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  :: ZnO Varistors
  :: °ü¸®ÀÚ 2007-06-13 17:14:15 , Á¶È¸ :116353  
  :: File download   [pdf : 1467 KB  Download: 7551]
THE MODELLING AND HARMONIC CONTENT OF THE RESISTIVE COMPONENT OF CURRENT IN Z. O VARISTORS
 
FJ van der Linde* and D.A Swift#
"University of Wales Coll ege, Nevrport # Unive rsity of Wales, Cardiff both fOlmerly University ofNataJ,
Durban
 

Abstract
Recent work on old and fziled arresters have shown that there is only a weak correlation between changes in the
paromelers of an ac model - based on microstnIcrural theories of conduction in ZnO vanstors - and high values
of the odd harmonics of lIle resistive component of the varistor leakage current. Here the extrapolation of
microstructural theories of conduction for bulk samples is validated. The harmon ic components of the Jeakase
current as modelled by the at power frequency model is found and compared to the experimental data.

 
l.introductton
Studies of varistor bloc ks from old and failed arresters removed from service has shown that th ere is only a weak correlation between the changes in the ac model parameters and the hannonic content of the resistive component of leakage current [van der Linde & Swift, 1998]. Eight varistor blocks from new arresters and 27 blocks from old and failed arresters were studied. The data W2S used to validate a model of conduct ion in bulk ZnO based on micrsotrucrural theories of conduction.
Changes in the parameters of the blocks from old and failed arresters were then quantified in lerms of changes
relative to the average va lues found for new blocks. The harmonic content of the resistive component of cw! ent
was also measured and quantified in terms of changes from the maximum harmonic values measured for the
new blocks. A comparison showed that large values of the harmonic magnitudes did not necessar ily coincide
with abnormal parameter values of the ac model.
Fucthennore, large values of the fifth harmonic were measured which is contrary to the fmdings of other researchers [Dengle r, Feser, Kohler, Richter & DchJschllloger, 1996; Dengler, Feser, Kohler, Schmidt & Richter, .1997].

Same explanations for these discrepancies such as errors in the measurement of the parameters [van der Linde &
Swift, 1996] and the difficulty in measuring the relatively small components of Current that are present in the harmonics [van de! Linde e: al, 1998J have already been explored. However, the statistical nature of the measu rement of both the parameters and the harmonics made in these studies, shodd lead 10 reasonably accurate results, particularly in the low-field region.

In chis report funher work to delennine the cause of these discrepancies is considered. TIle validity of the
extrapolation of the micrOSfrUctural theories from small to bulk samples is investigated. The theoretical harmonic
content of current for the ac model is determined and then compared with the existing experimental data.
 
2, Model
2. 1. Test Pracedure
The model under study here is a power freq uency model that consis ts of a voltage dependent capacitance in
parallel with two noo-linear resistive elements [van der Lillde et ai, 1998]. Only the resistive elements will be
considered here.The resistive elements are modelled using microstructural theories of the conduction in ZnD
material. The final temperature illdependent elements used have the following foons:
 
I is the resistive component of the leakage current tltrough the varistor in the low- (Equation 1) and highfield
-(Equation 2) regions respectively, va is the voltage applied to the varistor block and b2,c2 and 82 are constants dependent on the characteristics of tIle material . The equations are represented in the form chey were used to measure the constants.

TIlese two equations are simplificat ions of the electricfield- current density relationslJips for Schottky [D issado
& Fothergill, 1992, 222; Eda, 1978; Levinson& Philipp, 1975] and Fowler-Nordheim runneling [Eda, 1978; Levinson et at, 1975} conduction-mechanisms - valid in the low- and high-field case respectively. The original equations used are
where J is the current density, Fi is the applied electric-field. A" is Richardson=s constant, EB is me ilctivation energy, e is electron charge, Co and s.. are the permittivity of fre e space and the relative pennittivity
respectively, k is Boltzmann=s constant, T is temperature, m is the electron mass and.s is ~e modified
Planck constant. The h igh~field part of the model, as represented by equation 1, was fOWld to be accura e in
the region of the kne6point or for voltages higher than that depending on how the parameters were measured.
This 3;;.pect may be due to a lack of complexity in the behaviour of the model and a more suitable model may
be based on conduction such as that described by Mahan, Levinson & Philipp [1979].
 
3. Extrapolatio;,10 multiple boundaries
Equations 3 - 5 describe the behaviour of single insulating boundad~ that needs t be extrapolated to multiple boundaries as they are found in large samples of the material.
ZnO material does not consist of semiconducting ZnO grains with a continuous Bi-rich layer between them.
Instead, it has a sopltisticated structure involving various phases. As well as thin 8i-rich intergranular layers
between the ZnO grains, some of the ZnO grains are in dlrect contact with each other - with the interface areas
doped with Bi atoms [Olsson & Dunlop, 1989]. This structure can be simplified on the following asswnpt:ons:

  Only those boundaries containing thin Bi¡¤rich layers or with doped 2nD interfaces are actjve.
  Whichever type of boundary is active, it is continuous tluough the materiall.

Based on these aSS..nnpdons., the structure can be reduced to that illustrated in ftgure 3-14(a). If it is further
assumed that the volt drop only occurs in the intergranular layer that is pel1lendicular to the electric field, then litis smtcture can be reduced to that shown in figure 3-14(b) [Shirley & Paulson, 1979]. The smtcture represented in figure 3-14(b) can be further refmed by randomly varying the thickness of the intergranular layer and hence the size of the ZnO grains [Shirley et al, 1979]. Herein it is also assumed that the sample is large enough to pennit the use of the average dimensions throughout me simplified Structure,

Using this simplified struc ture, the complete volt drop over a sample can, therefore, be said to be the total volt
drop over the ZnO grains plus the volt drop at each intergranular layer/doped boundary (for Schottky and
PoolelFrenkel conduction respectively). The volt drop over the ZoO grains can be neglected in the region of operation that is of interest herein. Consequently, the volt drop will be the sum of the forward- and reversebias
bouudary volt drops or the swn of the volt drops over the doped boundaries. The barrier voltages have statistically distributed values, but the mean ones are usually used [Olsson et aI, 1989; van Kemenade & Eijnthoven, 1979].

If Schottky or PoolelFrenkel conduction is rigidly applied to the structure of Figure 3- 14(b), the complete device would not turn-on until the sum of all the barrier voltages has been exceeded by the applied voltage. That is, if there are n boundaries, each with a barrier field of E, and the total applied tiele ET is unifonn - conduction in phase wiman appliec. ac voltage will only occur once:

In reality, the process is probably much more complex - with the cmrent initially flowing along some parallel
paths that have very low total barrier fields. As the applied field increases, more of the boundaries will
become active, thereby increasing the number ofparalleJ paths available for conduction. TIlis process will
effectively create a system of parallel paths of current each with its own turn-on field. For p parallel paths, each
with its own total barrier field Ep, reflected in the constant bEp, equation 1 gives:

This expression for Scotiky conduction neglects the effect of the reverse-biased boundaries. It is similar in
fomito equation land the extrapolation is, therefore, valid in the low-field region.
Similarly, the current flowing when the fields are higher - and the conduction is dominated by tunneling - can be
calculated in large samples. Using equation 2, the total current under high-fields is:
 
4. Harmonic content of resistive component of current for specific parameter values
The study reported in ICLP >98 [ICLP98] found parameters of the resistive elements described by the voltage-current relationships for eight blocks from new arresters alld 27 blocks from old and failed arresters. The mean values of the arrester parameters and harmonic content of current for the new blocks are listed in Table 1 and 2. The parameters were found model the voltagecurrent characteristic well in the low-field region and reasonably well in the high-field region - depending on whether the model is optimised for the kneepoint region or voltages above that. TIle experimental parameters values will be used to calculate the theoretical hannonic content of the resistive component of the cunent which can then be compared with the experimental values. An interesting aspect of these results is the large magnitude of fifth harrnonic present in the current.

 
 Acknowledgement

Mr van del Linde would like to express his gratitude to Bowthorpe EMP for their support.
Refenmccs

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