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IntheACcase,astablePDwithatleasttwopulsesperperiodwasassumed,where-
asintheDCcase,thePDIVismuchtrickierduetotheultra-lowrepeatabilityas
comparedtotheACcase.Thus,thisshouldbeinterpretedasadetectionlevelin
thiscase.Inpractice,dischargemeasurementsareusuallymadewiththeapplied
DCvoltagebeingequaltoorseveraltimesgreaterthantheinceptionvoltage
[MELV65].Theoretically,thePDinceptionvoltagewithDCvoltageshouldreveal
similarvaluesforhomogenousspecimenswiththesamegeometry.Itismaterial-
independenttosomeextentandmainlyinfluencedbytheproportionofthelayer
thickness.However,thePDpulserepetitionrateisheavilyinfluencedbythemate-
rialresistivityandcapacitanceofthevoid.ItwasshownthatthestaticPDincep-
tionvoltageisdeterminedbytheresistivityofthedielectricmaterialadjacentto
thewallvoidandisnotinfluencedbythegasresistivity(usuallyafewordersof
magnitudehigher).Thisis,ofcourse,oneoftheinceptionconditionsapartfrom
thestartingelectronavailabilityandavalanchemultiplicationfulfillment.
TheapparentcapacitanceCcofagaseous(air-filled,ε=1)cavity(D=6mm,
d2=0.9mm)equals
C
c
=εε
0
π⎜⎟
⎛
⎝
d
D
2
2
⎞
⎠
2
=
0.3pF
(3.25)
Theterm“apparent”isused,sincethecavitydoesnothavemetallicwalls(which
arecharacteristicforarealcapacitor)[HAUS14,LEMK12,PAN18,PEDE89].Thecal-
culatedresistancesoflayer1forboththePKandXLPEspecimensbasedonmeasured
resistivityofbothmaterialsequals4.6⋅1012Ωand0.7⋅1014Ω,respectively.Hence,
theroughlyestimatedtimetpbetweenPDpulsesyields6secondsforPKand80seconds
forXLPE.
Thecomparisonoftimetpversustheappliedvoltagefordifferentspecimen
configurationsisshowninFigure3.14.Themeasurementresultsareshowninasemi-
-logarithmicplotandthetrendlinesapproximatedbyexponentialfunctions,yielding
thefollowingrelationshipsbetweentimetp(inseconds)andappliedvoltageU(in):
–XLPE
–PK
tp(U)=2.8o10
5e–0.48U
(3.26)
tp(U)=1o10
6e–0.64U
(3.27)
–XLPE-PK-XLPE
tp(U)=1.5o10
5e–0.61U
tp(U)=8o10
3e–0.47U
–PK-XLPE-PK
(3.28)
(3.29)
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