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U0
U0
U0
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mm2
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iPD(t , 0) =1
2Qapp(0)
IPD( , z) =IPD( , 0)e()z
IPD( , 0) = 12Qapp ()
T() = 2 ZC
ZC+ Zload
ZC Zload
V () =Zsens f() T() IPD( , z)
Zsens f()
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Qsens= 1
Zsens
F T1 (V ()) dt
=
F T1 (f() T() IPD( , z)) dt
U0
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U0
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eff
eff eff eff
eff
eff cable
eff
eff
eff
m m
P Ddens. (lm, tn) =j
i
qi, j
Teff,j/Tcycle
i, j
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eff cycle
eff cable eff
P Docc.rate. (lm, tn) = j
i ni, jTeff,j/Tcycle i,j
m eff cycle
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0 50 100 150 2000
500
1000
1500
Location [m]
Dischargemagnitude[pC]
(a)
050
100150
200 01Sep2007
01Oct2007
0
500
1000
1500
Location [m]
Dischargemagnitude[p
C]
(b)
Z0
Z0 =
l
c
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0 200 400 600 800 10000
20
40
60
80
100
Discharge magnitude [pC]
Pulse
count
q= 2
Z0
V(t)dt
V(t)
V(t)Z0
Z0
Z0
Z0 Z0
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f
q; , 2
= 12 2
e
(q)2
2 2
qR
f(q; k, ) =qk1 e q
k (k) qR+
k
f(q; , ) =
q1
e(
q )
qR+
2.6
2.6 3.7
3.7
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0 200 400 600 800 10000
0.5
1
1.5
2
2.5
3
x 103
PD magnitude [pC]
Density
PD magnitude
Weibull Distribution
Normal Distribution
Gamma Distribution
(a)
0 200 400 600 800 10000
0.2
0.4
0.6
0.8
1
PD magnitude [pC]
Cumulativeprobab
ility
PD magnitude
Weibull Distribution
Normal Distribution
Gamma Distribution
(b)
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0 50 100 150 2000
200
400
600
800
1000
1200
1400
Location [m]
Dischargemagnitude[pC]
2 2 8 8
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0 200 400 600 800 1000 12000
0.5
1
1.5
2
2.5
3
3.5
4x 10
3
PD magnitude [pC]
Density
PD magnitude
Weibull Distribution
Gamma Distribution
0 200 400 600 800 1000 12000
0.2
0.4
0.6
0.8
1
PD magnitude [pC]
Cumulativeprobab
ility
PD magnitude
Weibull Distribution
Weibull 95% confidence bounds
Gamma Distribution
Gamma 95%confidence bounds
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01Sep2007 01Oct20070
0.5
1
DateTime
ScaledAlphapara
meter[pC]
Scaled Alpha paramterer
Trend line
01Sep2007 01Oct20070
1
2
3
4
DateTime
Betaparam
eter
eff
P Dmax.dens. (lm, tn) = max j
i qi, jTeff, j/Tcycle
P Dmax.occ. (lm, tn) = max j
i
ni, j
Teff, j/Tcycle
max
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0 50 100 150 20001Sep2007
09Sep2007
16Sep2007
23Sep2007
01Oct2007
Location [m]
10
20
30
40
50
601
0
(b)
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0 50 100 150 2000
500
1000
1500
Location [m]
Dischargemagnitude[pC]
(a)
0 2000 4000 60000
1000
2000
3000
4000
5000
6000
Location [m]
Dischargemagnitude[pC]
(b)
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n
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0 2000 4000 6000 800010
5
0
5
10
15
20
25
30
Cable length [m]
Defectdispersion(numb
erofFTs)
FTs vs Cable length
Fitted line
95% confidence bound
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0 50 100 150 2000
10
20
30
40
50
60
Location [m]
PDrelatedparameter
PDrelated value
Moving average line(a)
0 2000 4000 60000
20
40
60
80
100
Location [m]
PDrelatedpar
ameter
PDrelated value
Moving average line(b)
130 135 140 1450
10
20
30
40
50
Location [m]
PDrela
tedparameter
PDrelated value
Moving average line
400 500 600 7000
10
20
30
40
50
Location [m]
PDrela
tedparameter
PDrelated value
Moving average line
200 205 2100
1
2
3
4
5
6
7
Location [m]
PDrelated
parameter
PDrelated value
Moving average line
2500 3000 3500 40000
5
10
15
20
Location [m]
PDrelated
parameter
PDrelated value
Moving average line
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th
th
limL = Q1 1.5 (IQR)limU = Q3+ 1.5 (IQR)
1 2 th
th
IQR = Q3
Q1
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0 50 100 150 2000
0.2
0.4
0.6
0.8
1
Location [m]
PDrelatedparameter
PDrelated value
25th Percentile
(a)
0 2000 4000 60000
20
40
60
80
100
Location [m]
PDrelatedparameter
PDrelated value
25th Percentile
(b)
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0 50 100 150 2000
1
Location [m]
PDc
hargedensity[pC/
powercycle]
0
1
Location [m]
PDc
hargedensity[pC/
powercycle]
fx; , 2
= A e
(x)2
22
x
R2 = 1
ni=1
(yi fi)2
ni=1
(yi y)2
yi fi
y
R2 R2
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050
100150
200 01Sep2007
01Oct2007
0
500
1000
1500
Location [m]
Dischargemagnitude
[pC]
(a)
0 50 100 150 200 01Sep2007
11Sep2007
21Sep2007
01Oct2007
0
1
Location [m]PDc
hargedensity[pC/powercycle]
(b)
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0 1000 2000 3000 4000 5000
6000 700001Aug2008
02Aug2008
0
1
Location [m]
PDc
hargedensity
0 1000 2000 3000 4000 5000 6000 70000
1
Location [m]
PDc
harg
edensity[pC/powercycle]
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01000
20003000
4000 01Aug2008
10Aug2008
17Aug2008
24Aug2008
01Sep2008
0
500
1000
1500
Dischargemagnitude
[pC]
Location [m]
(a)
0 1000 2000 3000 4000 01Aug2008
11Aug2008
21Aug2008
01Sep2008
0
1
Location [m]PDc
hargedensity[pC/powercycle]
0
1
(b)
R2 >0.7
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4
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F(z) = 1
1 + ez
F(z)
z
z
x
x0
r
z=r (xi x0)
r
RI= 1 (1 Fdens) (1 Focc.rate) (Fwidth) (Ftrenddens)
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Fdens
Focc.rate Fwidth
Ftrenddens
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0 200 400 600 800 1000 1200 1400 1600 18000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
PD charge density [pC / power cycle]
(a)
0 1 2 3 4 5 6 7 80
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
PD charge occurence rate [# / power cycle]
(b)
0 5 10 15 20 25 30 35 400
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
PD cluster width [0.1% of cable length]
(c)
0 10 20 30 40 50 60 70 800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Probability
PD Trend [pC / power cycle]
(d)
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01Sep2007 11Sep2007 21Sep20070.98
0.985
0.99
0.995
1
1.005
1.01
Risklevel
(a)
01Aug2008 11Aug2008 21Aug2008 01Sep20080
0.2
0.4
0.6
0.8
1
Ris
klevel
(b)
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P I= T P+ T N
F P+ T P+ T N+ F N
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0 50 100 150 200 2500
1000
2000
3000
4000
5000
6000
7000
PDmagnitude[pC
]
Location [m]
(a)
0100
200
0
4200
1000
2000
3000
4000
5000
6000
7000
Location [m]
Time [min]
PD
magnitude
[pC] (b)
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0 50 100 150 200 250 300
7
Location [m]
Time[hr]
0
100
200
300
400
500
600
0
1(a)
0 50 100 150 200 250 300
7
Location [m]
Time[hr]
0
0.02
0.04
0.06
0.08
0.1
0.12(b)
0
1
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0 1000 2000 3000 4000 5000 6000 70000
50
100
150
200
250
300
350
Discharge magnitude [pC]
Pulse
count
(a)
2 3 4 5 6 7 8 910
8
6
4
2
0
2
4
Logarithmic discharge magnitude
LogarithmicCDF
Experimental data
Maximum likelihood fit
95% Confidence interval
(b)
0 500 1000 1500 20000
5
10
15
20
25
30
35
Discharge magnitude [pC]
Pulse
cou
nt
(a)
3 4 5 6 7 88
6
4
2
0
2
Logarithmic discharge magnitude
Logarithmic
CDF
experimental data
Maximum likelihood fit
95% Confidence interval
(b)
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0 50 100 150 200 250 3000
200
400
600
800
1000
1200
Location [m]
Dischargemagnitude[p
C]
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0 50 100 150 200 2500
500
1000
1500
Location [m]
Dischargemagnitud
e[pC]
0 50 100 150 200 250 01Mar2008
01Apr2008
0
500
1000
1500
Location [m]
Dischargemagnitude[pC]
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01Mar2008 11Mar2008 21Mar2008 01Apr2008
0
0.2
0.4
0.6
0.8
1
Risklevel
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0 500 1000 1500 20000
500
1000
1500
2000
2500
Location [m]
Dischargemagnitude[pC]
(a)
0
1000
2000
01Feb2009
08Feb2009
15Feb2009
22Feb2009
01Mar20090
1000
2000
3000
Location [m]
Dischargem
agnitude[pC]
(b)
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01Feb2009 11Feb2009 21Feb200901Mar20090
0.2
0.4
0.6
0.8
1
Risklevel
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0 1000 2000 3000 4000 5000 56610
500
1000
1500
2000
2500
3000
3500
Location [m]
Dischargemagnitude[pC]
(a)
Discharging location
01000
20003000
400050005661 01May2009
01Jun20
0
1000
2000
3000
4000
Location [m]
Dischargemagnitude[pC]
Discharging location
(b)
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01May2009 01Jun20090
0.5
1
1.5
2
2.5
DateTime
BetaParameter
Estimated Beta parameter
2 3 4 5 6 76
4
2
0
2
Logarithmic discharge magnitude
LogarithmicCDF
experimental data
Maximum likelihood fit
95% Confidence interval
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01May2009 11May2009 21May2009 01Jun20090
0.2
0.4
0.6
0.8
1
R
isklevel
(b)
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0 200 400 600 800 10001200 140016000
2000
4000
6000
8000
Location [m]
Discharge
magnitude[pC]
(a)
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15Dec2010 25Dec2010 05Jan2011 20Jan20110
0.2
0.4
0.6
0.8
1
Risklevel
(b)
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f(qi; , ) =
qi
1 exp
qi
qi
F(qi; , ) = 1 expqi
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f(qi; , ) =
qi
1 exp
qi
n
f(q1, q2, . . . , q n; , ) =n
i=1
f(qi; , )
L=
n n
i=1
qi
n
1
exp
ni=1
qi
= ln (L) =n ln () + n ln () +
( 1)n
i=1
ln (qi)
ni=1
qi
= 0
= 0
n
nqi = 0
n ln () + n
+n
i=1
ln (qi) + ln ()
n
i=1
qi n
i=1
ln (qi) qi = 0
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=
ni=1
qi
n
1
n +n
ln (qi) n
nqi ln (qi)n
qi
= 0
U= expka var()
L=
exp
ka
var()
U= exp
ka var()
L=
exp ka
var(
)
ka
a= 1 (ka)
a= 12
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var cov
,
cov, var ()
=
2
2
1
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L
U
L
U
R
(0)
dens
i
occ.rate
trenddens
width
PD
PD
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a
eff
i,j
dens
max.dens
max.occ.rate
occ.rate
1
3
app
i,j
sens
2
pre
eff
i
0
C
load
sens
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yi
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