The Computing of the Influence of a Steady Element on the Polarization Spectrum

This paper describes computation of the influence of a steady current element on the current response of insulation material. The steady element is always present. When the insulation is dry, it can be neglected. When moisture is present, the steady element has to be calculated. A decision can be made after examining the spectrum.


Introduction
The insulation strength of a material can be scanned only by obsening the changes in the electro-physical structure oh the mate.ialwithout destroying it.The breakdown voltage can only be determined by performing an electrical strength test.'I'his is a destructive test on an insulation system made of solid material.This test is not suitable for service conditions   tll The relations between the quantities are evident' Changes in material structure due to service ageing necessarily change the material properties and electrical strength.In this way the determination of quantities closely connected to an electro- physical stmcture requires the quality of the material to be specified [2].
Many evaluation methods can be used to determine the state of an insulation material.There is no single method at present that can provide a full description.A set of methods hai to be used.Some of them involve observing the polarization spectrum.At Eg.I shows, the polarization spectrum is quite wide.

Infrrcd
Altcmating rncthods Drect mothods sp€trosmpy The available methods range from infiared sPectroscoPy to direct methods.Most information can be found between l0+ s and l0*5 s.This is the field where current or voltage responses can be observed mainly.There are tlvo way to access the polarization sPecrum [3]' 2 Two ways of accessing the polarization sPectrum The area of interest is in the range between 104 s and l0+5 s.We decided to monitor the polarization spectrum by means of current responses.Absorptive or resorptive current is a macroscopic exhibition of the polarization processes inside the material [4].

1 Macroscopic exhibition
Analysis of the polarization spectrum of the insulat- ing material is nowadays based on measuring the charging and discharging processes [5].
A method based on applying direct voltage will be de- scribed below.Direct methods are based on observing current or voltage time responses.Well-known methods are polarization indiies, absorptive or resorptive current analysis, recovery voltage or self-diicharge analysis.There is no problem with poruer supply, as in the case of the alternating diagnostic method.For example, when measuring a capacitive object with a capacity of 10 nF and applied voltage l0 kV the requisite .r.-,tt .,t is about 100 mA.A powerful supply is needed.
When applying external direct voltage forming an inter- nal electricil field inside the material, the total current shown in Fig. 2 consists of the following components' While charging with direct voltage current from the geometrical capaciry, absorptive and steady current are Present.After some time the material is discharged, but only two currents are presentresorptive current and current from the geometrical capacity' Steady current is not present because there is no external electrical field.Geometrical capacity current is so quick (about 10-12 S) that it cannot be neglected.Then the tota] eunem can be described as: For a macroscopic description of eurrent responses the equivalent Maxwell-Wagner model can be used for dielectric materials.The equivalent model of the insulating material shown in Fig. 3 is based on n independent Debye polarization processes.Each process has its own time constant of stabiJization 'tj and maximum of elementary current l mi , and by observing its changes we can obtain information about the state of the insulation system.
The values of the Rand C elements of the model are calculated from the observed absorptive ar resorptive currents.They represent ume independent elements -steady current i, and time dependent polarization element i a (t) .
The principle of analysis is described by following equations: s~s ion of negative charges from the trapping level with aetivation energy (9) energy of low conduction level, W T aetivation energy for charge emission from trapping level, WH energy of trapping level.
The observing current for a surface unit is initialization of occupation of trapping level, energy spectrum of trapping levels, charge, thickness of sample, Boltzmann's constant, temperature.
WH is time dependent because while occupying the energy level it retreats from the conducting level.Wr(t) is directJy proponional to time.
. e--.;q As we can see, the result is equation ( 12) with the steady state element in brackets 1 0 that no.resents the steady current i, from equation ( 3) Ol' element ---.2.from equation ( 4).Element !ai .e-:j represents the absorption current i a (t) i=l fmm equation (2) Ol' it is identical with the element from equation (3).
The conclusion is that macroscopic and microscopic views of the polarization processes when applying direct voltage lead to the same resuJts.

Microscopic exhibition
Basic baekground information ean be found in works of Simmons,Tamm and Ewers [6].The probability of the emis-In the past the polarization spectrum of an insulation material was scanned only by polarization indices.These are described very easily as a ratio of observing absorptive Ol' resorptive currents at a determined time.One-minute and 10-minute polarization indices are normally used.

Influence of steady current
Calculating the stabilization times of Debye independent polarization processes is one way to test the state of the insulation system.Another way to observe the polarization spectrum is transform the current response to the frequency domain.
The idea was to observe the intluence of the steady element in the poJarization current on two occasions.First, there were the modeling data.If the data is prepared in an anificial mode, the exact value of any element from equation (3) is known.This enables a correct comparison of the results obtained from calculations with the artificial input data [7].The data sets were prepared with and without the steady element, and the calculations were also done with two modes -ca!culation when the steady elements were present and also when they were not present.
Table 1 shows the components of the anificial data.Seven elemenrs were selected on the basis of our knowledge.For one set the steady element was added.This allows a very strict distinction of differences between the two models as the influence of the DC component.
Both models were analyzed with nvo modes of calculation.
First, without the presence of the DC component (model 0 and model l) two data sets were achieved.Then the same mode of calculation was performed, but with the presence of the DC component.
It is not easy to perform the calculation.It is virtually impossible to calculate seven elements directly.The computation process is very unstable and it is very sensitive to the initial conditions.A better way is to compute only one element first.This means that the total current will be replaced by a single polarization process.This process is represented by one element fiom equation ( 3), where parameter z= l.DC elements may or may not be present.Then another element is added and the calculation is repeated.The result replaces the total current with rwo elementary polarization processes (in the macroscopic mode there are nvo elementary current responses).Then more elements are added until all seven elements are used in the calculation.
The rcsults are shown in Frg. 4. It shows the data for model 0 and also the artificial data.There is only one elementary process in the calculation.The calculation is done without the steady element.There are large differences between them.Frg. 5 shows the same situation, except that the seven polarization processes are present in the computation.
It is hard to distinguish between the artificial data and the data achieved from modeling according to equation ( 3).
The situation is practically the same when the steady element is present in the calculation.
For one element the error is la1ge, and for seven elements the calculation and tie artificial data are the same.The conclusion is evident and no more results are needed.

Real cable
10000 -r -----------------charging time was 1000 s and for this reason the observing time constant 'i cannot be higher than IO-times.The reason for this is based on the physical background.If the charging lasts 1000 s, polarization processes with a level no higher than IO-times the time duration can be excited.Nevertheless the calculations only to five elementary processes were successful.No polarizations with a higher time constant were started.

Real cable
10000.,---------, Let us have a look at model O and the force calculation with the steady element (the first two columns of data) with expansion to seven elementary polarization processes (number of elements -7).It can be seen that the calculation is quite successful.Only srna]] differences appear between the artificial and calculated data.When the calculation was done without the steady component, the results exactly match with the artificial data.The conclusion is that the calculation really reveaIs the presence of the steady element, and its value can also be defined.
In the case of model I (artificiaI data with a steady element of magnitude 10 pA), the calculation with obligatory presence of the steady component is also successfu!.In the third column of data with 7 expansion elements can be seen that the calculation exactly revealed steady element 1 0 and determined its value.Tbe forth column belongs to calculation without forced of steady component.The results are completely wrong.Tbe time constants and amplitudes of the elementary polarization processes have large errors.This leads to the conclusion that if the steady element is present and the calculation does not require it, the result is completely wrong.
This situation was as expected.Tbe calculation can reveaI the steady element, and it is recommended to required calculation with it.If the element is present, the calculation reveals it.If the element is not present and the calculation is required to compute it, the result is a steady element with a magnitude ofO.
Tbe finaI situation was examined by measuring of real object.The cable was examined after accelerated thermal stress for a period of 7000 hours at a temperature of 100 oe.
Tbe cable was made from XPLE and for a 22 kV voltage operating leve!.The cable was charged with direct voltage at 100 Vand the current response was observed for a period of 1000 s.The observing time was selected to have the same time window of polarization processes as in the artificiaI data for model Oand model 1.Fig. 10 shows the measuring set.2. Fig. 12 shows the same situation but without a required steady component.The situations in the data values are completely changed.Although the data in graphic form seems to be the same, the magnitudes are different.The

Conc1usion
This paper deals with calculating elements of equivalent models for dielectric materials.The basic principles of the methods were described, together with the magnitudes of the e1ementary polarization currents and the time constant of their stabilization.First of all, the artificial data was verified.Tbe calculation was to the presence of a steady element.
Tben the approximation of real data was carried OUl successfully.It was demonstrated, that graphical fitting alone does not allow to claim that a model of a real object has been achieved.Tbe magnitudes of the observing e1ements have to be investigated with their electro-physical background.Although higher values were calculated and graphical fitting confirmed them, the physicaI processes did not start and they did not really exist.
Tbe real object has a direct element because it is at the end of its life after long-term accelerated thermal stress [8].Tbis is evident from graphical representation of real measured data.For this reason calculation with a required steady element must always be made, whether this steady component really exists or not.

Fig. l :
Fig. l: Common polarization sPecrum Fig. 2: Total current during charging and discharging

Fig. 3 :
Fig. 3: Maxwell-Wagner equivalent model for dielectric materials current at 15 s, magnitude of observing current at 60 s, magnitude of observing CUITent at 600 s.

Table l :
Components of artificial dataAs is shown in Thble l, model I is the same as model 0, except that the steady element is added for amplitude l0 pA.

Table 2 :
Results of the computation