Predicting Medium-Voltage Underground-Distribution Cable ...

Predicting Medium-Voltage

Underground-Distribution Cable

Failures

John P. Ainscough P. E., Member IEEE

Ian W. Forrest P. E., Member, IEEE Presented at the IEEE PES-ICC Fall Meeting, Nov. 11, 2009, Scottsdale, AZ

WG C26D

Predicting Medium-Voltage Underground-

Distribution Cable Failures


Ian W. Forrest P. E., Member, IEEE

Presented at the IEEE PES-ICC Fall Meeting,

Nov. 11, 2009, Scottsdale, AZ

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Introduction







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The Birth of Suburbia -

Starting in the 1950’s







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White House Conference on Natural Beauty

A solution to the problems of automobile junkyards

The possibility of underground installation of utility transmission lines

Policies of taxation which would not penalize or discourage conservation and the preservation of beauty

Areas in which the Federal Government could help communities develop their own programs of natural beauty

The possibility of a tree-planting program

Discussion Topics May 25-26, 1965







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History of MV-UD Cable Installations







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The Driver in the Installation of Underground

Primary Cable is New Housing

Housing Starts History

0

0.5

1

1.5

2

2.5

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

2009

Millio

ns

of

Ho

us

ing

Un

its







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Other Factors Impacting the Amount of

Underground Primary Cable Installed by Electrical

Utilities

Percentage of new housing units served by underground (a number that has steadily grown over the last five decades, and is now over 90% nationally).

Commercial expansion, with underground distribution, associated with new housing developments.

Increased construction of underground feeder lines.

An increasing amount of replacement activity as cable failure became an issue.







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Correlation Between Housing

Starts and Primary Cable

Electrical World Construction Surveys (1972 to 1986).

The Aluminum Association data on primary URD cable manufactured in the United States from 1971 to 1980.

AEIC supplied survey data on primary UD cable installed by year, with recorded failures (1964 to 1983).

NEMA Product Statistical Bulletins – reporting on pad-mounted and sub-surface type transformers.

Insulated Wire and Cable, periodic Current Industrial Reports, latest issue June 2007 by the US Census Bureau.

·







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Use of Regression Analysis Applied to the

Data Sources

US UTILITY MV-UD CABLE ESTIMATED INSTALLATIONS

HISTORY

0

50

100

150

200

250

300

350

400

450

500

1964

1966

1968

1970

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

YEAR INSTALLED

MIL

LIO

NS

OF

FE

ET

HMWPE

EPR

Replacement

EPR & TRXLP

TRXLPXLPE

To Estimate Medium-Voltage, Underground Cable installed annually

by US electrical utilities







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Existing Installed Population of Primary

Underground Cable

Insulation

Type

Millions of

Feet

Thousands of

Miles

HMWPE 882 167

XLPE 2,964 561

TRXLPE 2,742 519

EPR 2,245 425

Replacement 1,179 223

Total* 8,833 1,672

*Not including Replacement

Assuming a $30/ft replacement cost, and further assuming that only

the HMWPE and XLPE populations are subject to early failure, the

unavoidable pending replacement cost to US electrical utilities is

around $80 billion.







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MV-UD Cable Aging







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Aging Phenomenon

Insulation deterioration due to a combination of electro-chemical

and partial discharge processes

Because of the geometry of the deterioration from these

processes, it was described as “treeing” (electrical treeing and

water treeing)

Without a mechanism to resist insulation deterioration, the

process continues to the point where the size and density of the

deterioration causes an overall reduction in the ability of the

insulation to withstand voltage, and causing spontaneous

electrical failures to occur

Understanding that this proneness to fail is an aging

phenomenon is key to developing a failures predicting model







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Electrical Treeing







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Year* Action

1967 HMWPE began to be replaced with XLPE

1978 Increasing installation of cable in conduit

1981 Beginning of wide-spread use of PE jackets

1982 Introduction of tree-retardant XLPE

1983 Shift to increased use of EPR

1984 Triple-extruded cross-linked insulation shields

1985 Increasing application of elbow arresters at 15kV

1986 Focus on XLPE/TRXLP compound cleanliness

1988 Introduction of strand-fill technology

1989 Silicone injection “cable-cure” technology

1990 Increased use of 133% insulation level (RUS)

1991 “Clean-shield” technology introduced

1995 200vpm “discharge-free” requirement in standard

2004 New pellet inspection technology promoted *Approximate year when the practice became significant

Actions Taken to Increase the Life of MV-UD Cable







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Statistical Methodology

and Assumptions







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Single Year Curve FittingSingle Year Curve Fittingh(X,t) = Xa(t-g)b

Where h(X,t) = number of failures in population X in year t.

X = population in miles.

a = constant characteristic of the population.

g = grace period prior to the initial failures.

b = exponent characteristic of the population.

X

g

0

x

x x

x

xx

x

x xx

h(X,t)

Single Year of Installation Curve Fitting of Failure

Data to an Exponential Curve







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Multiple-Years of Installation Curve Fitting of

Failure Data to a Composite Exponential Curve







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Making the Connection to the Shape and Scale

Parameters of the Weibull Distribution

Connecting to the WeibullConnecting to the Weibull

distributiondistribution

h(X,t) = Xa(t-g)b or h(t) = a(t-g)b for a cable length

of one mile.

h(t) = ___

t - g is the above relationship in the

Weibull hazard function format.

Where b + 1

and b + 1a

b + 1

1







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The Weibull Probability Density Function

Weibull probability densityWeibull probability density

functionfunction

f(t) =

t - g exp[-( )] , t > g t - g

Where is refered to as the shape parameterof the

Weibull distribution and influences the spread of the

distribution,

and is the scale parameter and denotes the 63.2

percentile of the distribution for any value of the shape

parameter.







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Weibull Hazard Function and

Probability Density Function Superimposed

Wiebull Hazard and Probability Density Functions0 5 10

15

20

25

30

35

40

45

50

Years

Probability Density Function

Hazard Function







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Modifying the Weibull Probability

Density Function for

Varying Unit Length and Allowable Failures

Modifying the Weibull probabilityModifying the Weibull probability

density function for repairable cabledensity function for repairable cable

f(t) = ’’

’’

t - g exp[-( )’] , t > g t - g ’

Where ’ = b + n

and ’ = ( ) , x in miles

x = section length

n = failures allowed before section replacement

b + 1 xa/n

1

b + 1

(basically adjusting the model for repairable cable)







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Sources of Data and Verifying the Model







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Organizations Contributing

Data in the Early 1990’s

San Diego Gas and Electric

Duke Power

Iowa Lakes Electric

Public Service of New Hampshire

Jersey Central Power and Light

Public Service Company of Colorado

Florida Power and Light

Houston Lighting and Power

Baltimore Gas and Electric

RUS 1989 survey







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Verifying Goodness of the Data and Model

For the same construction, XLPE has longer life than HMWPE

220 mil insulations outperform 175 mil insulations of the same type

A cable with an overall jacket (whether PVC or PE) has a longer life than the same construction without a jacket

Cable of the same construction installed in regions of higher rainfall and lightning occurrence had shorter life than in a dry, lightning free area (e.g. North Carolina versus southern California)

MV-UD cable with a solid center conductor outperforms the same construction cable with an unfilled stranded conductor







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Model Generated Life Expectancy of

Early Vintage Cable Types

0

1

2

3

4

5

6

7

80 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84

Y e a rs In s ta lle d

Pe

rce

nta

ge

of

Fa

ilu

res

pe

r Y

ea

r

175 mil HMWPE, stranded conductor, no jacket


175 mil XLPE, stranded conductor, no jacket

175 mil XLPE, solid conductor, no jacket

175 mil XLPE, stranded conductor, jacket

0

1

2

3

4

5

6

7

80 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84


Pe

rce

nta

ge

of

Fa

ilu

res

pe

r Y

ea

r






Estimated MV-UD Cable Life ExpectancyBased on replacing a 2,500 ft half-loop following the third failure

0

1

2

3

4

5

6

7

80 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84


Pe

rce

nta

ge

of

Fa

ilu

res

pe

r Y

ea

r






0

1

2

3

4

5

6

7

80 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

84


Pe

rce

nta

ge

of

Fa

ilu

res

pe

r Y

ea

r






Estimated MV-UD Cable Life ExpectancyBased on replacing a 2,500 ft half-loop following the third failure







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Application of Model







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History of Representative MV-UD 175 mil XLPE

Cable Installations, Failures and Replacement

Year Failures

Actual

Miles

Replaced

and

Retired

Miles

Installed Year Failures

Actual

Miles

Replaced

and

Retired

Miles

Installed

1971 0 1990 88 169

1972 161 1991 180

1973 300 1992 167

1974 227 1993 206

1975 188 1994 330 6

1976 Unknown 237 1995 12

1977 Unknown 357 1996 18

1978 Unknown 611 1997 24

1979 Unknown 504 1998 30

1980 Unknown 421 1999 506 30

1981 Unknown 391 2000 469 30

1982 Unknown 425 2001 564 30

1983 Unknown 363 2002 586 30

1984 Unknown 397 2003 750 79.4

1985 Unknown 495 2004 821 53.3

1986 Unknown 359 2005 1023 82.4

1987 Unknown 257 2006 1158 91.1

1988 Unknown 152 2007 1272 37.9

1989 61 165 2008 1287 18.3







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Curve Fitting Results Using the Model

Tap 175mil XLPE

a= 0.0104 b= 1.28 g= 15 47164

Actual Failures Versus Model with 90% Confidence Limits

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

2020

2022

2024

Year

Nu

mb

er

of

Fa

ilure

s

Where the a, b, and g are selected based on minimizing the sum of

the squares of the differences between the actual and model

failures







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Selecting the Model Parameters Based on

Minimizing the Sum of the Squares

0

5e+4

1e+5

2e+5

2e+5

3e+5

3e+5

4e+5

4e+5

0.0099 0.0100 0.0101 0.0102 0.0103 0.0104 0.0105 0.01061.20

1.221.24

1.261.28

1.301.32

1.34

Constant a

Exponent b

Selecting a and b for g = 15 years







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90% Confidence Limits How the Spread

Increases With Poorer Fit of the

Data to the Model

Tap 175mil XLPE

a= 0.0104 b= 1.1 g= 15 935506


0

500

1000

1500

2000

2500

3000

3500

4000

19

72

19

74

19

76

19

78

19

80

19

82

19

84

19

86

19

88

19

90

19

92

19

94

19

96

19

98

20

00

20

02

20

04

20

06

20

08

20

10

20

12

20

14

20

16

20

18

20

20

20

22

20

24

Year

Nu

mb

er

of

Fa

ilu

res







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Replacement “Rules-of-Thumb” Reported by

Utility Respondents in 1996

C a b le R e p la c e m e n t “ R u le s o f T h u m b ”C a b le R e p la c e m e n t “ R u le s o f T h u m b ”

R e p la c e a f te r

O n e F a ilu re

T w o F a ilu re s

T h re e F a i lu re s

F o u r F a ilu re s

F iv e F a ilu re s

B a s e d o n E v a lu a tio n

R e s p o n s e s

6

1 6

2 6

3

1

6

T ra n s m is s io n & D is tr ib u t io n W o r ld , J u ly 1 9 9 6







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Impact on Annual Failures of Selecting a Retirement

Scenario of Replacing an Average 350 ft. Section

Following the Third Failure

Tap 175mil XLPE

a= 0.0104 b= 1.28 g= 15 47039

Identify the length of cable to be removed in feet 350

(If a feeder remember to multiply the trench feet by three.)

Allowable Failures per half-loop or feeder: 3


0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

2020

2022

2024

Year

Nu

mb

er

of

Fa

ilure

s







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Impact on Annual Failures of Selecting a

Retirement Scenario of Replacing an Average

2,500 ft. Half-loop Following the Fourth Failure

Tap 175mil XLPE

a= 0.0104 b= 1.28 g= 15 39024



Allowable Failures per half-loop or feeder: 4


0

500

1000

1500

2000

2500

197

2

197

4

197

6

197

8

198

0

198

2

198

4

198

6

198

8

199

0

199

2

199

4

199

6

199

8

200

0

200

2

200

4

200

6

200

8

201

0

201

2

201

4

201

6

201

8

202

0

202

2

202

4

Year

Nu

mb

er

of

Fa

ilure

s







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Weibull Hazard Function for 2500 ft. Half-loop

175 mil XLPE Tap Cable2,500 Ft Half-Loop Harzard Function

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

Year of Service

An

nu

al F

ailu

re R

ate

8 Failures per Year per 100 miles

(Point at which utilities became

aware there was a problem with

HMWPE

175 mil XLPE Tap Cable2,500 Ft. Half-Loop Cumulative Failures

0

5

10

15

20

25

30

0 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

Year of Service

Cu

mu

lati

ve

Fa

ilure

s

Replace 350 ft. Section following 3rd Failure

(21 Failures total in the 2,500 ft Half-Loop

Replace Half-Loop

following 4th Failure







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ICC Reported MV-UD Cable Failures

(HMWPE and XLPE) from 1984







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Comparison of the Two Retirement Scenarios:

Forcing Life by Repair

175 mil XLPE Tap Cable2,500 Ft Half-Loop Harzard Function

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

Year of Service

An

nu

al F

ailu

re R

ate

8 Failures per Year per 100 miles

(Point at which utilities became

aware there was a problem with

HMWPE

175 mil XLPE Tap Cable2,500 Ft. Half-Loop Cumulative Failures

0

5

10

15

20

25

30

0 4 8

12

16

20

24

28

32

36

40

44

48

52

56

60

64

68

72

76

80

Year of Service

Cu

mu

lati

ve

Fa

ilure

s

Replace 350 ft. Section following 3rd Failure

(21 Failures total in the 2,500 ft Half-Loop

Replace Half-Loop

following 4th Failure







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Life Distributions Resulting from Two Retirement

Scenarios of the Same Repairable Population

Comparison of Two Retirement Scenarios

For the Same Repairable Population

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 7

14

21

28

35

42

49

56

63

70

77

84

91

98

105

112

119

126

133

Years Installed

Pro

po

rtio

n o

f P

op

ula

tio

n

Rep

laced

per

Year

Replace an average 2,500 ft Half-loop

follow ing the fourth failure - average

section life 43 years

Replace an average 350 ft section

follow ing the third failure - average

section life 73 years







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Using the Model to Determine the Applied Retirement

Strategy Based on Actual Replacements

Tap 175mil XLPE

a= 0.0104 b= 1.28 g= 15 40173



Allowable Failures per half-loop or feeder: 3.23

To accept the Optimal Rehabilitation Scenario (ORS) type 'yes': yes

To accept the ORS with catch-up type 'yes': yes Amount* 0

(Catch-up works only if ORS is selected) *Negative amt. Means

actual is lagging the ORS

positive means actual is

ahead of the ORS


0

200

400

600

800

1000

1200

1400

1600

1800

2000

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

2020

2022

2024

Year

Nu

mb

er

of

Fa

ilure

s







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Replacement Scenario: Replacing One Mile After

Seven Failures

Original and Replacement Populations

0

100

200

300

400

500

600

700

1972

1975

1978

1981

1984

1987

1990

1993

1996

1999

2002

2005

2008

2011

2014

2017

2020

2023

Year Installed

Mil

es I

nsta

lled Planned Actual







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Guidelines for Using the Model

Annual results will occur over a range and, unlike a deterministic model, one years worth of results does not justify a change of plan

Updating the model with the latest consistently collected annual failure and replacement results is essential

When dealing with a small population a non-statistical approach is in order

It is not possible to predict monthly improvements to a problem that is going to take years to resolve

Solutions require a systematic approach to retiring the failing population

If the population under investigation is feeder cable, failures may be bi-modal







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Data Input FormNote to Users: There are three hidden sheets that are part of this statistical model.

Name of Company: Example If it becomes necessary to make changes on these sheets it is strongly recommended

Description of Cable: Tap 175mil XLPE that the user seek assistance from the author, email: [email protected]

Only enter data in shaded areas.

First Year of Installations 1972 Most recent year of data 2008

Year Failures

Actual

Miles

Replaced

and

Retired

Miles

Installed

Predicted

Failures

Predicted

Retirements

Only make changes in shaded areas. Range for curve fitting: 1999 to 2008

1972 161 0 0.0

1973 300 0 0.0

1974 227 0 0.0

1975 188 0 0.0

1976 237 0 0.0

1977 357 0 0.0

1978 611 0 0.0

1979 504 0 0.0

1980 421 0 0.0

1981 391 0 0.0

1982 425 0 0.0

1983 363 0 0.0

1984 397 0 0.0

1985 495 0 0.0

1986 359 0 0.0

1987 257 0 0.0

1988 152 2 0.0

1989 61 165 7 0.0

1990 88 169 17 0.0

1991 180 30 0.0 Tap 175mil XLPE1992 167 48 0.0

1993 206 73 0.0 a= 0.0104 b= 1.28 g= 15 40173

1994 330 6.0 106 -6.0 Identify the length of cable to be removed in feet 2500

1995 12.0 149 -12.0 (If a feeder remember to multiply the trench feet by three.)

1996 18.0 200 -18.0 Allowable Failures per half-loop or feeder: 3.23

1997 24.0 259 -24.0 To accept the Optimal Rehabilitation Scenario (ORS) type 'yes': yes

1998 30.0 326 -30.0 To accept the ORS with catch-up type 'yes': yes Amount* 0

1999 506 30.0 402 -30.0 (Catch-up works only if ORS is selected) *Negative amt. Means

2000 469 30.0 487 -30.0 actual is lagging the ORS

2001 564 30.0 582 -30.0 positive means actual is

2002 586 30.0 686 -30.0 ahead of the ORS

2003 750 79.4 786 -79.4

2004 821 53.3 897 -53.3

2005 1023 82.4 1005 -82.4

2006 1158 91.1 1113 -91.1

2007 1272 37.9 1240 -37.9

2008 1287 18.3 1377 -18.3

2009 1467 -149.3

2010 1543 -174.2

2011 1603 -199.8

2012 1644 -225.4

2013 1666 -249.9

2014 1667 -272.5

2015 1646 -292.2

2016 1605 -308.2

2017 1543 -319.7

2018 1465 -326.2

2019 1370 -327.3

2020 1263 -323.0

2021 1148 -313.4

2022 1026 -299.0

2023 903 -280.3

2024 780 -258.1

6179.0 -4890.8


0

200

400

600

800

1000

1200

1400

1600

1800

2000

1972

1974

1976

1978

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

2010

2012

2014

2016

2018

2020

2022

2024

Year

Nu

mb

er

of

Fa

ilure

s

Selecting the best combination of a , b , and g to achieve

the minimum sum-of-squares is an iterative process.

Since the exponent, b , should be greater than 1, and the grace

period, g , is in a range that can be surmised from the data, this

is a good starting point. A best a can then be selected followed

by iterations that vary each of the values slightly until a best fit

is achieved.







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Conclusions







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Conclusions

MV-UD cable failures result from accelerating

insulation deterioration due to electrical aging

Different types of MV-UD cable have different aging

characteristics

MV-UD cable aging failures follow an exponential

proneness-to-failure curve

Since MV-UD cable is repairable, the life expectancy

of installed cable is a function of both its proneness to

fail in the installed environment, and the retirement

policy of the utility







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Conclusions (continued)

The expense to repair, versus the expense to

replace, makes repair cost effective beyond the point

of acceptable customer service

Retirement policy at a utility will evolve from section

repair and replacement to more wholesale

replacement once failures reach a level that have too

much negative impact on service

The national scope of the MV-UD cable failure and

replacement issue is huge, growing and requires a

systemic approach by utilities







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Conclusions (continued)

It is assumed that MV-UD cable types installed in the

last twenty-five years have significantly better life

expectancy

Gaining knowledge of expected performance of the

younger generations of installed MV-UD cable (those

that have not been installed long enough to have

failure history), as well as cable with long service life

and no aging failures, would be a worthy industry

effort







WG C26D

Contact Information

John Ainscough is with Xcel Energy, Denver, CO

email: [email protected]

Ian W. (Bill) Forrest is with Forrest Associates,

Peterborough, NH

email: [email protected]

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