurement procedure. This spectrum isproduced by applying aseries of individualcharging volt-agesUCto the test object, followed by a short-circuitingperiod as explained in Figure 8, at each cycle or step in-creasing the charging period t1 = Tc as well as theshort-circuitingor groundingperiod (t2 - t1) = Td,andus-ingafixedratioof(Tc/Td)=2forthemeasurementseries.During the individual charging process as well as duringthe grounding period, no measurements are taken. After

Td haselapsed,therecoveryvoltage,UR(t),foraparticularcycle, is recorded and from itspeakvalue, the amplitudeURmaxis quantified together with the charging periodTcfor that cycle. As the charging periods are usually subdi-vided by cycles of 1, 2, and 5 for each decade in time, ei-ther a discontinuous graph,URmaxas a function ofTc, canbe drawn or a continuous function, if the individual mea-suring points are combined by some kind of interpola-

tion. The resulting curve is called the polarizationspectrum as each maximum appears at a Tc-value, whichapproximately corresponds to a singlerelaxation timeconstantRiCiof the equivalent circuit, see Figure 9, if allother time constants are neglected in this circuit. A pre-requisite for applying this method is the existence of a fi-nite, neithertoohigh nor too lowan insulation resistance

R0of the test object, which is responsible for the pro-nouncedpeakvalueinanindividualreturnvoltage,UR(t).Otherwise the return voltage will decay too quickly ornot decay at all. Such a simplified circuit with only fourelements can analytically be solved as shown in [23].There some computed return voltage curves are shown,but each only for a single relaxation time constant in ourequivalent circuit, see Figure 9. Such an individual returnvoltage starts development at about 0.1% of this timeconstant and becomes close to zero at about 20 times thistime constant, if an adequate insulation resistance (R0inFigure 9) is assumed. Therefore, the resolution of morethan one relaxation time constant, which differ by lessthan a factor of about 5 in magnitude, is very limited.

A fundamental drawback of this method is the timenecessary to perform a complete series of measurementsnecessary to obtain a polarization spectrum for any testobject: A series usually starts with the shortest charging

period Tc of 10ms, that is then changed insteps of2/5/10and up to the longest, at 10000 s. The insulation systemunder investigation must be adequately discharged be-tween each step before starting the next one. Thus, thetime necessary to execute one step is not only the time ofTc +Tc/2+ time ofUR(t) up toURmax , but there is also anadditional time to discharge the test object to zeroconditions.

As the RVM-technique is based on quantifying theeffects of a set of incomplete depolarizationcurrents andincomplete specific return voltage curves, it provides nodirect information about the insulation resistanceR0ofthe test object. It is, however, possible to calculate this re-sistance using the Newton iteration method if the initialreturnvoltage increase rate (dUR/dt) is also measured andquantified. The results of such calculations are subject touncertainty as was shown in [24].

Part II of this article will show some applications ofthis RVM-Technique. As this instrument is not able toperformmeasurementsontestobjectsofsmallsizeorlowcapacitance, calculated polarization spectra are shownin Figure 11, based on the results of the PDC measure-ments shown in Figure 4. As will be seen in Part II, such


Figu re 9. Equivalent circui t to mode l any l inear d ielect ric .


11/15

calculations are possible and accurate since the dielectricresponse functions f(t) of these samples are alreadyknown. The results demonstrate the influence of mois-ture content (m.c.) on the shape of the polarization spec-tra, i.e. the shifting of the peak values to shorter values ofcharging duration (TC) with increasing m.c.

Nevertheless, the RVM-technique is popular in di-agnosing oil-paper insulation in power transformers due

to the assumption that the moisture content in thepressboardcan reliably be identified. However, there hasbeen much controversy for some years surrounding thistechnique [25], which has been criticized for various rea-sons, e.g.: the moisture content of the pressboard evalu-ated from the polarization spectra very often yieldsmuch highervalues than that obtained by other methods;the recommendedinterpretation schemeis toosimplistic,and finally, the technique does not take into account theeffects of the geometry andproperties of the transformeroil. Therefore, in 1999 a CIGR Task Force (15.01.09)was set up to clarify these discrepancies. In Part II of thisarticle, an example of these investigations, a summary ofwhich was recently published [26], is provided.

If the insulation resistanceR0of the test object be-comes too large, the RVM-technique with its polar-ization spectrum will fail. This was experienced aboutten years ago, but onlyone publication asanexample willbe mentioned [27] in which someindividualreturn volt-ages with 15 minutes charging period displayed no peakvalue, URmax. Therefore, this technique and its evaluationprocedurebasedonthepolarizationspectrumcanonlybe applied fordielectrics whose insulation resistanceR0 isnot too large.

C) Isothermal Relaxation Current (IRC) AnalysisIn recent years, another alternative diagnostic tech-

nique appeared in the literature called IRC-Analysis.Originally mainly applied to the investigation of PE andXLPE cables [29]-[30], the authors currently use thismethod for the diagnostics of other kinds of insulationmaterials used in HV technology [31].

The method is based on adepolarizationcurrent mea-surement which is usually performed with a charging volt-age of 1 kV and a charging period of 1800 s followed by adischarging (short-circuiting) period of five seconds, dur-ing which no measurements are made [32]. The depolar-ization current, named relaxation current i

R(t), is then

measured and multiplied by the timetelapsed during thespecific measuring period which is in general equal to thedischarging period. But charging as well as dischargingtimes may be variableand set by the experienceof on-siteinvestigations [29]; as a result, numerical values of thesequantities are usually not indicated in the publications.From the results, an IRC-Plot,ttimesiR(t) as a functionoflog t, is made and used as an evaluation procedure. Thisprocedure is basedon thefollowing: ifiR(t) decays accord-ing to a single exponential function in the form of (a e-t/),

the specific IRC-Plot will show a bell-shaped curve whosemaximum appears at the time constant of this single ex-ponential function. As measured IRC-plots may also con-tain some local maxima, this measured plot is thenbymeans of somewhat complexandsophisticated evaluationproceduressimulated by the superposition of single ex-ponential functions with amplitudes ai and relaxationtimesias parameters. The latter parameter is related to

charge traps or trap energy levels in the insulation,which may change with material, temperature and, for ex-ample, aging products.

The shape of IRC-plots is quite different from theshape of the plots for the depolarization currents, as canbe seen in Figure 12. Again, some of the measured depo-larization currents in Figure 4 have been used to displaytypical shapes, but in this figure the time scale is muchlarger than those for other published results (see Part II),as the depolarization currents were available up to200000s, whereas thechargingperiods of commonmea-surementslastabout1800s.Theplotforanm.c.of2.5%indeed shows a bell-shaped curve whosemaximum is ob-

viously quite close to a dominant time constant in therange of some 1000 seconds which can also be identified


Figu re 10. Calculat ed re turn voltage s for one sample (2.5 % m.c.)

of Figure 4.

Figure 11 . Calcu lat ed polari zat ion spectra for 3 sample s of

Figu re 4.


12/15

from the relevant depolarization current in Figure 4 orthe relevant polarization spectrum in Figure 11.

Apart from the fact that this method cannot quantifythe dc insulation resistanceR0or the conductivity 0ofthe testobject, publishedresults very likely indicate a sys-tematic error of the evaluation procedure, as the maxi-mumwillalwaysbedependentonthechargingtime.Thiscan be well understood by the inherent behavior of a de-

polarization or relaxation current, which always de-cays more or less as an exponential function after abouthalf of the charging period which is not sufficient to get acomplete depolarization current up to the fulldischarging time, see Figure 5.

Alternative Frequency Domain TechniquesThe common measurement techniques for capaci-

tance,C, and the dielectric dissipation factor,tan , ac-cording to eq. (20) at power frequency (i.e. atone single

value in the frequency domain) by means of bridge cir-cuits, which are based on standard capacitors, are wellknown and explained in many textbooks related to HVtechnology [33]. Ingeneral, such measurement canrevealadverse effects in insulation systems. Depending on thetype of HV equipment under test, however, aging effectsare not always sensitive to a single set ofC- tan -valuesmeasured at power frequency. Manyinvestigations, espe-cially related to medium voltage power cables, haveshown that many kinds of aging phenomena are moreap-parent at a much lower frequency range [34]. Thus, forsome yearsC and tan have been measured at 0.1 Hz us-ing0.1HzHVtestequipment,whichhaslowpowercon-

sumption. One of the reasons for the development of lowfrequency techniques is that for diagnostic tests of me-dium-voltage PE/XLPE cables, the loss factors aremainlysensitive to water treeing [35].

Measurements performed at one or even two singlefrequencies, however, cannot be treated as an alternativemethod to an extended dielectric spectroscopy, apartfrom the additional expenses as necessary for the 0.1 HzHV test and measurement equipment.

The measurement ofC- tan - values (or complexpermittivity values, eq. (19)) within a large frequencyrange and high voltages up to some kilovolts is a difficult

task, as standard capacitors with precisely known andstable dielectric properties essentially in a frequencyrange of less than 1 Hz are not available. Higher voltagesare necessary to avoid EMC problems during on-sitemeasurements. This difficulty, which will be present inthe already mentioned instrument for the measurementsof Figures 6 and 7, was recently solved by the develop-ment of a new instrument based on frequency domainspectroscopy (FDS, [35]). Results of this, as well as ofother new instruments, will be discussed and shown inPart II of this article.

Coherency Between Different TechniquesFigures 10 to 12 have shown that results of alternative

measuring techniques can be computed if the dielectricresponse functionf(t) in an adequate time period is mea-

sured and known. Equation (14) also shows that anunique relationship exists between the time and fre-quency domains as long as thedielectric properties underinvestigation are linear. As most of the methods currentlyapplied are time-domain methods and, as for all conver-sions the equivalent circuit of Figure 9 is very important,the modeling procedures based on this circuit, and de-scribed in more detail in [9], are briefly explained.

For insulation systems in HV power equipment, allmeasured polarization and depolarization currentsseeeqs. (9) and (10)are governed, within the time periodsof interest, by monotonously decreasing functions. Thebehavior of the currents is essentially determined by the

dielectric response functionf(t)and the conductivity 0of the test object with its geometric capacitanceC0orCrespectively. Ifboth currents have been measured fortimeperiods large enough to identify the dc-componentwithin the polarization current, their sum can then beused to identify the dc resistanceR0(=C0 0/ 0) of thetest object. But the equivalent circuit of Figure 9 containsmany more circuit elements: The still unknown elements

Ri,Ciwith their corresponding time constants i=RiCirepresent the polarization and depolarization processesandmustnextbedeterminedbythemodelingprocedure.This can be done by fitting the depolarization currentwith the equation

i t A tdepol i ii

n

( ) exp( / ),= =

1 (21)

where

A U T R i i ni c c i i= =[ exp( / )] / , .1 1 for K (22)

In eq. (22),Tcis the period of time during which thestep voltageUcwas applied.


Figu re 12 . Calcula ted IRC-plots for 3 sampl es o f Figure 4 .


13/15

With a special, sequential algorithm not explainedhere, the a priori unknown coefficientsAiand time con-stants i, which are chosen equidistantly in the logarith-mic time scale, are determined. In general, only two orthree time constants per time decade are necessary to fitthe measured depolarization current with sufficientlyhigh accuracy. It shouldbe emphasized that by this proce-dure the currents are now simulated by algebraic equa-

tions covering the time scale from zero to infinityalthough their validity is restricted to the measured timeperiods only. Now our equivalent circuit with its knowncircuit elements can be used for all kinds oftransformations.

The transformation into the frequency domain mayeasiestbeunderstoodbyre-writingeq.(18)intheformofits relation between a measured sinusoidal current I( )and a measured sinusoidal voltageU( )as

I i C U( ) ( ) ( ). = (23)

Here, C() is the complex capacitance which is related to

the relative dielectric permittivity, eq. (19), as

C C iC

C ir r

( ) ( ) ( )

{ ( ) [ ( ) / ]}.

=

= +0 0 0 (24)

Here, C0 and 0 again represent the vacuumor geometriccapacitance and the dc conductivity of the test object, re-spectively.

The dissipation factor tan () can be re-written usingeq. (20) as:

tan ( ) ( )

( )

,

=

C

C (25)

as the losses due to dc conductivity are already includedin C( ).

For the equivalent circuit, Figure 9, the complex ca-pacitanceC() can now be calculated according to eq.(23) from its complex admittance,Y() as:

C Y

iC

i R

C

i R Ci

i ii

n

( ) ( )

.

= = + +

+ =1 10 1 (26)

TherealandimaginarypartsofC()arethengivenas

+ ++

=C C

C

R C

i

i ii

n

( )( )

1 21 (27)

and

= ++=

CR

R C

R C

i i

i ii

n

( )( )

.

1

10

2

21 (28)

Finally,tan () can be calculated from:

tan ( ) ( )

( )

=

++

++

=

11

1

0

2

21

2

R

R C

R C

C C

R C

i i

i ii

n

i

i ii=

1

n .

(29)

Equations (26) to (29) are simple algebraic equationsdependent only on frequency as all other magnitudes are

already known. A numerical computation of the resultsfor any frequency is thus straightforward.

Figures 6 and 7 display measured results of the testsample of Figure 4, and are thus not computed. As themeasurements of Figure 4 have only be made within atime period of five decades, it would not be possible tosimulateandcalculatemorethansevendecadesinthefre-quency domain. But the very good agreement of calcu-lated and measured results was already shown in [9] or[17].

Figures10 and11 showedcalculated results for returnor recovery voltages and polarization spectra respec-tively. As already explained, polarization spectra are

basedon the results of a series of return voltage measure-ments. The following calculation procedure, again basedon the equivalent circuit of Figure 9, can thus be appliedfor any transformation of a PDC measurement into re-turn voltages.

According to Figure 8, the return voltage uR(t) is mea-sured under open circuit after charging the sample with acharging voltage, UC, during a charging period, TC= t1,and a discharging (grounding) period of Td= t2- t1. Thetime scale for uR(t) will thus start for t t2. During TC notallofthecircuitelementsi=1...nmayhavebeenchargedcompletely and during the groundingperiod Td all of the

capacitors Cihave already been discharged to some ex-tent, so that the boundary conditions at time t = t2forsolving the differential equations are:

u tR( ) ,2 0= (30)

and for the remaining voltages at each RiCi element

u t U T R C T R Ci c c i i d i i( ) [ exp( / )]exp( / ).2 1=

(31)

The return voltage can now be computed by the fol-lowing differential equations:

du t

dt R Cu t u t i ni

i iR i

( )[ ( ) ( )],= =

11for K

(32)

and

du t

dt C

u t

R

u t u t

RR r r i

ii

n( ) ( ) ( ) ( ).=

=

1

0 0 1 (33)



14/15

As TC aswellasTd in these equations can have any val-ues, a PDC measurement from which the equivalent cir-cuit has been derived thus provides any kind of a returnvoltage measurement.

ForthecalculationofanIRC-plot,Figure12,notrans-formation but only a multiplication by the time t is neces-sary.

If Frequency Domain Spectroscopy is used, transfor-

mations into the time domain are also possible. The pro-cedures, however, are more difficult to apply. The readerinterested in such successfully investigated and appliedalgorithms can find an in-depth treatment in [36]-[37].

ConclusionsThis review introduces the theoretical background of

dielectric spectroscopy in the time and frequency do-mains and provides an overview about the specific mea-suring methods based on this background. The specificmethods treated are used for diagnosing electric insula-tion materialsused in power engineering.It indicates thatsome of these methods may not be sufficient to gain full

information about the actual conditions of a test objectand that either measurements ofpolarization and depo-larizationcurrents (PDC) in the time domain or measure-ments ofC-tan - values (or complex permittivity) in thefrequency domain (FDS) should be preferred to obtain adielectric response function which offers much moreinformation to judge the actual state of an insulationmaterial or system.

InPart II, the application of someof these methods aretreated in more detail and the results of some investiga-tions related to the PDC-, RVM- and FDS-methods willbe shown.

AcknowledgementSpecial thanks are due to my former student, V. Der

Houhanessian, for providing permission to publish someresultsofhisthesis[9],andforpreparingFigures10to12.

Walter S. Zaengl (SM1970-F1998),was born in 1931 and received hisDipl-Ing anddoctorate (Dr.-Ing.) in elec-trical engineering from the TechnicalUniversity of Munich/Germany in 1955and 1964 respectively.

In 1955 and 1956 he was with AEG,

Kassel, Germany, working on the devel-opment of HV power circuit breakers and HV testing.From 1956 to 1969 he worked with the Technical Uni-versity, Munich to support the construction of new HVlaboratories for research and testing, to perform researchon impulse voltage measurements for very high voltages(thesis on capacitor voltage dividers) and to teachcourses on HV measurement and testing techniques. In1969, he joined General Electric, in Pittsfield, MA, USA,for a special project.

In October 1969, he joined the Swiss Federal Instituteof Technology(ETH)ofZurich, Switzerlandas a full pro-fessorandhead of theHigh Voltage Laboratory. Researchunder his direction was mainly focused on the develop-ment of advanced techniques forHV measuringand test-ing systems, on basic research in gaseous discharges (SF6and gas mixtures), on applied research and diagnosticmethods forHVpower equipment, andon hazardousgas

treatment by means of non-thermal electrical discharges.He retired from full service at ETH in October 1996.ProfessorZaenglhasauthored about 120 publications

and is the co-author of three books on HV engineering.HeisaFellowoftheIEEEandamemberofVDE(Ger-

many), SEV(Switzerland) anda distinguishedmemberofCIGR. He was convenor of the IEC working group es-tablishing the latest IEC-Standard (No. 60270) for Par-tial Discharge (PD) Measurements, issued in 2000, andis member of a CIGR Task Force, Group (15-01-09),dealing with the application of dielectric phenomena fortransformer diagnostics.

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