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THE MODELLING AND HARMONIC
CONTENT OF THE RESISTIVE COMPONENT OF CURRENT IN Z. O VARISTORS |
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FJ van der Linde* and D.A Swift# "University
of Wales Coll ege, Nevrport # Unive rsity of Wales, Cardiff
both fOlmerly University ofNataJ,
Durban |
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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. |
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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. |
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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: |
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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 |
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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]. |
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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:
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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.
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Acknowledgement
Mr van del Linde would like to express his gratitude to
Bowthorpe EMP for their support. |
Refenmccs
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