NUREG/CR-6904 

 BNL-NUREG-75208-2005

Evaluation of the Broadband

r Impedance Spectroscopy

Prognostic/Diagnostic

Technique for Electric Cables

Used in Nuclear Power Plants

\

The Boeing Company and

Brookhaven National Laboratory 

U.S. Nuclear Regulatory Commission

Office of Nuclear Regulatory Research

Washington, DC 20555-0001
 

 NUREG/CR-6904 

 BNL-NUREG-75208-2005

Evaluation of the Broadband

Impedance Spectroscopy

Prognostic/Diagnostic

Technique for Electric Cables

Used in Nuclear Power Plants

Manuscript Completed: November 2005

Date Published: June 2006

Prepared by

D. Rogovin1

, R. Lofaro2

1 The Boeing Company

Huntington Beach, CA 92647

2

 Brookhaven National Laboratory

Upton, NY 11973-5000

J. Vora, NRC Project Manager

Prepared for

Division of Fuel, Engineering and Radiological Research

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington, DC 20555-0001

NRC Job Code Y6410
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ABSTRACT

Aging mechanisms can lead to degradation of electric cables and resultant failures of critical functions, as

well as losses of essential information for the decision-making process. Consequently, it would be highly

desirable to have a single universally effective prognostic, diagnostic technique that can be used in situ to

monitor the condition and predict the remaining useful life of installed electric cables of all types, in

operating nuclear power plant applications and environments. 

To address this issue, the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory

Research (RES), in collaboration with the Federal Aviation Administration (FAA) and the Boeing Company,

initiated a research study to evaluate the effectiveness of the broadband impedance spectroscopy (BIS)

technique for use in nuclear power plant cable diagnostics and condition monitoring. The results demonstrate

the effectiveness of this nonintrusive, nondestructive technique, which uses low-voltage signals at varying

frequencies to scan the length of an installed cable system to locate anomalies and degradation. Based

upon this study’s promising results, RES is considering follow-on collaborative research to demonstrate

the effectiveness of the BIS technique in operating nuclear power plant environments.
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TABLE OF CONTENTS

Page No.

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

FOREWORD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

TABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

EXECUTIVE SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix

ABBREVIATIONS ......................................................... xxxi

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxxiii

1. INTRODUCTION ..........................................................1

1.1 Background ......................................................1

1.2 Technical Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Research Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.5 Equipment Used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. REVIEW OF CONDITION MONITORING TECHNIQUES .........................7

2.1 General Criteria for an Effective Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Mechanical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Visual Inspection ............................................8

2.2.2 Elongation-At-Break .........................................8

2.2.3 Compressive Modulus ........................................9

2.3 Chemical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Oxidation Induction Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3.2 Fourier Transform Infrared (FTIR) Spectroscopy . . . . . . . . . . . . . . . . . . 10

2.4 Electrical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4.1 Insulation Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4.2 Dielectric Dissipation or Loss Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.4.3 Voltage Withstand Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.4 Time-Domain Reflectometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.5 Partial Discharge Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
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2.5 Reasons to Focus on an Electrical Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3. THEORY OF BROADBAND IMPEDANCE SPECTROSCOPY . . . . . . . . . . . . . . . . . . . . 15

3.1 Equivalent Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 Wire Properties and Wire Impedance Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 Approach to Extract Wire Properties from Impedance Data . . . . . . . . . . 17

3.2.2 Wire Properties from Impedance Data for Undamaged Wiring . . . . . . . 21

3.2.3 Wire Properties from Impedance Data for Damaged Wiring . . . . . . . . . 23

3.3 BIS Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3.1 Procedure for Making Impedance Measurements . . . . . . . . . . . . . . . . . . 27

3.3.2 Analysis and Interpretation of Impedance Data . . . . . . . . . . . . . . . . . . . 28

4. PREPARATION AND BASELINE TESTING OF CABLE TEST SPECIMENS . . . . . . . . 31

4.1 Selection of Cable Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.2 Preparation of Test Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3 Baseline Testing of Test Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.4 Accelerated Aging of Test Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5. RESULTS OF BIS TESTING OF CABLE SAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1 Application of BIS to Thermally Aged Cables . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.1 Detection of Degradation on Cables with Global Thermal Aging . . . . . 37

5.1.2 Development of Models for Cables with Thermal Degradation . . . . . . . 40

5.1.3 Detection of Localized Degradation on Cables . . . . . . . . . . . . . . . . . . . . 54

5.1.4 Locating Localized Degradation on Cables . . . . . . . . . . . . . . . . . . . . . . . 66

5.2 Application of BIS to Cables with Attached Loads . . . . . . . . . . . . . . . . . . . . . . . 71

5.2.1 Test Specimens Used for Testing with Attached Loads . . . . . . . . . . . . . 72

5.2.2 Low Frequency BIS Tests for Cables with Attached Loads . . . . . . . . . . 72

5.2.3 High Frequency BIS Tests for Cables with Attached Loads . . . . . . . . . . 75

5.2.4 Phenomenological Models of Cables with Attached Loads . . . . . . . . . . 77

5.2.5 Locating a Hot-Spot on a Cable with an Attached Load . . . . . . . . . . . . . 83

5.3 Application of BIS to Cables with Abrasion Damage . . . . . . . . . . . . . . . . . . . . . 84

5.3.1 Abrasion Test Specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.3.2 Evaluation of Low Frequency BIS Results on Cables with Abrasion . . . 85

5.3.3 Evaluation of High Frequency BIS Results on Cables with Abrasion . 101

5.3.4 Detection of Abrasion Damage Using BIS . . . . . . . . . . . . . . . . . . . . . . 110

5.3.5 Location of Abrasion Damage Using BIS . . . . . . . . . . . . . . . . . . . . . . . 113

5.4 Application of BIS to Cables with Cracking Damage . . . . . . . . . . . . . . . . . . . . 122

5.4.1 Test Specimens Used for Testing of Cables with Cracking . . . . . . . . . 123

5.4.2 Low Frequency BIS Measurements of Cables with Cracking . . . . . . . . 124

5.4.3 High Frequency BIS Measurements of Cables with Cracking . . . . . . . 128

5.5 Application of BIS to Cables with Varying Environments . . . . . . . . . . . . . . . . 130

5.5.1 Specimens Tested to Evaluate BIS for Cables with a Varying 

Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

5.5.2 Low Frequency BIS Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
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5.5.3 Phenomenological Models of Cables with Varying Environment . . . . 137

6. EVALUATION OF THE BIS METHOD FOR NUCLEAR PLANT CABLES . . . . . . . . . 149

6.1 Results for Global Thermal Aging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.2 Results for Global Plus Localized Thermal Aging (Hot-Spot) . . . . . . . . . . . . . 150

6.3 Results for Global Thermal Aging with an Attached Load . . . . . . . . . . . . . . . . 151

6.4 Results for Global Plus Localized Abrasion Damage . . . . . . . . . . . . . . . . . . . . 152

6.5 Results for Global Thermal Aging with Cracking Damage . . . . . . . . . . . . . . . . 153

6.6 Results for Global Thermal Aging with a Varying Environment . . . . . . . . . . . 153

7. CONCLUSIONS AND CONSIDERATIONS FOR FOLLOW-ON RESEARCH . . . . . . . 155

7.1 Conclusions on the Effectiveness of the BIS Method . . . . . . . . . . . . . . . . . . . . 155

7.2 Considerations for Follow-On Research to Demonstrate the Effectiveness of the

BIS Method in Nuclear Plant Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156

8. REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Appendix A: BIS Test Results for Cables with Global Thermal Aging Simulating

20 years and 40 years of Service . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Appendix B: BIS Test Results for Cables with Localized Thermal Aging (Hot Spots) . . . . . 203
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LIST OF FIGURES

Page No.

Figure 1 Wire system equivalent circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figure 2 Low frequency impedance spectra log magnitude for a 10 meter poly-x

twisted pair wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

Figure 3 Low frequency impedance spectra phase angle for a 10 meter poly-x twisted

pair wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 4 High frequency impedance spectra magnitude for a 10 meter poly-x twisted

pair wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 5 High frequency impedance spectra phase angle for a 10 meter poly-x twisted

pair wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

Figure 6 Frequency-dependent wire resistance and inductance . . . . . . . . . . . . . . . . . . . . . . 22

Figure 7 Micro picture of a poly-x wire cross section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Figure 8 Real and imaginary components of the wire insulation dielectric

function (open circuited) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Figure 9 Log magnitude and phase of the impedance spectra for moist and dry

wiring (open circuited) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

Figure 10 Ratio of the impedance spectra magnitude for moist and dry wiring

(open circuited) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

Figure 11 Ratio of the resistance and inductance for moist and dry wiring as a

function of frequency (R is S/m and L is H/m - open circuited) . . . . . . . . . . . . . . 25

Figure 12 Ratio of the real and imaginary components of the wiring insulation’s dielectric

function for moist and dry wiring as a function of frequency . . . . . . . . . . . . . . . . 27

Figure 13 Equipment and test setup for making impedance measurements . . . . . . . . . . . . . . 28

Figure 14 Typical aging chamber loading for global and hot-spot aging of cable test

specimens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Figure 15 Measured low frequency impedance phase spectra for cables with global 

thermal aging to simulate 60 years of service at various temperatures . . . . . . . . . 38
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Figure 16 Measured high frequency impedance phase spectra for cables with global

thermal aging to simulate 60 years of service at various temperatures . . . . . . . . . 39

Figure 17 Expanded view of impedance phase and magnitude per unit length spectra

over the frequency range from 78 MHz to 86 MHz for cables with global

thermal aging to simulate 60 years of service at various service temperatures . . . 40

Figure 18 Characteristic impedance magnitude per unit length and phase spectra 

for cables with global thermal aging to simulate 60 years of service at

various temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 19 Imaginary component and real component of propagation function for

cables with global thermal aging to simulate 60 years of service at various

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 20 Resistance per unit length and change in resistance per unit length for cables

with global thermal aging to simulate 60 years of service at various 

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 21 Comparison of resistance per unit length predicted by analytical model to

that extracted from measured impedance for cable with global thermal aging

to simulate 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Figure 22 Inductance per unit length and change in inductance per unit length for 

cables with global thermal aging to simulate 60 years of service at 70oC . . . . . . . 45

Figure 23 Comparison of inductance per unit length predicted by analytical model to

that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

Figure 24 Capacitance per unit length and change in capacitance per unit length for cables

with global thermal aging to simulate 60 years of service at various

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Figure 25 Conductance-to-frequency ratio per unit length and change in conductance-tofrequency ratio per unit length for cables with global thermal aging to

simulate 60 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . . . . 49

Figure 26 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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Figure 27 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 60 years of service at 70oC . . . . . . . . . . . . . . . . . 51

Figure 28 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 60 years of

service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 29 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from

measured impedance for cable with global thermal aging to simulate 

60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

Figure 30 High frequency characteristic impedance magnitude and phase spectra 

extrapolated from low frequency spectra for cables with thermal aging to

simulate 60 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . . . . 53

Figure 31 Imaginary and real components of the high frequency propagation function 

determined from the extrapolated characteristic impedance for cables with

thermal aging to simulate 60 years of service at various temperatures . . . . . . . . . 54

Figure 32 Impedance magnitude and phase spectra over the frequency range of

14MHz to 22MHz for cables with global thermal aging to simulate 60 years

of service at 50oC, plus additional thermal aging to simulate hot-spots of

different severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Figure 33 Impedance magnitude and phase spectra over the frequency range of 39MHz

to 45MHz for cables with global thermal aging to simulate 60 years of 

service at 50oC, plus additional thermal aging to simulate a hot-spot . . . . . . . . . . 57

Figure 34 Impedance magnitude and phase spectra over the frequency range from 

14MHz to 22MHz for cables with global thermal aging to simulate 60 years

of service at 50oC, plus additional thermal aging to simulate hot-spots of 

different sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Figure 35 Impedance magnitude and phase spectra over the frequency range of 

39MHz to 45MHz for cables with global thermal aging to simulate 60 years

of service at 50oC, plus additional thermal aging to simulate hot-spots of

different sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
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Figure 36 Impedance magnitude and phase spectra over the frequency range from 

14MHz to 22MHz for cables with global thermal aging to simulate 60 years

of service at 50oC, plus additional thermal aging to simulate hot-spots at 

different locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 37 Impedance magnitude and phase spectra over the frequency range from

39MHz to 45MHz for cables with global thermal aging to simulate 60 years

of service at 50oC, plus additional thermal aging to simulate hot-spots at 

different locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Figure 38 Example of average impedance phase spectrum over the frequency range from

100kHz to 100MHz for cable with global thermal aging . . . . . . . . . . . . . . . . . . . . 63

Figure 39 Schematic model of a cable with a hot-spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

Figure 40 Impedance phase and magnitude error functions for cable with thermal 

aging to simulate a 1 meter hot-spot located 7.0 to 8.0 meters from the

cable end representing 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . 69

Figure 41 Impedance phase zero crossing error functions for cable with thermal aging

to simulate a 1.0 meter hot-spot located 7.0 to 8.0 from the cable end

representing 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 42 Impedance phase and magnitude error functions for cable with thermal aging to

simulate a 1 meter hot-spot 2.0 to 3.0 meters from the end of the cable

representing 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Figure 43 Impedance phase zero crossing error functions for cable with thermal aging

to simulate a 1 meter hot-spot located 2.0 to 3.0 meters from the end

representing 60 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

Figure 44 Comparison of measured impedance magnitude for cable with and without an

attached load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 45 Comparison of the impedance phase spectra for cables with and without a

load attached . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 46 Comparison of impedance phase in the frequency range from 116kHz to

123kHz for cables with and without a load attached . . . . . . . . . . . . . . . . . . . . . . . 74

Figure 47 Change in impedance phase for cable system with a hot-spot from cable system

without a hot-spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
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Figure 48 Comparison of A(T) parameter in the vicinity of the first zero crossing

for cable systems with and without a hot-spot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Figure 49 Schematic of model for thermally aged cable with a load attached . . . . . . . . . . . . 78

Figure 50 Comparison of low frequency measured and predicted impedance magnitude

for a cable system with no hot-spots and an attached load . . . . . . . . . . . . . . . . . . . 79

Figure 51 Comparison of low frequency measured and predicted impedance phase 

spectra for a cable system with no hot-spots and an attached load . . . . . . . . . . . . . 79

Figure 52 Comparison of high frequency measured and predicted impedance magnitude

and phase for a cable system with a hot-spot and an attached load . . . . . . . . . . . . 80

Figure 53 Schematic of a cable system with a hot-spot and an attached load . . . . . . . . . . . . 80

Figure 54 Comparison of measured and modeled impedance magnitude for cable

system with a hot-spot and an attached load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

Figure 55 Comparison of low frequency measured and modeled impedance phase

spectra for a cable system with a hot-spot and an attached load . . . . . . . . . . . . . . 82

Figure 56 Comparison of high frequency impedance magnitude and phase spectra for

cable system with a hot-spot and an attached load . . . . . . . . . . . . . . . . . . . . . . . . . 82

Figure 57 Prediction of hot-spot location for a cable system with a load attached . . . . . . . . 83

Figure 58 Schematic of four cases studied to evaluate BIS for detecting and locating

abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

Figure 59 Low frequency impedance phase spectra for cables with and without abrasion

exposed to an environment of 20% Relative Humidity . . . . . . . . . . . . . . . . . . . . . 86

Figure 60 Low frequency impedance phase spectra for cables with and without abrasion

exposed to an environment of 85% Relative Humidity . . . . . . . . . . . . . . . . . . . . . 87

Figure 61 Impedance magnitude for cables with and without abrasion plus a conductive

contaminant exposed to an environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . 88

Figure 62 Impedance phase spectra for cables with and without abrasion plus a 

conductive contaminant exposed to an environment of 85% RH. . . . . . . . . . . . . . 88
xvi

Figure 63 Low frequency characteristic impedance magnitude for cables with and

without abrasion exposed to an environment of 85% RH . . . . . . . . . . . . . . . . . . . 89

Figure 64 Low frequency characteristic impedance phase spectra for cables with 

and without abrasion exposed to an environment of 85% RH . . . . . . . . . . . . . . . . 90

Figure 65 Imaginary component of the low frequency propagation function for cables

with and without abrasion exposed to an environment of 85% RH . . . . . . . . . . . 91

Figure 66 Real component of the low frequency propagation function for cables with

and without abrasion exposed to an environment of 85% RH . . . . . . . . . . . . . . . . 91

Figure 67 Capacitance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion exposed to an 

environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 68 Conductance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion exposed to an 

environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

Figure 69 Low frequency characteristic impedance magnitude for cables with and 

without abrasion plus a conductive contaminant exposed to an environment

of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

Figure 70 Low frequency characteristic impedance phase spectra for cables with and

without abrasion plus a conductive contaminant exposed to an environment 

of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

Figure 71 Imaginary component of the low frequency propagation function for cables

with and without abrasion plus a conductive contaminant exposed to an

environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure 72 Real component of the low frequency propagation function for cables with

and without abrasion plus a conductive contaminant exposed to an

environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

Figure 73 Capacitance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion plus a conductive

contaminant exposed to an environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . 96

Figure 74 Conductance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion plus a conductive

contaminant exposed to an environment of 85% RH . . . . . . . . . . . . . . . . . . . . . . . 97
xvii

Figure 75 Schematic of the localized cable interaction model for abraded cables plus a

conductive contaminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

Figure 76 Schematic representation of abraded cable with a conductive path between

conductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Figure 77 Impedance magnitude of conductivity path for abraded cable with conductive

path between conductors at various locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure 78 Comparison of magnitude for total impedance, interaction impedance, and

conductivity path impedance for abraded cable with a conductivity path at 

various locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 79 Comparison of conductivity path impedance phase, >(T), cable impedance

phase, 0(T), and total impedance phase, M(T), for abraded cable with a

conductivity path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure 80 Comparison of high frequency impedance magnitude and phase spectra for 

cables with and without abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

Figure 81 Comparison of high frequency impedance magnitude and phase spectra for

the frequency range from 8.4 MHz to 9.6MHz for cables with and 

without abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 82 Comparison of high frequency impedance magnitude and phase spectra in

the frequency range from 64MHz to 65.5MHz for cables with and without 

abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

Figure 83 Imaginary component of the high frequency propagation function for

cables with abrasion plus a conductive contaminant . . . . . . . . . . . . . . . . . . . . . . 105

Figure 84 Real component of the high frequency propagation function for cables

with abrasion plus a conductive contaminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

Figure 85 Resistance spectra for abraded cables in the high frequency range from

phenomenological model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 86 Inductance spectra for abraded cables in the high frequency range from

phenomenological models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

Figure 87 Capacitance spectra for abraded cables in the high frequency range from

phenomenological models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
xviii

Figure 88 Conductance spectra for abraded cables in the high frequency range from

phenomenological models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

Figure 89 Slope of the equation representing the imaginary component of the high

frequency propagation function for abraded cables . . . . . . . . . . . . . . . . . . . . . . . 111

Figure 90 Comparison of zero crossings in the frequency range 4.4MHz to 4.8MHz

for the second derivative of the impedance phase, A(T), for cables with

and without abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure 91 Comparison of the zero crossings of the second derivative of the impedance

phase, A(T), in the frequency range from 22.4MHz to 23.8MHz for cables

with and without abrasion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

Figure 92 Comparison of predicted and measured impedance phase in the range from

2.55MHz to 10.04MHz for unabraded cable (Specimen 15) . . . . . . . . . . . . . . . . 115

Figure 93 Comparison of predicted and measured impedance magnitude in the range

from 2.55MHz to 10.04MHz for unabraded cable (Specimen 15) . . . . . . . . . . . . 116

Figure 94 Characteristic impedance magnitude in the frequency range from 2.55MHz

to 10.04MHz for cables with and without abrasion . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 95 Characteristic impedance phase spectra in the frequency range from

2.55MHz to 10.04MHz for cables with and without abrasion . . . . . . . . . . . . . . . 117

Figure 96 Imaginary component of the propagation function in the frequency

range from 2.55MHz to 10.04MHz for cables with and without abrasion . . . . . . 118

Figure 97 Real component of the propagation function in the frequency range from

2.55MHz to 10.04MHz for cables with and without abrasion . . . . . . . . . . . . . . . 118

Figure 98 Measured impedance phase spectra in the frequency range from 4.048MHz to

15.04MHz for cables with and without abrasion on one conductor . . . . . . . . . . 120

Figure 99 Predicted location of abrasion damage for cable with one conductor abraded . . 121

Figure 100 Measured impedance phase spectra in the frequency range from 4.048MHz to

15.04MHz for cables with and without abrasion on both conductors . . . . . . . . . 122

Figure 101 Predicted location of abrasion damage on cable with both conductors abraded . 123

Figure 102 Schematic of cable with cracking damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
xix

Figure 103 Comparison of impedance phase for cables with and without cracking . . . . . . . . 125

Figure 104 Characteristic impedance log magnitude and phase for cables with and without

cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Figure 105 Imaginary and real components of the propagation function for cables with

and without cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Figure 106 Resistance per unit length for cables with and without cracking . . . . . . . . . . . . . 127

Figure 107 Inductance per unit length for cables with and without cracking . . . . . . . . . . . . . 127

Figure 108 Comparison of capacitance per unit length for cable with and without cracks . . 128

Figure 109 Conductance per frequency per unit length for cable with and without cracks . . 129

Figure 110 Comparison of second derivative of the impedance spectra, A(T), for

cables with and without cracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

Figure 111 Schematic of test setup for cables with varying environment . . . . . . . . . . . . . . . 131

Figure 112 Impedance magnitude for 100 meter cable with no aging or hot-spot and

external temperatures of 24oC (75oF), and 42oC (107.6oF) . . . . . . . . . . . . . . . . . . 132

Figure 113 Impedance phase spectra for 100 meter cable with no aging or hot-spot and

external temperatures of 24oC (75oF), and 42oC (107.6oF) . . . . . . . . . . . . . . . . . . 132

Figure 114 Impedance phase spectra for 100 meter cable with no aging or hot-spot and 

external temperatures of 24oC (75oF) low humidity, and 29oC (85oF) 

and 85% RH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

Figure 115 Impedance phase spectra for 100 meter cable with 1 meter hot-spot and

external temperatures of 24oC (75oF), and 42oC (107.6oF) . . . . . . . . . . . . . . . . . . 134

Figure 116 Impedance phase spectra for 100 meter cables with and without a 1 meter

hot-spot, and an external temperature of 24oC (75oF) . . . . . . . . . . . . . . . . . . . . . 134

Figure 117 Expanded view of the impedance phase spectra in the frequency range

from 425kHz to 445kHz for 100 meter cables with and without a 

1 meter hot-spot, and an external temperature of 24oC (75oF) . . . . . . . . . . . . . . . 135

Figure 118 Expanded view of the impedance phase spectra in the frequency range

from 425kHz to 445kHz for 100 meter cables with and without a

1 meter hot-spot, and an external temperature of 42oC . . . . . . . . . . . . . . . . . . . . 136
xx

Figure 119 Summary comparison of impedance phase spectra for 100 meter cables

with and without a 1-meter hot-spot and external temperatures of

24oC (75oF) and 42oC (107.6oF) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

Figure 120 Comparison of impedance magnitude in the frequency range from 1kHz to

1MHz for cables aged to simulate 60 yrs @ 50oC and 60 yrs @ 90oC . . . . . . . . . 137

Figure 121 Comparison of impedance phase spectra for 10 meter cables aged to

simulate 60 yrs @ 50oC and 60 yrs @ 90oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

Figure 122 Comparison of extracted characteristic impedance magnitude for 10 meter

cables aged to simulate 60 yrs. @ 50oC and 60 yrs @ 90oC . . . . . . . . . . . . . . . . 139

Figure 123 Comparison of extracted characteristic impedance phase spectra for 10 m

cables aged to simulate 60 yrs.@50oC and 60 yrs@90oC . . . . . . . . . . . . . . . . . . 139

Figure 124 Comparison of imaginary component of the propagation function for

10 m cables aged to simulate 60 yrs.@50oC and 60 yrs@90oC . . . . . . . . . . . . . . 140

Figure 125 Comparison of the real component of the propagation function for 

10 meter cables aged to simulate 60 yrs. @ 50oC and 60 yrs @ 90oC . . . . . . . . . 140

Figure 126 Comparison of resistance per unit length and relative difference in

resistance per unit length for 10-meter cables aged to simulate 60 yrs.

@ 50oC and 60 yrs @ 90oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Figure 127 Comparison of inductance per unit length and relative difference in

inductance per unit length for 10m cables aged to simulate 60yrs.@50oC 

and 60yrs@90oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Figure 128 Comparison of capacitance per unit length and relative difference in

capacitance per unit length for 10m cables aged to simulate 60 yrs

@50oC and 60 yrs@90oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Figure 129 Comparison of conductance per unit length and relative difference in

conductance per unit length for 10m cables aged to simulate 60 yrs

@50oC and 60 yrs@90oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144

Figure 130 Schematic of model for 100-meter cable containing a hot-spot . . . . . . . . . . . . . . 144

Figure 131 Error in predicted impedance phase as a function of assumed hot-spot 

location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
xxi

Figure 132 Error in predicted impedance phase as a function of assumed hot-spot

location over the cable length from 90 meters to 99 meters . . . . . . . . . . . . . . . . . 147
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xxiii

LIST OF TABLES

Page No.

Table 1 Cable Test Specimens for Broadband Impedance Spectroscopy Research . . . . . . 33

Table 2 Specimens tested to evaluate BIS for detecting global thermal aging . . . . . . . . . . 38

Table 3 Parameters for analytical model of resistance for cables thermally aged 

to simulate 60 years of service at various service temperatures . . . . . . . . . . . . . . . 44

Table 4 Parameter values for analytical model of inductance for cables aged to

simulate 60 years of service at various service temperatures . . . . . . . . . . . . . . . . . 46

Table 5 Parameter values for dielectric function analytical model for cables

thermally aged to simulate 60 years of service at various service temperatures . . 50

Table 6 Specimens tested to evaluate BIS for locating localized areas of thermal aging . . 55

Table 7 Average impedance phase magnitude for cables with global thermal aging to

simulate 60 years of service at 50oC, plus additional thermal aging to simulate

hot-spots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

Table 8 Differences in zero crossing frequencies between cable with no hot-spot 

(cable 26) and cables with hot-spots (cables 27 to 30) at odd number zero

crossings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Table 9 Impedance phase zero crossing line spacing for cables with global thermal

aging to simulate 60 years of service, with and without hot-spots . . . . . . . . . . . . . 66

Table 10 Specimens tested to evaluate BIS for testing cables with attached loads . . . . . . . . 72

Table 11 Specimens tested to evaluate BIS for detecting abrasion . . . . . . . . . . . . . . . . . . . . 84

Table 12 Fitting constants for equation representing the real component of the high

frequency propagation function for cables with abrasion plus a conductive

contaminant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

Table 13 Fitting constants for equations representing the high frequency electrical 

properties of abraded cables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Table 14 Specimens tested to evaluate BIS for testing cables with a varying environment 131
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xxv

EXECUTIVE SUMMARY

Aging of electric cables has been studied for decades and it is well known that aging degradation

can lead to failures of electric cable systems. Periodic replacement of installed cables is not

practical due to the costs involved, and the potential for introducing unforseen anomalies due to

installation deficiencies and modifications. As such, a prognostic/diagnostic technique that can

be used in situ to monitor the condition of installed electric cables and predict their remaining

useful life is highly desirable. While a number of prognostic/diagnostic techniques are currently

available to test installed cables, each has its limitations on the types of cables for which it can

be used and the extent of the age-related degradation it can detect. Currently, there is no single

viable in situ technique available that can be used to monitor the condition of all types of electric

cables in a nuclear power plant, especially the low-voltage instrumentation and control (I&C)

cables.

Existing regulatory requirements relevant to electric cables:

• 10CFR, part 50, Appendix A, GDC 18 - Inspection and testing of electric power systems.

Electric power systems important to safety shall be designed to permit appropriate

periodic inspection and testing of important areas and features, such as, wiring,

insulation, connections, and switchboards, to assure the continuity of the systems and the

condition of their components. The systems shall be designed with a capability to test

periodically the operability and functional performance of the components of the

systems, such as onsite power sources, relays, switches, and buses, and the operability of

the system as a whole.

• 10CFR, part 50, Appendix B, Criterion XI 

 A test program shall be established to assure that all testing required to demonstrate that

structures, systems and components will perform satisfactorily in service is identified and

performed in accordance with written test procedures which incorporate the requirements

and acceptance limits contained in applicable design documents.

• 10CFR, Part 54, License Renewal, GALL Report - XI E3 Inaccessible medium voltage

cables not subject to 10CFR 50.49 environmental qualification requirements

Testing and condition monitoring based aging management program is acceptable to the

staff. 

The utilization of the research results and the applicability of an effective diagnostics and

condition monitoring method for installed cable systems in operating nuclear power plants:

• The research results show that the BIS method has potential for being a non-intrusive,

non-destructive and an effective in situ diagnostics and condition monitoring method for

installed cable systems in operating nuclear power plants. 
xxvi

• The BIS method has potential for satisfying the aging management requirements of

inaccessible/underground cables for the current license term and for license renewal

considerations.

• The research results provide technical bases for:

(a) evaluating the licensees programs for aging management of cables within the scope of

license renewal (10CFR Part 54),

(b) supporting the development of appropriate IEEE standards, and 

(c) for the development of a dedicated regulatory guide on cable diagnostics and

condition monitoring

The BIS technique - applied to electric cable diagnostics and condition monitoring:

The Broadband Impedance Spectroscopy (BIS) technique was developed by the Boeing

Company under the sponsorship of the United States Federal Aviation Administration (FAA) to

monitor the condition of installed aircraft wiring. In the study reported herein, which was

sponsored by the Office of Nuclear Regulatory Research (RES) of the U.S. Nuclear Regulatory

Commission (NRC), the BIS technique was evaluated for application to electric cables used in

nuclear power plants. Cable samples, which are representative of a commonly used type of lowvoltage instrumentation and control cable in nuclear power plants, were prepared and received

accelerated aging to simulate various types of degradation expected in actual plant service

conditions, including the following:

• Global thermal degradation,

• Global thermal degradation plus localized hot-spots,

• Thermal degradation with cracking, and 

• Abrasion damage

The cable samples were then tested in the laboratory using the BIS method, and the data were

analyzed to draw conclusions on the effectiveness of the method. Several test configurations

were evaluated, including:

• Constant temperature and humidity along the cable with no load attached,

• Constant temperature and humidity along the cable with a load attached, and

• Varying environments along the length of the cable with no load attached

For the cable type tested, pre-aging measurements were used to develop models that represent

the impedance response of the cable. These models were then used to determine the post-aging

condition of the cables. In applying the BIS method, a model is useful for each type of cable to

be tested.
xxvii

The results demonstrated that the BIS method can be used on nuclear power plant cables, and

may represent a breakthrough in the prognostics and diagnostics of installed cable systems. The

technique provides a non-destructive means of monitoring cable systems in their installed

configuration. Age-related degradation can be detected in an incipient stage prior to failure.

Specific conclusions from this research are:

• The BIS method was clearly able to detect the presence of thermal degradation

associated with the cables used in this study. Specifically, the impedance phase

spectra of the cables tested were observed to increase as the amount of thermal

degradation on the cable increased. This increase can be used as an indicator of

global thermal degradation.

• The BIS method was able to detect the presence of localized thermal degradation,

or hot-spots on the cables. Specifically, a shift in the zero crossings of the

impedance phase spectra was observed when a hot-spot was present on the cable.

• An approach was developed for locating hot-spots within a cable using models of

the cable’s electrical properties. The models were able to predict the hot-spot

location within ±10%.

• The BIS method was not sensitive enough to distinguish between the different

severities and sizes of hot-spots simulated at low frequencies. However, high

frequency data were able to distinguish between the severity levels. Additional

research is warranted to establish the sensitivity limits for this technique.

• The BIS method was able to detect and locate the presence of abrasion-related

damage on a cable. The models and approach used are similar to that for

detecting and locating thermal hot-spots.

• The BIS method was demonstrated to be effective for detecting and locating

degradation on cables with an attached load. This is important since it is

desirable to have a technique that can test cables in their installed configuration,

without having to disconnect them from attached equipment.

• The BIS method was able to detect simulated cracking damage on cables. 

However, the simulation method used in this study was determined not to

accurately represent the cracking phenomena. Additional research is warranted to

more accurately evaluate the BIS method on actual cable cracking.

• The BIS method was able to detect the presence of localized thermal degradation,

or hot-spots on the cables even with a varying environment along the external

surface of the cables. For the example presented herein, the model’s prediction of

hot-spot location is within a few percent of the correct position.

While the BIS method shows great promise as a prognostic and diagnostic technique for installed

cable systems, additional research is desirable before it can be applied in the field. Specifically,

the following additional items should be considered for future research:
xxviii

• Research on the detection and location of cracking damage in cables using more

realistic simulation of the cracking damage,

• The technique should be demonstrated on additional types of cable to determine

its usefulness for other materials and cable configurations,

• The technique should be demonstrated in an actual plant environment to

determine the impact of the various environmental factors that may impact the

BIS measurements, and

• The technique should be demonstrated on blind test samples in which the type,

severity, size, and location of the degradation are unknown

Based upon the promising results obtained from this research effort, the Office of Nuclear

Regulatory Research is considering follow-on research, preferably in a collaborative manner, to

demonstrate the applicability of the BIS method in nuclear plant environment.
xxix

ACKNOWLEDGMENTS

The authors would like to thank the NRC program manager, Jitendra Vora for his technical

guidance and support throughout this project.

We would also like to thank Martin Kendig of Rockwell Scientific for his assistance in the

performance of the impedance measurements, and the processing of the data.

We also thank Michael Villaran of Brookhaven National Laboratory for his assistance in

reviewing the report and providing technical comments.

The assistance of Louis Gerlach in the preparation of the cable test specimens is also greatly

appreciated.

We also express our appreciation to Susan Signorelli for her assistance in the preparation of this

manuscript.
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ABBREVIATIONS

AWG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . American Wire Gauge

BIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Broadband Impedance Spectroscopy

BNL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Brookhaven National Laboratory

CM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Condition Monitoring

DZC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detection Zero Crossing

EAB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Elongation-at-Break

EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethylene Propylene Rubber

FAA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Federal Aviation Administration

FTIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fourier Transform Infrared Spectroscopy

I&C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumentation and Control

IR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Insulation Resistance

NRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear Regulatory Commission

OIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oxidation Induction Time

OSTP . . . . . . . . . . . . . . . . . . . . . . . . . . . White House Office of Science and Technology Policy

RES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . U.S. NRC, Office of Nuclear Regulatory Research

TDR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time Domain Reflectometry

XLPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-Linked Polyethylene
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xxxiii

LIST OF SYMBOLS

d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diameter of cable conductors (cm/in.)

l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . total length of cable (meters/ft.)

la . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . length to start of defect (meters/ft.)

lb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . length to end of defect (meters/ft.)

lc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . length to abraded portion of cable (meters/ft.)

ri . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inside radius of coaxial cable insulation (cm/in.)

ro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outside radius of coaxial cable insulation (cm/in.)

r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radius of cable conductor (cm/in.)

s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Center-to-center distance of cable conductors (cm/in.)

x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Distance along cable specimen (meters/feet)

C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Capacitance (Farads)

G............................................................Conductance (mho)

I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current (Amperes)

L ...........................................................Inductance (Henries)

Lk ...................Inductance for cable aged to simulate service temperature k (Henries)

R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistance (Ohms)

Rs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resistance of a single conductor (Ohms)

Rk . . . . . . . . . . . . . . . . . . . . Resistance of a cable aged to simulate service temperature k (Ohms)

V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Voltage (Volts)

Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impedance (Ohms)

Z0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic Impedance (Ohms)

* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Difference between parameters

*s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Depth of conductor skin effect (cm/in)

g0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dielectric constant of vacuum

g1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Real component of the dielectric function

g2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaginary component of the dielectric function

(i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaginary component of the propagation function

(r . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Real component of the propagation function

H . . . . . . . . . Slope of linear function representing imaginary component of propagation function

J . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Time constant (seconds)

7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structure factor

A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Second derivative of the impedance phase

M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impedance phase (Degrees)

Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic impedance phase (Degrees)

T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Frequency (Hertz)

Tk . . . . . . . . . . . . . . . . . . . . . Frequency for cable aged to simulate service temperature k (Hertz)
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1

1. INTRODUCTION

1.1 Background

Condition monitoring of electric cables is of particular interest for application to nuclear power

plants, in which miles of electric cables are used to perform numerous operational and safety

functions. Aging studies have shown that, as these cables age, there is the possibility that their

performance may degrade making them susceptible to failure (Lofaro, et al., 2002; Villaran and

Lofaro, 2003). Since replacement of all the cables would be expensive and impractical, an

effective technique to characterize their condition is highly desirable. To be useful, the

technique would have to be unobtrusive, non-destructive and able to be performed in situ. 

Currently, there is no single in situ condition monitoring technique that has been proven to be

effective at determining the installed condition and the remaining useful service life of all the

various types of electric cables, particularly low-voltage instrumentation and control (I&C)

cables, in a typical nuclear power plant.

The issue of cable system safety was brought to the forefront with the issuance of the U.S. White

House Office of Science and Technology Policy (OSTP) Report containing a review of Federal

Programs related to the safety of installed electric cable systems, which was published in

November 2000. The report concluded that cable system safety is an important public health and

safety issue that transcends government agencies. One of the recommendations from that report

is to perform collaborative research to develop effective condition monitoring techniques.

In response to the White House OSTP report recommendation, the U.S. Nuclear Regulatory

Commission, Office of Nuclear Regulatory Research (NRC/RES) organized the International

Conference on Wire System Aging in April 2002 [Lofaro, November 2002] to provide a forum

for researchers from around the world to meet and discuss issues related to wire system aging,

including promising new condition monitoring techniques for cable systems. One of the

techniques discussed was broadband impedance spectroscopy.

Broadband impedance spectroscopy (BIS) is a technique being developed by the Boeing

Company, under the sponsorship of the U.S. Federal Aviation Administration (FAA) to monitor

the condition of wiring in aircraft. It utilizes impedance measurements of the wiring to obtain

information on the dielectric properties of the wire insulation. Impedance measurements are

made in situ at relatively low voltages and over a broad range of frequencies. Using algorithms

and computer models developed by Boeing, the dielectric properties are extracted from these

impedance measurements to characterize the condition of the wiring. The information extracted

can be used to identify and locate areas of degradation.

Based on the initial success of the FAA research, NRC/RES sponsored a research program to

evaluate the feasibility of using BIS to monitor nuclear power plant cables. While the

construction of nuclear plant cables is different than aircraft wiring, conceptually there are

similarities; therefore, condition monitoring techniques developed for aircraft may be suitable for

use in nuclear power plants. The feasibility study demonstrated that BIS was able to distinguish
2

between aged and un-aged nuclear plant electric cables. Also, the technique was able to locate

localized areas of degradation. Based on these results it was determined that BIS is a promising

new technique for application to nuclear plant cables and further research was initiated to

evaluate this technique in more detail. This report documents the results of this research.

In this report, an overview of the types of electric cables used in nuclear power plants is

presented. The theory behind BIS is then discussed, along with the procedures for performing

the test and evaluating the data. Finally, results from tests on actual nuclear plant cables are

presented, from which conclusions regarding the effectiveness of the technique are drawn.

Recommendations are made for future research, as well as demonstrations of the BIS method in

nuclear plant environments.

1.2 Technical Issues

There are several important technical issues related to condition monitoring of cables in nuclear

power plants that should to be addressed through research. These include the following:

• Detection of age-related degradation that could impact cable performance,

• Location of localized damage due to “hot-spots” along the cable route,

• Handling of connected loads to allow testing cables in situ without de-termination,

• Identification and location of localized damage, such as abrasion or cracking, and

• Handling of varying environments along a cable due to routing through different areas

and environmental zones of the plant

The first issue relates to the ability to determine the installed condition of a cable. Typically,

electric cables used in nuclear power plants perform numerous operational and safety functions

in the plant. The service environments to which the cables are exposed vary from benign indoor

conditions, to adverse localized environments, including high temperatures, humidity, radiation,

and pressures. Some safety-related cables are expected to operate under harsh environments and

accident conditions. These cables must be qualified through testing to provide assurance that

they can perform their safety function for the licensed life of the plant. Once qualified, the

cables are typically installed and receive minimal attention thereafter. For license renewal,

acceptable options are provided for demonstrating continued qualification for qualified cables. 

Aging management programs are required for non-qualified cables that are in the scope of

license renewal.

As plants approach the end of their original licensed life, many utilities are applying for license

extensions to continue operation of the plant. The basis for the license renewal is that aging

degradation will be managed through the implementation of effective aging management

programs. For electric cables, current aging management programs rely on visual inspection of

cables to determine their condition and whether they are fit for continued service. While visual
3

inspections provide some assurance that the cables are not damaged, these inspections provide

very little information on sections of the cables that are not visible. For these hidden sections of

cable, techniques that can interrogate an entire cable system would be useful to detect

degradation that could potentially cause a loss of function. 

The second technical issue that must be addressed is related to areas along the cable route that

expose the cable to adverse localized environments. Such areas can be caused by routing of a

cable near a hot steam pipe, or through a high radiation area. Installations that place the cables

in areas with localized adverse environments, or “hot-spots,” can result in localized damage to a

cable. Even though the majority of a cable may appear to be in good condition, a hot-spot can

cause localized degradation of the cable that can impair its performance. Therefore, a viable and

preferred condition monitoring technique must be able to locate localized damage caused by

these hot-spots.

Another important issue related to condition monitoring of cables is the ability to test the cables

in situ without disturbing them. Ideally, the cable would not have to be de-terminated from its

load for the testing process since this could introduce undesirable stresses on the cable and its

connectors due to repeated disconnecting and re-connecting of the terminations. Since each

cable will have a load attached, it is desirable that the condition monitoring technique be able to

correct for the impact of the load on any measurement data obtained from the cable.

Studies have shown that exposure to aging stressors can degrade the insulating materials

commonly used in the construction of electric cables. This degradation can be global in nature,

such as a reduction in ductility of the insulation, or it can be localized, such as cracking. 

Mechanical damage has also been observed on installed cables, such as due to abrasion. This

localized damage can adversely impact the ability of a cable to perform its function, particularly

under abnormal operating or accident conditions when moisture is present. Therefore, it is

important that a condition monitoring technique be able to detect localized damage, such as

cracking and abrasion.

Finally, the cable runs in nuclear power plants can be very long, and one cable can traverse many

different areas of the plant. As such, the environment along the cable may vary. Therefore, it is

important that the condition monitoring technique be capable of accounting for this varying

environment along the cable.

Each of these technical issues was addressed in the research program discussed herein.

1.3 Objectives
4

The objectives of the research program reported herein were to evaluate the effectiveness and

sensitivity of the BIS technique with respect to the technical issues discussed above. To

maintain a manageable scope for this effort, the issues were reviewed and selected ones were

chosen to be addressed in this program based on their importance to demonstrating the

usefulness of the BIS method for nuclear plant cables. For this research effort the objectives

were to evaluate the BIS technique capabilities for the following:

• Detecting and locating areas of localized degradation (hot-spots) on nuclear plant

cables caused by stressors commonly found in nuclear plants.

• Detecting and locating localized damage on nuclear plant cables with a load

attached

• Detecting and locating localized damage on nuclear plant cables in the form of

abrasion and cracking

• Detecting and locating localized damage on nuclear plant cables with a varying

environment along the length of the cable

Additional issues not covered in this program are intended to be addressed in future research.

1.4 Research Approach

The research approach used to meet the project objectives involved the testing of cable samples

that were exposed to accelerated thermal aging to simulate degradation caused by exposure to

service conditions. A test matrix was developed that included tests of cable specimens to

address each of the issues identified above. The testing was divided into five sections; 1)

detection and location of thermal degradation (both global and localized), 2) detection of

degradation with attached loads on the cable, 3) detection of abrasion damage, 4) detection of

cracking damage, and 5) detection of degradation with varying environments along the cable. In

each case, appropriate test specimens were prepared and broadband impedance measurements

were made. 

Analytical models were developed, the data were analyzed, and correlations were established.

The cable test specimens were prepared and baseline tested at BNL. Once preparation of the

cable test specimens was completed, the specimens were shipped to the Boeing test facilities in

Thousand Oaks, California. There, BIS testing of the specimens was performed and the data

obtained were analyzed. Measurements were made on un-aged cable specimens, and the data

were used to develop models that represent the impedance response of the un-damaged cables. 

The models were then validated by comparison of the model predictions to the actual data

obtained. These models can be used to identify the level and location of degradation on other

cables constructed of similar materials and with similar conductor configurations. The theory

and process for developing and using the models is discussed in Section 3 of this report.
5

Once the models were completed, testing of the aged specimens was performed. The models

were then used to analyze the data obtained and predict the aged condition of the cables.

1.5 Equipment Used

The impedance measurements were made using a commercially available instrument, and an

instrument built for the FAA for BIS measurements. The former instrument was used for lowfrequency measurements ranging from 100Hz to 1MHz. The later instrument was used for the

high-frequency measurements ranging from 1MHz to 100MHz. Both instruments were

controlled by laptop computer using a LabVIEW® software graphical interface. Data were

downloaded and stored on the laptop for subsequent distribution and analysis.
6

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7

2. REVIEW OF CONDITION MONITORING TECHNIQUES

In this section a discussion on what constitutes effective cable condition monitoring is presented,

along with a brief overview of several currently available condition monitoring techniques. The

techniques are categorized as mechanical, chemical, and electrical based on the properties they

monitor. The advantages and limitations of each technique are discussed. The purpose of this

discussion is to present the current state-of-the-art in cable monitoring at the time of this

research. This section is not intended to be a comprehensive listing of all condition monitoring

techniques. It is acknowledged that there are other techniques available, and significant

advancements are being made in the refinement of the existing technologies. However, thus far

these techniques are subject to similar limitations as the techniques discussed herein.

2.1 General Criteria for an Effective Technique

Condition monitoring of an electric cable involves the observation, measurement, or trending of

one or more indicators, which can be correlated to the condition or functional performance of the

cable. The intention is to provide information that can be used to determine the current ability of

a cable to perform within specified acceptance criteria, as well as to make predictions about its

remaining useful life. Ideally, the technique should have the following attributes:

• Non-destructive and non-intrusive (i.e., it does not require that the cable be disconnected

or disturbed),

• Capable of measuring property changes or indicators that are trendable and can be

consistently correlated to functional performance during normal service,

• Applicable to cable types and materials commonly used in existing nuclear power plants,

• Capable of being performed in situ under field conditions,

• Capable of detecting age-related degradation at levels that are low enough to allow

sufficient time to take corrective actions prior to cable failure,

• Capable of locating localized areas of degradation on a cable due to hot-spots, and

• Provides information that can be used to predict the remaining useful life of the cable.

In practice, there are no condition monitoring techniques currently available that have all of the

above attributes. Each has its own uses, as well as limitations that make it unsuitable as a

general tool for monitoring installed cables.

The following sections provide an overview of several currently available techniques. The

advantages of each technique are discussed, along with its limitations.

2.2 Mechanical Techniques
8

Techniques classified as mechanical involve the measurement or monitoring of some physical

attribute of the cable. Examples of mechanical techniques include visual inspections,

elongation-at-break, and compressive modulus measurement. Each of these techniques is

discussed below.

2.2.1 Visual Inspection

Visual inspection is an effective technique for providing a qualitative assessment of a cable’s

condition. While no quantitative data is obtained, the results can be trended to provide an

assessment of how fast a cable is degrading under the operating conditions to which it is

exposed. This technique can be used to evaluate the condition of a cable and determine if more

extensive testing is required to characterize its condition. Past studies have found that, in most

cases, cables that appear to be in good physical condition through visual inspection show

acceptable electrical performance.

The major advantage of the visual inspection is that it is inexpensive to perform and it does not

require any expensive equipment. It is recommended that a standardized procedure be

developed to ensure that a consistent inspection approach is used and that all of the important

cable attributes are inspected.

The most serious limitation of this technique is that the cable to be inspected must be accessible

and visible. In some cases, cables may be installed in closed conduits or buried beneath other

cables in a cable tray. In these cases, visual inspection would not be directly useful. Also, even

for visually accessible cables, usually only the jacket can seen. Therefore, inspection of the

insulation would probably not be possible. However, visual inspection of representative cables

that are accessible could be used to provide an indirect measure of the condition of the

inaccessible cables.

2.2.2 Elongation-At-Break

Elongation-at-break (EAB) is a measure of a material's resistance to fracture under an applied

tensile stress. It is often termed the "ductility" of a material and is defined as the percent

increase in elongation at the time of fracture. EAB is a valuable parameter for monitoring aging

in cable materials because of its sensitivity to microstructural changes in polymers brought about

by service aging. It is a widely accepted measure of polymer aging and is used as a reference in

evaluating other techniques.

In general, EAB measurements provide a useful quantitative assessment of the remaining

integrity of a cable. As the EAB decreases to a low value, and crack initiation and propagation

become possible from in-service stresses, moisture intrusion and current leakage could become

a problem. At this time there does not appear to be any commonly accepted criterion for the

minimum EAB of a cable material that will define the end of its useful service life. A

conservative value of $50 percent has been used as an acceptance criterion, even though there is

usually some useful service life remaining.
9

The major concern with EAB testing is that it is a destructive test, and relatively large amounts

of cable are required. They can only be obtained if cable is removed from service, or if

sacrificial cable samples are available for periodic evaluation.

2.2.3 Compressive Modulus

Compressive modulus is a material property defined as the ratio of compressive stress to

compressive strain below the proportional limit. As cable insulation and jacket materials age

they tend to harden, which will cause the compressive modulus of the materials to increase. By

monitoring this change in compressive modulus, an estimate of the degradation rate of the

material can be made. Compressive modulus is measured using a device developed by EPRI

known as the polymer indenter.

In many instances, cables are not easily accessible in nuclear plants. Often they may be stacked

in cable trays or run through conduits, which severely limits access to perform CM testing. For

cables which are accessible, the indenter can be used to determine the modulus of the outer

jackets. For those cables that are not accessible, it is not desirable nor possible, in some

instances, to excessively handle the cables to permit indenter testing. To monitor the modulus of

individual jackets or insulation, access would be desirable at a termination point. This is not the

optimum situation, since the termination points may be physically located in a different plant

location and exposed to very different ambient conditions than the remainder of the cable.

Measurement of compressive modulus is a non-destructive test that does not affect the continued

operation of the cable. The indenter is computer controlled and the software prevents the probe

from penetrating the material being tested, from leaving residual marks, or from causing any

other type of damage. It is suitable for use on various materials (XLPE, EPR, Hypalon® and

Neoprene). However, not every material produces significant age-induced changes in

compressive modulus that can easily be correlated with thermal or radiation exposure. For low

levels of aging, relatively small modulus changes can be seen, which, in the absence of baseline

measurements, might be difficult to correlate with aging. Cable construction and manufacture

were also found to produce different modulus results for the same aging. Compressive modulus

data correlate well with EAB measurements, which is an indication of this technique’s

usefulness.

2.3 Chemical Techniques

Techniques classified as chemical involve the measurement or monitoring of some attribute of

the cable’s insulation related to changes in its chemistry or molecular makeup. Examples of

chemical techniques include oxidation induction time (OIT) and Fourier Transform Infrared

Spectroscopy (FTIR). Each of these techniques is discussed below.

2.3.1 Oxidation Induction Time
10

Polymeric materials used to insulate cable conductors typically include an anti-oxidant in their

formulation to mitigate oxidation, which will degrade the polymer over time. As the cables age,

the anti-oxidant additives are gradually lost from the polymers due to diffusion and volatilization

from the surface. As the additives are depleted, oxidation will gradually increase.

Oxidation induction time is a technique for measuring the time required for a polymer to begin to

oxidize under controlled conditions. When compared to values from new cables, the OIT

provides an indication of the amount of aging on the cable. The process involves the controlled

heating of a small scraping of insulation material from the cable. As the sample is heated under

an oxygen environment, the amount of energy liberated is measured. An increase in this energy

indicates the onset of oxidation, which is an exothermic reaction. The time to oxidation onset is

measured and represents the oxidation induction time.

OIT has been shown to provide useful correlations to EAB values for some cable insulation

materials. However, access to the cable is required to obtain the test specimen. Also, the test

must be performed in a laboratory setting, and the results only provide data on a localized

portion of the cable.

2.3.2 Fourier Transform Infrared (FTIR) Spectroscopy

FTIR Spectroscopy is a technique for analyzing the structure of molecules. The principle

involves the measurement of absorbance or transmittance of infrared radiation by molecular

structures, including those for polymers. As the radiation passes through a polymer, atoms

absorb radiation and begin to vibrate. For a particular chemical bond, maximum vibration

occurs for a specific wavelength of radiation. Therefore, by irradiating a specimen with a

continuous spectrum of infrared radiation, and measuring the peaks (wavelengths) at which

maximum absorbance or transmittance occurs, the chemical bonds that are vibrating may be

identified from standard wavelengths that are available from the open literature. The presence of

certain molecular bonds that develop as a result of oxidation can be used as an indicator of aging.

One of the potential problems with the FTIR spectroscopy technique is that it is a surface

examination procedure in which the infrared radiation passes into the surface of the specimen

and is refracted back into the crystal. By analyzing the intensity of the incident and reflected

rays, the transmittance is determined. Since accelerated thermal aging at elevated temperatures

will produce an oxidation gradient at the specimen surface, the spectroscope will detect a higher

amount of oxidation that the average bulk value. The technique would, therefore, be expected to

give a more accurate estimate of bulk aging for naturally-aged specimens, for which oxidation

gradients will be minimized at the lower service aging temperatures.

2.4 Electrical Techniques
11

Techniques classified as electrical involve the measurement or monitoring of some electrical

property of the cable. Examples of electrical techniques include insulation resistance (IR),

dielectric loss, voltage withstand testing, time-domain reflectometry, and partial discharge

testing. Each of these techniques is discussed below.

2.4.1 Insulation Resistance

Insulation resistance measurements are commonly performed to determine the current condition

of cable insulation. By applying a voltage from the conductor to ground, the resistance of the

insulation separating them can be measured. The advantages of this test are that it is relatively

easy to perform and requires inexpensive equipment. If the insulation resistance decreases in a

predictable manner as the insulation ages, trending of this parameter could be useful as a

condition monitoring technique for electric cables.

When a dc voltage is applied to a test specimen, the total current flowing in the insulation from

the conductor to ground is equal to the sum of the capacitive charging current, leakage current,

and dielectric absorption current. These three component currents change with time. The

capacitive charging current and the dielectric absorption current will initially be relatively high

when the test voltage is first applied to the test specimen. Once the insulation, which behaves

like a capacitor, is energized and charges have aligned across the insulation, these currents will

taper off and eventually approach zero. However, leakage current will typically start at zero and

gradually increase. In high integrity insulation, leakage current will reach and maintain a steady

value after a certain amount of time. If the insulation is badly deteriorated, wet, or contaminated,

the leakage current will be greater than that found in good insulation and it could continue to

increase over time. As a result, the total current flowing in a test specimen will start out high

when a test voltage is first applied, and taper off in different ways over the next several minutes

depending on the condition of the insulation. 

In high integrity insulation the insulation resistance will gradually increase after the test voltage

is applied, then a steady value will be reached. Because of this behavior, insulation resistance

measurements are taken using an ohmmeter first at one minute and again at ten minutes. The

ratio of the insulation resistance at ten minutes to the value measured at one minute is called the

polarization index.

One disadvantage of making insulation resistance measurements is that the cable under test must

be disconnected in order to attach the test instrument. However, this can be controlled by test

procedures with independent verification steps, as are commonly used for surveillance and

maintenance procedures in nuclear power plants.

The major factor affecting insulation resistance measurements is temperature. The effect of

temperature is predictable and can be corrected by normalizing the raw insulation resistance

readings to a common temperature, such as 16oC (60oF), for purposes of comparison. Using the

ratio of the 10 minute insulation resistance to the 1 minute reading, the polarization index can

provide a measure of dielectric condition that eliminates temperature effects. Consequently, in
12

order to collect data that are trendable, accurate time and temperature data must accompany the

raw quantitative insulation resistance measurements. For this reason, plant personnel often look

upon the insulation resistance test as a simple pass/fail test for the dielectric integrity of electrical

equipment and cables, but too irregular for trendable condition monitoring.

2.4.2 Dielectric Dissipation or Loss Factor

When a steady-state ac test voltage is applied to an insulated cable, the resulting apparent total

current that flows consists of a charging current due to the capacitance of the cable insulation

and a leakage current. The phase angle between the applied test voltage and the total current is

known as the dielectric phase angle. The complement of the phase angle is called the dielectric

loss angle.

The leakage current for electric cables is normally much smaller than the charging current, but it

is more sensitive to the condition of the insulation. As insulation deteriorates it is expected that

the leakage current will increase, while the capacitive current remains approximately constant. 

Thus, the ratio of the magnitudes will increase. The ratio is called the dielectric dissipation

factor and is commonly used as a measure of insulation condition. Another means of describing

insulation condition is the dielectric power factor, expressed as the cosine of the dielectric phase

angle. At very low power factors (<10 percent), the dielectric power factor is approximately

equal to the dielectric dissipation factor.

Dielectric loss measurement is a very simple and straightforward condition monitoring

technique. Using a signal analyzer, an internal source provides an applied ac voltage signal to

the test specimen over a range frequencies, while measuring and recording the dielectric phase

angle at each increment. The phase angle data can then be used to calculate the dielectric loss or

power factor. Studies have shown that dielectric loss can be correlated to cable degradation.

Another advantage of this test is that it can be used to interrogate an entire cable system. The

data obtained provide information on the global condition of the cable, and can provide insights

into the condition of the entire cable system.

Some of the factors that affect the dielectric loss measurement technique include cable length,

humidity or moisture within the cable and insulation, and electrical equipment operating in the

vicinity of the test cable. The effect of length is very uniform and predictable, resulting in a

relative increase in insulation power factor as the length of cable increases. This effect is most

easily accounted for by making in situ baseline measurements for each cable to be monitored to

serve as a standard for comparison with similar measurements in the future. The effect of other

operating electrical equipment or energized cables in the same tray is typically concentrated at

the frequency of the operating equipment. In most cases, this is the 60Hz power frequency and it

has a more pronounced effect on longer cables than short ones. This problem can be avoided by

making measurements at an applied ac test voltage with a frequency below 50Hz or above 70Hz.
13

The major advantage of the dielectric loss technique is that the cable being tested does not have

to be completely accessible. The test equipment can be connected to the ends of the cable, and

the test can be performed without physically touching the length of the cable. Also, no material

samples are taken from the cable.

A disadvantage of the dielectric loss technique is that the cable under test must be disconnected

in order to attach the test instrument. However, this can be controlled by test procedures with

independent verification steps, as are commonly used for surveillance and maintenance

procedures in nuclear power plants.

2.4.3 Voltage Withstand Test

The high potential voltage withstand test is a measure of a cable insulation’s ability to withstand

a high applied voltage stress. To perform this test, the cable is connected to a source of high

voltage. The test voltage is applied to each individual conductor of the cable specimen and held

for five minutes, during which time the leakage current between the conductor and electrical

ground is recorded. The leakage current provides a measure of the insulation’s condition.

As with any electrical test, an advantage of this test is that it can interrogate an entire cable

system to identify weak points.

A disadvantage of this test is that, due to the high voltages applied, the test itself can degrade the

insulation. If this test is repeated a number of times, the dielectric strength may become so

weakened that the cable could fail because of the testing. As such, this test would not normally

be used in situ by nuclear power plant technicians to assess and trend the dielectric integrity of a

cable’s insulation system. Since it is a high voltage test, it has the potential to destroy a cable if

a voltage breakdown should occur. Even at lower levels of applied test voltage, within the

voltage rating of the cable, the cable insulation is incrementally weakened by each high potential

test. Thus, the risks of causing either catastrophic or incipient damage to cable insulation make

this an unsuitable condition monitoring method.

2.4.4 Time-Domain Reflectometry

Time-domain reflectometry (TDR) works on the same principle as radar. A pulse of low-voltage

energy is transmitted down a cable and the reflected waveform is captured on the instrument

scope. When the pulse reaches the end of the cable, or a fault along the cable, part or all of the

pulse energy is reflected back to the instrument. The TDR measures the time it takes for the

signal to travel down the cable and reflect back. The TDR then converts this time to distance

and displays the information as a waveform and/or distance reading. Knowing the length of the

cable, the reflected pulse can be interpreted as the end of the cable, or a fault in the cable.

The primary use of the TDR is for locating defects in a cable. Little information is provided on

the condition of un-faulted cable insulation.
14

2.4.5 Partial Discharge Testing

Another type of electrical test is the partial discharge test. When an insulation defect such as a

void is present, the defect will display a localized corona or ionization during exposure to a

high-voltage stress. As voltage builds up across a void, once the partial discharge inception

voltage is reached, the gas in the void will ionize and a discharge will occur. The discharge

redistributes electrical charge within the dielectric and is known as partial discharge.

The inception voltage for these voids tends to be constant, so that the measurement of total

charge being redistributed within the dielectric is believed to be a good indicator of the size of

the voids and their likelihood of becoming an incipient failure. Partial discharge testing requires

the measurement of small current pulses (<5 pC) while applying a relatively high test voltage.

2.5 Reasons to Focus on an Electrical Technique

From the previous overview of currently available condition monitoring techniques it can be

seen that there are advantages and limitations to each. Of the three categories of techniques

presented, the electrical techniques appear to have the highest potential of meeting the criteria

for an effective in situ technique discussed previously. Advantages of the electrical techniques

are the following:

• An entire cable system can be interrogated with one test to detect degradation,

• The cable does not have to be accessible along its entire length,

• Results can be correlated to other monitoring parameters, such as EAB,

• The data obtained can be used to locate localized defects,

• Hardware can be installed to provide continuous on-line monitoring without connecting

test equipment, and 

• Material samples are not required to perform the test

• Loads at either end of an installed cable system can remain connected

• Non-intrusive, non-destructive voltage signals can be applied for examination

Based on these advantages, an electrical technique was focused on for this research. In

particular, broadband impedance spectroscopy was selected for evaluation.
15

G iC i () () () ω ω ω ωε ω + =Λ

Figure 2 Wire system equivalent circuit

3. THEORY OF BROADBAND IMPEDANCE SPECTROSCOPY

This section presents an overview of the theory behind broadband impedance spectroscopy

(BIS), and how impedance measurements are used to determine the electrical properties of

cables.

3.1 Equivalent Circuit

Over the past 70 years or more electric impedance models enabled the analysis of the dielectric

properties for numerous materials (for example, see Vaughan, 1969). Figure 2 depicts the

system being analyzed, which consists of two wires of length l with a voltage potential V(T )

across them.

The core concept of transmission theory is that a set of wires can be viewed as a distributed

system that is endowed with a frequency dependent resistance, R(ω) per meter, inductance, L(ω)

per meter, conductance, G(ω) per meter, and capacitance, C(ω) per meter. Note, the

conductance and capacitance are related to the wire insulation dielectric function, ε(ω) via

(3.1-1)

Here “i” represents the imaginary operator (square root of -1), and “Λ”is a structure factor that is

independent of frequency and is a real number. For example, for two identical wires whose

diameter is “d” and the center-to-center separation between the conductors is “s” the structure

factor would be:
16

(3.1-2a)

If the system is a coaxial cable, with inner and outer radii r0 and r1, respectively, then 

(3.1-2b)

If a voltage is established between the wires, then the system’s electrodynamics obey the

following equations (Durney and Johnson, 1969):

(3.1-3)

(3.1-4)

Here, V(x, t) is the voltage established between the two wires at the space-time point (x, t) and

I(x, t) is the current flowing in the wires. The solutions of these equations define a set of normal

modes A(x, t) 

(3.1-5)

The propagation function is defined as follows:

(3.1-6a)

Here α(ω) is the dissipation (per meter) and 2π/β(ω) is the wavelength of the normal mode.

Furthermore, we can rewrite the propagation function as

( ) Λ = −

π

cosh 1 s

d

Λ = ⎛

⎝

⎜ ⎞

⎠

⎟

2

0

1

π

ln r

r

∂

∂

∂

x ∂

V xt RI xt L

t

(,) (,) (,) =− − Ixt

∂

∂

∂

x ∂

I x t GV x t C

t

(,) (,) (,) =− − V xt

Axt x i t ( , ) exp = − [γω ω ± ( ) ( )]

( ) [ ][ ]

[ ]

γω ω ω ω ω ω ω

αω βω

± =± + +

=± +

R iL G iC

i

() () () ()

() ()
17

(3.1-6b)

The impedance for open-circuited and short-circuited wires is given by the following equations:

(3.1-7a)

(3.1-7b)

Here the wire length is l, and Z0(ω), the characteristic impedance, is given by the following

equation:

(3.1-8)

3.2 Wire Properties and Wire Impedance Spectra

In this section, the approach for extracting wire properties from impedance data is presented. An

example is then given describing how this approach is used for wire prognostics by extracting

the wire properties from the impedance data of healthy wiring and from damaged wiring.

Specifically, the cases of damage due to (1) humidity and (2) abrasion are examined. The data

presented in this section were obtained from a research program sponsored by the FAA, as well

as Boeing's IR&D on aircraft wiring and are used herein for demonstration purposes.

3.2.1 Approach to Extract Wire Properties from Impedance Data

First, the wire properties are extracted from the measured broadband impedance spectra for the

following wiring configurations: open-circuited and short-circuited. The product of the

short-circuited and open-circuited impedances and their ratio yield the characteristic impedance

and the propagation function, as follows:

(3.2-1a)

(3.2-1b)

γ ω ω ω ω εω ± () () () () =± + [ ] R iL i Λ

Z Z open () () () ω ω γω = 0 Coth[ l]

Z Z short() () () ω ω γω = 0 Tanh[ l]

Z ( ) R iL

G iC 0 ω

ω ωω

ω ωω = ++

() ()

() ()

ZZZ o short open

2

() () () ω ωω =

γ ω

ω

ω

( ) ( )

( )

l = − Tanh 1 Z

Z

short

open
18

Using equations (3.1.6b) and (3.1.8) for the propagation function and characteristic impedance,

respectively, the above equations can be written as:

(3.2-2a)

(3.2-2b)

Therefore, the wire properties per length are related to the characteristic impedance and the

propagation function via the following equations:

(3.2-3a)

(3.2-3b)

(3.2-3c)

(3.2-3d)

Here, ε1(ω) and ε2(ω) are the real and imaginary portion of the dielectric function, respectively.

Before an example of a wiring system is presented, the behavior of the characteristic impedance

and propagation function will be discussed, as well as the open-circuited and short-circuited

impedance spectra. At low frequencies, the characteristic impedance is dominated by the wire’s

capacitance and therefore is large. Conversely, the propagation function is very small such that

γ(ω) l << 1. Thus, the open-circuited and short-circuited impedance spectra approach the

following limiting forms at low frequencies:

(3.2-4a)

γω ω ω ω ω () () () () Z R iL 0 = +

γ ω

ω

ωεω ( )

( ) ( ) Z

i

0

= Λ

R Z () () () ω γω ω = Re [ 0 ]

L Z () () () ω [ ] ω = γω ω

1

0 Im

ε ω γ ω

ω ω

1

0

( ) ( )

( ) =

⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥ Re

Λ Z

ε ω γ ω

ω ω

2

0

( ) ( )

( ) = − ⎡

⎣

⎢ ⎤

⎦

⎥ Im

Λ Z

Z

i open ( ) ( )

ω

ω εω

→

1

Λ l
19

(3.2-4b)

Thus, at low frequencies the open-circuited wire impedance is dominated by the wire’s

capacitance. The magnitude of the open-circuited impedance depends nearly inversely on the

frequency and, therefore is large, whereas its phase is determined by the ratio ε2(ω)/ε1(ω). On

the other hand, at low frequencies the short-circuited impedance is independent of frequency

(ω → 0), is dominated by the wire’s resistance, and is small. At higher frequencies, the shortcircuited impedance exhibits a linear dependence on frequency with a slope determined by the

wire’s inductance. Thus, the low frequency portion of these spectra is completely dominated by

the wire’s electrical properties.

As an example, Figures 3 and 4 depict the log magnitude and phase of the impedance spectra at

low frequencies for a ten meter poly-x twisted pair wire that was open-circuited and shortcircuited. Here, the frequency ranges from 1kHz to 1MHz. 

Z R iL short() () () ω ω ωω → + l [ ]

3 4 5 6

4

5

6

3 4 5 6

0.25

0.5

0.75

1

1.25

1.5

Log10 ω Log10 ω

Log10 |Z(

ω)|

Log10 |Z(

ω)|

Open-Circuited Short-Circuited

Figure 3 Low frequency impedance spectra log magnitude for a 10 meter poly-x

twisted pair wire
20

In the region where γ(ω) l > π, the impedance spectra exhibit oscillations with a period of

2π/[γ(ω) l]. Electrical waves now propagate on the wiring and the impedance is dominated by

wave interference. Furthermore, noting that ε1(ω) >> ε2(ω), the characteristic impedance and the

propagation function approach the following limits:

(3.2-5a)

(3.2-5b)

Examination of the open-circuited and short-circuited cable impedances, described by

Equations (3.1.7a) and (3.1.7b), reveal that the period of these oscillations is determined by the

inductance and the real component of the dielectric function. Information on the location of

defects, such as “hot-spots,” is contained in this portion of the impedance spectrum.

As an example, Figures 5 and 6 depict the impedance magnitude and phase spectra at high

frequencies for a ten meter poly-x twisted pair wire that was open-circuited and short-circuited. 

Here the frequency ranged from 1MHz to 40MHz. 

Open-Circuited Short-Circuited

Log10 ω Log10 ω

3 4 5 6

-87.5

-87

-86.5

-86

3 4 5 6

20

40

60

80

Φ(ω)

Φ(ω)

Figure 4 Low frequency impedance spectra phase angle for a 10 meter poly-x

twisted pair wire

Z L

0

1

→ ( )

( )

ω

Λ ε ω

γω ω ε ω ω () ()() → i L Λ 1
21

1 ́ 107 2 ́ 107 3 ́ 107 4 ́ 107

-75

-50

-25

25

50

75

1 ́ 107 2 ́ 107 3 ́ 107 4 ́ 107

-75

-50

-25

25

50

75

Open Circuited Short Circuited

Φ(ω)

ω

Φ(ω)

ω

Figure 6 High frequency impedance spectra phase angle for a 10 meter poly-x

twisted pair wire

1 ́ 107 2 ́ 107 3 ́ 107 4 ́ 107

200

400

600

800

2 ́ 107 4 ́ 107 6 ́ 107 8 ́ 107 1 ́ 108

200

400

600

800

Open-Circuited Short-Circuited

ω ω

|Z(

ω)|

|Z(

ω)|

Figure 5 High frequency impedance spectra magnitude for a 10 meter poly-x

twisted pair wire

3.2.2 Wire Properties from Impedance Data for Undamaged Wiring

The wire electrical properties can be extracted from impedance data using equations (3.2-3a)

through Eq. (3.2-3d). The frequency dependent resistance and inductance are shown in Figure 7.

Examination of the resistance, R(ω), shows that it increases significantly at frequencies over

50kHz due to the skin effect. Analysis shows that the resistance varies as ω1/2, as expected. The

skin effect manifests itself when the conductor’s skin depth, δs(ω), is on the order or less than the

radius of the conductor, r (here r~10-4m), i.e. δs(ω) < r. At that point, the electrical currents are

confined near the surface of the conductor within the skin depth. This occurs when ω ≈ 50kHz. 
22

The inductance also exhibits frequency dependence. However, L(ω) does not follow the usual

skin effect frequency dependence due to the wire’s complex microstructure, depicted in Figure 8.

Specifically, there are nineteen strands, all of which conduct current, and their associated

magnetic fields interfere with each other. Furthermore, their individual radii are over twenty

times smaller than the wire conductor itself. Thus, the skin depth is on the order of 100μ−300μ. 

As a result, the frequency dependence is very weak. Finally, the low frequency behavior

(100Hz-1kHz) of the inductance (shown in Figure 7) is probably not valid. In particular, the

contribution of the inductance to the wire’s impedance is very small compared to that of the

resistance and dielectric function. As a result, the low-frequency portion of the inductance

(100Hz-1kHz) suffers from noise.

Figure 9 depicts the real and imaginary components of the wire’s dielectric function (times the

structure factor, Λ) in the frequency range from 100kHz to 1MHz. Examination of this figure

3 4 5 6

0.15

0.2

0.25

0.3

4.5 5 5.5 6

3.4 ́ 10-6

3.5 ́ 10-6

3.6 ́ 10-6

3.7 ́ 10-6

R(ω) L(ω)

Log10ω Log10ω

Figure 7 Frequency-dependent wire resistance and inductance

Figure 8 Micro picture of a poly-x wire

cross section
23

3.5 4.5 5 5.5 6

4.815  ́ 10-11

4.82  ́ 10-11

4.825  ́ 10-11

4.83  ́ 10-11

4.835  ́ 10-11

3.5 4.5 5 5.5 6

6 ́ 10-14

8 ́ 10-14

1 ́ 10-13

1.2 ́ 10-13

1.4 ́ 10-13

1.6 ́ 10-13

ε1(ω)

ε

2(ω)

Log10ω Log10ω

Figure 9 Real and imaginary components of the wire insulation dielectric

function (open circuited)

reveals that the real component is about 500-1000 times larger than the imaginary component.

Note that both components exhibit significant frequency dependence in the vicinity of 100Hz.

These structures arise from a slow, Debye ion process on the order of 100ms, in which ions

move in response to the ac electric fields associated with the probe voltage, V(ω). Furthermore,

there is a broad background that arises from very fast electronic processes, on the order of 0.1μs.

Analysis of the dielectric data reveals that this process is nearly independent of frequency and is

the largest contribution to the dielectric function. This electronic dielectric process follows the

fraction power law, in which the following relationship applies:

(3.2-6)

Here A1 is a fitting constant representing the strength of the process with a typical value ranging

from 2 to 4, ε0 is the dielectric constant of vacuum, τ is the time scale of the electronic dielectric

process, and p is a fitting constant ≈ 0.05. Note that as the frequency increases, the wire

insulation becomes more lossy. Finally, there is a small structure in the vicinity of 30kHz that

mirrors another process that is midway between the electronic and ion dielectric processes. The

origin of this process is unclear.

3.2.3 Wire Properties from Impedance Data for Damaged Wiring

An important element of a successful cable condition monitoring technique is its ability to detect

damage on the cable due to exposure to a stressor. As part of the initial feasibility study for this

project, impedance data were evaluated for wiring that was damaged by exposure to elevated

humidity levels. Humidity was chosen as the damage stressor since models were already

available for this damage mechanism from previous research on aircraft wires (Rogovin and

Kendig, 2002).

[ ] ε ω

ε

ω τ

electronic p

A

i

( ) ( ) ≈ +

1 0

1

1

g1(T)

g2(T)
24

If the wiring is damaged by exposure to elevated levels of humidity, corrosion and other new

microscopic processes may occur that are reflected in the wire’s electrical properties. As an

example, the case of poly-x twisted pair wiring exposed to humidity is examined.

Figure 10 depicts the log magnitude and phase of the impedance over the low frequency portion

(100Hz-1MHz) of the spectra for the cases in which the wires are open-circuited. Three

conditions are evaluated: (1) healthy wiring, (2) wiring exposed to 85%/85°F for 24 hours, and

(3) wiring exposed to 85%/85°F for 168 hours.

Examination of Figure 10 reveals that humidity changes the impedance spectra significantly.

Specifically, at low frequencies the impedance phase for the healthy wire Φdry(ω) ≈-90°, which

implies that little energy is dissipated in the wiring. When the wiring is exposed to humidity for

a period of time, the impedance phase migrates to more dissipative states where its value varies

from -85° < Φhumidity (ω) < -75°. Furthermore, the magnitude of the impedance is reduced

drastically. This is shown in Figure 11 where the ratio of the magnitude of the impedances are

plotted as a function of frequency. Note that the longer the wiring is exposed to humidity the

more conductive it becomes. Clearly, the wire’s dielectric properties can be seriously

compromised by humidity.

3 4 5 6

4

5

6

3 4 5 6

-88

-86

-84

-82

-80

-78

-76

Log10ω Log10ω

Log10|Z(

ω)|

Φ(ω)

Healthy wiring

24 hours in humidity

168 hours in humidity

1

1

2

3

2

3

2

3

1

Figure 10 Log magnitude and phase of the impedance spectra for moist and

dry wiring (open circuited)
25

Next, the electrical properties for dry and moist wiring are compared. Figure 12 depicts the

resistance and inductance of dry and moist wiring in the frequency range from 100Hz to 1MHz.

3 4 5 6

0.15

0.25

0.3

0.35

0.4

0.45

0.5

24 hours in humidity

168 hours in humidity

|Zhumidity(ω)|/ |Zdry(ω)|

Log10ω

3

2 2

3

Figure 11 Ratio of the impedance spectra magnitude for moist and dry wiring

(open circuited)

3 4 5 6

0.12

0.14

0.16

0.18

0.2

0.22

0.24

3 4 5 6

3.5 ́ 10-6

4.5 ́ 10-6

5 ́ 10-6

Log10ω Log10ω

R(ω)L(ω)

Healthy wiring

24 hours in humidity

168 hours in humidity

1

2

3

Healthy wiring

24 hours in humidity

168 hours in humidity

1

2

3

1

2 3

1

2

3

Figure 12 Ratio of the resistance and inductance for moist and dry wiring as

a function of frequency (R is S/m and L is H/m - open circuited)
26

ρ εω εω = 2 1 ( )/ ( )

Referring to Figure 11, it should be noted that both of these electric properties are changed by

humidity. For example, the resistance of moist wiring is about 20% larger that dry wiring. To

understand this, the following model describing the resistance for a pair of twisted wires is

examined:

(3.2-7)

Here “s” is the distance between the wire centers, Rs(ω) is the resistance for a single wire

(s → ∞) and “d” is the diameter of the wire insulation. Note that equation (3.2-7) demands that

the resistance will increase as s/d increases. Since humidity swells the wire’s insulation, the

resistance will increase, as shown in Figure 12.

Figure 13 compares the real and imaginary components of the wire insulation’s dielectric

function. Note that the imaginary component increases by a factor of several hundred to over one

thousand with exposure to humidity. This behavior implies that new and significant microscopic

processes occur. These processes occur throughout the spectrum, implying both ionic and

electronic dielectric processes. Note that the real component of the dielectric function has

increased as well.

More important, these processes are different than those that occur in a dry wire. This can be

seen by examining the ratio of the imaginary to the real component of the dielectric function,

(3.2-8)

Examination of Figure 13 reveals that the ratio increases from 10-3 for dry wire to the range of

0.15 < ρ(ω) < 0.25 for wire exposed to humidity. Clearly, the exponent (p), response time (τ) and

the strength (A1) in the fraction power law, as represented by Eq. (3.2-6), have changed.

Furthermore, the imaginary component of the dielectric function shows structure near ω ≈

104

Hz. Note that the longer the wiring is exposed to humidity, the further this peak migrates to

higher frequencies. 

R R

d

s

d

s

d

s ( ) ( )

( )

ω

ω

π =

−

⎡

⎣

⎢

⎢

⎢

⎤

⎦

⎥

⎥

⎥

2

1 2
27

3456

0.05

0.1

0.15

0.2

0.25

Healthy wiring

24 hours in humidity

168 hours in healthy

Log10ω

1

2

3

1

2

3

Healthy wiring

24 hours of humidity 168 hours humidity

ρ(ω)

3456

0.05

0.1

0.15

0.2

0.25

3456

0.05

0.1

0.15

0.2

0.25

Healthy wiring

24 hours in humidity

168 hours in healthy

Log10ω

Healthy wiring

24 hours in humidity

168 hours in healthy

Log10ω

Healthy wiring

24 hours in humidity

168 hours in healthy

Log10ω

1

2

3

1

2

3

Healthy wiring

24 hours of humidity 168 hours humidity

ρ(ω)

Figure 13 Ratio of the real and imaginary components of the wiring

insulation’s dielectric function for moist and dry wiring as a function of

frequency

3.3 BIS Test Procedure

The process for using the BIS technique to evaluate a cable’s condition involves two steps;

1) performing impedance measurements on the cable, and 2) analysis and interpretation of the

impedance data obtained using analytical models. Each of these steps is discussed in the

following sections.

3.3.1 Procedure for Making Impedance Measurements

Impedance measurements were made on the cable being evaluated over a broad range of

frequencies in the open circuited configuration. In this study, frequencies ranging from 100 Hz

to 100 MHz were used. The measurements were broken up into two frequency ranges; low

frequency, which included frequencies from 100Hz to 1MHz, and high frequencies, which

included frequencies from 1MHz to 100MHz. The use of two frequency ranges was determined

to be the best approach for taking impedance measurements due to the limitations of the test

equipment available. In the low frequency range, a Hewlett-Packard instrument was used since

it provided better impedance data accuracy in this range of frequencies. However, at higher

frequencies, the impedance data obtained from the HP instrument were “noisy” and lacked

adequate resolution. Therefore, in the high frequency range, an Eclypse instrument was used
28

that was specially designed to provide accurate impedance measurements at high frequencies. 

Figure 14 shows the Eclypse instrument (top) and the HP instrument (bottom) used to perform

the impedance measurements.

For the laboratory measurements, the cable being evaluated was prepared by stripping

approximately 1⁄2 inch of insulation from the ends of each conductor. The conductors were then

connected to terminals on the instrument being used for the impedance measurement, as

discussed above. The actual impedance measurements were performed automatically by a laptop

computer based software program, which controlled the actual measurements and downloading

of the data obtained. The measurements involved the input of a sinusoidal voltage signal into the

cable with an amplitude of 1-volt. The frequency of the input signal was varied over the desired

range of measurement. Data points were obtained at 2000 discrete frequencies in each

measurement range, and included the impedance magnitude and phase angle. The data points

were downloaded to the computer for subsequent retrieval and analysis.

3.3.2 Analysis and Interpretation of Impedance Data

After the impedance measurements were obtained, the data were analyzed using analytical

models. Different models were developed for each specific type of degradation being evaluated,

and were used to interpret the data for purposes of detecting and locating degradation on the

cable.

Figure 14 Equipment and test setup

for making impedance measurements
29

In practice, the application of BIS would involve starting with a known condition of the cable in

an un-degraded (baseline) state. The impedance measurements of the cable after being degraded

would be compared to the baseline condition. An appropriate model would then be selected to

explain any differences in the cable’s impedance. Based on the model that best fits the data, the

type of degradation would be identified.

The development of analytical models for various types of cable degradation was one of the

main objectives of this research effort, and is discussed in the following sections of this report. 

It should be noted that only one cable type was evaluated in this study. Therefore, the models

developed may not be applicable to other types of cables. The suitability of the models

developed in this study to other cable types is the subject of a future research program.
30

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31

4. PREPARATION AND BASELINE TESTING OF CABLE TEST SPECIMENS

This section of the report discusses the process used to prepare the cable test specimens that were

used in this study.

4.1 Selection of Cable Types

A number of different types of cables are used in nuclear power plants, and a great deal of

knowledge is available concerning their construction and performance (see for example Thue,

1999; Moore, 1997; and Grayson, 2000). For this research, cable samples were prepared using

Rockbestos Firewall® III, 2/C #12 AWG instrumentation and control cable, which is a

commonly used type of cable in nuclear power plants. The cables had a cross-linked

polyethylene (XLPE) insulation on each conductor, and an overall Neoprene jacket covering the

bundle of insulated conductors. The testing was limited to one type of cable to allow a full range

of testing to be performed within the budget and schedule allocated for this study. Future

research is desirable to investigate the effectiveness of the BIS technique on other types of

cables.

4.2 Preparation of Test Samples

The test specimens were prepared using a single reel of cable stored at BNL. The cable reel was

obtained from the warehouse stock of a decommissioned nuclear power plant as part of a

previous research program for the NRC. A single reel of cable was used as the source of all of

the test specimens for this study to avoid differences in cable properties that can occur between

different batches of cable.

Lengths of cable were cut from the reel to prepare the test specimens. The test specimens ranged

in length from 10 meters (32.8 feet) to 100 meters (328 feet). Approximately 15 cm (6 inches) of

the outer jacket was stripped from each end of the test specimen, along with approximately

2.5 cm (1 inch) of insulation from each conductor end.

4.3 Baseline Testing of Test Samples

Prior to aging, each test specimen was tested to determine its baseline performance. The tests

used were insulation resistance and dielectric loss. These tests were chosen since they are well

established, traditional tests that can be used for comparison purposes with the BIS test data. The

tests were repeated after aging of the test specimens was completed.
32

4.4 Accelerated Aging of Test Samples

Thermal aging was applied to the cable test specimens using convection ovens at BNL to

simulate exposure to a service temperature of 50oC (122oF) for durations of 20 years, 40 years,

and 60 years. The aging duration was determined using the Arrhenius equation with an

activation energy of 1.33 eV, which is the value used in the original qualification tests for these

cables. The thermal aging was applied globally to the entire length of the test specimen. Cable

specimens with no thermal aging were also tested to provide baseline data on the cable

performance.

In addition to global aging, selected specimens received thermal aging over a portion of their

length to simulate exposure to hot-spots at predetermined locations on the cable. The hot-spot

lengths simulated were 0.5 meters (1.64 feet) and 1.0 meters (3.3 feet) long. The hot-spots were

simulated by inserting only a portion of the test specimen in the aging chamber. Figure 15

shows a typical aging chamber loading used to perform the global and hot-spot aging. Table 1

provides a matrix of the test specimens prepared for this study.

Figure 15 Typical aging chamber loading for global and hot-spot

aging of cable test specimens
33

Cable Type = Rockbestos I&C, 2 Conductor, #12 AWG with XLPE Insulation and Neoprene Oute

No. Specimen ID No. Length meters (inches)

Global Accelerated Thermal Aging Applied 1 Localized Accelerated Thermal Ag

Aging Parameters

(hours @ Temp)

Service Life

Simulated

(years @ Temp.)

Aging Parameters 2

(hours @ Temp.)

Size

(meters)

Ho

Sim

(years 

1. PNI-79-RB-188-801 1.0 (39.4) None None None - N2, PNI-79-RB-188-802 2.0 (78.7) None None None - N3, PNI-79-RB-188-803 9.0 (354.3) None None None - N4. PNI-79-RB-188-804 1.0 (39.4) 31.6 @121oC (250oF) 20 @ 50oC (122oF) None - N5. PNI-79-RB-188-805 2.0 (78.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) None - N6. PNI-79-RB-188-806 9.0 (354.3) 31.6 @121oC (250oF) 20 @ 50oC (122oF) None - N7. PNI-79-RB-188-807 1.0 (39.4) 63.1 @121oC (250oF) 40 @ 50oC (122oF) None - N8. PNI-79-RB-188-808 2.0 (78.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) None - N9. PNI-79-RB-188-809 9.0 (354.3) 63.1 @121oC (250oF) 40 @ 50oC (122oF) None - N10. PNI-79-RB-188-810 1.0 (39.4) 94.7 @121oC (250oF) 60 @ 50oC (122oF) None - N11. PNI-79-RB-188-811 2.0 (78.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) None - N12. PNI-79-RB-188-812 9.0 (354.3) 94.7 @121oC (250oF) 60 @ 50oC (122oF) None - N13. PNI-79-RB-188-813 10.0 (393.7) None None None - N14. PNI-79-RB-188-814 10.0 (393.7) None None None - N15. PNI-79-RB-188-815 10.0 (393.7) None None None - N

Table 1 Cable Test Specimens for Broadband Impedance Spectroscopy Research
Table 1 Cable Test Specimens for Broadband Impedance Spectroscopy Research (continued

No. Specimen ID No. Length meters (inches)

Global Accelerated Thermal Aging Applied 1 Localized Accelerated Thermal Ag

Aging Parameters

(hours @ Temp)

Service Life

Simulated

(years @ Temp.)

Aging Parameters 2

(hours @ Temp.)

Size

meters

(inches)

Ho

Sim

(years 

16. PNI-79-RB-188-816 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) None - N17, PNI-79-RB-188-817 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 6.96 @150oC (302oF) 1.0 (39.4) 20 @ 618, PNI-79-RB-188-818 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 6.96 @150oC (302oF) 0.5 (19.7) 20 @ 619. PNI-79-RB-188-819 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 33.1 @150oC (302oF) 1.0 (39.4) 20 @ 720. PNI-79-RB-188-820 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 33.1 @150oC (302oF) 0.5 (19.7) 20 @ 721. PNI-79-RB-188-821 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) None - N22. PNI-79-RB-188-822 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 13.9 @150oC (302oF) 1.0 (39.4) 40 @ 623. PNI-79-RB-188-823 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 13.9 @150oC (302oF) 0.5 (19.7) 40 @ 624. PNI-79-RB-188-824 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 66.2 @150oC (302oF) 1.0 (39.4) 40 @ 725. PNI-79-RB-188-825 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 66.2 @150oC (302oF) 0.5 (19.7) 40 @ 726. PNI-79-RB-188-826 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) None - N27. PNI-79-RB-188-827 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 20.9 @150oC (302oF) 1.0 (39.4) 60 @ 628. PNI-79-RB-188-828 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 20.9 @150oC (302oF) 0.5 (19.7) 60 @ 629. PNI-79-RB-188-829 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 99.3 @150oC (302oF) 1.0 (39.4) 60 @ 730. PNI-79-RB-188-830 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 99.3 @150oC (302oF) 0.5 (19.7) 60 @ 731. PNI-79-RB-188-831 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 418.8 @150oC (302oF) 1.0 (39.4) 20 @ 932. PNI-79-RB-188-832 10.0 (393.7) 31.6 @121oC (250oF) 20 @ 50oC (122oF) 418.8 @150oC (302oF) 0.5 (19.7) 20 @ 933. PNI-79-RB-188-833 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 837.6 @150oC (302oF) 1.0 (39.4) 40 @ 934. PNI-79-RB-188-834 10.0 (393.7) 63.1 @121oC (250oF) 40 @ 50oC (122oF) 837.6 @150oC (302oF) 0.5 (197) 40 @ 9

34
Table 1 Cable Test Specimens for Broadband Impedance Spectroscopy Research (continued

No. Specimen ID No. Length meters (inches)

Global Accelerated Thermal Aging Applied 1 Localized Accelerated Thermal Ag

Aging Parameters

(hours @ Temp)

Service Life

Simulated

(years @ Temp.)

Aging Parameters 2

(hours @ Temp.)

Size

meters

(inches)

Ho

Sim

(years 

35

35. PNI-79-RB-188-835 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 1256.4 @150oC (302oF) 1.0 (39.4) 60 @ 936. PNI-79-RB-188-836 10.0 (393.7) 94.7 @121oC (250oF) 60 @ 50oC (122oF) 1256.4 @150oC (302oF) 0.5 (19.7) 60 @ 937. PNI-79-RB-188-837 10.0 (393.7) 9.1 @121oC (250oF) 20 @ 60oC (140oF) None - N38. PNI-79-RB-188-838 10.0 (393.7) 35.3 @121oC (250oF) 20 @ 70oC (158oF) None - N39. PNI-79-RB-188-839 10.0 (393.7) 18.3 @121oC (250oF) 40 @ 60oC (140oF) None - N40. PNI-79-RB-188-840 10.0 (393.7) 70.6 @121oC (250oF) 40 @ 70oC (158oF) None - N41. PNI-79-RB-188-841 10.0 (393.7) 27.4 @121oC (250oF) 60 @ 60oC (140oF) None - N42. PNI-79-RB-188-842 10.0 (393.7) 105.8 @121oC (250oF) 60 @ 70oC (158oF) None - N43. PNI-79-RB-188-843 10.0 (393.7) 1256.4 @150oC (302oF) 60 @ 90oC (158oF) None - N44. PNI-79-RB-188-847 100.0 (3937) None - 1256.4 @150oC (302oF) 1.0 (39.4) 60 @ 945. PNI-79-RB-188-848 100.0 (3937) None - None - N

1. Calculations based on activation energy of 1.33 eV.2. Hot-spot aging time is in addition to global aging time.3. Measured from right end of cable, as determined by orienting wording on cable so it can be read normally from left to right.
36

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37

5. RESULTS OF BIS TESTING OF CABLE SAMPLES

This section presents the results of the BIS tests performed on the cable test specimens with

various types of degradation. The models developed for each type of degradation are presented

and, comparisons with actual test data are made.

5.1 Application of BIS to Thermally Aged Cables

The initial research to evaluate BIS was focused on the detection of degradation on cables that

had been exposed to thermal aging. This is a fundamental requirement of an effective cable

condition monitoring technique for nuclear plant cables since thermal aging is one of the

predominant stressors in such plants. Section 5.1.1 presents the results of tests on cables that

received global thermal aging to simulate various service conditions. These cables were tested

to characterize their impedance spectra, and demonstrate the capability of the BIS method for

detecting thermal degradation. Subsequently, models were developed to represent the measured

impedance spectra and the electrical properties of the cables.

In Section 5.1.2, the results from tests on cables with localized thermal aging, or hot-spots, is

presented. These tests were performed to determine if the BIS technique is capable of locating

localized degradation on a cable. The models and process used to locate degradation are

presented and discussed.

5.1.1 Detection of Degradation on Cables with Global Thermal Aging

The BIS technique was evaluated for its ability to detect global thermal aging on cables using the

test specimens shown in Table 2. These cables were aged to simulate 20, 40 and 60 years of

service at service temperatures of 50oC (122oF), 60oC (140oF), and 70oC (158oF). For each test

specimen, broadband impedance measurements were made over the low frequency range (100

Hz to 1 MHz) and over the high frequency range (1 MHz to 100 MHz).

Figure 16 shows the measured impedance phase spectra in the low frequency range for the cables

aged to simulate 60 years of service (Specimens 26, 41, and 42). In performing these

measurements, the cables were placed in a humidity chamber, which was maintained at a

constant temperature of 25o (77oF) and a pressure of 1 atmosphere to minimize atmospheric

effects on the measurements. The cables were tested with the conductors connected to the test

instrument on one end, and “open” (unconnected) at the opposite end.

Referring to Figure 16, it is seen that as the amount of degradation on the cable increases, which

is represented by the higher simulated service temperature, the greater the cable’s impedance

phase shifts away from -90 degrees. This suggests that as the degradation on the cable increases,

the cable becomes more dissipative, which is expected. Similar results were obtained for cables

aged to simulate 20 years and 40 years of service (Appendix A).
38

No. Specimen ID

Length

meters

(inches)

Service Life Simulated Hot-Spot Simulated

16. PNI-79-RB-188-816 10 (393.7) 20 @ 50oC (122oF) None

37. PNI-79-RB-188-837 10 (393.7) 20 @ 60oC (140oF) None

38. PNI-79-RB-188-838 10 (393.7) 20 @ 70oC (158oF) None

21. PNI-79-RB-188-821 10 (393.7) 40 @ 50oC (122oF) None

39. PNI-79-RB-188-839 10 (393.7) 40 @ 60oC (140oF) None

40. PNI-79-RB-188-840 10 (393.7) 40 @ 70oC (158oF) None

26. PNI-79-RB-188-826 10 (393.7) 60 @ 50oC (122oF) None

41. PNI-79-RB-188-841 10 (393.7) 60 @ 60oC (140oF) None

42. PNI-79-RB-188-842 10 (393.7) 60 @ 70oC (158oF) None

Table 2 Specimens tested to evaluate BIS for detecting global thermal aging

200000 400000 600000 800000 1x106

-89.4 

-89.2 

-88.8 

-88.6 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

A B 

C 

Φ(ω) [Deg.] 

ω [Hz]

Figure 16 Measured low frequency impedance phase spectra for cables with

global thermal aging to simulate 60 years of service at various temperatures
39

Figure 17 shows the impedance phase spectra for these cables in the high frequency range. 

Examination of this figure reveals that the impedance phase for these cables differs significantly

as degradation increases, particularly for frequencies above 60MHz where large differences in

the zero crossings of the impedance phase spectra are seen. An expanded view for the frequency

range from 78 MHz to 86 MHz is shown in Figure 18 for both the impedance phase and

magnitude. The shift in both phase and magnitude to lower frequencies with increasing

degradation is readily observed. Similar results were obtained for cables aged to simulate 20

years and 40 years of service (Appendix A).

These results demonstrate that thermal degradation has an impact on a cable’s electrical

impedance spectra. By measuring the impedance over a range of frequencies and comparing the

impedance spectra to a known spectra for an undamaged cable, changes in the impedance phase

and magnitude can be observed and used as an indicator of cable degradation. 

In the next section, models are developed that can be used to describe the changes in the

impedance spectra. These models can be used to characterize a cable’s electrical properties after

being exposed to global thermal degradation. The models can also be used to locate localized

areas of degradation on the cable, such as would be caused by environmental “hot-spots” along

the cable.

2x107

-75 

-50 

-25 

25 

50 

75 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

4x107 6x107 8x107 1x108

Φ(ω) [Deg.] 

ω [Hz] 

C 

B 

A 

Figure 17 Measured high frequency impedance phase spectra for cables with

global thermal aging to simulate 60 years of service at various temperatures
40

5.1.2 Development of Models for Cables with Thermal Degradation

Analytical models are used to determine the electrical properties of a cable, thereby providing an

assessment of the cable’s health. In addition, the models are required to determine the location

of localized degradation on a cable. The development of analytical models for cables exposed to

thermal aging is discussed in this section.

In order to develop an analytical model, it is important to understand the basic approach to

modeling a cable. If a cable is exposed to an aging stressor uniformly along its length, it will be

in a “single state” and can be represented by two frequency dependent functions; the

characteristic impedance, Z0 (T), and the propagation function, ( (T). However, if a cable is

exposed to different levels of an aging stressor along its length, it will have sections with

different amounts of aging degradation and the cable will be in multiple states. In this case, each

section will have its own characteristic impedance and propagation function, and the cable must

be modeled as a complex combination of these parameters.

At low frequencies the cable’s impedance is non-oscillatory and, as discussed in Section 3.2.1,

the characteristic impedance and propagation function can be directly extracted from the

measured impedance spectra using equations 3.2-1a and 3.2-1b. At high frequencies, where the

cable’s impedance oscillates, it is not possible to directly extract the characteristic impedance

and propagation function. Instead, one of the following two approaches can be used:

7.8x107

-40 

-20 

20 

40 

100 

150 

200 

250 

300 

Φ(ω) |Z(ω)|/l [S/m] [Deg.] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

8.2x107 8.6x107

7.8x107

 8.2x107 8.6x107

ω [Hz]

ω [Hz]

A 

B 

C 

C 

B 

A 

Figure 18 Expanded view of impedance phase and magnitude per unit length

spectra over the frequency range from 78 MHz to 86 MHz for cables with global

thermal aging to simulate 60 years of service at various service temperatures
41

• Extrapolative approach, or

• Physical modeling approach

The extrapolative approach is used here to model cables with thermally induced aging

degradation. In this approach, the function representing the cable’s characteristic impedance in

the low frequency range is first determined using equation 3.2-1a. This function is then

extrapolated to high frequencies ranging from 1MHz to 15MHz. By substituting the

extrapolated characteristic impedance into equation 3.1-7a, the propagation function for the high

frequency range can then be determined using the following equation:

(5.1-1)

where Zopen is the measured cable impedance in the open configuration, and Z0, extrapolated (T) is the

extrapolated characteristic impedance for the cable.

5.1.2.1 Extraction of Cable Properties from Measured Impedance Spectra

As discussed in Section 3.2.1, a cable’s characteristic impedance and propagation function can

be extracted from measured impedance data. The cable’s impedance is measured in the open

configuration and the shorted configuration, then equations 3.2-1a and 3.2-1b can be used to

obtain the cable’s characteristic impedance and propagation function . Once these functions are

known, the cable’s electrical properties can be determined using equations 3.2-3a to 3.2-3d. This

was performed for the thermally aged cable test specimens in Table 2. Results for the cables

aged to simulate 60 years of service are presented below. Similar results were obtained for the

remaining cables in Table 2 and are included in Appendix A.

In Figure 19, the magnitude,*Z0(T)*, and phase, Q(T), of the characteristic impedance spectra

are presented for the cables thermally aged to simulate 60 years of service (Specimens 26, 41,

and 42). Examination of this figure shows that the thermal aging has only a small effect on the

cable’s characteristic impedance, as evidenced by the changes in magnitude of less than 5%.

Figure 20 compares the real component, (r

, and imaginary component, (i, of the propagation

function spectra for the cables aged to simulate 60 years of service. As shown, the real

component of the propagation function increases as the aging degradation increases (higher

simulated service temperature). This reflects the fact that the thermal aging process produces

chemical changes in the cable’s insulation.

γ ω

ω

ω

( ) ( )

( ) ,

= ⎡

⎣

⎢

⎢

⎤

⎦

⎥

⎥

− Coth

Z

Z

open

extrapolated

1

0
42

104

106

108

110

112

-3

-2

-1

4.6 4.8 5.2 5.4 5.6 5.8 6 

Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

Log10(ω) 

4.6 4.8 5.2 5.4 5.6 5.8 6 

Log10(ω) 

C A 

B 

C 

A 

B 

|Z0(ω)|/l [S/m]

Figure 19 Characteristic impedance magnitude per unit length and phase spectra for

cables with global thermal aging to simulate 60 years of service at various temperatures

0.015

0.020

0.025

0.030

0.035

0.0002

0.0004

0.0006

0.0008

4.6 4.8 5.2 5.4 5.6 5.8 6 

50 oC (122 oF)

C

60 oC (140 oF)

70 oC (158 oF)

A

Log10(ω) B

4.6 4.8 5.2 5.4 5.6 5.8 6 

Log10(ω) 

C 

A 

B 

C 

A 

B 

γ

r

(ω) γ

i

(ω)

Figure 20 Imaginary component and real component of propagation function for cables

with global thermal aging to simulate 60 years of service at various temperatures

With the characteristic impedance and propagation function now known, the cable’s electrical

properties can be determined. First, equation 3.2-3a is used to obtain the resistance of the cables,

as shown in Figure 21. The left-hand side of the figure shows the resistance per unit length of

the cable in ohms/meter, while the right-hand side shows the percent change in resistance for an

increase in service temperature from 50oC to 60oC, and from 50oC to 70oC. The percent change

was calculated using the following equation:
43

200000 600000 1x106

0.02

0.04 

0.06

0.08

0.10

0.12

0.14 

ω

-0.02

-0.01

0.01

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A 

B 

C 

E 

50 to 60 oC 

50 to 70 oC 

D 

D 

E 

200000 600000 1x106

δR(ω)/l [S/m] R(ω)/l [S/m] 

ω [Hz]

ω [Hz]

Figure 21 Resistance per unit length and change in resistance per unit length for cables

with global thermal aging to simulate 60 years of service at various temperatures

5.1-2

where Rk(T) is the resistance for service temperatures of 60oC (140oF) (k=60) and 70oC (158oF)

(k=70), and R50(T) is the resistance for a service temperature of 50oC (122oF).

Referring to the left-hand side of Figure 21, it is seen that an increase in thermal aging (i.e.,

higher service temperature) results in a small but perceptible decrease in the cable’s resistance. 

This implies that shrinkage of the insulation is greatest with the higher simulated service

temperature. The right-hand side of Figure 21 shows that the resistance decreases as service

temperature increases, which results in a negative percent change. Also, the percent change in

resistance increases (i.e., becomes more negative) at the higher frequencies.

Using the extracted resistance, an analytical model can now be developed to represent this

resistance spectra. The analytical model is based upon the knowledge that resistance is primarily

governed by the skin effect, which is a function of T1⁄2. Therefore, an equation of the following

form was fitted to the resistance spectra presented in Figure 21:

5.1-3

where Rk(T) is the resistance for a cable aged to simulate service temperature k, Tk is the skin

δ ω ω ω

ω

R R R

R k

k ( ) () ()

( ) = − 50

50

R R k k

k

( ) ω ,

ω

ω

= +

⎛

⎝

⎜ ⎞

⎠

⎟ 0 1
44

frequency for a cable aged to simulate service temperature k, and R0,k is an adjustable constant. 

The values for the skin frequency and R0,k for the cables evaluated are shown in Table 3.

The cable resistance determined using the analytical model is compared to the extracted cable

resistance in Figure 22 for the cable thermally aged to simulate 60 years of service at 50oC

(122oF). As shown, the analytical model is within 5% of the extracted resistance over the

frequency range from 400kHz to 1 MHz, which demonstrates reasonably good accuracy for this

model. Similar results were obtained for the other cables in Table 2, which are included in

Appendix A. The error in the analytical model arises from the fact that the classical relationship

of the skin effect was approximated by equation 5.1-3. However, the error introduced by this

approximation is acceptable for the purposes of this study.

A similar process was followed to obtain an analytical model for the cable inductance. Equation

3.2-3b was used to extract the inductance from the measured characteristic impedance and

propagation function spectra. The results are presented in Figure 23. The left-hand side shows

the inductance per unit length, L(T) Henries/meter, for the cables aged to simulate 60 years of

service. The right-hand side shows the percent change in inductance, *L(T), for an increase in

service temperature from 50oC to 60oC, and from 50oC to 70oC. The percent change was

calculated using the following equation:

5.1-4

where Lk(T) is the inductance for cables aged to simulate service temperatures of 60oC (140oF)

(k=60) and 70oC (158oF) (k=70), and L50(T) is the inductance for the cable aged to simulate a

service temperature of 50oC (122oF).

Simulated Service

Temperature Skin Frequency (Tk) Constant (R0,k)

50 oC (122 oF) 12,589.3 sec-1 0.0150 S/m

60 oC (140 oF) 12,589.3 sec-1 0.0143 S/m

70 oC (158 oF) 14,125.4 sec-1 0.0150 S/m

1. Parameters determined by fitting equation 5.1-3 to resistance data in Figure 20

Table 3 Parameters for analytical model of resistance for cables thermally aged to simulate 60

years of service at various service temperatures 1

δ ω ω ω

ω

L L L

L k

k ( ) () ()

( ) = − 50

50
45

400000 600000 800000 1x106

0.06

0.08

0.12

0.14

Extracted 

B Model 

A 

B 

A 

R(ω)/l [S/m] 

ω [Hz]

Figure 22 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to simulate 60

years of service at 70oC

3.8

4.2

4.4

4.6

-0.02

-0.01

0.01

0.02

400000 800000

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

400000 800000 

L(ω)/l [H/m] δL(ω)/l [H/m] 

ω [Hz] ω [Hz]

Figure 23 Inductance per unit length and change in inductance per unit length for cables

with global thermal aging to simulate 60 years of service at 70oC

Examination of the left-hand side of Figure 23 shows that the inductance tends to increase with
46

increasing thermal degradation, as evidenced by comparing the inductance for the 50oC (122oF)

service temperature (curve A) with that for the 60oC (140oF) service temperature (curve B). This

supports the notion that shrinkage of the insulation is greater with increased amounts of thermal

aging. A further increase in service temperature to 70oC (158oF) (curve C) results in a decrease

in inductance for this case. The reason for this decrease is not readily apparent. It is also noted

that the inductance decreases with increasing frequency. This is consistent with the skin effect,

although the inductance decreases with frequency as T-0.2, whereas the skin effect predicts a T-0.5

dependence.

An analytical model of the cable’s inductance is now developed based on the extracted

inductance spectra. Since the inductance does not behave as the classical skin effect, the

following phenomenological relation is used.

5.1-5

where L0,k is the very low frequency inductance per unit length of the cable, and ak, Jk, and mk

are adjustable constants. The values for these parameters were determined for the cables aged to

simulate 60 years of service by fitting equation 5.1-5 to the extracted inductance spectra

presented in Figure 23 over the frequency range from 429 kHz to 1MHz. The rms error between

the model prediction and extracted data was minimized to determine the parameter values, which

are presented in Table 4.

Figure 24 compares the inductance extracted from the measured impedance spectra with the

inductance predicted by the analytical model for the cable aged to simulate 60 years of service at

70oC (158oF). As shown, the predicted inductance is within 1% of the extracted inductance over

the frequency range from 429 kHz to 1 MHz, which demonstrates good accuracy for the

analytical model. Similar results were obtained for the other cables in Table 2, which are

presented in Appendix A.

L La k kk

k

m

k

m

k

k

( ) ( )

( )

ω ,

ω τ

ω τ = − +

⎛

⎝

⎜ ⎞

⎠ 0 ⎟ 2 1

1

Service Temperature

Simulated

Very Low Frequency

Inductance (L0,k) ak Jk mk

50 oC (122 oF) 4.84 :H/m 0.612 0.10 :sec-1 0.18

60 oC (140 oF) 4.84 :H/m 0.612 0.10 :sec-1 0.18

70 oC (158 oF) 5.00 :H/m 0.675 0.10 :sec-1 0.18

1. Parameters determined by fitting equation 5.1-5 to the inductance spectra presented in Figure 22.

Table 4 Parameter values for analytical model of inductance for cables aged to simulate 60 years

of service at various service temperatures 1
47

3.75x10-6

3.85x10-6

3.90x10-6

3.95x10-6

400000 600000 800000 1x106

Extracted 

B Model 

A 

A 

B 

L(ω)/l [H/m] 

ω [Hz] 

Figure 24 Comparison of inductance per unit length predicted by analytical model

to that extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 70oC

The capacitance and conductance are linked by the cable’s dielectric function, which is given by

equation 3.1-1. Therefore, these two electrical properties will be considered together. Using

equations 3.2-3c and 3.2-3d, the real and imaginary components of the dielectric function are

extracted from the characteristic impedance and propagation function. The capacitance and

conductance are then determined using equation 3.1-1.

Figure 25 presents the capacitance per unit length, C(T) Farads/meter, for the cables aged to

simulate 60 years of service. The left-hand side presents the capacitance per unit length for each

of the different service temperatures simulated. The right-hand side presents the percent change

in capacitance for an increase in service temperature from 50oC to 60oC (curve D), and 50oC to

70oC (158oF) (curve E). Examination of this figure shows that the capacitance, and therefore, the

real component of the dielectric function, g1(T), decreases slowly with frequency and has an

average value of 0.35 to 0.38 nF/m. The effect of higher simulated service temperatures is

mixed; the capacitance of the cable aged to simulate a service temperature of 60oC (140oF)

shows a decrease compared to the cable aged to simulate 50oC (122oF). However, an increase is

noted when the capacitance for the cable aged to simulate 70oC (158oF) is compared to the cable

aged to simulate 50oC (122oF). This behavior is non-intuitive and the explanation is not readily

obvious.
48

200000 600000 1x106

3.5

3.6

3.7

3.8

200000 600000 1x106

0.02

0.04

0.06

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

C(ω)/l [x10-10 F/m] δC(ω)/l [x10-10 F/m]

ω [Hz] ω [Hz]

Figure 25 Capacitance per unit length and change in capacitance per unit length for

cables with global thermal aging to simulate 60 years of service at various temperatures

Figure 26 presents the conductance per unit length for the cables aged to simulate 60 years of

service. The left-hand side of the figure shows the conductance per unit length normalized by

the frequency, G(T)/T mho-sec/m. The right-hand side shows the change in conductance,

*G(T), for an increase in service temperature from 50o to 60oC (curve D), and from 50o to 70oC

(curve E). As shown, the conductance increases with frequency and has an average value on the

order of 6x10-3 mho-sec/m. Also, as the simulated service temperature increases, the

conductance increases. The right-hand side of the figure shows that the conductance for the

cable aged to simulate 70oC (158oF) increased by approximately 40% above that for the cable

aged to 50oC (122oF). This indicates that the cable’s insulation has probably passed through a

glass transition phase and become more dissipative.

Using the capacitance and conductance spectra, analytical models for the cable’s dielectric

function are now developed. These models are based upon the fraction power law, which has

been used extensively over the past two decades to model dielectric materials. The model is

defined in the following equation:

5.1-6

[ ] ( ) [ ] ( )

ε

ωτ ωτ

= +

+

+

+

⎛

⎝

⎜

⎜

⎞

⎠

⎟

⎟ c

A

i

A

i

0 n n

1

1

2

2

1

1 1 1 2
49

5.0

6.0

7.0

8.0

200000 600000 1x106

0.1

0.3

0.5

0.7

1x106

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

200000 600000 

G(ω)/ω-l [x10-12mho-s/m] 

δG(ω)/ω-l [x10-12mho-s/m] 

ω [Hz] ω [Hz]

Figure 26 Conductance-to-frequency ratio per unit length and change in conductance-tofrequency ratio per unit length for cables with global thermal aging to simulate 60 years

of service at various temperatures

where the second and third terms in the equation refer to electronic processes and mixed

processes that govern the insulator’s dielectric response to electrical forces. The constants c0,

A1, J1, n1, A2, J2, and n2 are determined based upon physical considerations. For example,

2#A2#4 due to the fact that the electronic processes dominate the material’s dielectric response

to electrical forces throughout the frequency range. Furthermore, these processes are very fast

(J2=0.1 :s) and nearly independent of frequency (0#n2#0.1). On the other hand, ionic processes

are not included in equation 5.1-6 since they are too slow (0.01s#J2#1s) and cannot affect the

material’s dielectric response to electrical forces. Also, the ionic processes are Debye in nature

and are about 5% less than A2 even at low frequencies (i.e., 1kHz or less, whereas we are

interested in the frequency range from 429kHz and above). Finally, the mixed processes are

midway between the ionic and electronic processes. Typically, the following ranges are found

for these parameters: 0.1#A1#1.0, 0.1#n1#0.5, and 10:s#J1#100:s.

The parameter values for the dielectric function analytical model were determined by fitting

equation 5.1-6 to the extracted capacitance and conductance over the frequency range from

429 kHz to 1 MHz, and minimizing the rms error between the modeled values and the extracted

values. The parameter values are presented in Table 5.
50

3.58

3.59

3.61

3.62

3.63

3.64

400000 800000 

Extracted 

B Model 

A 

A 

B 

300000 500000 600000 700000 

C(ω)/l [x10-10 F/m]

ω [Hz] 

Figure 27 Comparison of capacitance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 70oC

Figure 27 compares the capacitance predicted by the model to the capacitance extracted from the

measured impedance spectra for the cable aged to simulate 60 years of service at 70oC (158oF). 

As shown, the predicted capacitance is within 1% of the extracted capacitance over the

frequency range from 429 kHz to 1MHz, which demonstrates good accuracy for the model.

Service

Temperature

Simulated

c0 A1 J1 n1 A2 J2 n2

50 oC (122 oF) 0.2920 1.00 31.6 0.2500 6.00 0.10 0.010

60 oC (140 oF) 0.2874 0.85 31.6 0.2489 6.80 0.10 0.018

70 oC (158 oF) 0.2880 1.50 31.6 0.2500 5.75 0.01 0.125

1. Parameter values determined by fitting equation 5.1-6 to the capacitance and conductance spectra presented in Figures 24 and 25,

respectively.

Table 5 Parameter values for dielectric function analytical model for cables thermally aged to

simulate 60 years of service at various service temperatures 1
51

400000 600000 800000 

Extracted 

B Model 

A 

B 

A 

300000 500000 700000 

6.50

6.75

7.25

7.50

7.75

8.00

8.25

G(ω)/ω-l [x10-12mho-s/m]

ω [Hz] 

Figure 28 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 60 years of service at 70oC

Similarly, Figure 28 compares the conductance-to-frequency ratio, G(T)/T, predicted by the

model to the conductance-to-frequency ratio extracted from the measured impedance spectra for

the cable aged to simulate 60 years of service at 70oC (158oF). As shown, the predicted spectra

is within 10% of the extracted spectra over the frequency range from 429 kHz to 1MHz, which

demonstrates good accuracy for the model.

With the electrical properties modeled, the characteristic impedance and propagation function

can now be modeled using equations 3.1-8 and 3.2-2, respectively. Figure 29 compares the

characteristic impedance predicted by the analytical model to that extracted from the measured

impedance spectra for the cable thermally aged to simulate 60 years of service at 70oC (158oF). 

As shown, the characteristic impedance predicted by the analytical model is within 1% of the

extracted spectra over the frequency range from 429 kHz to 1 MHz, which demonstrates good

accuracy for the model. Similarly, Figure 30 compares the propagation function predicted by the

analytical model to that extracted from the measured impedance spectra for the cable thermally

aged to simulate 60 years of service at 70oC (158oF). Again, good accuracy is demonstrated for

the model, with predicted values within 1% for the imaginary part, and within 7% for the real

part of the propagation function.
52

101.6

101.7

101.8

101.9

-2.25

-1.50

-1.25

-1.00

-0.75

-0.50

Extracted 

Model B 

A 

600000 700000 800000 

Ψ(ω)

400000 600000 800000 

A B 

B 

A 

-1.75

101.5

101.4

|Z0(ω)|/l [S/m] 

ω [Hz] ω [Hz]

Figure 29 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 60 years of service at 70oC

0.015

0.020

0.025

0.030

0.035

0.0004

0.0006

0.0008

200000 600000 1x106

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

B 

A 

A B 

400000 600000 800000 

0.010

ω [Hz]

ω [Hz]

Figure 30 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 60 years of service at 70oC

5.1.2.2 Extrapolation of Cable Properties to High Frequency
53

0.004

0.005

0.006

0.007

0.008

98

100

102

104

106

2x107 6x107 1x108

Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A

B 

A B 

C 

A 

B 

C 

2x107 6x107

 1x108

|Z0(T)|/l [S/m] 

ω (Hz)

ω (Hz)

Figure 31 High frequency characteristic impedance magnitude and phase spectra

extrapolated from low frequency spectra for cables with thermal aging to simulate 60

years of service at various temperatures

Next, the high frequency cable properties are determined by using the extrapolative approach,

which was discussed previously. The characteristic impedance and propagation function for the

cables aged to simulate 60 years of service are presented and discussed below. Similar analyses

were performed for the cables aged to simulate 20 years and 40 years of service, and these

results are presented in Appendix B.

The high-frequency characteristic impedance spectra were determined by extrapolating the lowfrequency spectra. Figure 31 presents the extrapolated high-frequency characteristic impedance

magnitude, *Z0(T)*, and phase, Q(T), spectra for cable specimens 26, 41 and 42. The limiting

value of the characteristic impedance magnitude (i.e., as T64) for the cables are as follows:

Specimen 26 (50oC): Z0(T64) = 77.42 S

Specimen 41 (60oC): Z0(T64) = 79.46 S

Specimen 42 (70oC): Z0(T64) = 75.12 S

Using Equation 5.1-1, each cables’ propagation function at high frequency was determined, as

shown in Figure 32. Examination of this figure shows that both the real and imaginary

components of the propagation function exhibit a number of oscillations, starting in the vicinity

of 10 MHz. These oscillations are a consequence of the extrapolative approach used, and do not

represent reality. Specifically, the impedance spectra are strong functions of the frequency in the

vicinity of the phase zero crossings. Thus, small differences between the actual characteristic
54

0.02

0.04

0.06

0.08

0.1

0.5

1.5

2.5

3.5

2x107 6x107 1x108

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A 

B 

C 

A 

B 

C 

2x107 6x107 1x108

ω ω (Hz) (Hz)

γ

i

(ω)

γ

r

(ω)

Figure 32 Imaginary and real components of the high frequency propagation

function determined from the extrapolated characteristic impedance for cables

with thermal aging to simulate 60 years of service at various temperatures

impedance and the extrapolated value give rise to these fictitious oscillations. Furthermore, as

the frequency increases, the differences between the actual and extrapolated values also increase. 

To mitigate the impact of these anomalies on the evaluations performed herein, the extrapolated

propagation function data used in the evaluations were restricted to values in the frequency range

from 1 MHz to 10 MHz. The results in this frequency range are reliable.

5.1.3 Detection of Localized Degradation on Cables

In this section, the use of BIS for detecting a localized area of degradation on a cable is

discussed. For purposes of this study, the localized area of degradation was simulated by

exposing a small section of a cable to elevated temperature in addition to the global thermal

aging applied to the cable. The cable specimens tested for this portion of the study are identified

in Table 6.

First, the high frequency impedance spectra for cables with and without hot-spots are compared

to demonstrate that localized damage does impact the cable’s impedance. This difference in

impedance spectra can be used to detect and locate localized degradation. The data presented

were obtained from BIS measurements on cables in the open configuration. Next, three tests are

presented that can be used to detect localized degradation. These tests do not provide absolute

values for cable properties; rather, the tests are based upon the differences between cables with

and without localized degradation.
55

5.1.3.1 Comparison of Impedance Spectra With and Without Localized Degradation

In this section, the impact of localized degradation on a cable’s impedance spectrum is

examined. The effect of degradation severity, size, and location are evaluated.

No. Specimen ID

Length

meters

(inches)

Service Life Simulated

(Global Aging)

Hot-Spot Simulated

Conditions Simulated/

Location on Cable (meters

from left end)

16. PNI-79-RB-188-816 10 (393.7) 20 @ 50oC (122oF) None

17. PNI-79-RB-188-817 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 60oC/8.0m to 9.0m

18. PNI-79-RB-188-818 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 60oC/8.0m to 8.5m

19. PNI-79-RB-188-819 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 70oC/8.0m to 9.0m

20. PNI-79-RB-188-820 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 70oC/8.0m to 8.5m

31. PNI-79-RB-188-831 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 90oC/8.0m to 9.0m

32. PNI-79-RB-188-832 10 (393.7) 20 @ 50oC (122oF) 20 yrs. @ 90oC/8.0m to 9.0m

21. PNI-79-RB-188-821 10 (393.7) 40 @ 50oC (122oF) None

22. PNI-79-RB-188-822 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 60oC/1.0m to 2.0m

23. PNI-79-RB-188-823 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 60oC/1.5m to 2.0m

24. PNI-79-RB-188-824 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 70oC/1.0m to 2.0m

25. PNI-79-RB-188-825 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 70oC/1.5m to 2.0m

33. PNI-79-RB-188-833 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 90oC/1.0m to 2.0m

34. PNI-79-RB-188-834 10 (393.7) 40 @ 50oC (122oF) 40 yrs. @ 90oC/1.5m to 2.0m

26. PNI-79-RB-188-826 10 (393.7) 60 @ 50oC (122oF) None

27. PNI-79-RB-188-827 10 (393.7) 60 @ 50oC (122oF) 60 yrs. @ 60oC/7.0m to 8.0m

28. PNI-79-RB-188-828 10 (393.7) 60 @ 50oC (122oF) 60 yrs. @ 60oC/7.0m to 7.5m

29. PNI-79-RB-188-829 10 (393.7) 60 @ 50oC (122oF) 60 yrs. @ 70oC/7.0m to 8.0m

30. PNI-79-RB-188-830 10 (393.7) 60 @ 50oC (122oF) 60 yrs. @ 70oC/7.0m to 7.5m

35. PNI-79-RB-188-835 10 (393.7) 60 @ 50oC (122oF) 60 yrs. @ 90oC/7.0m to 8.0m

36. PNI-79-RB-188-836 10 (393.7) 60 @ 50oC (122oF) 40 yrs. @ 90oC/7.0m to 7.5m

Table 6 Specimens tested to evaluate BIS for locating localized areas of thermal aging
56

1.4x107

300

600

80

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs]

ω [Hzs] 

1.8x107 2.2x107

1.4x107 1.8x107 2.2x10 A 7

B A 

B 

C 

C 

60

40

20

-20

-40

-60

700

500

400

200

100

Figure 33 Impedance magnitude and phase spectra over the frequency range of 14MHz

to 22MHz for cables with global thermal aging to simulate 60 years of service at 50oC,

plus additional thermal aging to simulate hot-spots of different severity

The impact of hot-spot severity was examined by comparing cables with simulated hot-spots

representing 60 years of exposure to thermal environments of 60oC and 70oC. The impedance

spectra for these cables were compared to each other, and to a cable with no hot-spot. Figure 33

presents the impedance magnitude and phase spectra over the frequency range of 14MHz to

22MHz for three cables; one with no hot-spot (curve A), one with a 1-meter hot-spot

representing 60 years at 60oC (curve B), and one with a 1-meter hot-spot representing 60 years at

70oC (curve C). Examination of this figure shows that the double peak structure present in the

impedance magnitude spectrum for the cable with no hot-spot (curve A) disappears when a hotspot is introduced onto the cable. Furthermore, the zero crossing of the impedance phase spectra

are shifted to lower frequencies when a hot-spot is present. In this case, the increase in

degradation severity from 60o (curve B) to 70oC (curve C) appears to have very little effect, as

shown by the very similar impedance spectra.

Figure 34 presents the impedance magnitude and phase spectra over the frequency range of

39MHz to 45MHz for the same three cables. As shown in this figure, a shift toward lower

frequencies is noted for both the magnitude and phase spectra when a hot-spot is present. In this

case, the increase in degradation severity from 60oC (curve B) to 70oC (curve C) is more

pronounced with the less severe degradation resulting in an impedance spectrum that is closer to

that of the baseline cable with no hot-spot (curve A). The hot-spot with more severe degradation

tends to shift the impedance spectrum to lower frequencies.
57

3.9x107

50

100

150

60

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

4.5x107 4.3x107 4.1x107

3.9x107

 4.5x107 4.3x107 4.1x107

40

20

-40

-60

A A 

B 

B 

C 

C 

Figure 34 Impedance magnitude and phase spectra over the frequency range of 39MHz

to 45MHz for cables with global thermal aging to simulate 60 years of service at 50oC,

plus additional thermal aging to simulate a hot-spot

These results demonstrate that the presence of localized degradation does impact the cable’s

impedance spectra. Further, the impedance spectrum appears to be sensitive to the severity of

the hot-spot degradation at higher frequencies. Thus, comparison of a cables’s broadband

impedance spectrum to that for a cable with a known condition may be useful as an indicator of

the presence and severity of a hot-spot.

The impact of hot-spot size was investigated by comparing cables with hot-spots of 0.5 meters

and 1.0 meters. Again, the cables are compared to each other, as well as to a cable with no hotspot. Figure 35 presents the impedance magnitude and phase spectra over the frequency range of

14MHz to 22MHz for three cables; one with no hot-spot (curve A), one with a 0.5-meter hotspot representing 60 years at 70oC (curve B), and one with a 1-meter hot-spot representing 60

years at 70oC (curve C). Examination of this figure shows that the increase in degradation size

from 0.5 meters (curve B) to 1.0 meters (curve C) appears to have very little effect, as shown by

the very similar impedance spectra.
58

1.4x107

600

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs]

ω [Hzs] 

A 

A 

B 

B 

C 

C 

400

200

80

60

40

20

-20

-40

1.8x107

 2.2x107

1.4x107

 1.8x107 2.2x107

Figure 35 Impedance magnitude and phase spectra over the frequency range from

14MHz to 22MHz for cables with global thermal aging to simulate 60 years of service at

50oC, plus additional thermal aging to simulate hot-spots of different sizes

Figure 36 presents the impedance magnitude and phase spectra over the frequency range of

39MHz to 45MHz for the same three cables. As shown in this figure, the increase in degradation

size from 0.5 meters (curve B) to 1.0 meters (curve C) is more pronounced with the smaller hotspot resulting in an impedance spectrum that is closer to that of the baseline cable with no hotspot (curve A). The larger size hot-spot tends to shift the impedance spectrum to lower

frequencies.

These results demonstrate that a cable’s impedance spectrum appears to be sensitive to the size

of the hot-spot at higher frequencies, as reflected by a shift to lower frequencies as the hot-spot

size increases. Thus, comparison of a cables’s broadband impedance spectrum to that for a cable

with a known condition may be useful as an indicator of the size of a hot-spot.

Finally, the impact of hot-spot location on a cable’s impedance spectrum was examined. This

testing was performed using a cable with a simulated 1-meter long hot-spot representing 60 years

at 70oC located from 8.0 to 9.0 meters from the left end of the cable. The cable’s impedance was

measured twice; once with the point of measurement (POM) at the left end of the cable, and once

with the POM at the right end of the cable. This effectively yielded impedance spectra for a hotspot located 8.0 to 9.0 meters from the POM, and for a hot-spot located 1.0 to 2.0 meters from

the POM. These measurements were compared to each other, as well as to the impedance

spectrum from a cable with no hot-spot.
59

3.9x107

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

A 

A 

B B 

C C 

60

40

20

-40

50 -20

150

125

100

75

4.1x107 4.3x107

175

4.5x107

3.9x107 4.1x107 4.3x107

 4.5x107

Figure 36 Impedance magnitude and phase spectra over the frequency range of 39MHz

to 45MHz for cables with global thermal aging to simulate 60 years of service at 50oC,

plus additional thermal aging to simulate hot-spots of different sizes

Figure 37 presents the impedance magnitude and phase spectra over the frequency range of

14MHz to 22MHz for three cases; one with no hot-spot on the cable (curve A), one with a

1.0-meter hot-spot representing 60 years at 70oC located 8.0m to 9.0 m from the POM (curve B),

and one with a 1-meter hot-spot representing 60 years at 70oC located 1.0m to 2.0m from the

POM (curve C). Examination of this figure shows that the location of the hot-spot does impact

the impedance spectrum for the cable. With the hot-spot located close to the POM (curve B), the

two peak structure observed for the cable with no hot-spot (curve A) is not present. Also, the

maxima for the impedance magnitude, and the zero crossing for the impedance phase are shifted

to a lower frequency. With the hot-spot farther from the POM (curve C), the two peak structure

is still present; however, the impedance magnitude and phase zero crossing are also shifted to a

lower frequency.

Figure 38 presents the impedance magnitude and phase spectra over the frequency range of

39MHz to 45MHz for the same three cables. As shown in this figure, a consistent trend is not

readily apparent since the impedance spectra for the case in which the hot-spot is farther from

the POM (curve C) is very similar to the base line cable with no hot-spot (curve A), while that

for the case in which the hot-spot is close to the POM (curve B) shows a shift toward lower

frequencies.

These results demonstrate that the location of a hot-spot also impacts the cable’s impedance

spectrum as evidenced by a shift in the spectrum to lower frequencies. The data suggest that the

closer the hot-spot is to the POM, the greater is the impact on the measured impedance.
60

1.4x107

600

80

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

ω [Hzs]

ω [Hzs] 

A 

A 

B B 

C 

C 

400

200

1.8x107

 2.2x107

1.4x107

 1.8x107 2.2x107

60

40

20

-40

-20

No Hot Spot 

C 

70 oC (158 oF) Hot Spot at 1.0m-2.0m from POM 

70 oC (158 oF) Hot Spot at 8.0m-9.0m from POM 

A 

B 

Figure 37 Impedance magnitude and phase spectra over the frequency range from

14MHz to 22MHz for cables with global thermal aging to simulate 60 years of service at

50oC, plus additional thermal aging to simulate hot-spots at different locations

3.9x107

150

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) Hot Spot at 1.0m-2.0m from POM 

70 oC (158 oF) Hot Spot at 8.0m-9.0m from POM 

A 

B 

ω [Hzs] 

ω [Hzs] 

A 

A 

B 

B 

C 

C 

100

50

4.1x107

 4.3x107

60

40

20

4.5x10 -40 7

3.9x107

 4.1x107 4.3x107 4.5x107

Figure 38 Impedance magnitude and phase spectra over the frequency range from

39MHz to 45MHz for cables with global thermal aging to simulate 60 years of service at

50oC, plus additional thermal aging to simulate hot-spots at different locations
61

5.1.3.2 Numerical Tests for Detecting Localized Degradation

In this section three numerical tests that can be used to detect the presence of a hot-spot based on

measured impedance spectra are presented. These tests are 1) average dissipation, 2) zero

crossing location, and 3) zero crossing line spacing. Each of these tests are discussed below.

5.1.3.2.1 Average Dissipation Test

As demonstrated in the previous evaluation of impedance spectra for the thermally aged cables,

as the degradation on the cable increases, the cable’s conductance per Hertz also increases. 

Therefore, cables with a higher level of degradation are expected to show more dissipation when

the cable is subjected to an ac voltage. Since the presence of a hot-spot on a cable implies that

some portion of the cable was degraded more than the remainder of the cable, a cable containing

a hot-spot is expected to show more dissipation than a cable without a hot-spot. The phase

spectrum for the cable should reflect this increased dissipation by forcing the phase spectrum

further away from ±90°. This should be the case throughout the frequency range used to probe

the cable. However, since cable physics in the oscillatory region is dominated by wave

phenomena, the impedance phase is not expected to decrease at every discrete frequency when a

hot-spot is present on the cable. Rather, the average value of the absolute phase magnitude,

<*M(T)*>, should exhibit the aforementioned behavior and can be used as an indicator of the

presence of a hot-spot. This is defined by the following equation

5.1-7

In Equation 5.1-7, the integration is performed over the frequency range from T1=1MHz to

T2=100MHz since this is the range of frequencies over which the impedance is measured.

5.1.3.2.2 Phase Zero Crossing Frequency Test

Changes in the zero crossing frequencies of the impedance phase spectra are useful as indicators

of cable degradation. At high frequencies, the impedance phase is a strong function of the

propagation function phase since the characteristic impedance phase is essentially zero. 

Consequently, the frequencies at which the impedance phase zero crossings occur can be

determined by the following equation:

5.1-8

( ) ( )

Φ

Φ

ω

ω ω

ω

ω

ω

ω

ω ≡ ∫

∫

d

d

1

2

1

2

( ) () () γ ω

ω ω

i π

L C

n ≈ ≈ 1
62

From the low frequency impedance data presented previously, it was shown that the cable

inductance and capacitance increase with increasing degradation of the cable. Although that data

are restricted to the non-oscillatory region of the impedance spectrum, it is reasonable to assume

that this behavior extends to higher frequencies. Based on this assumption, it is expected that the

zero crossings of the impedance phase spectrum will exhibit a shift to lower frequencies when

the spectrum for a cable containing a hot-spot is compared to that for a cable without a hot-spot.

The impedance data presented previously showed that, in some cases, the cable’s impedance

spectra contain a double peak structure. Also, in some cases additional zero crossings occur. To

compare the various zero crossings between different spectra, it is desirable to average the

spectra over a range of frequencies as follows: 

5.1-9

where j=T±)T, and )T=1.30MHz.

5.1.3.2.3 Phase Zero Crossing Line Spacing Test

In the phase zero crossing line spacing test the sum of the spacing between zero crossings is

compared. The line spacing of the zero crossings is defined by the following equation:

5.1-10

where n is the zero crossing being evaluated, k is the total number of zero crossings in the

frequency interval of interest, Tn is the frequency of the nth zero crossing, and )Tmeas is the

frequency spacing between measured data points. For this study, measurements were taken at

2000 equally spaced data points over the frequency range from 100kHz to 100MHz; therefore,

)Tmeas = (100x106 - 0.1x106)/2000 = 49,950.

Figure 39 shows an example of the averaged impedance phase spectrum, <*M(T)*>, over the

frequency range from 100kHz to 100MHz. Examination of this figure shows that the frequency

increments between the individual zero crossings can be viewed as line spacings.

( ) ( ) Φ

Φ

∆

∆

∆

ω ∆

π π

π

ω ω

ω ω

ω ω

ω ω = −

+

−

+

∫

∫

d

d

( )

θ

ω ω

ω n

n n

n

k

meas

=

− −

=

∑ 1

2

∆
63

2x107

20 

40 

60

80 

<|Φ(ω)|> 

ω [Hz]

ω1

ω2

4x107

 6x107 8x107 1x108

Figure 39 Example of average impedance phase spectrum over

the frequency range from 100kHz to 100MHz for cable with

global thermal aging

5.1.3.2.4 Results of the Numerical Tests

Each of the three tests discussed above were applied to the cable test samples to determine their

effectiveness for detecting a hot-spot on a cable. Results for the cables with global thermal

aging to simulate 60 years of service are discussed below. Results for the cables with thermal

aging to simulate 20 years and 40 years of service are included in Appendix B.

First, the average of the phase magnitude was determined for each of the cables. Table 7

presents the results of this test, which compares the values for each of the cables aged to simulate

60 years of service, both with and without hot-spots. For this test, the frequency range was

restricted and included data from 7MHz to 100MHz since data measurements below 7MHz were

found to be unreliable. In the table the change in average impedance phase magnitude,

*<*M(T)*>, is determined by the following equation:

5.1-11 ( ) ( ) ( )

( ) δφω

φω φω

φ ω =

− B

B
64

where +*M(T)*,B represents the average impedance phase magnitude for the baseline cable and

+*M(T)*, represents the average impedance phase magnitude of the cable being tested.

Examination of Table 7 shows that 7 of the 8 cables with hot-spots had an average impedance

phase magnitude lower than that for the baseline cable without a hot-spot. These results support

the finding that the average dissipation of the cable decreases with increased degradation, thus

suggesting that the average dissipation test may be a useful indicator for detecting hot-spots. 

Next, the zero crossing frequencies are compared between the baseline cable with no hot-spot

(cable 26) and each of the cables with a hot-spot (cables 27 to 30). To make this comparison, a

matrix of zero crossing frequency differences is created using the following relationship:

5.1-12

where Tzc, n, 26 is the zero crossing frequency for the nth impedance phase zero crossing for cable

26 (baseline), Tzc, n, x is the zero crossing frequency for the nth impedance phase zero crossing for

cable x (x = 27, 28, etc. for cables with hot-spots), and )Tmeas is the frequency spacing between

measured data points, which for this study is 49,950Hz, as discussed previously. Positive

Cable Hot-spot

Temperature

Hot-spot

Size

Hot-spot

Location

<*N(T)*> * <*N(T)*>

26. None None None 37.0340 -

27A. 60oC (140oF) 1.0m 1.0m to 2.0m 36.7463 + 0.78%

27B. 60oC (140oF) 1.0m 8.0m to 9.0m 36.5958 + 1.18%

28A. 60oC (140oF) 0.5m 1.5m to 2.0m 36.1382 + 2.42%

28B. 60oC (140oF) 0.5m 8.5m to 9.0m 35.6967 + 3.61%

29A. 70oC (158oF) 1.0m 1.0m to 2.0m 36.7463 + 0.78%

29B. 70oC (158oF) 1.0m 8.0m to 9.0m 35.5958 + 3.88%

30A. 70oC (158oF) 0.5m 1.5m to 2.0m 36.8930 + 0.38%

30B. 70oC (158oF) 0.5m 8.5m to 9.0m 37.2820 - 0.67%

Table 7 Average impedance phase magnitude for cables with global thermal aging to simulate

60 years of service at 50oC, plus additional thermal aging to simulate hot-spots

∆

∆

ω

ω ω

ω zc n x

zc n zc n x

meas

, ,

,, ,, = 26 −
65

differences would indicate a downshift in frequency for the zero crossing for the cables with hotspots. The results are presented in Table 8.

Examination of Table 8 shows that there is no clear trend in the zero crossing frequencies. For

zero crossings 1, 3, 5, and 7 on the cables with hot-spots, each is either the same or downshifted

to a lower frequency relative to the baseline cable. For the higher zero crossings the results are

mixed with some showing a downshift and others showing a shift toward higher frequencies. 

These results suggest that this test may not be effective at detecting hot-spots.

Finally, the phase zero crossing line spacing test is applied to the cables with global thermal

aging to simulate 60 years of service. Again, each cable with a hot-spot is compared to the

baseline cable without a hot-spot. The results are presented in Table 9.

Examination of Table 9 shows that the line spacing for most of the cables with hot-spots is

smaller (positive change) than that for the baseline cable. These results support the finding that

the zero crossings occur closer together for cables with hot-spots. Therefore, the line spacing

test may be a useful indicator of the presence of hot-spots on cables.

Cable

Frequency Difference for Zero Crossing No.

1 3 5 7 9 11 13 15 17 19 21

27A 0 0 0 + 2 - 4 - 4 - 2 - 2 - 7 + 4 0

27B + 1 + 1 + 1 0 - 2 - 2 + 1 + 1 0 - 7 + 10

28A + 1 + 4 + 7 + 4 0 + 3 + 2 + 6 + 4 + 10 + 20

28B + 1 0 + 1 + 5 - 1 0 + 2 + 1 - 2 0 + 12

29A 0 0 0 + 2 - 4 - 4 - 2 - 2 - 7 + 4 0

29B + 1 + 1 + 1 0 - 2 - 1 + 1 + 1 0 - 7 + 10

30A + 1 + 2 + 3 + 6 + 2 + 1 + 7 + 5 + 7 + 1 + 19

30B + 2 + 3 + 6 + 5 + 7 + 7 + 8 + 11 + 4 + 22 + 25

Table 8 Differences in zero crossing frequencies between cable with no hot-spot (cable 26) and

cables with hot-spots (cables 27 to 30) at odd number zero crossings
66

5.1.4 Locating Localized Degradation on Cables

This section presents the results of research on the use of BIS to locate localized areas of

degradation, or hot-spots, on a cable. The cables shown in Table 6 were also used for this

portion of the research. First, the theory behind hot-spot location is discussed. Subsequently,

results from the application of this theory are presented.

5.1.4.1 Theory Behind Hot-spot Location in Thermally Aged Cables

The formation of a hot-spot in a thermally aged cable occurs when a segment of the cable is

exposed to higher temperatures than the other portions of the cable. This could occur, for

example, if the cable is routed near a hot steam line in the plant. Figure 40 presents a schematic

depicting a model for a two-conductor cable with a hot-spot. In this figure, “H” represents the

healthy portion of the cable exposed to normal operating conditions, and “D” represents the

damaged portion of the cable exposed to elevated temperature conditions (i.e., hot-spot). The

total length of the cable is denoted by l, and the length of the hot-spot is indicated by la to lb. 

The cable has a frequency dependent voltage applied to the two conductors represented by V(T).

Cable Line Spacing Percent Change from

Baseline Cable

26 (Baseline) 93.60 -

27A 93.60 0

27B 93.15 + 0.48%

28A 92.65 + 1.01%

28B 93.05 + 0.59%

29A 93.60 0

29B 93.15 + 0.48%

30A 92.70 + 0.96%

30B 92.45 + 1.23%

Table 9 Impedance phase zero crossing line spacing for cables with global thermal aging to

simulate 60 years of service, with and without hot-spots
67

D 

V(T) 

x=0 x=la x=lb x=l

H H 

Figure 40 Schematic model of a cable with a hot-spot

In Section 5.1, it was shown that aging degradation will alter the cable’s electrical properties. 

Furthermore, the cable’s characteristic impedance and propagation function depend upon the

severity of the degradation. To model this dependence, the following equation can be used:

5.1-13

where Z0,H(T) and (H(T) represent the cable’s characteristic impedance and propagation function

in the healthy portion of the cable, and Z0,D(T) and (D(T) represent the cable’s characteristic

impedance and propagation function in the damaged (hot-spot) portion of the cable.

In Section 5.1.2 of this report, models for the thermally aged cables were developed that can be

used to approximate the cable’s actual electrical properties. Specifically, models were developed

based on low frequency impedance data and were extrapolated to high frequencies. Equation

5.1-1 was then used to obtain the cable’s high frequency propagation function. Although the

model has the correct cable impedance, since it is built into the model, the extrapolated

characteristic impedance is an approximation of the real function; therefore, the propagation

function is also an approximation of the real function. To minimize the introduction of modeling

error into the evaluation, the modeling is limited to the frequency range from 1MHz to 10MHz. 

This is sufficient since the first three or four zero crossings of the impedance phase occur within

this frequency range.

The most direct method of determining a hot-spot location would be to invert equation 5.1-13

and solve for la and lb. However, inverting the equation yields a transcendental equation that

includes la and lb in a non-linear way. An easier method of locating a hot-spot is to calculate the

cable’s impedance using equation 5.1-13 based on assumed values of la and lb and compare the

result to the measured impedance. Based on the root mean square (rms) error between the value

predicted by the model and the measured value, new values of la and lb are chosen and the

process is repeated. The final hot-spot location is determined by minimizing the rms error.

() () () ( ) [ ] () ( ) [ ]

() () ( ) [ ] [ ] ( ) Z Z

Z Z

Z Z MODEL H

H H a D Db a

D H H b Db a

ω ω

ωγ ωγ

ω ωγ γ = −+ −+ −−

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪ 0

0 0

0 0

,

, ,

, ,

coth coth

coth tanh
68

The following process is used to determine a hot-spot location:

1. Measure the cable impedance

2. Calculate the cable impedance using equation 5.1-13 using an assumed hot-spot location

3. Compare the impedance predicted by the model with the measured value and calculate a

rms error

4. Based on the rms error, assume a new hot-spot location and repeat steps 2 and 3.

5. Repeat steps 2 through 4 until the rms error is minimized

In comparing the modeled impedance to the measured impedance, four different parameters are

calculated. These are defined by the following equations:

5.1-14

5.1-15

5.1-16

5.1-17

where NMODEL(T) and NMEASURED (T) are the predicted and measured values of the cable

impedance phase, ZMODEL (T) and ZMEASURED (T) are the predicted and measured cable impedance

magnitude, and <n, MODEL and <n, MEASURED are the predicted and measured frequency of the nth

impedance phase zero crossing, and 1 and S are parameters developed specifically to represent

the model accuracy.

The relationships defined by equations 5.1-14 to 5.1-17 are referred to as the “error functions”

since they represent the error between the cable’s properties predicted by the model to the actual

measured value. Each of the error functions is evaluated in making a determination as to the

correct location of a hot-spot.

The process for locating a hot-spot is demonstrated below for cable 29. This cable has a 1 meter

( ) ( ) ( )

( ) δφ ω φ ωφ ω

ω φ ω

ω

≡ −

=

=

∑ MODEL n MEASURED n

MEASURED n

MHz

MHz

n

n

1

10

( ) ( ) ( )

( ) δ ω

ω ω

ω ω

ω

Z

Z Z

Z

MODEL N MEASURED n

MEASURED n

MHz

MHz

n

n

≡ −

=

=

∑ 1

10

δ ω δφ ω ω Θ≡ + ( ) ( ) ( ) 2 2Z

δ

ν ν

ν ω

ω

Ω ≡ −

=

=

∑ n MODEL n MEASURED

n MEASURED

MHz

MHz

n

n , ,

,

1

10
69

2 4 6 8 10

0.010

0.015

0.020

<δΦ> <δ|Ζ|> 

X [m]

Actual position of the hot spot: 7m to 8m from the POM 

X [m]

2 4 6 8 10

0.020

0.025

0.030

0.015

Figure 41 Impedance phase and magnitude error functions for cable with thermal aging

to simulate a 1 meter hot-spot located 7.0 to 8.0 meters from the cable end representing

60 years of service at 70oC

hot-spot representing 60 years of service at 70oC (158oF). The hot-spot is located 7.0 to 8.0

meters from the left end of the cable. In this demonstration, the cable impedance point of

measurement is first taken at the left end of the cable (29A), then at the right end of the cable

(29B). Thus, one cable is used to demonstrate two hot-spot locations; namely, 7.0 to 8.0 meters

from the POM and 2.0 to 3.0 meters from the POM. In each case, a hot-spot location is assumed

and the error functions are calculated. The results are plotted as a function of length along the

cable to facilitate the identification of maxima and minima.

Figures 41 presents the results of the impedance phase error function calculations, <*M(T)>, and

impedance magnitude, <**Z(T)*>, for cable 29A as a function of distance along the cable. 

Examination of this figure shows that the impedance phase error has an absolute minimum at

6.0 meters, while the impedance magnitude also has an absolute minimum at 6.0 meters. These

minima are relatively close to the actual hot-spot location of 7.0 to 8.0 meters from the POM.

Figures 42 presents the results of the error function calculations, <*1(T)>, and zero crossing

frequency change, <*S>, for cable 29A as a function of distance along the cable. Examination

of this figure shows that <*1(T)> has an absolute minimum at 6.0 meters, while the zero

crossing frequency change, <*S>, has an absolute minimum at 5.0 to 7.0 meters. Again, these

minima are relatively close to the actual hot-spot location of 7.0 to 8.0 meters from the POM.
70

0.015

0.020

0.025

0.002

0.004

0.006

0.008

2 4 6 8 10

<δΘ> <δS> 

X [m]

Actual position of the hot spot: 7m to 8m from the POM 

X [m]

2 4 6 8 10 

0.010

Figure 42 Impedance phase zero crossing error functions for cable with thermal aging to

simulate a 1.0 meter hot-spot located 7.0 to 8.0 from the cable end representing 60 years

of service at 70oC

2 4 6 8 10

0.02

0.03

0.04

<δΦ> <δ|Ζ|> 

X [m]

Actual position of the hot spot: 2m to 3m from POM 

X [m]

2 4 6 8 10 

0.02

0.03

0.04

Figure 43 Impedance phase and magnitude error functions for cable with thermal aging

to simulate a 1 meter hot-spot 2.0 to 3.0 meters from the end of the cable representing 60

years of service at 70oC

From an evaluation of the four error functions obtained for this cable, a hot-spot location of 5.0

to 7.0 meters from the POM would be predicted. This is in excellent agreement with the actual

hot-spot location of 7.0 to 8.0 meters from the POM.

Figures 43 presents the results of the impedance phase error function calculations, <*M(T)>, and

impedance magnitude, <**Z(T)*>, for cable 29B as a function of distance along the cable. 

Examination of this figure shows that the impedance phase error has an absolute minimum at 4.0

meters, while the impedance magnitude has an absolute minimum at 3.0 meters. These minima

are relatively close to the actual hot-spot location of 2.0 to 3.0 meters from the POM.
71

0.015

0.025

0.030

0.002

0.004

0.006

0.008

2 4 6 8 10

<δΘ> <δS> 

X [m]

Actual position of the hot spot: 2m to 3m from the POM 

X [m]

2 4 6 8 10 

Figure 44 Impedance phase zero crossing error functions for cable with thermal aging to

simulate a 1 meter hot-spot located 2.0 to 3.0 meters from the end representing 60 years

of service at 70oC

Figures 44 presents the results of the error function calculations, <*1(T)>, and zero crossing

frequency change, <*S>, for cable 29B as a function of distance along the cable. Examination

of this figure shows that <*1(T)> has an absolute minimum at 3.0 meters, while the zero

crossing frequency change, <*S>, has an absolute minimum at 2.0 meters. Again, these minima

are relatively close to the actual hot-spot location of 2.0 to 3.0 meters from the POM. It is also

noted that <*S> has a second minima at 7.0 meters; however, based on the other error function

minima, this one is seen to be inconsistent and can be eliminated.

From an evaluation of the four error functions obtained for this cable, a hot-spot location of 2.0

to 4.0 meters from the POM would be predicted. Again, excellent agreement with the actual hotspot location of 2.0 to 3.0 meters from the POM is obtained. Additional examples of hot-spot

location are included in Appendix B.

5.2 Application of BIS to Cables with Attached Loads

When cables are monitored in a nuclear power plant environment it is very likely that they will

be connected to a piece of equipment. Rather than disconnect the cable from the equipment, it

would be desirable to monitor the cable as installed. To determine the impact of attached loads

on the BIS method, tests were performed with a load attached to the test cables to determine if

degradation can be detected and located without disconnecting the cable. The results are

reported in this section.
72

5.2.1 Test Specimens Used for Testing with Attached Loads

For this portion of the research the cable test specimens presented in Table 10 were used. 

Two different loads were used for these tests; 1) a small induction motor, and 2) a solenoid coil. 

Both loads have very broad impedance spectra and produced very similar results. Therefore,

most of the testing was focused on the motor and those results are reported herein. The results

apply equally well to the coil or any load that has a capacitance and inductance in parallel. The

combination of test cable with load attached is referred to as the “cable system” in the following

discussion.

5.2.2 Low Frequency BIS Tests for Cables with Attached Loads

Impedance measurements were made on the cables alone in the open circuit configuration, and

with the load attached to determine their frequency response. The load used was a 1 Hp, 3-phase

ac induction motor. Figure 45 compares the low frequency impedance magnitudes for the cable

specimen with no hot-spot (Specimen 26), the load, and the cable system (cable connected to the

load). As shown, the impedance magnitude of the motor is less than that of the cable for

frequencies less than the crossing frequency, Tc, which is the point at which the impedance

curves cross (approximately 126kHz). As a result, most of the current will flow through the

motor and not through the cable’s capacitance. As the cable’s length increases, the crossing

frequency decreases. 

Figure 45 also shows that as the frequency increases, the magnitude of the cable’s impedance

magnitude continues to decrease as 1/T, whereas the cable system’s impedance magnitude

decreases as 1/(T-Tc)

2

. Once the load’s impedance is greater than the cable’s impedance, less

current flows through the motor and more flows through the cable’s capacitance. As a result, the

cable system’s impedance will be dominated by the physics of the cable.

No. Specimen ID Length

meters (inches)

Service Life

Simulated

Hot-Spot

Simulated

26. PNI-79-RB-188-826 10 (393.7) 60yrs. @ 50oC None

27. PNI-79-RB-188-827 10 (393.7) 60yrs. @ 50oC 60yrs. @ 60oC

29. PNI-79-RB-188-829 10 (393.7) 60yrs. @ 50oC 60yrs. @ 70oC

Table 10 Specimens tested to evaluate BIS for testing cables with attached loads
73

Figure 46 compares the impedance phase spectra for the cable, load, and cable system. As

shown, the motor’s impedance phase is nearly 90 degrees at 100Hz and gradually decreases until

100kHz, at which point it drops below 0 degrees. This behavior implies that the motor can be

viewed as a simple L-C circuit with the inductance and capacitance in parallel. It is noted that

the motor’s impedance phase has a zero crossing at 200kHz and that the cable system itself has a

zero crossing at 120kHz. Thus, at low frequencies the cable system’s impedance is heavily

dominated by the motor. However, the zero crossing of the impedance phase does react to the

presence of a hot-spot.

Figure 47 compares the impedance phase spectra of a cable system consisting of an aged cable

without a hot-spot connected to a load to that of a system consisting of an aged cable with a

hot-spot connected to a load. The severity of the hot-spot is varied. As shown, the presence of a

hot-spot does affect the system’s impedance in the region of the zero crossing, although the

effect is small. Specifically, the hot-spot decreases the frequency at which the cable system’s

impedance phase has a zero crossing. The more severe the hot-spot, the greater the downshift in

zero crossing frequency.

3.5 4 4.5 5 5.5 6 

3

4

5

Log10ω

Cable aged to 60yrs@50°C 

Motor alone 

Cable aged to 60yrs@50°C 

plus motor

Log10|Z(ω|

A

A

B

B

C

C

Figure 45 Comparison of measured impedance magnitude for cable with

and without an attached load
74

-75

-50

-25

25

50

Φ(ω)

3.5 4 4.5 5 5.5 6 

Log10ω

Cable aged to 60yrs@50°C

Motor alone 

Cable aged to 60yrs@50°C 

plus motor

A

A

B

B

C

C

Figure 46 Comparison of the impedance phase spectra for cables with and

without a load attached

5.065 

-5

-2.5

2.5

5

7.5

Φ(ω)

5.075 5.084 5.085 5.090 

Log10ω

System with no hot spot 

System with hot spot of 

60yrs@60°C 

System with hot spot of 

60yrs@70°C 

A

A

B

B

C

C

Figure 47 Comparison of impedance phase in the frequency range from 116kHz to

123kHz for cables with and without a load attached
75

0.2

0.4

0.6

0.8

1

1.2

δΦ(ω)

3.5 4 4.5 5 

Log10ω

System with hot spot of 

60yrs@60°C 

System with hot spot of 

60yrs@70°C 

5.5 6 

A

A

B B

Figure 48 Change in impedance phase for cable system with a hot-spot from

cable system without a hot-spot

Figure 48 presents the difference in the impedance phase between the cable system with the hotspot and the cable system without the hot-spot. As shown, the differences are localized to the

vicinity of the impedance phase zero crossing. Also, as the severity of the hot-spot increases, the

difference also increases. Therefore, an accurate model of the cable system impedance can be

used to examine the behavior of the impedance phase in the vicinity of the low frequency zero

crossings and this can be used as an indicator for the presence of a hot-spot on the cable’s

insulation.

5.2.3 High Frequency BIS Tests for Cables with Attached Loads

In evaluating the high frequency BIS measurements, the frequency averaged second derivative of

the impedance phase spectra was found to provide useful information for detecting hot-spots on

a cable connected to a load. Specifically, the zero crossings of this parameter were found be to

downshifted when the cable’s insulation contains a hot-spot.

The second derivative of the impedance phase, A(T), is developed as follows. At each

frequency Tn at which a measurement is taken, M(Tn) is the measured impedance phase. This

phase value is averaged over a frequency range of Tn ± n0, where n0 = 0.749625MHz (15

frequency steps) for this parameter. This averaged impedance phase is represented by the

following equation:
76

5.2-1

The second derivative of the impedance phase can then be developed as follows:

5.2-2

This is then averaged over a frequency range of Tn ± s0, where s0 = 1.22429MHz (25 frequency

steps) for this parameter to form the second derivative parameter as follows:

5.2-3

The parameter A(T) is the second derivative in frequency of the cable’s phase impedance. It is

observed that attached loads downshift the zero crossings of A(T). These zero crossings are

referred to herein as the “Detection Zero Crossings” (DZC). For a 10 meter cable, there are 14

DZCs between 1MHz and 100MHz.

The A(T) parameter was compared for the cable systems with and without a hot-spot. An

examination of the A(T) spectra showed that a frequency downshift occurs at all of the 14 DZCs

when a hot-spot is present on the cable. Figure 49 presents an example in which the A(T)

parameter is compared for the cable systems with and without a hot-spot in the vicinity of the

first DZC, which occurs at 11.4MHz. It is observed that a frequency downshift occurs when the

hot-spot is present. Similar results were found for the remaining DZCs. 

Figure 49 also shows that the location of the hot-spot relative to the point of measurement also

affects the zero crossing frequency. As shown, the farther the hot-spot is from the POM, the

greater the downshift in frequency of the zero crossing. Thus, in principle, a cable system’s

impedance phase spectra are sensitive to the location of the hot-spot.

( )

( )

0

m n

m -n

n m

n 2 n

0

0

∑

=

=

Φ +

Φ =

ω

ω

( ) ( ) ( ) ( ) n n 10 2 n n-10 Ω ω = Φ ω + - Φ ω + Φ ω

( )

( )

0

m s

m -s

n m

n 2 s

0

0

∑

=

=

Ω +

Π =

ω

ω
77

5.2.4 Phenomenological Models of Cables with Attached Loads

In this section a model for predicting the properties of a thermally aged cable with an attached

load is developed. The model is based on the phenomenological approach and, therefore, is

valid in the frequency range from 10Hz to 1MHz. Models are developed for the following two

cases:

• Thermally aged cable with no hot-spots and a load attached

• Thermally aged cable with a 1 meter hot-spot and a load attached

The first scenario modeled is shown schematically in Figure 50. The cable is 10 meters long and

has been thermally aged to simulate 60 years of service at 50oC (specimen 26). No hot-spots are

present on the cable, and a load is attached to the far end of the cable, represented by an

impedance, ZL(T). The cable system’s impedance, Zmodel(T), is given by the following equation:

5.2-4

-0.04 

-0.02 

0.02

Π(ω)

ω [Hz]

1.08x107

System with no hot spot 

System with 1m hot spot at

1 to 2 m from POM 

System with 1m hot spot at

8 to 9 m from POM 

1.12x107 1.14x107 1.16x107

A 

A 

B 

B 

C 

C 

Figure 49 Comparison of A(T) parameter in the vicinity of the first zero

crossing for cable systems with and without a hot-spot

() () ( ) ( ) [ ( ) ]

Z () () () Z Tanh [ ]l

Z Z Tanh l Z Z

0 L

L 0

Model 0

ω ω γ ω

ω ω γ ω

ω ω

+

+ =
78

V(ω) ZL(ω)

Cable

Load 

x = l 

Figure 50 Schematic of model for thermally aged cable with a load

attached

In Equation 5.2-4 Z0(T) and ((T) are the cable’s characteristic impedance and propagation

function, and ZL(T) is the impedance of the load.

In Section 5.1 phenomenological models were developed for thermally aged cables and the

characteristic impedance and propagation function were extracted from measured impedance

spectra using Equations 3.2-1a and 3.2-1b. Using that information and the measured impedance

of the load, the modeled impedance of the cable system can be constructed. The results are

shown in Figures 51 and 52, which compare the modeled versus measured impedance magnitude

and phase, respectively.

Figure 51 shows that in the frequency range from 100Hz to 1MHz, the modeled impedance

magnitude is within approximately 3% of the measured impedance magnitude. The error is

concentrated in the vicinity of the spectrum’s peak at approximately 126MHz. The model’s peak

is slightly downshifted relative to the measured peak.

Figure 52 shows that in the frequency range from 100Hz to 1MHz, the modeled impedance

phase spectra is within approximately 6% of the measured impedance phase. The error is

concentrated in the vicinity of the spectrum’s zero crossing at approximately 126MHz. The

model’s zero crossing is slightly downshifted relative to the measured zero crossing.

Figure 53 provides a comparison of the modeled and measured impedance magnitude and phase

for the cable system without a hot-spot.
79

500

1000

1500

2000

2500

3000

3.5 4 4.5 5 5.5 6 

Log10ω

Measured 

Predicted 

|Z(ω)|

B

A

B

A

Figure 51 Comparison of low frequency measured and predicted

impedance magnitude for a cable system with no hot-spots and an

attached load

-75

-50

-25

25

50

3.5 4 4.5 5 5.5 6 

Log10ω

Φ(ω)

Measured 

Predicted B

A

B

A

Figure 52 Comparison of low frequency measured and predicted impedance phase

spectra for a cable system with no hot-spots and an attached load
80

-40

-20

20

5.025 

3200 Log10ω

Φ(ω)

Measured 

Predicted B

A

B

A

⏐Z(ω)⏐

A

B

3000

2800

2600

5.075 5.125 5.175 

5.025 5.075 5.125 5.175 

Log10ω

Figure 53 Comparison of high frequency measured and predicted impedance magnitude

and phase for a cable system with a hot-spot and an attached load

ZL(ω)

x = lb

V(ω)

Cable

Hot-Spots Load 

x = la x = l 

Figure 54 Schematic of a cable system with a hot-spot and an attached

load

Next, the model for a cable system with a hot-spot is developed. This case is shown

schematically in Figure 54. The cable is 10 meters long and has been thermally aged to simulate

60 years of service at 50oC (specimen 29). A 1 meter hot-spot representing 60 years at 70oC is

present on the cable, and a load is attached to the far end of the cable, represented by an

impedance, ZL(T). 
81

500

1000

1500

2000

2500

3000

3.5 4 4.5 5 5.5 6 

Log10ω

Measured 

Predicted 

|Z(ω)|

B

A

B

A

Figure 55 Comparison of measured and modeled impedance

magnitude for cable system with a hot-spot and an attached load

Figure 55 compares the measured and modeled impedance magnitude for the cable system in the

frequency range from 1kHz to 1MHz. As shown, the model is within approximately 1% of the

measured impedance magnitude, indicating good agreement.

Figure 56 compares the measured and modeled impedance phase for the cable system in the

frequency range from 1kHz to 1MHz. As shown, the model is within approximately 1% of the

measured impedance phase, indicating good agreement. It is also observed that the modeled

impedance phase in the vicinity of the zero crossing is slightly larger than the measured peak and

is downshifted relative to the measured value.

Figure 57 provides a comparison of the modeled and measured impedance magnitude and phase

for the cable system with a hot-spot.
82

-75

-50

-25

25

50

3.5 4 4.5 5 5.5 6 

Log10ω

Φ(ω)

Measured 

Predicted B

A

B

A

Figure 56 Comparison of low frequency measured and modeled impedance

phase spectra for a cable system with a hot-spot and an attached load

-40

-20

20

5.02 

3200 Log10ω

Φ(ω)

Measured 

Predicted B

A

B

A

⏐Z(ω)⏐

A

B 3000

2800

5.06 5.10 5.14 

Log10ω

5.02 5.06 5.10 5.14 

Figure 57 Comparison of high frequency impedance magnitude and phase spectra for

cable system with a hot-spot and an attached load

5.2.5 Locating a Hot-Spot on a Cable with an Attached Load
83

2 4 6 8 

x (meters) 

0.15

0.05

0.10

0.20

Actual and 

Predicted 

Location 

<δΦ(x)> 

Figure 58 Prediction of hot-spot location for a cable system with a load

attached

Here, an approach is developed to locate the position of a hot-spot on a cable with an attached

load using the low frequency impedance spectrum. This work is based on the models developed

in the previous sections for a cable with an attached load. As a demonstration of the approach,

specimen 29 is used, which is thermally aged to simulate 60 years of service @ 50oC, and has a

1 meter hot-spot representing 60 years @ 70oC.

For this demonstration, the impedance phase spectrum in the vicinity of the zero crossing at

120kHz is focused on. The cable system’s impedance in the frequency range from 110kHz to

142kHz is calculated based on an assumed location of the hot-spot, and the relative difference

between the modeled phase and measured phase is calculated. Using an iterative procedure, the

assumed hot-spot location is incremented and the difference between measured and modeled

phase values is again calculated. The predicted hot-spot location is obtained when this

difference is a minimum. Figure 58 presents the results of the difference calculations as a

function of assumed hot-spot location. As shown, the hot-spot location is correctly predicted.

These results demonstrate that the low frequency BIS can be used to predict the location of a

hot-spot on a cable that has a load attached. Relatively good accuracy was demonstrated in the

example presented.

5.3 Application of BIS to Cables with Abrasion Damage

This section presents the results of testing performed to evaluate the use of the BIS method for
84

detecting and locating abrasion damage on cables. First, a discussion of the cables tested is

presented. Subsequently, results of tests performed at low frequency are discussed followed by

the results of tests performed at high frequency.

5.3.1 Abrasion Test Specimens

In this portion of the research, the cable test specimens shown in Table 11 were used.

Specimen 15 was used as the baseline representing a healthy cable with no aging or abrasion. 

On specimen 22, one of the conductors was abraded using a Dremel tool to grind the cable’s

insulation down to the bare metal conductor over a length of 2mm (0.08in.). On specimens 29

and 30, both conductors were abraded as previously described. A conductive contaminant was

applied to the abraded portion of specimen 30. In all cases, the abrasion was located in the

middle of the cable at 5m (196.85in.) from the end. The following four cases were studied:

• Case A: Unabraded cable

• Case B: Cable with one conductor abraded

• Case C: Cable with two conductors abraded

• Case D Cable with two conductors abraded and a conductive contaminant applied

to the abraded portion of the cable

Case D represents a typical scenario expected in a power plant since a number of contaminants

are commonly found on cables that have not been touched in many years. These contaminants

can absorb moisture and hold it near the cables resulting in a conductive pathway between cables

and ground. For this study, the contaminant used was a mixture of 85% Skydrol hydraulic fluid,

11% iron filings, and 4% carbon black powder. This mixture had as a jelly-like consistency and

was applied directly to the cables in the location of the abrasion. Figure 59 presents a schematic

of the four cases studied.

No. Specimen ID Length

meters (inches)

Service Life

Simulated

Hot-Spot

Simulated

15. PNI-79-RB-188-815 10 (393.7) None None

22. PNI-79-RB-188-822 10 (393.7) 40yrs. @ 50oC 40yrs. @ 60oC

29. PNI-79-RB-188-829 10 (393.7) 60yrs. @ 50oC 60yrs. @ 70oC

30. PNI-79-RB-188-830 10 (393.7) 60yrs. @ 50oC 60yrs. @ 70oC

Table 11 Specimens tested to evaluate BIS for detecting abrasion
85

BIS measurements were made by placing the test specimen in a humidity chamber so that the

temperature and humidity surrounding the cable could be controlled. Test leads were connected

to the cables by extending the cable ends through ports in the wall of the humidity chamber. 

Measurements were taken at various humidity levels while holding the temperature at 30oC

(86oF).

The BIS measurements were performed over two frequency ranges: 1) the low frequency or nonoscillatory range, which was 1kHz to 1MHz, and 2) the high frequency or oscillatory range,

which was 1MHz to 100MHz. In the non-oscillatory range, the measurements were performed

with the HP-5094 device, which provided data points at 401 discrete frequencies equally spaced

over the range. In the oscillatory region the measurements were made with the Eclypse

instrument, which provided data points at 2000 discrete frequencies equally spaced over the

range.

5.3.2 Evaluation of Low Frequency BIS Results on Cables with Abrasion

The impedance response of abraded cables in the low frequency range is evaluated in the

following sections.

5.3.2.1 Low Frequency Impedance Measurements on Abraded Cables

Figure 59 Schematic of four cases studied to evaluate BIS

for detecting and locating abrasion
86

3.5 4 4.5 5 5.5 6 

-89.6

-89.5

-89.4

-89.3

-89.2

-89.1

Φ(ω)

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

C 

B 

A 

Figure 60 Low frequency impedance phase spectra for cables with and

without abrasion exposed to an environment of 20% Relative Humidity

Figure 60 compares the measured impedance phase spectra for cables with and without abrasion

exposed to an environment of 20% relative humidity (RH). As shown, the abrasion does not

affect the cables’ impedance phase in the non-oscillatory frequency range.

Figure 61 compares the impedance phase spectra for cables with and without abrasion exposed

to an environment of 85% RH. As shown, when a higher level of humidity is present, all of the

phase spectra have a new structure; i.e., a peak in the vicinity of 5kHz to 10kHz. This structure

arises from the increased humidity level, which provides a conductive pathway for leakage

currents. It is also observed that the abraded cable’s peak is shifted to higher frequencies relative

to the unabraded cable. This frequency shift may be attributable to the fact that the averaged

dielectric function of the abraded cable is smaller than that for the unabraded cable. As a result,

any structures must occur at higher frequencies. It is further observed that there is no readily

observable difference between the phase spectra of the cables with one and two conductors

abraded.

It should be noted that, while the change in the low frequency impedance phase spectra can be

used to detect abrasion under high humidity levels, this may not be practical in a nuclear power

plant environment since the humidity levels may not be high enough to observe these changes. 

For example, the peaks previously discussed were not observed when BIS measurements were

made under conditions of 70% RH.
87

3.5 4 4.5 5 5.5 6 

-88.75

-88.50

-88.25

-87.75

-87.50

-87.25

-87.00 

Φ(ω)

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

A

B

C

Figure 61 Low frequency impedance phase spectra for cables with and

without abrasion exposed to an environment of 85% Relative Humidity

Next, the case in which a conductivity path is present in the vicinity of the abraded portion of the

cables is evaluated (Case D). Figure 62 compares the measured impedance magnitude for cables

with and without abrasion, including cables with abrasion and a conductive contaminant applied

to the cables. The environment was 85% RH for these measurements. As shown, at the low end

of the frequency range (1kHz) the impedance decreases from approximately 245S to 7000S

when the conductive contaminant is present. This is consistent with the loss of insulation, which

degrades the cable’s insulating capability.

Figure 63 presents the impedance phase spectra for the cables with and without abrasion and a

conductive contaminant. Again the environment is 85% RH. As shown, the impedance phase

near the low end of the frequency range increases from approximately -89.5 degrees to -16.7

degrees when the conductive contaminant is placed on the abraded portion of the cable. This

supports the concept that there is a conductivity path between the abraded conductors since the

impedance phase behaves more like a resistor (which has zero degree phase) than a capacitor

(which has a 90 degree phase).
88

3.5 4 4.5 5 5.5 6 

2.5

3.5

4

4.5

5

Log10 T

A 

B

C

Log10 Z(T) Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant 

D 

D 

Figure 62 Impedance magnitude for cables with and without abrasion plus a

conductive contaminant exposed to an environment of 85% RH

3.5 4 4.5 5 5.5 6 

-80

-70

-60

-50

-40

-30

-20

A B C Log10 T

M(T)

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

2mm abrasion on both conductors 

plus conductive contaminant 

D

D

Figure 63 Impedance phase spectra for cables with and without

abrasion plus a conductive contaminant exposed to an environment of

85% RH.
89

3.5 4.0 4.5 5.0 5.5 6 

120

140

160

180

200

0.5

1

1.5

2

2.5

|Ζ0(ω)| 

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A 

B C Log10 T

δ|Ζ0(ω)|

3.5 4.0 4.5 5.0 5.5 6 

B

C

Figure 64 Low frequency characteristic impedance magnitude for cables with and

without abrasion exposed to an environment of 85% RH 

Further examination of the previous two figures shows that, as the frequency increases, the effect

of the conductivity path on the cable’s properties decreases to the point where all of the

impedance spectra converge. This implies that the micro-processes taking place are slow; i.e.,

on the order of milli-seconds, which is reasonable since the contaminant used contained iron

particles.

5.3.2.2 Low Frequency Models of Abraded Cables

A phenomenological approach was used to model the characteristic impedance and propagation

function for abraded cables. First, the characteristic impedance and propagation function for

cables with abrasion only were extracted from the low frequency impedance measurements made

at 85% RH. Figure 64 presents the magnitude of the characteristic impedance for each of the

cables with and without abrasion. The difference from the unabraded case is also presented for

each abraded cable. As shown, the differences are very small (on the order of 1S to 2S or less).

Figure 65 presents the characteristic impedance phase spectra for cables with and without

abrasion exposed to an environment of 85% RH. The change from the baseline (unabraded) case

is also presented. Again, the changes are very small ( on the order of ±2 degrees or less).
90

-35

-30

-25

-20

-15

-10

-5

-0.2

-0.1

0.1

0.2

Ψ(ω) δΨ(ω)

3.5 4.0 4.5 5.0 5.5 6 

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A 

B 

C 

Log10 T

3.5 4.0 4.5 5.0 5.5 6 

B

C

Figure 65 Low frequency characteristic impedance phase spectra for cables with and

without abrasion exposed to an environment of 85% RH

Figures 66 and 67 present the imaginary and real components of the propagation function for

each of the cables with and without abrasion. The difference from the unabraded case is also

presented for each abraded cable. As shown, the differences are very small (on the order of 1%

to 2% or less).

It should be noted that, while the parameter changes are on the order of 1% to 2%, only 0.02% of

the cable’s insulation was removed in these tests. Thus, the measured changes are two orders of

magnitude greater than the amount of insulation removed.

Next, the cables’ electrical properties were extracted from the measured low frequency

impedance spectra. Figure 68 compares the cables’ capacitance with and without abrasion

exposed to an environment of 85% RH. The relative change from the baseline (unabraded) case

is also presented. It is observed that the changes are on the order of 2%.

Figure 69 compares the cables’ conductance with and without abrasion exposed to an

environment of 85% RH. The relative change from the baseline (unabraded) case is also

presented. It is observed that the changes are relatively large; on the order of 15%.

It is noted that abrasion of a small portion of a cable’s insulation cannot by itself change the

cable’s electrical and material properties. However, abrasion down to the metallic conductor of

a cable allows the environment to enter the cable’s insulation and degrade its insulating

capabilities. Specifically, humidity can moisten the insulation and increase its dielectric

function. Also, humidity can form a weak conductivity path between the conductor and ground. 

This behavior would not occur when the humidity is low.
91

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.001

-0.0008

-0.0006

-0.0004

-0.0002

γ

i

(ω)

3.5 4.0 4.5 5.0 5.5 6 

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A 

B

C

Log10 T

3.5 4.0 4.5 5.0 5.5 6 

B 

C 

δγ

i

(ω)

Figure 66 Imaginary component of the low frequency propagation function for cables

with and without abrasion exposed to an environment of 85% RH 

0.002

0.004

0.006

0.008

-0.0002

-0.00015

-0.0001

-0.00005

γ

r

 (ω)

3.5 4.0 4.5 5.0 5.5 6 

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A 

B

C

Log10 T

3.5 4.0 4.5 5.0 5.5 6 

B 

C 

δγr

 (ω)

Figure 67 Real component of the low frequency propagation function for cables with and

without abrasion exposed to an environment of 85% RH
92

4.1x10-9

0.005

0.01

0.015

0.02

C(ω)/l [F/m] 

4.0 5.0 6.0

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A B

Log10 T

3.5 4.5 5.5 

B C 3.8x10-9

3.6x10-9

δC(ω)

4.0 5.0 6.0

Figure 68 Capacitance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion exposed to an environment of

85% RH

1.8x10-10

G(ω)/ ω−l (mho-sec/m) 

Log10 T

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

A 

B 

Log10 T

3.5 4.5 5.5 

B 

C

4.0 5.0 6.0 

3.5 4.5 5.5 4.0 5.0 6.0

0.1

-0.1

-0.2

δG(ω)/ ω−l

1.4x10-10

1.0x10-10

Figure 69 Conductance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion exposed to an environment of

85% RH
93

200

-0.8

-0.6

-0.4

-0.2

|Ζ0(ω)| [S] Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A 

D Log10 T

3.5 4.5 5.5 

D 

4.0 5.0 6.0

3.5 4.5 5.5 4.0 5.0 6.0

150

100

δ|Ζ0(ω)| [S]

Figure 70 Low frequency characteristic impedance magnitude for cables with and

without abrasion plus a conductive contaminant exposed to an environment of 85% RH 

Next, models for cables with both abrasion and a conductive contaminant are developed. The

characteristic impedance, propagation function, and electrical properties can be calculated based

on two scenarios, as follows:

1. Assume the cable is degraded uniformly along its entire length

2. Assume an interaction between the abraded cable conductors, localized at the

point where the conductive contaminant was placed

Since the actual phenomena can best be described as a composite of the above two scenarios,

two models were developed; 1) a spatially averaged degradation model, and 2) a localized cable

interaction model. These models are presented below.

For the spatially averaged cable degradation model, a phenomenological approach is used to

extract the cable’s characteristic impedance, propagation function, and electrical properties from

measured impedance data. Here, the extracted cable parameters represent the quantities spatially

averaged over the length of the cable.

Figure 70 presents the magnitude of the characteristic impedance for each of the cables with and

without abrasion plus a conductive contaminant. The difference from the unabraded case is also

presented for each abraded cable. As shown, the addition of a conductive contaminant greatly

decreases the magnitude of the cable’s characteristic impedance at low frequencies (on the order

of 80%). As the frequency approaches 1MHz, the magnitude of the characteristic impedance for

the cables with and without abrasion merge, as expected.
94

Ψ(ω) δΨ(ω)

20

Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A 

D 

Log10 T

3.5 4.5 5.5 

D

4.0 5.0 6.0 

3.5 4.5 5.5 4.0 5.0 6.0

10

-10

-20

-30

-10

-20

-30

Figure 71 Low frequency characteristic impedance phase spectra for cables with and

without abrasion plus a conductive contaminant exposed to an environment of 85% RH 

Figure 71 presents the characteristic impedance phase spectra for cables with and without

abrasion plus a conductive contaminant exposed to an environment of 85% RH. The difference

from the baseline (unabraded) case is also presented. As shown, the characteristic impedance

phase is significantly changed by the presence of a conductivity path. Specifically, the change in

phase, *Q(T), approaches zero as the frequency approaches 1MHz.

Figures 72 and 73 present the imaginary and real components of the propagation function for

each of the cables with and without abrasion plus a conductive contaminant. The difference

from the unabraded case is also presented for each abraded cable. As shown, the imaginary

component of the propagation function increases when a conductive path is present. Again, the

larger changes occur at the very low frequencies (1kHz) and as the frequency increases the

change approaches zero. Similarly, the real component increases by a factor as large as eight at

the low frequencies when the conductive path is present. These results clearly show that the

cable is very dissipative and is on the verge of shorting out.

An examination of the cables resistance and inductance show that these properties show little or

no change in the presence of a conductive path. However, the cable insulation’s dielectric

function (averaged over the length of the cable) is greatly changed by the conductive path. 

Figure 74 compares the cables’ capacitance per unit length with and without abrasion plus a

conductive contaminant exposed to an environment of 85% RH. The relative change from the

baseline (unabraded) case is also presented. It is observed that at low frequencies, the cable’s

capacitance per unit length increases by a factor of approximately eight when the conductive

path is present. This difference approaches zero as the frequency approaches 1MHz.
95

0.35

0.2

γ

i

(ω)

Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A

D

Log10 T

3.5 4.5 5.5 

D

4.0 5.0 6.0 3.5 4.5 5.5 4.0 5.0 6.0

0.25

0.15

0.05

0.4

0.6

0.8

δγ

i

(ω)

Figure 72 Imaginary component of the low frequency propagation function for cables

with and without abrasion plus a conductive contaminant exposed to an environment of

85% RH 

0.035 8

γ

r

(ω)

Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A

D

Log10 T

3.5 4.5 5.5 

D

4.0 5.0 6.0 3.5 4.5 5.5 4.0 5.0 6.0

0.025

0.015

0.005

7

6

5

4

δγ

r

(ω)

Figure 73 Real component of the low frequency propagation function for cables with and

without abrasion plus a conductive contaminant exposed to an environment of 85% RH 
96

3.0x10-8

8

δC (ω) 

Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A 

D 

Log10 T

3.5 4.5 5.5 

D

4.0 5.0 6.0 

3.5 4.5 5.5 4.0 5.0 6.0

2.0x10-8

1.0x10-8

C (ω)/l [F/m] 

6

4

2

Figure 74 Capacitance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion plus a conductive

contaminant exposed to an environment of 85% RH

Figure 75 compares the cables’ conductance per unit length with and without abrasion plus a

conductive contaminant exposed to an environment of 85% RH. The relative change from the

baseline (unabraded) case is also presented. It is observed that at low frequencies, the cable’s

conductance increases by a factor of approximately 1,000 or more when the conductive path is

present. This difference approaches a factor of eight as the frequency approaches 1MHz.

For the localized cable interaction model, the conductivity path is viewed as a point structure in

which current can flow from one conductor to the other at a specified point located in the area of

the abrasion. Thus, it is assumed that the cable is not degraded throughout its entire length; only

a small region is degraded and this is approximated by a point at the location of the conductive

contaminant. Furthermore, it is assumed that the cable interaction that arises from the

conductive contaminant can be represented by a localized impedance, Zc(T), located at a point in

the cable where the conductive contaminant was placed. This model is depicted in Figure 76.
97

2.0x10-8

100

G(ω)/ω−l [mho-sec/m] 

Log10 T

Unabraded 

2mm abrasion on both conductors 

plus a conductive contaminant

A 

D 

A 

D 

Log10 T

3.5 4.5 5.5 

D

4.0 5.0 6.0

3.5 4.5 5.5 4.0 5.0 6.0

6.0x10-8

1.0x10-7

1.4x10-7

δG(ω)

300

500

700

Figure 75 Conductance per unit length extracted from measured low frequency

impedance spectra for cables with and without abrasion plus a conductive

contaminant exposed to an environment of 85% RH

Z0(ω), γ(ω)

Total current I(ω)

Current flowing in the conductivity path Ic(ω)

Current flowing in the cable after the conductivity 

Z0(ω), γ(ω)

Z0(ω), γ(ω) Z0(ω), γ(ω)

V(ω) Zc(ω)

Z0(ω), γ(ω) Cable baseline parameters

 lc

 l

Figure 76 Schematic of the localized cable interaction model for abraded

cables plus a conductive contaminant
98

(ω) (ω) (ω) cable C I = I + I

Figure 77 Schematic representation of abraded cable with a conductive

path between conductors

( ) ( ) ( )

() () ω ω

ω ω

ω

cable C

cable C

Load Z Z

Z Z Z

+ =

In this model, the current flowing in the cable is separated into two different components, as

follows:

5.3-1

where I(T) is the total current flowing in the cable, Ic(T) is the current that flows through the

localized impedance Zc(T), and Icable is the remaining current that continues to flow in the cable

after the localized area of abrasion. Therefore, the impedances due to the localized interaction,

Zc(T), and the cable length after the abraded point, Zcable(T), are in parallel with each other. This

can be modeled by treating the portion of cable after the conductivity path as a load, as shown in

Figure 77. Here, lc is the distance from the cable end to the abraded portion of the cable, and the

load represents the portion of cable after the conductivity path. The impedance of the portion of

the cable represented by the load, Zcable(T), is determined by the following equation:

5.3-2

where l represents the length of the whole cable. In this equation it is assumed that the system is

in the open configuration. It should be noted that, if the impedance of the conductive path is less

than that for the remainder of the cable, the current will short through the conductive path.

The total impedance for the load is represented by the following equation:

5.3-3

Z Z Coth cable c ( ) ( ) ( )( ) ω ω γω = − 0 [ ]
99

The impedance for a system consisting of a cable connected to a load is represented by the

following equation:

5.3-4

Thus, using the measured impedance for Zmodel(T), and the above equations, the impedance of the

conductive path, Zc(T), can be determined. Figure 78 presents the frequency dependence of the

magnitude of Zc(T) in the frequency range from 1kHz to 1MHz for cables with abrasion and

various locations of a conductive path between conductors. As shown, there is no significant

difference in the impedance for the different locations. Therefore, in the non-oscillatory region,

the modeled impedance, Zmodel(T), is essentially independent of the point at which the conductive

path is located, and it decreases with increasing frequency.

It is noted from equations 5.3-2 that Zcable(T) depends on its location on the cable, (l - lc). This is

physically reasonable since, in this region of the frequency spectrum, the electrical waves that

are used to probe the cable’s impedance have wavelengths that are much larger than the cable’s

length. However, the currents that flow in the cable and the conductivity path depend upon the

relative size of the impedances of these two paths. Furthermore, the cable’s total impedance

should react to the location of the conductivity path. This is discussed below.

() () ( ) ( ) [ ( ) ]

() () () [ ] l

l

Z Z Tanh

Z Z Tanh Z Z

0 Load

Load 0

Model 0

ω ω γ ω

ω ω γ ω

ω ω

+

+ =

3.5 4 4.5 5 5.5 6 

7000

|ZC(ω)|

Log10 ω

1 

zc= 0.0m 

2 

3 

4 

5 

zc= 2.5m 

zc= 5.0m 

zc= 7.5m 

6000 zc= 10.0m

5000

4000

3000

1 2 

3 4 

5 

Figure 78 Impedance magnitude of conductivity path for abraded cable

with conductive path between conductors at various locations
100

4 

5 

6 

7 

8 

3.5 4 4.5 5 5.5 6 

Log10 ω

A 

zc= 0.0m 

B 

C 

D 

E 

zc= 2.5m 

zc= 5.0m 

zc= 7.5m 

zc= 10.0m 

Log10 Z(ω) F 

G 

Interaction 

Impedance 

Total 

Impedance 

A B C D 

E 

G F 

Figure 79 Comparison of magnitude for total impedance, interaction

impedance, and conductivity path impedance for abraded cable with a

conductivity path at various locations

Figure 79 compares the impedances of the conductivity path and the cable as a function of

frequency for the case in which the location of the conductivity path varies. As shown, at very

low frequencies, the magnitude of Zcable(T) is two to three orders of magnitude larger that ZC(T) 

for all locations on the cable. Thus, for frequencies below 1kHz, most of the current flows

through the conductivity path and the total impedance is the same as ZC(T). At higher

frequencies ZC(T) approaches Zcable(T), depending upon the frequency and location of the

conductivity path; therefore, more current flows through the cable and less through the

conductivity path. In this region, the total impedance approaches Zcable(T). At frequencies near

1MHz, ZC(T) becomes larger than Zcable(T), and little current flows through the conductivity

path; therefore, the total impedance merges with the impedance Zcable(T).

Figure 80 presents the frequency dependence of the impedance phase for the conductivity path,

>(T), in the frequency range from 1kHz to 1MHz, along with the impedance phase for the total

impedance, M(T), and the impedance phase of Zcable(T), 0(T). As shown, at low frequencies

where most of the current flows through the conductivity path, M(T) is approximately equal to

>(T). As the frequency increases, M(T) approaches 0(T). This is to be expected since the ion

particles cannot follow the probe frequency and, therefore, less current flows in the conductivity

path. Also, if ZC(To) # Zcable(To), where To is the operating frequency of the system, a significant

portion of the current will flow through the conductivity path and the cable will short.
101

3.5 4 4.5 5 5.5 6 

-80

-60

-40

-20

η(ω)

ξ(ω)

Φ(ω)

Log10 T

Figure 80 Comparison of conductivity path impedance phase,

>(T), cable impedance phase, 0(T), and total impedance phase,

M(T), for abraded cable with a conductivity path

5.3.3 Evaluation of High Frequency BIS Results on Cables with Abrasion

This section presents the results of BIS testing in the high frequency range (1MHz to 100MHz)

for abraded cables. The same cable test specimens used for the low frequency testing were used

for this portion of the research. Phenomenological models of the abraded cables are presented

that can be used at high frequency, and are the basis for detecting abrasion on cables. An

approach for locating abrasion on cables is also presented.

5.3.3.1 High Frequency Impedance Measurements on Abraded Cables

The open configuration impedance was measured for each of the cables using the Eclypse

instrument, as discussed previously. Figure 81 presents the averaged high frequency impedance

magnitude and phase spectra for cables with and without abrasion exposed to an environment of

85% RH. The impedance spectra were averaged over a frequency range of ±800MHz to remove

small structures in the spectra associated with additional zero crossings. These small structures

would prevent an accurate analysis of the spectra. As shown, small but significant changes

occur in the impedance spectra when abrasion is present on the cable.
102

2x107

100

300

500

700

-75

-50

-25

25

50

75

|Ζ(ω)| Φ(ω)

ω (Hz)

A 

B C 

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant 

D 

D

4x107 6x107 8x107

ω (Hz)

2x107 4x107 6x107 8x107

Figure 81 Comparison of high frequency impedance magnitude and phase

spectra for cables with and without abrasion

Figure 82 shows an expanded view of the high frequency impedance magnitude and phase for

the frequency range from 8.4 MHz to 9.6 MHz, in the vicinity of the first zero crossing. As

shown, the phase zero crossing and the first maxima of the impedance magnitude are shifted to a

higher frequency when the cable is abraded. The largest change is observed for the case in

which the abrasion is covered by a conductive contaminant, thus establishing a conductivity

path.

Figure 83 shows an expanded view of the high frequency impedance magnitude and phase for

the frequency range from 64 MHz to 65.5 MHz. As shown, the phase zero crossing and the

maxima of the impedance magnitude are again shifted to a higher frequency when the cable is

abraded. The changes in this region of the spectra are larger than those in the vicinity of the first

zero crossing. This implies that a small portion of the process remains that is due to the iron

particles in the contaminant. It is noted that the frequency shift in the zero crossing of the cable

with one conductor abraded is larger than that for the cable with both conductors abraded. Thus,

there is no simple pattern in these spectra.
103

Φ(ω)

-40

-20

20

40

60

650

700

750

8.4x106

|Ζ(ω)|

ω (Hz)

A B 

C 

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant 

D 

D 

ω (Hz)

D

8.8x106 9.2x106

8.4x106 8.8x106 9.2x106

Figure 82 Comparison of high frequency impedance magnitude and phase spectra for the

frequency range from 8.4 MHz to 9.6MHz for cables with and without abrasion

Φ(ω)

260

6.46x107

|Ζ(ω)|

B

C 

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus contaminant

D 

D 

ω (Hz)

D

6.48x107 6.52x107 6.54x107

270 

280 

A 

B

C

A

30

20

10

-10

6.46x107 6.48x107 6.52x107 6.54x107

ω (Hz)

Figure 83 Comparison of high frequency impedance magnitude and phase spectra in the

frequency range from 64MHz to 65.5MHz for cables with and without abrasion
104

5.3.3.2 High Frequency Phenomenological Models of Abraded Cables

In Section 5.2 the propagation function for thermally degraded cables was extracted from the

high frequency portion of the cable’s measured impedance by extrapolating the low frequency

characteristic impedance to higher frequencies. However, the extrapolated characteristic

impedance exhibited incorrect behavior due to its strong dependence on frequency in the vicinity

of 1MHz. While the extracted characteristic impedance is correct, its form does not lend itself to

extrapolation.

To model the high frequency response of abraded cables, the high frequency portion of the

characteristic impedance is approximated by a constant, z0, which is equal to the value of the

characteristic impedance at a frequency of 1MHz, Z0(T=106

). The resulting propagation

function is given by the following equation:

5.3-5

Figure 84 presents the extracted imaginary component of the propagation function for the cables

with and without abrasion. As shown, only small differences are noted when abrasion is present.

Examination of the real component of the propagation function reveals that, similar to the results

for cables with thermal degradation discussed in Section 5.2, the real component of the

propagation function exhibits large oscillations that are unphysical in nature and arise from the

approximation of the characteristic impedance. To overcome this anomalous behavior, the real

component of the propagation function is fitted to the following function:

5.3-6

where $ and 6 are fitting constants with the values shown in Table 12.

Figure 85 presents the real component of the propagation function for the cables based on

equation 5.3-6. As shown, the abraded cables are similar to the unabraded cables in terms of

dissipation; however, when the conductive contaminant is applied, the cable becomes much

more dissipative.

( ) γ ω

ω

( ) = ⎡

⎣

⎢ ⎤

⎦

⎥ 1 −1

0 l

Coth

Z

z

open

γ ω β δω ( ) r = +
105

γ

i

(ω)

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant 

D 

30 

20 

10 

ω (Hz)

5 

15 

25 

4x107

 6x107 8x107 1x108

A

B

C

D 

Figure 84 Imaginary component of the high frequency

propagation function for cables with abrasion plus a conductive

contaminant

Case $ 6

A: Unabraded -0.00380219 0.0115745

B: One Conductor Abraded -0.00518014 0.0115005

C: Two Conductors Abraded -0.00552897 0.0116347

D: Two Conductors Abraded Plus

Conductive Contaminant

-0.00398439 0.0123597

Table 12 Fitting constants for equation representing the real component of

the high frequency propagation function for cables with abrasion plus a

conductive contaminant
106

γ

r

(ω)

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant 

D 

ω (Hz)

0.5

4x107

 6x107 8x107 1x108

0.4

0.3

0.2

0.1

A

B

C

D

Figure 85 Real component of the high frequency propagation function

for cables with abrasion plus a conductive contaminant

A similar approach is used to model the electrical properties of the abraded cables at high

frequencies. The following equations are used:

5.3-7

5.3-8

5.3-9

5.3-10

The values of the fitting constants are presented in Table 13.

Resistance: R(ω β δω ) = +

Inductance: ( ) . L ω β δ

ω

= + 0 05

Capacitance: ( ) C ω β . .

δ

ω

α

ω

=+ + 0 05 0 5

Conductance: ( ) G ω β . .

δ

ω

α

ω

=+ + 0 05 0 5
107

The following figures present the electrical properties of the abraded cables as represented by

Equations 5.3-7 to 5.3-10.

Case Fitting Constant

$6"

Resistance

Case A: Unabraded Cable 0.2 0.005955662 0

Case B: One Conductor Abraded 0.2 0.005955662 0

Case C: Two Conductors Abraded 0.2 0.005955662 0

Inductance

Case A: Unabraded Cable 4.0 x 10-6 1.11936 0

Case B: One Conductor Abraded 4.0 x 10-6 1.11936 0

Case C: Two Conductors Abraded 4.0 x 10-6 1.11936 0

Capacitance

Case A: Unabraded Cable 1.86 x 10-10 2.97289 x 10-8 1.04147 x 10-9

Case B: One Conductor Abraded 1.86 x 10-10 1.48645 x 10-8 0.52073 x 10-9

Case C: Two Conductors Abraded 1.86 x 10-10 0 0

Conductance

Case A: Unabraded Cable 0 2.97289 x 10-8 3.60049 x 10-11

Case B: One Conductor Abraded 0 1.48645 x 10-8 1.80024 x 10-11

Case C: Two Conductors Abraded 0 0 0

Table 13 Fitting constants for equations representing the high frequency electrical properties of

abraded cables
108

R(ω)/l [S/m]

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contaminant

D 

ω (Hz)

80 A

B

C

60 D

40

20

4x107

 6x107 8x107 1x108

Figure 86 Resistance spectra for abraded cables in the high frequency

range from phenomenological model

3.7x10-5

L(ω)/l [H/m]

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

2mm abrasion on both conductors 

plus conductive contaminant 

D

ω (Hz)

A B C

D 

20

4x107

 6x107 8x107 1x108

3.6x10-5

3.5x10-5

3.4x10-5

3.3x10-5

Figure 87 Inductance spectra for abraded cables in the high frequency range

from phenomenological models
109

C(ω)/l [F/m]

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

2mm abrasion on both conductors 

plus conductive contaminant 

D

ω (Hz)

A B

C 

D

4x107 6x107 8x107 1x108

3.8x10-9

3.7x10-9

3.6x10-9

3.5x10-9

Figure 88 Capacitance spectra for abraded cables in the high frequency range from

phenomenological models

G(ω)/ω−l [mho-sec/m]

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

2mm abrasion on both conductors 

plus conductive contaminant 

D

ω (Hz)

A 

B

C 

D

4x107 6x107 8x107 1x108

1.25x10-10

0.75x10-10

0.50x10-10

0.25x10-10

1.00x10-10

Figure 89 Conductance spectra for abraded cables in the high frequency range from

phenomenological models

5.3.4 Detection of Abrasion Damage Using BIS
110

( ) ( )

ω

γ ω

ω

d

d

v

i

-1

p ≡

Two different approaches were developed for the detection of abrasion on cables using BIS. The

first involves the properties of the propagation function; specifically the inverse of the velocity

of propagation of electrical signals that propagate on the cable, vp

-1(T), which is defined by the

following equation:

5.3-11

The second approach is phenomenological in nature and involves the zero crossings of the

second derivative of the impedance phase, A(T), which is defined by the following equation:

5.3-12

In Equation 5.3-12, <M> implies an average of the impedance phase over a frequency range of

±600kHz.

It can be shown that the slope of vp

-1(T) increases whenever the cable’s insulation is abraded. 

From Equation 5.3-11 the imaginary component of the propagation function is required in the

oscillatory region of the frequency spectrum. However, the slope of the extracted parameter

exhibits large oscillations that are unphysical in nature. This behavior arises from the

approximation used for the cable’s characteristic impedance. To overcome this anomalous

behavior, the imaginary component of the propagation function is fitted to a linear function, as

follows:

5.3-13

In this equation, discrete x values from 1 to 2000 replace the continuous frequency spectra, T,

over the range from 1MHz to 100MHz. Recall that the impedance measurements were made at

2000 discrete frequencies in the high frequency range. These individual data points correspond

to the x values from 1 to 2000. This approximation ignores the propagation velocity’s

dispersion. Figure 90 presents the slope of this equation, H. As shown, the slope for the

unabraded cable is smaller than that for any of the abraded cables. As a result the slope for each

abraded cable can be compared to the baseline (unabraded) cable as an indicator for the presence

of abrasion on the cable. These results imply that the velocity of propagation for electrical

signals traveling on the cable decreases when the insulation is abraded.

( ) 2

2

d

d

ω

ω

Φ

Π ≡

γ (x) α x ς i = +
111

ς

2x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

2mm abrasion on both conductors 

plus conductive contaminant 

D

ω (Hz)

A 

B 

C 

D 4x107

 6x107 8x107 1x108

0.01676

0.01678

0.01674

Figure 90 Slope of the equation representing the imaginary component of the high

frequency propagation function for abraded cables

The approach using the zero crossings of the second derivative of the impedance phase, A(T), to

detect abrasion is now discussed. Figure 91 compares the zero crossings of A(T) for the cables

with and without abrasion. It is observed that the zero crossings are downshifted to lower

frequencies when abrasion is present on the cables. The reason for this behavior is not

understood. This behavior is not observed for the impedance phase spectra. In general, the zero

crossing of the impedance phase depends upon the product [L(T) C(T)]-1⁄2, and this is true for

A(T) as well. However, in the oscillatory region of the frequency spectrum the impedance is

dominated by wave phenomena, especially interference. As a result, the behavior of the zero

crossings when the cable’s properties are changed is complex and cannot easily be explained.

Figure 92 presents A(T) in the frequency range from 4.2MHz to 5.2MHz. As shown the zero

crossing of the abraded cables is downshifted relative to the unabraded cable. It is noted that the

zero crossing of the abraded cables are the same, despite the differences in the cable’s insulation.
112

-1

Π (ω)

4.5x106

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors 

plus conductive contam inant 

D 

ω (H z)

A

B

C

D

4.6x106 4.7x106 4.8x106

-2

-3

Figure 91 Comparison of zero crossings in the frequency range 4.4MHz

to 4.8MHz for the second derivative of the impedance phase, A(T), for

cables with and without abrasion

Π 4 (ω)

2.26x107

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

2mm abrasion on both conductors plus 

conductive contaminant 

D 

ω (Hz)

A 

D C B 

2.28x107 2.32x107 2.34x107

-2

2

Figure 92 Comparison of the zero crossings of the second derivative of the

impedance phase, A(T), in the frequency range from 22.4MHz to 23.8MHz for

cables with and without abrasion
113

Similar results were found for other zero crossings examined. These results show that a select

number of zero crossings of A(T) can be used to determine if the cable’s insulation is abraded. 

When abrasion is present, the zero crossings for A(T) are downshifted in frequency. For the

tests performed in this study, 28 out of 29 zero crossings examined followed this rule.

5.3.5 Location of Abrasion Damage Using BIS

The high frequency phenomenological models developed previously for abraded cables are not

useful for locating this damage. This is due to the following observation. The cable insulation’s

dielectric function follows the fractional power law for dielectric materials, which is:

5.3-14

The first term in the above equation refers to ionic processes, while the second and third terms

refer to electronic processes that contribute to the cable insulation dielectric function. Here, g0 is

the dielectric function of vacuum, and A1, A2 and A3 refer to various micro processes that

dominate the insulation’s dielectric function. When a portion of the insulation is abraded down

to the metallic conductor, the parameters A1 = A2 = A3 = 0, and g(T) = g0. The

phenomenological models developed previously deal with the capacitance between two

conductors in a cable via the structure factor, 7, and knowledge of this structure factor is

imprecise. Therefore, a model is required that includes knowledge of all the parameters

contained in the cable’s capacitance. Also, if only one of the wires is abraded, then the

capacitance per unit length and conductance per unit length are given by the following equation:

5.3-15

If both of the conductors are abraded to the metallic conductor (thus there is no insulation

present), the capacitance per unit length and conductance per unit length are given by the

following equation:

5.3-16

The phenomenological models developed previously cannot accurately represent this scenario.

As such, at high frequencies the following models for resistance per unit length and inductance

per unit length can be used:

( ) ( ) ( ) ( ) ( ) ( ) ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+

+

+

+ = + 1 2 n3

3

3

n

2

2

n

1

1

0 1

A

1

A

1

A 1

ω τ ω τ ω τ

ε ω ε

i i i

() () ( ) ( ) ( ) ( ) ( ) ( ) ⎟

⎟

⎟

⎟

⎠

⎞

⎜

⎜

⎜

⎜

⎝

⎛

+

+

+

+

+

+ = Λ + 1 2 3 n

3

3

n

2

2

n

1

1

0 1

A

2

1

1

A

2

1

1

A

2

1

G C 1

ω τ ω τ ω τ

ω ω ω ε

i i i

i

( ) ( ) G C 0 ω + i ω ω = Λ ε
114

5.3-17

5.3-18

At high frequencies the inoic portion of g(T) can be ignored since the ions are too slow to react

to the high frequency fields, and the fractional power law for the insulation’s dielectric function

reduces to the following equation:

5.3-19

For a cable with a twisted pair of conductors, the structure factor becomes:

5.3-20

Here “s” is the distance between the centers of the conductors and “d” is their diameter. The

various constants in the above equations arise from various physical processes. At high

frequencies the cable’s resistance is dominated by the skin effect and Equation 5.3-17 is the

asymptotic form of the skin effect, with Ts being the skin frequency. The various constants can

be determined by obtaining the cable’s characteristic impedance and propagation function from

the measured impedance spectra, and then calculating the open configuration impedance using

assumed values for the constants. The measured impedance can then be compared to the

calculated impedance and the error calculated. Using an iterative process, the final value of the

constants can be determined by minimizing the rms error between the calculated impedance and

the measured impedance.

For the unabraded cable (Specimen 15) the best fit values for the constants are the following:

Resistance per unit length: R0 = 0.02S/m

Ts = 28.183kHz

Inductance per unit length L0 = 4.1:H/m

T1 = 10MHz

n1 = 0.275

Dielectric Function 7g0 = 0.185nF/m

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ = +

s

R R0 1

ω

ω

ω

( ) ( )

( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+ = l

l

2n

l

n

l

0 1 /

/ L L 1- 0.5

ω ω

ω ω

ω

( ) ( ) ( ) ( ) ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+

+ = Λ + 2 n3

3

3

n

2

2

0

1

A

1

A 1 ω τ ω τ

ε ω ε

i i

( ) Λ = π

Arc Coth s

d
115

2x106

75

Φ(ω) [Degrees]

50

25

-25

-50

-75

4x106

 6x106 8x106 1x107

Predicted 

Measured A

B

A

B

ω [Hz]

Figure 93 Comparison of predicted and measured impedance phase in the

range from 2.55MHz to 10.04MHz for unabraded cable (Specimen 15)

A2 = 1.2, J2 = 2.82:s, n2 = 0.5

A3 = 3.94 J3 = 0.1:s, n3 = 0.022

The characteristic impedance and propagation function are then calculated using Equations

3.2-1a and 3.2-1b. The open configuration impedance is then calculated using Equation 3.2-7a.

Figure 94 compares the cable impedance phase predicted by the model to the measured

impedance. The rms error of the impedance phase is 4.76%, indicating good agreement between

the predicted and measured values. As shown, the impedance phase predicted by the model

deviates slightly from the measured impedance after the first zero crossing. Also, there is a

small deviation between the model and the measured values in the vicinity of 1MHz to 2MHz. 

Since the model was developed in the frequency range from 2.55MHz to 10.04MHz it is not

surprising that deviations appear outside this range.

Figure 94 compares the cable impedance magnitude predicted by the model to the measured

impedance. Again, good agreement is observed between the predicted and measured values.
116

500

1000

1500

2000

2500

2x106

|Z(ω)|/l [S/m]

4x106 6x106 8x106 1x107

Predicted 

Measured A

B

A

B

ω [Hz]

Figure 94 Comparison of predicted and measured impedance magnitude in

the range from 2.55MHz to 10.04MHz for unabraded cable (Specimen 15)

Next, the characteristic impedance and propagation function for cables with one or both

conductors abraded is determined. This is useful since the abraded cable is modeled as if it is in

two states; 1) the conductor has all of its insulation (i.e., unabraded), and 2) the conductor is

bare.

Figures 95 and 96 present the characteristic impedance magnitude and phase in the frequency

range from 2.55MHz to 10.04MHz for the cables with and without abrasion. As shown, the

characteristic impedance magnitude increases when the insulation is abraded. The characteristic

impedance phase decreases when the insulation is abraded.

Figures 97 and 98 present the imaginary and real components of the propagation function in the

frequency range from 2.55MHz to 10.04MHz for the cables with and without abrasion. In all

cases the behavior of the propagation function is as expected in light of the fact that the cable’s

capacitance and conductance decrease when the insulation is abraded.
117

70

80

90

100

|Z0(T)| 

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

ω (Hz) A

B

C

4x106 6x106 8x106 1x107

Figure 95 Characteristic impedance magnitude in the frequency range

from 2.55MHz to 10.04MHz for cables with and without abrasion

-0.6

-0.4

-0.2

0.2

Ψ(ω)

Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A

B

C

ω (Hz)

4x106 6x106 8x106 1x107

A

B

C

Figure 96 Characteristic impedance phase spectra in the frequency range

from 2.55MHz to 10.04MHz for cables with and without abrasion
118

0.05

0.1

0.15

0.2

0.25

0.3

0.35

γi(ω) Unabraded 

2mm abrasion on one conductor 

2mm abrasion on both conductors 

A 

B 

C 

ω (Hz)

4x106 6x106 8x106 1x107

A

B

C

Figure 97 Imaginary component of the propagation function in the frequency

range from 2.55MHz to 10.04MHz for cables with and without abrasion

0.001

0.002

0.003

0.004

0.005

γ

r

(ω) Unabraded

2mm abrasion on one conductor

2mm abrasion on both conductors 

A

B

C

ω (Hz)

4x106 6x106 8x106 1x107

A

B

C

Figure 98 Real component of the propagation function in the frequency

range from 2.55MHz to 10.04MHz for cables with and without abrasion
119

In this section, an approach for locating abrasion damage is presented using the cable models

developed in the previous section. Specifically, two cases are evaluated; 1) a cable with the

insulation abraded on one conductor, and 2) a cable with the insulation abraded on both

conductors. In both cases, the models are able to predict the location of the abrasion within 10%.

The approach used is the same as that used to locate insulation damage when the cable is

thermally aged, which is discussed in Section 5.2. As such, different models are developed for

each of the two cases being studied.

5.3.5.1 Model for Cable with One Conductor Abraded

The scenario evaluated here is depicted in Figure 44 as Case B. A 2mm (0.08in.) length of

insulation is abraded from one conductor in the middle of the cable. The total cable length is

10m (393.7in.) and the start and end points of the abraded section are labeled la and lb,

respectively. The cable is not shorted at the point of abrasion.

For this case, the abraded cable is in two states; the abraded portion is in a “damaged” state, and

the unabraded portion is in a “healthy” state. The model for the impedance of the cable is

represented by the following equation:

5.3-21

In Equation 5.3-21, the subscript “d” refers to the cable property in the damaged state, and the

subscript “h” refers to the cable property in the healthy state. The parameter “l” is the total

length of the cable. This model will be used together with the measured impedance to locate the

abrasion damage on the cable.

Figure 99 presents the measured impedance phase spectra in the frequency range from

4.048MHz to 15.04MHz for the cables with and without abrasion. As shown, the cables are very

similar with small differences in the spectra after the first zero crossing. These differences are

on the order of the deviations observed between the models presented in the previous section.

[ ] [ ]

[ ] Z

Z Coth h ha

model 0 h

0 0d d

0d 0h h d

Z()

Z Tanh

Z ( ) Z ( ) Coth Tanh [ ( ) ( ) ( )( ) ( ) ( )( )( )( ) ( )( )

ω ω

ω γω ω γω

ω ω γω γω = −+ −+ −− ,

, ,

, ,

b a

b ba ]
120

-75 

-50 

-25 

25 

50 

75 

Φ(ω) Unabraded

2mm abrasion on one conductor 

A

B

ω (Hz)

0.8x107 1.0x107 1.2x107 1.4x107

A

B

1.6x107

Figure 99 Measured impedance phase spectra in the frequency range from

4.048MHz to 15.04MHz for cables with and without abrasion on one conductor

To locate the abrasion damage on the cable, the following procedure is used:

• Calculate the impedance of the cable using Equation 5.3-21 and an assumed location for

the abrasion

• Compare the calculated impedance to the measured impedance and compute the rms error

in the values at each data point

• Using an iterative process, assume new locations for the abrasion along the cable and

compute the rms error between the predicted and measured impedance for each location

• The location that minimizes the rms error is the predicted location of the abrasion

For this example, abrasion locations were assumed every 1 meter (39.37in.) along the cable. The

impedance phase values were compared at discrete frequencies in the range from 4.048MHz to

15.04MHz. The error in the predicted phase values was computed using the following equation:

5.3-22 ( ) ()

∑ ( )

∑

=

=

=

=

Φ

Φ Φ

Φ = n 15.04MHz

4.048MHz

Measured

n 15.04MHz

4.048MHz

Model n b Measured , -

n

n

n

n

ω

ω

ω

ω

ω

ω ω

δ

l
121

2 4 6 8 10 

x (meters) 

0.0855

0.0865

0.087

0.0875

0.088

Actual Location 

Predicted 

Location 

<δΦ(x)> 

Figure 100 Predicted location of abrasion damage for cable with one conductor

abraded

In this example, the model predicts that the abrasion is located at 6 meters from the end of the

cable and the correct location is 5 meters. Figure 100 presents the results of the error

calculations showing the minima at 6 meters, which represents the predicted damage location. It

is noted that the error at this predicted location is 8.55%.

5.3.5.2 Model for Cable with Two Conductors Abraded

The scenario evaluated here is depicted in Figure 44 as Case C. A 2mm (0.08in.) length of

insulation is abraded from both conductors in the middle of the cable. The total cable length is

10m (393.7in.) and the start and end points of the abraded section are labeled la and lb,

respectively. The cable is not shorted at the point of abrasion.

Figure 101 presents the measured impedance phase spectra in the frequency range from

4.048MHz to 15.04MHz for the cables with and without abrasion. As shown, the cables are very

similar with small differences in the spectra before the first zero crossing and in the region

before and after the third zero crossing. Again, these differences are on the order of the

deviations observed between the models presented previously.
122

-75 

-50 

-25 

25 

50 

75 

Φ(ω) Unabraded

2mm abrasion on two conductors 

A

B

ω (Hz)

0.8x107 1.0x107 1.2x107 1.4x107

A

B

1.6x107

Figure 101 Measured impedance phase spectra in the frequency range from

4.048MHz to 15.04MHz for cables with and without abrasion on both

conductors

Using the appropriate characteristic impedance and propagation function, the iterative process

described previously in this section was used to predict the location of the abrasion. The results

predict a location of 6 meters, while the correct location is 5 meters. Figure 102 presents the

error calculations and the predicted versus actual location of the abrasion.

These results demonstrate the BIS method can be used to predict the location of abrasion damage

with relatively good accuracy.

5.4 Application of BIS to Cables with Cracking Damage

Cracking of the insulation on aged cables is a potential problem in nuclear power plants since it

can lead to leakage currents that may cause the system to fail. This is particularly true under

humid or wet conditions, during which moisture can enter the crack and create a conductive path

between the cable conductor and ground. Therefore, it is desirable for a condition monitoring

technique to be able to detect and locate cracking in cables.

In this section, the BIS method is evaluated for its ability to detect and locate cracking damage

on cables. 
123

2 4 6 8 10 

x (meters) 

0.0927

0.0928

0.0929

0.0931

Actual Location 

Predicted 

Location 

<δΦ(x)> 

Figure 102 Predicted location of abrasion damage on cable with both conductors

abraded

5.4.1 Test Specimens Used for Testing of Cables with Cracking

For this portion of the research, unaged cables were used. To simulate the cracking damage a

knife was used to slice the insulation on both conductors of the cable. A total of 12 simulated

cracks were placed on the cable over a length of 2.54 cm (1in.). The crack location was 4 meters

from the left end of the cable. Figure 103 shows a schematic of the scenario evaluated.

Baseline impedance measurements were obtained using the Eclypse instrument and the HP

instrument. Measurement parameters used were a 1-Volt oscillation level, medium integration

time, and 4-samples of averaging. High frequency measurements were collected at 2000 discrete

frequency points between 1MHz and 100MHz. Low frequency measurements were collected at

logarithmically spaced points over the frequency range from 1kHz to 1MHz. Measurements

were made with the conductors in both the open and the shorted configuration, and from both

ends of the cable. The cable was coiled and placed in a humidity chamber that was maintained at

60%RH and 30oC for all measurements.
124

V(T) 

4m 

9m 

12 cracks over 2.54 cm 

A B

Figure 103 Schematic of cable with cracking damage

After baseline impedance measurements were made, the cable was removed from the

environmental chamber and 12 cracks were simulated on each conductor of the cable. Each

simulated crack was equally spaced at 0.21mm, with a width of 0.1mm. The cracks were first

made to a depth of 50% of the insulation thickness and measurements were made. A conductive

contaminant consisting of 85% Skydrol hydraulic fluid, 11% iron particles, and 4% carbon black

powder was applied to the cracked portion of the cable and the impedance measurements were

repeated. The cracks were then extended completely through the insulation (100%) and

additional conductive contaminant was applied, after which the impedance measurements were

again performed. Thus, four sets of impedance measurements were made on the cable.

5.4.2 Low Frequency BIS Measurements of Cables with Cracking

Figure 104 compares the impedance phase spectra in the low frequency range from 1kHz to

1MHz for cables with and without cracking. As shown, there is only a small difference between

the uncracked cable and the cable with cracks. Even the conductive path does not appear to

impact the impedance phase. This can be attributed to the lack of a conductivity path between

the conductors, even with the conductive contaminant applied. A possible reason for this is the

size of the iron filings used, which were on the order of 100:. This is approximately the same

dimension as the crack width. Thus, it is believed that the iron particles could not enter the crack

and make a connection with the cable conductor.
125

ω

Φ(ω)

200000 400000 600000 80000

0 

1x106 

-89.5 

-89.4 

-89.3 

-89.2 

-89.1 

ω [Hz]

B

No 

50% Cracking

100% Cracking plus a 

conductive contaminant

A

B 

C

C A

Φ(ω) [Hz]

Figure 104 Comparison of impedance phase for cables with and without

cracking

Although the differences in the impedance spectra are very small, the data were analyzed to

determine the spatially averaged electrical properties of the cable. Figures 105 and 106 present

the characteristic impedance magnitude and phase spectra, and the propagation function,

respectively, for the cable with and without cracking. As shown, only small differences are

observed between the cable with no cracking and the cable with cracking.

Figure 107 compares the resistance per unit length for the cable with and without cracking. As

shown the resistance per unit length does not change when the cable contains cracks, even when

a conductive contaminant is applied to the cracks.

Figure 107 compares the inductance per unit length for the cable with and without cracking. As

shown the inductance per unit length increases slightly when the cable contains cracks and a

conductive contaminant is applied to the cracks. This change is more apparent near the upper

end of the low frequency region.

Figure 108 compares the capacitance per unit length for the cable with and without cracking. As

shown the capacitance per unit length increases slightly when the cable contains cracks and a

conductive contaminant is applied to the cracks. This change is also more apparent near the

upper end of the low frequency region. It is observed that the capacitance per unit length for the

cable with cracking but no conductive contaminant was higher than the baseline cable with no

cracking, and the cable with cracking plus a conductive contaminant.
126

3.5 4 4.5 5 5.5 6

2.05 

2.1 

2.15 

2.2 

2.25 

2.3 

2.35 

200000 600000 

1

-4

-3

-2

-1

Ψ(ω)

ω [Hz] 

ω

Log10|Z(T)|

No 

50% Cracking

100% Cracking plus a 

conductive contaminant

A 

B 

C 

1x10

6

ω [Hz] 

Figure 105 Characteristic impedance log magnitude and phase for cables with and

without cracking

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.0002

0.0004

0.0006

0.0008

0.0012

γ

i

 (ω)

20000 60000

ω [Hz] 

No Cracking 

50% Cracking 

100% Cracking plus a 

conductive contaminant

A

B

C

1x106

ω [Hz]

γ

r

 (ω)

20000 60000 1x106

A

B

C

A B

C

Figure 106 Imaginary and real components of the propagation function for

cables with and without cracking
127

0.025

0.05

0.075

0.125

0.15

0.175

R(ω)/l [Ω/m]

200000 600000 1x106

No Cracking 

50% Cracking 

100% Cracking plus a 

conductive contaminant

A

B

C

ω [Hz] 

A

B

C

Figure 107 Resistance per unit length for cables with and without cracking

100000 200000 300000 400000 

4.4x10-6

L(ω)/l [H/m]

3.8x10-6

4.2x10-6

No Cracking 

50% Cracking 

100% Cracking plus a 

conductive contaminant

A

B

C

ω [Hz] 

A

B

C

Figure 108 Inductance per unit length for cables with and without cracking
128

3.58x10-10

C(ω)/l [F/m]

50000 100000 150000 200000 

3.56x10-10

3.54x10-10

3.52x10-10

No Cracking 

50% Cracking 

100% Cracking plus a 

conductive contaminant

A

B

C

A ω [Hz] 

B

C

Figure 109 Comparison of capacitance per unit length for cable with and

without cracks

Figure 110 compares the conductance per frequency per unit length for the cable with and

without cracking. As shown the conductance per unit length increases slightly when the cable

contains cracks and a conductive contaminant is applied to the cracks. This change is also more

apparent near the upper end of the low frequency region. It is observed that the capacitance per

unit length for the cable with cracking but no conductive contaminant was higher than the

baseline cable with no cracking, and the cable with cracking plus a conductive contaminant.

5.4.3 High Frequency BIS Measurements of Cables with Cracking

In this section the high frequency impedance spectra of the cable test specimens is analyzed to

develop an approach for detecting cracking on cables. Specifically, a similar approach to that

used in Section 5.2 for evaluating attached loads is used here in which the zero crossings of the

second derivative of the impedance phase spectra, A(T), are examined for differences. These

differences are then used as indicators for the presence of cracking. The development and

definition of the parameter A(T) was presented previously in Equations 5.2-1 through 5.2-3.

It is observed from the test results that, for a 9-meter cable, there are eight detection zero

crossings (DZCs) in the high frequency range used for the cracking tests (i.e., 1MHz to

100MHz).

Figure 111 compares the first DZC for A(T) for the cables with and without cracking. As

shown, the DZC is downshifted to lower frequencies when cracking is present on the cables. 
129

4.25x10-12

G(ω)/ω−l [mho-sec/m]

50000 100000 150000 200000 

4.00x10-12

3.75x10-12

3.50x10-12

3.25x10-12

2.75x10-12

No Cracking 

50% Cracking 

100% Cracking plus a 

conductive contaminant

A

B

C

ω [Hz] A

B

C

Figure 110 Conductance per frequency per unit length for cable with and

without cracks

Similar results were observed for the other seven DZCs. These results suggest that monitoring

the zeros crossings of the parameter A(T) may be an effective indicator for the presence of

cracking on a cable.
130

Π(ω)

1.48x107

4

2

ω [Hz] 

No Cracking 

50% Cracking 

50% Cracking plus a 

conductive contaminant 

A

B

C

B A

C

-2

-4

-6

1.52x107 1.54x107 1.56x107 1.58x107

100% Cracking plus a 

conductive contaminant 

D

D

Figure 111 Comparison of second derivative of the impedance spectra,

A(T), for cables with and without cracking

It should be noted that cracking of a cable’s insulation arises when a cable that has been

embrittled by long-term exposure to environmental stresses is physically stressed. For example,

bending or crushing of an embrittled cable can lead to cracking of the insulation. In the

experiments performed as part of this research, cracking was simulated by slicing the cable’s

insulation using a knife. This approach was selected since it was an efficient method of

simulating the physical characteristics of a crack; however, the approach does not accurately

capture the physics or the chemistry of the cracking. As a result, the results demonstrate the

potential for detecting cracking using the BIS method; however, accurate models for real world

cracking are not currently available, thus, a model for locating cracking could not be developed

as part of this study. Additional research using more realistically simulated cracking is

recommended to further evaluate the BIS method for detecting this type of degradation. 

Continuous BIS measurement during the aging process would be beneficial to understanding and

modeling the cracking process. Chemical analysis of the cable’s insulation would also be useful.

5.5 Application of BIS to Cables with Varying Environments

Electric cables in nuclear power plants can be very long and can traverse several different areas

of the plant. Thus, the environment along the length of the cable may vary. In order to apply a

condition monitoring technique to cables in their installed configuration, the impact of this

varying environment on the measurements must be evaluated. To investigate the impact of
131

varying environments, long runs of cable were tested. Several different environments were

imposed on sections of the cable during the tests to determine the impact on the test results.

5.5.1 Specimens Tested to Evaluate BIS for Cables with a Varying Environment

For this portion of the research, the cable test specimens shown in Table 14 were tested. The 10

meter cables were used to provide data for developing the phenomenological models for the 100

meter cables. The 100 meter cables were tested with constant temperature and humidity on the

external surface of the cables, and with a varying environment along their length. Comparisons

were made between the test results not only for the different environments, but also for the

cables with and without the hot-spot.

BIS tests were performed over the frequency range from 1kHz to 1MHz using the HP

instrument. Due to the length of test specimens 47 and 48, these cables were tested with the first

10 meters inside the test facility building, and the remainder outside the building. As a result,

the cables were exposed to two different environments. Inside the building, the temperature was

maintained at approximately 20oC (68oF) with low humidity. The portion of cable inside the

building was also placed in a humidity chamber for several tests. The temperature outside the

building varied several degrees as a function of location, and as a function of time of day.

Figure 112 depicts the test setup schematically.

No. Specimen ID Length

meters (inches)

Service Life

Simulated

Hot-Spot

Simulated

26. PNI-79-RB-188-826 10 (393.7) 60yrs. @ 50oC None

43. PNI-79-RB-188-843 10 (393.7) 60yrs. @ 90oC None

47. PNI-79-RB-188-847 100 (3,937) None 60yrs. @ 90oC

48. PNI-79-RB-188-848 100 (3,937) None None

Table 14 Specimens tested to evaluate BIS for testing cables with a varying environment
132

Hot spot at 

96m to 97m 

50m 

Humidity 

Chamber 

Inside the building 

Figure 112 Schematic of test setup for cables with varying environment

5.5.2 Low Frequency BIS Results

Figure 113 compares the measured impedance magnitude for the 100 meter cable without any

aging or hot-spot (specimen 47) using external temperatures of 24oC (75oF), and 42oC (107.6oF)

along the entire length of the cable. The results presented cover a frequency range of 400kHz to

1MHz. As shown, the impedance magnitude peak value is downshifted slightly for the case in

which the higher external temperature was used.
133

Figure 114 compares the impedance phase spectra for the 100 meter cable with no aging or hotspots (specimen 48) and external temperatures of 24oC (75oF), and 42oC (107.6oF). As shown,

the higher external temperature causes a downshift in the first zero crossing of the impedance

phase.

400000 600000 800000 1x106

200

400

600

800

1000

1200

|Ζ(ω)|

ω [H z]

24oC (75oF)

42oC (108oF)

A

A

B

B

Figure 113 Impedance magnitude for 100 meter cable with no aging or

hot-spot and external temperatures of 24oC (75oF), and 42oC (107.6oF)

432000 434000 436000 438000 440000 442000 444000 

-30

-20

-10

10

20

Φ(ω)

A

24oC (75oF)

42oC (108oF)

A

B

B

Figure 114 Impedance phase spectra for 100 meter cable with no aging or

hot-spot and external temperatures of 24oC (75oF), and 42oC (107.6oF)
134

Figure 115 compares the impedance phase spectra for the 100 meter cable with no aging or hotspot and varying humidity levels over the first 10 meters of cable. For this test, the first 10

meters of the cable were placed in a humidity chamber and the conditions were maintained at

29oC (85oF) and 85% RH. As shown, the higher external humidity causes a downshift in the first

zero crossing of the impedance phase, similar to that observed for the elevated temperature case.

Next, the impact of a varying external temperature on a cable with a 1 meter hot-spot (specimen

47) was examined. Figure 116 compares the measured impedance phase spectra for the 100

meter cable with a 1 meter hot-spot and external temperatures of 24oC (75oF), and 42oC

(107.6oF). As shown, the higher external temperature causes an upshift in the zero crossing of

the impedance phase. This is contrary to previous observations and the reason for this behavior

is not readily apparent.

Finally, a comparison of the two 100 meter cables was made to examine the impact of the hotspot on the cables properties, particularly in the vicinity of the zero crossings. Figure 117

compares the measured impedance phase spectra for the two 100 meter cables. For this

measurement, the external temperature was maintained at 24oC (75oF). As shown, the zero

crossing of the impedance phase is downshifted by the presence of the 1 meter hot-spot. It

should be noted that for this figure, the impedance phase is limited to the range from -90 to +90,

since this is the physical range of the impedance phase. Measured values outside this range are

438000 440000 442000 444000 

-30

-20

-10

10

20 No humidity 

Humidity

432000 434000 436000 

Φ(ω)

ω [Hz]

A

A

B

B

Figure 115 Impedance phase spectra for 100 meter cable with no aging or

hot-spot and external temperatures of 24oC (75oF) low humidity, and 29oC

(85oF) and 85% RH.
135

unphysical in nature and arise from instrument error, therefore, they are eliminated from the

figure. However, the zero crossing frequencies presented are correct.

430000 435000 440000 445000 

-30

-20

-10

10

20

Φ(ω)

ω [Hz]

24oC (75oF)

42oC (108oF)

30

-40

A

A

B

B

Figure 116 Impedance phase spectra for 100 meter cable with 1 meter

hot-spot and external temperatures of 24oC (75oF), and 42oC (107.6oF)

-75

-50

-25

25

50

75

400000 600000 800000 1x106

Φ(ω)

ω [Hz]

No Hot-Spot

1m Hot-Spot

A

A

B

B

Figure 117 Impedance phase spectra for 100 meter cables with and

without a 1 meter hot-spot, and an external temperature of 24oC (75oF)
136

Figure 118 shows an expanded view of the measured impedance phase spectra for the two 100

meter cables in the vicinity of the first zero crossing with an external temperature of 24oC (75oF). 

The downshift in the zero crossing of the impedance phase is clearly visible with the presence of

the 1 meter hot-spot.

Figure 119 shows an expanded view of the measured impedance phase spectra for the two 100

meter cables in the vicinity of the first zero crossing with an external temperature of 42oC

(107.6oF). Again, a downshift in the zero crossing of the impedance phase is observed with the

presence of the 1 meter hot-spot.

Figure 120 summarizes the comparison of the impedance phase spectra for the various cases

examined above; namely, 100 meter cables with and without a hot-spot, and external temperature

of 24oC (75oF) and 42oC (107.6oF). This figure shows the different behavior that these two

cables exhibit when the mean outside temperature changes. For the cable without a hot-spot,

increasing the external temperature results in a downshift in the impedance phase zero crossing,

while the reverse is true for the cable with the 1-meter hot-spot. This reverse behavior is

attributed to the presence of the hot-spot.

430000 435000 440000 445000 

-30

-20

-10

10

20

Φ(ω)

ω [Hz]

24oC (75oF)

42oC (108oF)

-40

A

A

B B

Figure 118 Expanded view of the impedance phase spectra in the

frequency range from 425kHz to 445kHz for 100 meter cables with

and without a 1 meter hot-spot, and an external temperature of 24oC

(75oF)
137

430000 435000 440000 445000 

-40

-30

-20

-10

10

20

Φ(ω)

ω [Hz]

No Hot-Spot

A 1m Hot-Spot

A

B

B

Figure 119 Expanded view of the impedance phase spectra in the

frequency range from 425kHz to 445kHz for 100 meter cables with and

without a 1 meter hot-spot, and an external temperature of 42oC (107.6oF)

Φ(ω)

430000 435000 440000 445000 

-40

-30

-20

-10

10

20

ω [Hz]

B A 

C A 24oC No Hot-Spot 

42oC No Hot-Spot

24oC 1m Hot-Spot 

42oC 1m Hot-Spot

B 

C 

D 

D 

Figure 120 Summary comparison of impedance phase spectra for 100

meter cables with and without a 1-meter hot-spot and external

temperatures of 24oC (75oF) and 42oC (107.6oF)
138

5.5.3 Phenomenological Models of Cables with Varying Environment

In this section a phenomenological model for a cable containing a hot-spot with a varying

external environment is developed. The approach taken is to consider the cable to be in two

states; namely a healthy state with no hot-spots, and a degraded state with the hot-spot. Each

state is then modeled separately accounting for a varying environment, then the models are

combined to represent the cable with a hot-spot. To develop the separate models, impedance

results from test specimen 43, which was thermally aged to simulate 60 yrs @ 90oC , and

specimen 26, which was thermally aged to simulate 60 yrs @ 50oC were used.

Figure 121 compares the measured impedance magnitude for the two 10 meter cables in the

frequency range from 1kHz to 1MHz. As shown, the impedance magnitude for the cable with

the more severe aging is lower. Thus, the more severe aging has made the cable’s insulation

more conductive.

Figure 122 compares the measured impedance phase spectra for the two 10 meter cables in the

frequency range from 1kHz to 1MHz. As shown, the impedance phase for the cable with the

more severe aging is higher than that for the cable with less aging for frequencies less than

approximately 400kHz. Again, this indicates that the more severe aging has made the cable’s

3.5 4 4.5 5 5.5 6 

2.5

3.5

4

4.5

5

5.5

Log10 ω

Log10 ⏐Z(ω)⏐

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Figure 121 Comparison of impedance magnitude in the frequency

range from 1kHz to 1MHz for cables aged to simulate 60 yrs @ 50oC

and 60 yrs @ 90oC
139

insulation more conductive. It is observed that the impedance phase for specimen 43 drops

significantly over 0.5MHz. The reason for this is not clear.

The cables characteristic impedance and propagation function are now extracted from the

measured impedance in the frequency range from 1kHz to 1MHz. Figure 123 compares the

extracted characteristic impedance magnitude for the 10-meter cables. As shown, the more

severe aging results in a decrease in the characteristic impedance magnitude.

Figure 124 compares the extracted characteristic impedance phase spectra for the 10-meter

cables. As shown, the more severe aging results in a decrease in the characteristic impedance

phase. The largest difference occurs at the lowest frequencies in this range, i.e., 1kHz. This

behavior arises from the fact that more severe aging degrades the cable’s electrical properties.

Figures 125 and 126 compare the extracted imaginary and real components, respectively, of the

propagation function for the 10-meter cables. As shown, the more severe aging results in an

increase in these parameters.

-89.4

-89.3

-89.2

-89.1

-88.9

-88.8

-88.7

3.5 4 4.5 5 5.5 6 

Log10 ω

Φ(ω) 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B A

Figure 122 Comparison of impedance phase spectra for 10 meter

cables aged to simulate 60 yrs @ 50oC and 60 yrs @ 90oC
140

3.5 4 4.5 5 5.5 6 

220

Z0(ω)

Log10 ω

200

180

160

140

120

100

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Figure 123 Comparison of extracted characteristic impedance magnitude

for 10 meter cables aged to simulate 60 yrs. @ 50oC and 60 yrs @ 90oC
141

-30

-20

-10

3.5 4 4.5 5 5.5 6 

Log10 ω

Ψ(ω) 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Figure 124 Comparison of extracted characteristic impedance phase

spectra for 10 m cables aged to simulate 60 yrs.@50oC and 60 yrs@90oC

200000 400000 600000 800000 1x106

0.01

0.02

0.03

0.04

ω [Hz] 

γi

 (ω) Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Figure 125 Comparison of imaginary component of the propagation

function for 10 m cables aged to simulate 60 yrs.@50oC and 60 yrs@90oC
142

The electrical properties of the cables are now determined for the 10-meter cables aged to

simulate 60 yrs. @ 50oC and 60 yrs @ 90oC. Figure 127 compares the resistance per unit length

for the cables, along with the relative difference in resistance per unit length. It is observed that

both resistance curves follow the square root frequency dependence due to the skin effect. As

shown, at very low frequencies, the resistance for the cable with the more severe aging is larger. 

For direct currents, the resistance per unit length depends on the geometry of the twisted

conductor pair according to the following equation:

5.5-1

where “s” is the distance between the cable conductor centers, “d” is the wire insulation’s

diameter, and Rs is the skin resistance of a single conductor. Thus, the smaller the diameter of

the conductor insulation, the larger the resistance at direct current. These results imply that the

insulation shrinkage increases when the aging becomes more severe, which is consistent with

intuition. It is observed that for frequencies above 100kHz, the relative difference in resistance

per unit length is negative, which implies that the resistance for the cable with the more severe

aging becomes smaller that the cable with less aging. This behavior is an anomaly for which no

readily apparent explanation is available.

200000 400000 600000 800000 1x106

0.0002

0.0004

0.0006

0.0008

ω [Hz] 

γ

r

 (ω) 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

0.0012

Figure 126 Comparison of the real component of the propagation function

for 10 meter cables aged to simulate 60 yrs. @ 50oC and 60 yrs @ 90oC

( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

−

=

/d 1

/d

d

2 R R

2

s

dc

s

s

π
143

Figure 128 compares the inductance per unit length for the cables, along with the relative

difference in inductance per unit length. As shown, the inductance is smaller when the aging

severity is increased. This behavior does not reflect the standard formula for the dc inductance

per unit length dependence on the cable geometry, which is defined by the following equation:

5.5-2

This behavior is not currently understood; however, cables have a very complicated structure

that involves a number of wire strands that form the conductor. Each strand creates its own

magnetic field and it is possible that the individual contributions from each strand to the cables’s

magnetic field may interfere with each other. In that case, Equation 5.5-2 would not describe the

cable’s inductance.

200000 600000 1x107

0.12

0.14

R(ω)/l [Ω/m]

ω [Hz] 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

ω [Hz] 

B

δR(ω)

0.08

0.06

0.04

0.02

0.15

0.10

0.05

-0.05

200000 600000 1x107

Figure 127 Comparison of resistance per unit length and relative difference in resistance

per unit length for 10-meter cables aged to simulate 60 yrs. @ 50oC and 60 yrs @ 90oC

⎟

⎠

⎞ ⎜

⎝

⎛ = d

s L Cosh -1

π

μ
144

Figure 129 compares the capacitance per unit length for the cables, along with the relative

difference in capacitance per unit length. As shown, the capacitance is increased when the aging

severity is increased. This behavior does not reflect the dc capacitance per unit length

dependence on the cable’s geometry, as defined by the following equation:

5.5-3

In the above equation, g1(T) refers to the real component of the insulation’s dielectric function. 

However, the thermal aging can change the insulation’s chemistry. Throughout this frequency

range, the thermally degraded cable’s insulation has a capacitance that is larger than for the less

degraded cable. Furthermore, the capacitance exhibits a weak dependence on frequency. That

implies that the more severe aging degradation affected all of the microprocesses that control the

insulation’s dielectric function.

3.5 4 4.5 5 5.5 6

-0.075

-0.07

-0.065

-0.06

4.4x10-6 -0.055

L(ω)/l [H/m]

ω [Hz] 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Log10 ω B

δL(ω)

200000 600000 1x107

4.2x10-6

3.8x10-6

3.6x10-6

3.4x10-6

Figure 128 Comparison of inductance per unit length and relative difference in

inductance per unit length for 10m cables aged to simulate 60yrs.@50oC and

60yrs@90oC

( ) ( )

⎟

⎠

⎞ ⎜

⎝

⎛ =

d

s Cosh

C -1

πε 1 ω

ω
145

Figure 130 compares the conductance per unit length for the cables, along with the relative

difference in conductance per unit length. As shown, the conductance is increased when the

aging severity is increased. This behavior does not reflect the dc conductance per unit length

dependence on the cable’s geometry, as defined by the following equation:

5.5-4

In the above equation, g2(T) refers to the imaginary component of the insulation’s dielectric

function. However, the thermal aging can change the insulation’s chemistry. Throughout this

frequency range, the degraded cable’s insulation has a capacitance that is larger than for the

cable that is less severely degraded.

0.585

0.59

0.595

0.605

3.5 4 4.5 5 5.5 6

5.5x10-10

C(ω)/l [F/m]

ω [Hz] 

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A

Log10 ω

B

δC(ω)

200000 600000 1x107 5.0x10-10

4.5x10-10

4.0x10-10

Figure 129 Comparison of capacitance per unit length and relative difference in

capacitance per unit length for 10m cables aged to simulate 60 yrs@50oC and

60 yrs@90oC

( ) ( )

⎟

⎠

⎞ ⎜

⎝

⎛ =

d

s Cosh

G -1

π ω ε 2 ω

ω
146

With the electrical properties of the individual 10-meter cables modeled, a model can be

developed for the 100 meter cable with a hot-spot. The model is then applied to the impedance

measurements made on the cables shown schematically in Figure 1. The geometry of the model

is shown schematically in Figure 131.

Referring to the above figure, Sh refers to the healthy section of cable with no aging, and Sd

refers to the damaged section of cable thermally aged to simulate a hot-spot. Also, la and lb refer

to the start and end location, respectively, of the damaged hot-spot section of cable.

The modeled impedance for this configuration is represented by the following equation:

1x10-11

1.2

3.5 4 4.5 5 5.5 6

G(ω)/ω−l [mho-sec/m]

ω [Hz]

Aged to Simulate 60 yrs. @ 50°C

Aged to Simulate 60 yrs. @ 90°C

A

B

B

A Log10 ω

B

δG(ω)/ω

200000 600000 1x107

1.0

0.8

0.6

0.4

0.2

8x10-10

7x10-10

6x10-10

5x10-10

9x10-10

Figure 130 Comparison of conductance per unit length and relative difference in

conductance per unit length for 10m cables aged to simulate 60 yrs@50oC and 60 yrs@90oC

x=0 la

Sd

V(ω)

lb x=l

Sh Sh

Figure 131 Schematic of model for 100-meter cable containing a hot-spot
147

5.5-5

where Z0,h(T) and Z0,d(T) are the characteristic impedances, and (h(T) and (d(T) are the

propagation functions for the healthy and damaged sections of cable, respectively. In applying

this model, the impedance data from the 10-meter cable aged to simulate 60yrs @ 50oC are used

to represent the healthy section, and the impedance data from the 10-meter cable aged to

simulate 60yrs @ 90oC are used to represent the damaged section. It should be noted that the

impedance measurements for the 10-meter cables were performed with the cables in a humidity

chamber and the conditions maintained at 30oC (85oF) and 20% RH. Thus, there is some error

introduced in using impedance data from these cables to model the 100 meter cables, which were

measured under slightly different conditions of 24oC (75oF) and low humidity.

To determine the hot-spot location relative to the point of measurement, it is first assumed that la

is zero. The model is used to calculate the impedance and the results are compared to the

measured impedance. In the frequency range from 1kHz to 1MHz. The assumed hot-spot

location is then changed and the impedance calculation is repeated. This process is continued

until the hot-spot location is varied over the entire length of the cable. For each calculation, the

error in the impedance phase is calculated using the following equation:

5.5-6

where MMeasurement (Tm) is the measured impedance phase at the frequency Tm and MModel (Tm, la)

is the model’s impedance phase at the frequency Tm based on the assumption that the hot-spot

location is la. In addition, Tn0=437,419Hz and the lower and upper frequencies were 429, 949Hz

and 445, 020Hz, respectively. The results are shown in Figure 132.

() () () ( ) [ ] () ( ) [ ]

() () ( ) [ ] [ ] ( ) ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+ =

0,d 0,h h b b a

0,h a 0,d b a

model 0,h Z Z coth - tanh -

Z coth - Z coth - Z Z l l l l

l l l l

d

h d

ω ω γ γ

ω γ ω γ

ω ω

( )

() ( )

∑ ( )

∑

= +

= −

= +

= −

Φ

Φ Φ

Θ ≡ m n n

m n n

m

m n n

m n n

Measurement m Model m a

a 0

0

0

0

- ,

ω

ω ω

δ

l

l
148

Examination of the above figure shows that the model predicted the hot-spot location to be

within 90 meters to 99 meters from the point of measurement. The error varies from

approximately 56% down to approximately 5% near the correct location. To more accurately

locate the hot-spot, the calculations were repeated in the region from 90 meters to 99 meters

using refined assumptions for the hot-spot location. The predicted location is then found to be

99 meters from the point of measurement. This is in good agreement with the correct location of

96 meters. Thus, the model’s prediction is within 3% of the correct location. Figure 133

presents the results of this calculation. As shown, the model is within 4.2% of the correct

location.

These results demonstrate that BIS can be used to locate hot-spots on cables even when the

environment is variable along the external surface of the cable. For the example presented

herein, the model’s prediction of hot-spot location is within a few percent of the correct position. 

This is particularly interesting in light of the fact that parameters from the 10 meter cables aged

at slightly different conditions were used to represent the 100 meter cable being modeled. In

addition, 90% of the 100 meter cable was outside the building during testing, which resulted in a

dynamic external environment. In spite of these adverse factors, the model was able to predict

the hot-spot location with good accuracy.

20 40 60 80 

0.1

0.2

0.3

0.4

0.5

δΘ (x)

x [m] 

Figure 132 Error in predicted impedance phase as a function of

assumed hot-spot location
149

96 98 

0.042

0.044

0.046

0.048

0.050

δΘ (x)

x [m] 

92 94 

Correct 

Location

Predicted 

Location 

Figure 133 Error in predicted impedance phase as a function of

assumed hot-spot location over the cable length from 90 meters to 99

meters
150

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151

6. EVALUATION OF THE BIS METHOD FOR NUCLEAR PLANT CABLES

The goal of this research program was to evaluate the effectiveness of the BIS method for

detecting and locating degradation in electric cables in nuclear power plant applications. To

achieve this goal, a commonly used low-voltage instrumentation and control (I&C) cable was

selected to prepare cable test specimens, which were exposed to accelerated aging to simulate

various types of service conditions in a typical nuclear power plant application. Specific types of

degradation were inflicted on the cable after which the cable test specimens were tested using the

BIS method. The types of degradation evaluated are the following;

• Global thermal aging of the cable

• Global plus localized thermal aging of the cable (i.e., hot-spots)

• Thermal degradation with cracking, and 

• Abrasion damage to the cable

In testing the cables, the following three different cable configurations were evaluated to provide

a representative sampling of the applications commonly expected in a nuclear power plant

setting:

• Constant temperature and humidity along the cable with no load attached

• Constant temperature and humidity along the cable with a load attached

• Varying environments along the length of the cable with no load attached

For each configuration, BIS measurements were made and the data were analyzed to determine if

the degradation could be detected and located. Detection and location of the degradation is

based on the use of the measured impedance data, the governing equations for the electrical

properties of an electric cable, and models developed to analytically represent the cable

properties. The results for each of the different configurations are discussed below.

6.1 Results for Global Thermal Aging

The test results on the cables with global thermal aging clearly show that the BIS method is

capable of detecting thermal degradation of a cable. In the low frequency range, comparison of

the measured impedance phase spectra show an increase in the impedance phase angle when

thermal aging is present on the cable. This increase in impedance phase indicates that the cable

is more dissipative, and can be used as an indicator of aging degradation on the cable.

The high frequency BIS data show that, as thermal aging is applied to the cable, the impedance

magnitude and phase spectra are downshifted to lower frequencies. Therefore, by measuring the
152

impedance of a cable and comparing it to a baseline for a known cable in good condition, this

downshift in frequency can also be used as an indicator of thermal degradation on the cable.

Analytical models were developed to predict the electrical properties of a degraded cable based

on measured impedance data. The approach used is based upon the fact that, at low frequencies

the cable’s impedance is non-oscillatory and the characteristic impedance and propagation

function can be directly extracted from the measured impedance spectra. At high frequencies,

where the cable’s impedance oscillates, it is not possible to directly extract the characteristic

impedance and propagation function. Instead, the cable’s characteristic impedance in the low

frequency range is first determined. This function is then extrapolated to the high frequency

range. The propagation function for the high frequency range can then be determined. Once the

characteristic impedance and propagation function are known, the models developed for the

cable’s electrical properties can be used to predict the electrical properties of the cable. Results

showed relatively good accuracy for the models developed.

These results demonstrate that the BIS method can detect thermal degradation and predict the

electrical properties of the degraded cable with relatively good accuracy for the type of cable

tested in this study. It should be noted that this testing was performed in a laboratory

environment. Testing in a actual plant environment is recommended to verify the effectiveness

of the BIS method for detecting this type of degradation.

6.2 Results for Global Plus Localized Thermal Aging (Hot-Spot)

The results from the testing of cables with global thermal aging were used as the basis for

detecting and locating localized thermal aging (i.e., hot-spots) in cables. The high frequency

impedance spectra for cables with and without hot-spots were compared and they demonstrated

that localized damage does impact the cables impedance characteristics. The presence of a hotspot tends to downshift the frequency of the impedance spectra. This difference in impedance

spectra can be used to detect and locate localized degradation. 

The impact of hot-spot severity, size, and location were also investigated in this study. Tests

were performed to compare the impedance response of cables with a hot-spot representing

60 years of service at 60oC (140oF) and 60 years of service at 70oC (158oF). The results indicate

that the difference in hot-spot severity was not significant enough for the low frequency

impedance spectra to show a measurable difference. However, the high frequency spectra did

show a downshift in frequency. This change is useful for estimating the size of a hot-spot. 

Cables with hot-spots 1.0 meters in length and 0.5 meters in length were also compared to

evaluate the impact of hot-spot size, and similar results were obtained.

To determine the sensitivity of the BIS method to hot-spot location, test cables were measured

from both ends. This effectively provided data for a hot-spot at two different distances from the

point of measurement. Results demonstrated that the location of the hot-spot does impact the
153

impedance spectra, and this difference can be used to locate the degradation. The closer the hotspot is to the point of measurement, the greater is the change in the impedance spectra.

A method for locating a hot-spot was developed based on the models for the cable’s properties. 

Specifically, the cable’s impedance is calculated using equation 5.1-13 based on assumed values

of the hot-spot location. This calculated value is compared to the measured impedance. Based

on the root mean square (rms) error between the value predicted by the model and the measured

value, new values of hot-spot location are chosen and the process is repeated. The final hot-spot

location is determined by minimizing the rms error.

In comparing the modeled impedance to the measured impedance, four different parameters are

used, which are based on the impedance magnitude and the impedance phase zero crossings. 

Results show that this approach can be used to predict hot-spot location with an accuracy of

10%.

It should be noted that this testing was performed in a laboratory environment with a known,

well defined hot-spot on the test specimen. Also, only one hot-spot was present on the cable.

Therefore, generalization of these results to cables with multiple hot-spots would not be

appropriate. However, these results do show promise that the BIS method is a powerful tool for

locating localized damage in an installed cable system.

6.3 Results for Global Thermal Aging with an Attached Load

Impedance measurements were made on cables with localized thermal aging both with and

without a load attached to the cable. The goal was to determine the impact of the load on the

ability of the BIS method to detect and locate a hot-spot. The results showed that, at low

frequencies, the cable system’s impedance is heavily dominated by the load. However, the zero

crossing of the impedance phase does react to the presence of a hot-spot. Therefore, an accurate

model of the cable system impedance can be used to examine the behavior of the impedance

phase in the vicinity of the low frequency zero crossings. This can be used as an indicator for

the presence of a hot-spot on the cable’s insulation even with a load attached to the cable.

In evaluating the high frequency BIS measurements for cables with an attached load, the

frequency averaged second derivative of the impedance phase spectra was found to provide

useful information for detecting hot-spots. Specifically, the zero crossings of this parameter

were found to be downshifted when the cable’s insulation contains a hot-spot. An examination

of the A(T) spectra showed that a frequency downshift occurs at all of the 14 DZCs when a hotspot is present on the cable. Thus, detection of a hot-spot appears to be feasible for cables with a

load attached.

Models were also developed to predict the electrical properties for cables with hot-spots and an

attached load. Using these models and an approach similar to that used for the detection of hotspots without an attached load, the location of a hot-spot was correctly predicted. These results
154

demonstrate that the BIS method is capable of detecting and locating localized degradation on

cables even if there is a load attached to the cable. Some knowledge of the impedance response

of the load is useful.

6.4 Results for Global Plus Localized Abrasion Damage

The testing on cables with simulated abrasion damage showed that the low frequency impedance

spectra do not respond to the presence of abrasion unless a high humidity level is present to

create a conductivity path. When a higher level of humidity is present, all of the phase spectra

have a new structure (i.e., a peak) in the vicinity of 5kHz to 10Khz. This structure arises from

the increased humidity level, which provides a conductive pathway for leakage currents. 

It is also observed that the abraded cable’s impedance peak is shifted to higher frequencies

relative to the unabraded cable. This frequency shift may be attributable to the fact that the

averaged dielectric function of the abraded cable is smaller than that for the unabraded cable. As

a result, any changes to the spectra must occur at higher frequencies. It is further observed that

there is no readily observable difference between the phase spectra of the cables with one and

two conductors abraded.

It should be noted that, while the change in the low frequency impedance phase spectra can be

used to detect abrasion under high humidity levels, this may not be practical in a nuclear power

plant environment since the humidity levels may not be high enough to observe these changes. 

For example, the peaks previously discussed were not observed when BIS measurements were

made under conditions of 70% RH.

An evaluation of the high frequency data shows that the phase zero crossing and the first maxima

of the impedance magnitude are shifted to a higher frequency when the cable is abraded. The

largest change is observed for the case in which the abrasion is covered by a conductive

contaminant, thus establishing a conductivity path.

Models were developed to represent the electrical properties of the abraded cable. Using these

models together with the measured impedance spectra, abrasion damage was located on a test

specimen with an accuracy of 15%. An iterative approach similar to that used for detecting hotspots was used in which an assumed damage location is used to calculate the cable impedance. 

This is compared to a measured value and an iterative process is used to minimize the rms error

between predicted and measured values. These results demonstrate that the BIS method is

potentially useful for detecting and locating abrasion damage on a cable.

6.5 Results for Global Thermal Aging with Cracking Damage
155

Testing of cables with simulated cracking was performed to evaluate the effectiveness of the BIS

method for detecting and locating this type of degradation. The impedance phase spectra in the

low frequency range from 1kHz to 1MHz for cables with and without cracking show that there is

only a small difference between the uncracked cable and the cable with cracks. Even a

conductive contaminant applied to the cable does not appear to impact the impedance phase. 

This can be attributed to the lack of a conductivity path between the conductors, even with the

conductive contaminant applied. A possible reason for this is the size of the iron filings used,

which were on the order of 100:. This is approximately the same dimension as the crack width. 

Thus, it is believed that the iron particles could not enter the crack and make a connection with

the cable conductor.

The high frequency impedance spectra of the cable test specimens showed that the zero crossings

of the second derivative of the impedance phase spectra, A(T), did show differences that may be

useful as indicators for the presence of cracking. Monitoring the zero crossings of the parameter

A(T) may be an effective indicator for the presence of cracking on a cable.

In the experiments performed herein, cracking was simulated by slicing the cable’s insulation

using a knife. This approach was selected since it was an efficient method of simulating the

physical characteristics of a crack; however, the approach does not accurately capture the

physics or the chemistry of cracking that would occur in real plant environments. As a result,

the results demonstrate the potential for detecting cracking using the BIS method; however,

accurate models for real world cracking are not currently available. Additional research using

more realistically simulated cracking is recommended to further evaluate the BIS method for

detecting this type of degradation. Continuous BIS measurement during the aging process would

be beneficial to understanding and modeling the cracking process. Chemical analysis of the

cable’s insulation would also be useful.

6.6 Results for Global Thermal Aging with a Varying Environment

Testing of long cables (100 meters) was performed to evaluate the impact of varying

environments along the external surface of the cables on BIS measurements. One of the cables

contained a 1-meter hot-spot that simulated 60 years of service at 90oC. The hot-spot was

located at 96 meters from the end of the cable. Two different environments were simulated

during the testing process.

The predicted location using BIS was 99 meters from the point of measurement. This is in good

agreement with the correct location of 96 meters. Thus, the model’s prediction is within 3% of

the correct location. The results demonstrate that the BIS method can be used to locate hot-spots

on cables even with varied environments along the external surface of the cable. For the

example presented herein, the model’s prediction of hot-spot location is within a few percent of

the correct position.
156

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157

7. CONCLUSIONS AND CONSIDERATIONS FOR FOLLOW-ON RESEARCH

7.1 Conclusions on the Effectiveness of the BIS Method

The research program reported herein evaluated the BIS method as a prognostic and diagnostic

tool for monitoring installed electric cable systems in nuclear power plants. The results

demonstrated that this method is effective for nuclear plant cables, and that it is capable of

detecting and locating localized degradation within a cable in its incipient stage prior to failure. 

Various degradation scenarios were evaluated, including the following:

• global thermal aging damage,

• localized thermal aging damage,

• abrasion damage, and 

• cracking damage

The following conclusions are drawn based on the results of this research:

• The BIS method was clearly able to detect the presence of thermal degradation on

the cables used in this study. Specifically, the impedance phase spectra of the

cables tested were observed to increase as the amount of thermal degradation on

the cable increased. This increase can be used as an indicator of global thermal

degradation.

• The BIS method was able to detect the presence of localized thermal degradation,

or hot-spots on the cables. Specifically, a shift in the zero crossings of the

impedance phase spectra were observed when a hot-spot was present on the cable.

• An approach was developed for locating hot-spots on a cable using models of the

cables electrical properties. The models were able to predict the hot-spot location

with an accuracy of 10%.

• The BIS method was not sensitive enough to distinguish between the different

severities and sizes of hot-spots simulated in the low frequency range; however,

measurements in the high frequency range did detect the differences. Additional

research is warranted to establish the sensitivity limits for this technique

• The BIS method was able to detect and locate the presence of abrasion damage on

a cable. The models and approach used are similar to that for detecting and

locating thermal hot-spots.

• The BIS method was demonstrated to be effective for detecting and locating

degradation on cables with an attached load. This is important since it is

desirable to have a technique that can test cables in their installed configuration,

without having to disconnect them from attached equipment.
158

• The BIS method was able to detect the simulated cracking damage on cables. 

However, the simulation method used in this study was determined not to

accurately represent the cracking phenomena. Additional research should be

considered to more accurately evaluate the BIS method on actual cable cracking.

• The BIS method was able to detect the presence of localized thermal degradation,

or hot-spots on the cables even with a varying environment along the external

surface of the cables. For the example presented herein, the model’s prediction of

hot-spot location is within a few percent of the correct position.

The results from this study suggest that the technology that makes use of BIS may represent a

breakthrough in the condition monitoring of installed electric cables. In a laboratory setting, this

technique was able to detect and locate the various forms of aging degradation commonly found

in nuclear power plant applications. This technique has the capability to provide a means of

scanning an entire cable system to determine its acceptability for continued service. The

technique can be applied in situ with low voltage signals that will not damage the cable under

test, and can detect aging damage in an incipient state prior to a failure occurring.

7.2 Considerations for Follow-On Research to Demonstrate the Effectiveness of the BIS

Method in Nuclear Plant Environment

While the BIS method shows great promise as a prognostic and diagnostic technique for installed

cable systems, additional research is desirable before it can be applied in the field. Specifically,

the following additional items should be considered during future research, preferably in a

collaborative manner:

• Research on the detection and location of cracking damage in cables using more

realistic simulation of the cracking damage,

• The technique should be demonstrated on additional types of cable to determine

its usefulness for other materials and cable configurations

• The technique should be evaluated with different types of loads attached to the

cables to determine the impact of loads encountered in a plant environment

• The technique should be demonstrated in an actual plant environment to

determine the impact of the various environmental factors that may impact the

BIS measurements

• The technique should be demonstrated on blind test samples in which the type,

severity, size, and location of the degradation are unknown

Based upon the promising results obtained from this phase of the research effort, the Office of

Nuclear Regulatory Research (RES) is considering a follow-on research effort. The primary

focus of the next phase of the research should be on the demonstration of the BIS method for

installed cable systems in operating nuclear power plant environment. 
159

8. REFERENCES

Durney, C. and Johnson, C., “Introduction to Modern Electromagnetics,” McGraw-Hill, 1969.

Grayson, S.J., et al., “Fire Performance of Electric Cables,” Interscience Communications, Ltd.,

United Kingdom, 2000.

Lofaro, R.J., “Proceedings of the International Conference on Wire System Aging,”

NUREG/CP-0179, Brookhaven National Laboratory, November 2002.

Lofaro, R.J., et al., “Assessment of Environmental Qualification Practices and Condition

Monitoring Techniques for Low-voltage Electric Cables,” NUREG/CR-6704, Brookhaven

National Laboratory, Upton, NY, USA, February 2001.

Moore, G.F., “Electric Cables Handbook,” Blackwell Science, Inc., Malden, MA, USA, 3rd

Edition, 1997.

National Science and Technology Council, Committee on Technology, United States White

House, “Review of Federal Programs for Wire System Safety,” Wire System Safety Interagency

Working Group, November 2000.

Rogovin, D. and Kendig, M., “Diagnostic/Prognostics of Aged Wiring Using Broadband

Frequency Impedance,” 6th Joint FAA/DOD NASA Conference on Aging Aircraft, San

Francisco, 2002.

Thue, W.A., “Electric Power Cable Engineering,” Marcel Dekker, Inc., New York, NY, USA,

1999.

Vaughan, W., “Dielectric Properties and Molecular Behavior,” Chap. 2, Van Nostrand, 1969.

Villaran, M. and Lofaro, R.J., “Evaluation of Aging and Environmental Qualification Practices

for Power Cables Used in Nuclear Power Plants” NUREG/CR-6794, Brookhaven National

Laboratory, Upton, NY, USA, January 2003.
160

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161

Appendix A

BIS Test Results for Cables with Global Thermal Aging Simulating 20 years and 40 years

of Service
162

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163

List of Figures

Page No.

Figure A-1 Low frequency impedance phase spectra for cables globally aged to simulate 20

years of service at various service temperatures . . . . . . . . . . . . . . . . . . . . . . . . 168

Figure A-2 High frequency impedance phase spectra for cables with global thermal aging to

simulate 20 years of service at various service temperatures . . . . . . . . . . . . . . 169

Figure A-3 Expanded view of impedance phase and magnitude per unit length spectra for the

frequency range from 78 MHz to 86 MHz for cables with global thermal aging to

simulate 20 years of service at various service temperatures . . . . . . . . . . . . . . 169

Figure A-4 Characteristic impedance magnitude per unit length and phase spectra for cables

with global thermal aging to simulate 20 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Figure A-5 Imaginary and real components of the propagation function spectra for cables

with global thermal aging to simulate 20 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

Figure A-6 Resistance per unit length and change in resistance per unit length for cables with

global thermal aging to simulate 20 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Figure A-7 Comparison of resistance per unit length predicted by analytical model to

resistance extracted from measured impedance for cable with global thermal

aging to simulate 20 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . 171

Figure A-8 Comparison of resistance per unit length predicted by analytical model to

resistance extracted from measured impedance for cable with global thermal

aging to simulate 20 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Figure A-9 Comparison of resistance per unit length predicted by analytical model to

resistance extracted from measured impedance for cable with global thermal

aging to simulate 20 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . 172

Figure A-10 Inductance per unit length and change in inductance for cables with global

thermal aging to simulate 20 years of service at various service temperatures . 173

Figure A-11 Comparison of inductance per unit length predicted by analytical model to

inductance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 50oC . . . . . . . . . . . . . . 173
164

Figure A-12 Comparison of inductance per unit length predicted by analytical model to

inductance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 60oC . . . . . . . . . . . . . . 174

Figure A-13 Comparison of inductance per unit length predicted by analytical model to

inductance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 70oC . . . . . . . . . . . . . . 174

Figure A-14 Capacitance per unit length and change in capacitance per unit length for cables

with global thermal aging to simulate 20 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175

Figure A-15 Comparison of capacitance per unit length predicted by analytical model to

capacitance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 50oC . . . . . . . . . . . . . . 175

Figure A-16 Comparison of capacitance per unit length predicted by analytical model to

capacitance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 70oC . . . . . . . . . . . . . . 176

Figure A-17 Conductance-to-frequency ratio per unit length and change in conductance-tofrequency ratio per unit length for cables with global thermal aging to simulate 

20 years of service at various service temperatures . . . . . . . . . . . . . . . . . . . . . . 176

Figure A-18 Comparison of capacitance per unit length predicted by analytical model to

capacitance per unit length extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 60oC . . . . . . . . . . . . . . 177

Figure A-19 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 20 years of service at 50oC . . . . . . . . . . . . . . . . . . . . 177

Figure A-20 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 20 years of service at 60oC . . . . . . . . . . . . . . . . . . . . 178

Figure A-21 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 20 years of service at 70oC . . . . . . . . . . . . . . . . . . . . 178

Figure A-22 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cables with global thermal aging to simulate 20 years of service at 50oC . . 179
165

Figure A-23 Comparison of imaginary and real components of the propagation function

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 50oC . . . . . 179

Figure A-24 Comparison of characteristic impedance magnitude and phase spectra predicted

by analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 60oC . . . . . . . . . . . . . . 180

Figure A-25 Comparison of imaginary and real components of the propagation function

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 60oC . . . . . 180

Figure A-26 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 20 years of service at 70oC . . 181

Figure A-27 Comparison of imaginary component and real component of the propagation

function for cable with global thermal aging to simulate 20 years of service at

70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

Figure A-28 Low frequency impedance phase spectra for cables with global thermal aging to

simulate 40 years of service at various service temperatures . . . . . . . . . . . . . . 182

Figure A-29 High frequency impedance phase spectra for cables with global thermal aging to

simulate 40 years of service at various service temperatures . . . . . . . . . . . . . . 183

Figure A-30 Expanded view of impedance phase and magnitude per unit length spectra over

the frequency range from 78 MHz to 86 MHz for cables with global thermal

aging to simulate 40 years of service at various service temperatures . . . . . . . 183

Figure A-31 Characteristic impedance magnitude and phase spectra for cables with global

thermal aging to simulate 40 years of service at various service temperatures . 184

Figure A-32 Imaginary and real components of the propagation function for cables with global

thermal aging to simulate 40 years of service at various service temperatures . 184

Figure A-33 Resistance per unit length and change in resistance per unit length for cables with

global thermal aging to simulate 40 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185

Figure A-34 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
166

Figure A-35 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Figure A-36 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186

Figure A-37 Inductance per unit length and change in inductance per unit length for cables

with global thermal aging to simulate 40 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Figure A-38 Comparison of inductance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

Figure A-39 Comparison of inductance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

Figure A-40 Comparison of inductance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188

Figure A-41 Capacitance per unit length and change in capacitance per unit length for cables

with global thermal aging to simulate 40 years of service at various service

temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Figure A-42 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189

Figure A-43 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Figure A-44 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 40 years of service at 70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Figure A-45 Conductance-to-frequency ratio per unit length and change in conductance-tofrequency ratio per unit length for cables with global thermal aging to simulate 

40 years of service at various service temperatures . . . . . . . . . . . . . . . . . . . . . . 191
167

Figure A-46 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 50oC . . . . . . . . . . . . . . . . . . . . 191

Figure A-47 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 60oC . . . . . . . . . . . . . . . . . . . . 192

Figure A-48 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 70oC . . . . . . . . . . . . . . . . . . . . 192

Figure A-49 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 50oC . . 193

Figure A-50 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 60oC . . 193

Figure A-51 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 70oC . . 194

Figure A-52 Comparison of the imaginary component and real component of the propagation

function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at

50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

Figure A-53 Comparison of the imaginary component and real component of the propagation

function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at

60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Figure A-54 Comparison of the imaginary component and real component of the propagation

function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at

70oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

Figure A-55 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
168

Figure A-56 Comparison of resistance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Figure A-57 Comparison of inductance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Figure A-58 Comparison of inductance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Figure A-59 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Figure A-60 Comparison of capacitance per unit length predicted by analytical model to that

extracted from measured impedance for cable with global thermal aging to

simulate 60 years of service at 60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199

Figure A-61 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 60 years of service at 50oC . . . . . . . . . . . . . . . . . . . . 199

Figure A-62 Comparison of conductance-to-frequency ratio per unit length predicted by

analytical model to that extracted from measured impedance for cable with global

thermal aging to simulate 60 years of service at 60oC . . . . . . . . . . . . . . . . . . . . 200

Figure A-63 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 60 years of service at 50oC . . 200

Figure A-64 Comparison of characteristic impedance magnitude per unit length and phase

spectra predicted by analytical model to that extracted from measured impedance 

for cable with global thermal aging to simulate 60 years of service at 60oC . . 201

Figure A-65 Comparison of the imaginary component and real component of the propagation

function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 60 years of service at

50oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

Figure A-66 Comparison of the imaginary component and real component of the propagation

function predicted by analytical model to that extracted from measured
169

impedance for cable with global thermal aging to simulate 60 years of service at

60oC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
170

200000 400000 600000 800000 1x106

-89.4

-89.2

-88.8

-88.6

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

C 

B 

B 

A 

A 

Φ(ω) [Deg.] 

ω [Hz]

Figure A-1 Low frequency impedance phase spectra for cables globally

aged to simulate 20 years of service at various service temperatures

A.1 Test Results for Cables with Global Thermal Aging to Simulate 20 Years of Service

The following figures present the results of broadband impedance tests performed on cables with

global thermal aging to simulate 20 years of service in a nuclear power plant at service

temperatures of 50oC (122oF), 60oC (140oF), and 70oC (158oF). These results supplement the

data presented in Section 5 of this report.
171

2x107

-75

-50

-25

25

50

75

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

A 

B 

C 

4x107 6x107 8x107 1x108

Φ(ω) [Deg.] 

ω [Hz] 

Figure A-2 High frequency impedance phase spectra for cables with global

thermal aging to simulate 20 years of service at various service

temperatures

-40 

-20 

20 

40 

100 

150 

200 

250 

300 

|Z(ω)|/l [S/m] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

7.8x107 8.2x107 8.4x107 8.6x107

7.8x107 8.2x107

 8.4x107 8.6x107

A 

A 

B 

C B 

C 

Φ(ω) [Deg.] 

ω [Hz]

ω [Hz]

Figure A-3 Expanded view of impedance phase and magnitude per unit length

spectra for the frequency range from 78 MHz to 86 MHz for cables with global

thermal aging to simulate 20 years of service at various service temperatures
172

4.6 4.8 5.2 5.4 5.6 5.8 6 

104 

105 

106 

107 

108 

109 

110 

4.6 4.8 5.2 5.4 5.6 5.8 6 

-4 

-3 

-2 

-1 

|Z0(ω)|/l [S/m]

Log10(ω)

Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

Log10(ω) 

A 

A 

B 

B 

C 

C 

Figure A-4 Characteristic impedance magnitude per unit length and phase spectra for

cables with global thermal aging to simulate 20 years of service at various service

temperatures

4.6 4.8 5.2 5.4 5.6 5.8 6 

0.015 

0.020 

0.025 

0.030 

0.035 

0.0002 

0.0004 

0.0006 

0.0008 

Log10(ω) 

γ

r

(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B

A 

Log10(ω) 

γ

i

(ω)

4.6 4.8 5.2 5.4 5.6 5.8 6 

A 

A 

B C 

C 

B 

Figure A-5 Imaginary and real components of the propagation function spectra for

cables with global thermal aging to simulate 20 years of service at various service

temperatures
173

400000 600000 800000 1x106

0.06 

0.08 

0.12 

0.14 

400000 600000 800000 

-0.015 

-0.010 

-0.005 

δR(ω)/l [S/m]

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

0.10 

A 

B C 

E 

50 to 60 oC 

50 to 70 oC 

D 

D 

E 

R(ω)/l [S/m] 

ω [Hz]

ω [Hz]

Figure A-6 Resistance per unit length and change in resistance per unit length for

cables with global thermal aging to simulate 20 years of service at various service

temperatures

600000 700000 800000 900000 1x106

0.11

0.12

0.13

0.14

Extracted 

Model 

A 

B 

A B 

R(ω)/l [S/m] 

ω [Hz] 

Figure A-7 Comparison of resistance per unit length predicted by

analytical model to resistance extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 60oC
174

600000 700000 800000 900000 1x106

0.11

0.12

0.13

0.14

Extracted 

Model 

A 

B 

A B 

R(ω)/l [S/m] 

ω [Hz]

Figure A-8 Comparison of resistance per unit length predicted by analytical

model to resistance extracted from measured impedance for cable with global

thermal aging to simulate 20 years of service at 70oC

600000 700000 800000 900000 1x106

0.11 

0.12 

0.13 

0.14 

R (ω)/l [S/m] 

ω [H z]

Extracted 

M odel 

A 

B 

A B 

Figure A-9 Comparison of resistance per unit length predicted by analytical

model to resistance extracted from measured impedance for cable with global

thermal aging to simulate 20 years of service at 50oC
175

400000 600000 800000

3.9

0.008

0.012

0.016

0.020

δL(ω)/l [H/m] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

3.8

3.7

400000 600000 800000 

A B C 

D 

E 

L(ω)/l [H/m] 

ω [Hz]

ω [Hz]

Figure A-10 Inductance per unit length and change in inductance for cables with global

thermal aging to simulate 20 years of service at various service temperatures

600000 700000 800000 900000 1x10-6

3.72x10-6

Extracted 

Model 

A 

B 

3.68x10-6

3.66x10-6

3.64x10-6

3.62x10-6

A 

B 

L(ω)/l [H/m] 

ω [Hz]

Figure A-11 Comparison of inductance per unit length predicted by

analytical model to inductance per unit length extracted from measured

impedance for cable with global thermal aging to simulate 20 years of service

at 50oC
176

600000 700000 800000 900000 1x106

Extracted 

Model 

A 

B 

3.72x10-6

3.68x10-6

3.66x10-6

3.64x10-6

3.74x10-6

B 

L A (ω)/l [H/m] 

ω [Hz] 

Figure A-12 Comparison of inductance per unit length predicted by

analytical model to inductance per unit length extracted from measured

impedance for cable with global thermal aging to simulate 20 years of

service at 60oC

600000 700000 800000 900000 1x106

3.80x10-6

L(ω)/l [H/m] 

Extracted 

B Model 

A 

3.78x10-6

3.76x10-6

3.74x10-6

3.72x10-6

A B 

ω [Hz]

Figure A-13 Comparison of inductance per unit length predicted by

analytical model to inductance per unit length extracted from measured

impedance for cable with global thermal aging to simulate 20 years of service

at 70oC
177

400000 600000 800000

3.52

0.005

0.010

0.015

0.020

0.025

C(ω)/l [x10-10 F/m] δC(ω)/l [x10-10 F/m]

ω [Hz]

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

3.48

3.46

3.44

3.42

3.54

400000 600000 800000 

A 

B 

C 

D 

E 

ω [Hz]

Figure A-14 Capacitance per unit length and change in capacitance per unit length for

cables with global thermal aging to simulate 20 years of service at various service

temperatures

600000 700000 800000 900000 1x106

3.450

C(ω)/l [x10-10 F/m]

Extracted 

B Model 

A 

3.445

3.440

3.435

3.430

3.425

3.415

A 

B 

ω [Hz] 

Figure A-15 Comparison of capacitance per unit length predicted by

analytical model to capacitance per unit length extracted from

measured impedance for cable with global thermal aging to simulate

20 years of service at 50oC
178

600000 700000 800000 900000 1x106

3.46

3.47

3.48

3.49

3.51

C(ω)/l [x10-10 F/m] 

Extracted 

B Model 

A 

A 

B 

ω [Hz] 

Figure A-16 Comparison of capacitance per unit length predicted by

analytical model to capacitance per unit length extracted from

measured impedance for cable with global thermal aging to simulate

20 years of service at 70oC

400000 600000 800000

0.1

0.2

0.3

0.4 G(ω)/ω-l [x10-12mho-s/m] 

δG(ω)/ω-l [x10-12mho-s/m] 

ω [Hz]

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

7.0

6.5

6.0

5.5

5.0

7.5

400000 600000 800000 

A 

B 

C 

D 

E 

ω [Hz] 

Figure A-17 Conductance-to-frequency ratio per unit length and change in

conductance-to-frequency ratio per unit length for cables with global

thermal aging to simulate 20 years of service at various service

temperatures
179

600000 700000 800000 900000 1x106

3.425

3.430

3.435

3.440

3.445

Extracted 

B Model 

A 

A 

B 

C(ω)/l [x10-10 F/m]

ω [Hz]

Figure A-18 Comparison of capacitance per unit length predicted by analytical

model to capacitance per unit length extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 60oC

600000 700000 800000 900000 1x106

5.2

5.4

5.6

5.8

Extracted 

B M odel 

A 

A 

B 

G(ω)/ω-l [x10-12mho-s/m]

ω [Hz]

Figure A-19 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 50oC
180

600000 700000 800000 900000 1x106

5.4

5.6

5.8

6.2

Extracted 

B Model 

A 

B 

A 

G(ω)/ω-l [x10-12mho-s/m]

ω [Hz] 

Figure A-20 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 20 years of service at 60oC

600000 700000 800000 900000 1x106

6.6

6.8

7.2

7.4

7.6

Extracted 

B Model 

A 

B 

A 

G(ω)/ω-l [x10-12mho-s/m]

ω [Hz]

Figure A-21 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for cable

with global thermal aging to simulate 20 years of service at 70oC
181

400000 600000 800000 103

104

105

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

|Z0(ω)|/l [S/m] Ψ(ω)

ω [Hz]

Extracted 

B Model 

A 

400000 600000 800000 

B 

A 

B 

A 

ω [Hz]

Figure A-22 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cables with global thermal aging to simulate 20 years of service at 50oC

600000 800000 1x106

0.015

0.025

0.030

0.035

0.0006

0.0007

0.0008

0.0009

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1x106

B 

A A B 

ω [Hz]

ω [Hz]

Figure A-23 Comparison of imaginary and real components of the propagation function

predicted by analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 50oC
182

Extracted 

B Model 

A 

400000 600000 800000 103

104

105

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

Ψ(ω)

400000 600000 800000 

B 

A 

B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz] ω [Hz]

Figure A-24 Comparison of characteristic impedance magnitude and phase spectra

predicted by analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 60oC

600000 800000 1X106

0.015

0.025

0.030

0.035

0.0006

0.0007

0.0008

0.0009

γ

i

(ω)

ω

ω

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1X106

A B A B 

Figure A-25 Comparison of imaginary and real components of the propagation function

predicted by analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 20 years of service at 60oC
183

Extracted 

B Model 

A 

400000 600000 800000 

103

104

105

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

Ψ(ω)

400000 600000 800000 

B 

A 

B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz] ω [Hz]

Figure A-26 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 20 years of service at 70oC

600000 800000 1x106

.015

0.025

0.030

.035

0.0006

0.0007

0.0008

0.0009

γ

i

(ω)

ω [Hz]

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1x106

A B A B 

ω [Hz]

Figure A-27 Comparison of imaginary component and real component of the

propagation function for cable with global thermal aging to simulate 20 years of service

at 70oC
184

200000 400000 600000 800000 1x106

-89.4 

-89.2 

-88.8 

-88.6 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

B A 

C 

Φ(ω) [Deg.] 

ω [Hz]

Figure A-28 Low frequency impedance phase spectra for cables with global

thermal aging to simulate 40 years of service at various service

temperatures

A.2 Test Results for Cables with Global Thermal Aging to Simulate 40 Years of Service

The following figures present the results of broadband impedance tests performed on cables with

global thermal aging to simulate 40 years of service in a nuclear power plant at service

temperatures of 50oC (122oF), 60oC (140oF), and 70oC (158oF). These results supplement the

data presented in Section 5 of this report.
185

-75 

-50 

-25 

25 

50 

75 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

C 

B 

A 

2x107 4x107 6x107 8x107 1x108

Φ(ω) [Deg.] 

ω [Hz] 

Figure A-29 High frequency impedance phase spectra for cables with global

thermal aging to simulate 40 years of service at various service

temperatures

7.8x107

-40 

-20 

20 

40 

75

100

125

150

175

200

225

|Z(ω)|/l [S/m] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

B 

A 

8.2x107

7.8x107

8.6x107

8.2x107

 8.6x107

A A 

B B 

C C 

Φ(ω) [Deg.] 

ω [Hz]

ω [Hz]

Figure A-30 Expanded view of impedance phase and magnitude per unit length spectra

over the frequency range from 78 MHz to 86 MHz for cables with global thermal aging to

simulate 40 years of service at various service temperatures
186

4.6 4.8 5.2 5.4 5.6 5.8 6 

104

106

108

110

112

-4

-3

-2

-1

Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

Log10(ω) 

4.6 4.8 5.2 5.4 5.6 5.8 6 

Log10(ω) 

C 

A 

B 

C 

A 

B 

|Z0(ω)|/l [S/m] 

Figure A-31 Characteristic impedance magnitude and phase spectra for cables with

global thermal aging to simulate 40 years of service at various service temperatures

0.005

0.015

0.020

0.025

0.030

0.035

0.0002

0.0004

0.0006

0.0008

4.6 4.8 5.2 5.4 5.6 5.8 6 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

Log10(ω) 

4.6 4.8 5.2 5.4 5.6 5.8 6 

Log10(ω) 

C A 

B C 

A 

B 

γ

r γ (ω) i

(ω)

Figure A-32 Imaginary and real components of the propagation function for cables with

global thermal aging to simulate 40 years of service at various service temperatures
187

400000 600000 800000 1x106

0.06

0.08

0.12

0.14

-0.022

-0.018

-0.014

-0.010

R(ω)/l [S/m] δR(ω)/l [S/m]

ω [Hz]

ω [Hz]

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A B C 

E 

50 to 60 oC 

50 to 70 oC 

D 

D 

E 

400000 600000 800000 

Figure A-33 Resistance per unit length and change in resistance per unit length for

cables with global thermal aging to simulate 40 years of service at various service

temperatures

400000 600000 800000 1x106

0.06

0.08

0.12

0.14

R(ω)/l [S/m] 

ω [Hz]

Extracted 

B Model 

A 

B 

A 

Figure A-34 Comparison of resistance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 50oC
188

600000 700000 800000 900000 1x106

0.11

0.12

0.13

0.14

R(ω)/l [S/m] 

ω [Hz]

Extracted 

B Model 

A 

B 

A 

Figure A-35 Comparison of resistance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 60oC

600000 700000 800000 900000 1x106

0.11

0.12

0.13

0.14

R(ω)/l [S/m] 

ω [Hz]

Extracted 

B Model 

A 

B 

A 

Figure A-36 Comparison of resistance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 70oC
189

400000 600000 800000 1x106

3.65

3.70

3.75

3.80

3.85

3.90

3.95

0.015

0.025

0.030

0.035

L(ω)/l [x10-6H/m] δL(ω)/l [x10-6 H/m] 

ω [Hz]

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

400000 600000 800000

ω [Hz]

Figure A-37 Inductance per unit length and change in inductance per unit length for

cables with global thermal aging to simulate 40 years of service at various service

temperatures

600000 700000 800000 900000 1x106

3.62x10-6

3.64x10-6

3.66x10-6

3.68x10-6

3.7x10-6

L(ω)/m (H/m)

ω (Hz)

Extracted 

B Model 

A 

A 

B 

Figure A-38 Comparison of inductance per unit length predicted by

analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 40 years of service at 50oC
190

3.72x10-6

3.74x10-6

3.76x10-6

3.78x10-6

3.82x10-6

600000 700000 800000 900000 1x106

Extracted 

B Model 

A 

A 

B 

L(ω)/m (H/m)

ω (Hz)

Figure A-39 Comparison of inductance per unit length predicted by

analytical model to that extracted from measured impedance for cable with

global thermal aging to simulate 40 years of service at 60oC

3.64x10-6

3.66x10-6

3.68x10-6

3.72x10-6

3.74x10-6

600000 700000 800000 900000 1x106

Extracted 

B Model 

A 

A 

B 

L(ω)/m (H/m)

ω (Hz)

Figure A-40 Comparison of inductance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global

thermal aging to simulate 40 years of service at 70oC
191

400000 800000 

3.35

3.45

3.50

3.55

3.60

400000 600000 800000 

-0.03

-0.02

-0.01

0.01

0.02

C(ω)/l [x10-10 F/m] δC(ω)/l [x10-10 F/m]

ω [Hz] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

ω [Hz] 

Figure A-41 Capacitance per unit length and change in capacitance per unit length for

cables with global thermal aging to simulate 40 years of service at various service

temperatures

400000 600000 800000 1x106

3.46

3.47

3.48

3.49

3.51

3.52

C(ω)/l [x10-10 F/m] 

ω [Hz]

Extracted 

B Model 

A 

A 

B 

Figure A-42 Comparison of capacitance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 40 years at 50oC
192

3.36

3.38

3.42

3.44

400000 600000 800000 1x106

Extracted 

B Model 

A 

A 

B 

C(ω)/l [x10-10 F/m] 

ω [Hz]

Figure A-43 Comparison of capacitance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 40 years of service at 60oC

3.53

3.54

3.55

600000 800000 1x106

Extracted 

B Model 

A 

A 

B 

C(ω)/l [x10-10 F/m] 

ω [Hz] 

Figure A-44 Comparison of capacitance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 40 years of service at 70oC
193

1x106

5.5

6.0

6.5

7.0

7.5

8.0

8.5

0.1

0.2

0.3

G(ω)/ω-l [x10-10 mho-s/m] δG(ω)-l [x10-10 mho-s/m]

ω [Hz] 

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

E 

50 to 60 oC 

50 to 70 oC 

D 

A 

B 

C 

D 

E 

400000 600000 800000 400000 600000 800000

ω [Hz] 

Figure A-45 Conductance-to-frequency ratio per unit length and change in conductanceto-frequency ratio per unit length for cables with global thermal aging to simulate 40

years of service at various service temperatures

5.25

5.50

5.75

6.00

6.25

6.50

400000 600000 800000 1x106

Extracted 

B Model 

A 

B 

A 

G(ω)/ω-l [x10-10 mho-s/m]

ω [Hz] 

Figure A-46 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 40 years of service at 50oC
194

3.36

3.38

3.42

3.44

400000 600000 800000 1x106

Extracted 

B Model 

A 

B 

A 

G(ω)/ω-l [x10-10 mho-s/m]

ω [Hz] 

Figure A-47 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 40 years of service at 60oC

7.25

7.50

7.75

8.00

8.25

8.50

600000 700000 800000 1x106

Extracted 

B Model 

A 

B 

A 

900000 

G(ω)/ω-l [x10-10 mho-s/m]

ω [Hz] 

Figure A-48 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 70oC
195

102.5

103.0

103.5

104.0

104.5

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

Extracted 

B Model 

A 

400000 600000 800000 

Ψ(ω)

B 400000 600000 800000 A 

B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz]

ω [Hz]

Figure A-49 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 50oC

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

105.5

106.0

106.5

107.0

107.5

Extracted 

B Model 

A 

400000 600000 800000 

Ψ(ω)

400000 600000 800000 

B 

A B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz]

ω [Hz]

Figure A-50 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 60oC
196

102.5

103.0

103.5

-1.75

-1.50

-1.25

-1.00

-0.75

-0.50

Extracted 

B Model 

A 

400000 600000 800000 

Ψ(ω)

400000 600000 800000 

B 

A B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz] ω [Hz]

Figure A-51 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 40 years of service at 70oC

0.015

0.020

0.025

0.030

0.035

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

600000 800000 1X106

γ

i

(ω)

ω [Hz] 

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1X106

B 

A A B 

ω [Hz]

Figure A-52 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at 50oC
197

0.015

0.020

0.025

0.030

0.035

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

600000 800000 1X106

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1X106

B 

A A B 

ω [Hz] 

ω [Hz]

Figure A-53 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at 60oC

 ́

0.015

0.020

0.025

0.030

0.035

0.0004

0.0006

0.0008

600000 800000 1X106

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

600000 800000 1X106

B 

A 

B A 

ω [Hz] 

ω [Hz]

Figure A-54 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 40 years of service at 70oC

A.3 Test Results for Cables with Global Thermal Aging to Simulate 60 Years of Service
198

400000 600000 800000 1x106

0.06

0.08

0.12

0.14

Extracted 

B Model 

A 

B 

A 

R(ω)/l [S/m] 

ω [Hz] 

Figure A-55 Comparison of resistance per unit length predicted by analytical model to

that extracted from measured impedance for cable with global thermal aging to simulate

60 years of service at 50oC

The following figures present the results of broadband impedance tests performed on cables with

global thermal aging to simulate 60 years of service in a nuclear power plant at service

temperatures of 50oC (122oF), 60oC (140oF), and 70oC (158oF). These results supplement the

data presented in Section 5 of this report.
199

400000 600000 800000 1x106

0.06

0.08

0.12

0.14

Extracted 

B Model 

A 

B 

A 

R(ω)/l [S/m] 

ω [Hz] 

Figure A-56 Comparison of resistance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 60oC

3.75 x10-6

3.80 x10-6

3.85 x10-6

400000 600000 800000 1x106

Extracted 

B Model 

A 

A 

B 

L(ω)/m (H/m)

ω (Hz)

Figure A-57 Comparison of inductance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 50oC
200

400000 600000 800000 1x106

3.75 x10-6

3.85 x10-6

3.90 x10-6

3.95x10-6

Extracted 

B Model 

A 

A 

B 

L(ω)/m (H/m)

ω (Hz)

Figure A-58 Comparison of inductance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 60oC

3.39

3.41

3.42

3.43

3.44

3.45

400000 600000 800000 1x106

Extracted 

B Model 

A 

A 

B 

C(ω)/l [x10-10 F/m] 

ω [Hz] 

Figure A-59 Comparison of capacitance per unit length predicted by analytical

model to that extracted from measured impedance for cable with global thermal

aging to simulate 60 years of service at 50oC
201

Figure A-60 Comparison of capacitance per unit length predicted by analytical model to

that extracted from measured impedance for cable with global thermal aging to simulate

60 years of service at 60oC

5.25

5.50

5.75

6.00

6.25

6.50

6.75

400000 600000 800000 1x106

Extracted 

B Model 

A 

B 

A 

G(ω)/ω-l [x10-10 mho-s/m]

ω [Hz] 

Figure A-61 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 60 years of service at 50oC
202

6.50

6.75

7.25

7.50

7.75

8.00

8.25

400000 600000 800000 

Extracted 

B Model 

A 

B 

A 

300000 500000 700000 

G(ω)/ω-l [x10-10 mho-s/m]

ω [Hz] 

Figure A-62 Comparison of conductance-to-frequency ratio per unit length

predicted by analytical model to that extracted from measured impedance for

cable with global thermal aging to simulate 60 years of service at 60oC

104.5

105.0

105.5

106.0

-2.25

-1.75

-1.50

-1.25

-1.00

-0.75

Extracted 

B Model 

A 

400000 600000 800000 

Ψ(ω)

400000 600000 800000 

B 

A B 

A 

|Z0(ω)|/l [S/m] 

ω [Hz]

ω [Hz]

Figure A-63 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 60 years of service at 50oC
203

106.5

107.0

107.5

108.0

-2.25

-1.50

-1.25

-1.00

-0.75

-0.50

Extracted 

B Model 

A 

400000 600000 800000 

Ψ(ω)

400000 600000 800000 

A B 

B 

A 

-1.75

|Z0(ω)|/l [S/m] 

ω [Hz]

ω [Hz]

Figure A-64 Comparison of characteristic impedance magnitude per unit length and

phase spectra predicted by analytical model to that extracted from measured impedance

for cable with global thermal aging to simulate 60 years of service at 60oC

0.015

0.020

0.025

0.030

0.035

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

400000 600000 1x106

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

B 

A A B 

800000

400000 600000 1x106 800000 

ω [Hz] 

ω [Hz] 

Figure A-65 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 60 years of service at 50oC
204

0.015

0.020

0.025

0.030

0.035

0.0004

0.0005

0.0006

0.0007

0.0008

0.0009

400000 600000 1x106

γ

i

(ω)

Extracted 

B Model 

A 

γ

r

(ω)

B 

A 

B 

A 

800000

400000 600000 800000

ω [Hz] 

ω [Hz]

Figure A-66 Comparison of the imaginary component and real component of the

propagation function predicted by analytical model to that extracted from measured

impedance for cable with global thermal aging to simulate 60 years of service at 60oC
205

Appendix B

BIS Test Results for Cables with Localized Thermal Aging (Hot Spots)
206

(This page intentionally left blank)
207

List of Figures

Page No.

Figure B-1 Characteristic impedance magnitude per unit length and phase spectra over the

frequency range from 1MHz to 100MHz for cables with global thermal aging to

simulate 20 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . 207

Figure B-2 Imaginary and real components of the propagation function over the frequency

range from 1MHz to 100MHz for cables with global thermal aging to simulate 

20 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

Figure B-3 Impedance magnitude per unit length and phase spectra over the frequency range

from 39MHz to 45 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Figure B-4 Imaginary and real components of the propagation function over the frequency

range from 1MHz to 100MHz for cables with global thermal aging to simulate 

 40 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . 208

Figure B-5 Characteristic impedance magnitude per unit length and phase spectra over the

frequency range from 1MHz to 100MHz for cables with global thermal aging to

simulate 40 years of service at various temperatures . . . . . . . . . . . . . . . . . . . . 209

Figure B-6 Impedance magnitude per unit length and phase spectra over the frequency range

from 14MHz to 22 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Figure B-7 Impedance magnitude per unit length and phase spectra over the frequency range

from 14MHz to 22 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Figure B-8 Impedance magnitude per unit length and phase spectra over the frequency range

from 41MHz to 42 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

Figure B-9 Impedance magnitude per unit length and phase spectra over the frequency range

from 39MHz to 45 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots at different

locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
208

Figure B-10 Impedance magnitude per unit length and phase spectra over the frequency range

from 14MHz to 22 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots at different

locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Figure B-11 Impedance magnitude per unit length and phase spectra over the frequency range

from 39MHz to 45 MHz for cables with global thermal aging to simulate 40 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Figure B-12 Impedance magnitude per unit length and phase spectra over the frequency range

from 14MHz to 22 MHz for cables with global thermal aging to simulate 40 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

Figure B-13 Impedance magnitude per unit length and phase spectra over the frequency range

from 14MHz to 22 MHz for cables with global thermal aging to simulate 40 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Figure B-14 Impedance magnitude per unit length and phase spectra over the frequency range

from 41MHz to 42 MHz for cables with global thermal aging to simulate 40 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213

Figure B-15 Impedance magnitude per unit length and phase spectra over the frequency range

from 39MHz to 45 MHz for cables with global thermal aging to simulate 40 years

of service at 50oC, plus additional thermal aging to simulate hot spots at different

locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
209

2x107 6x107 1x108

98

100

102

|Z0(T)|/l [S/m] Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A B 

C 

A 

B 

C 

2x107 6x107 1x108

0.2

0.3

0.4

ω ω (Hz) (Hz)

Figure B-1 Characteristic impedance magnitude per unit length and phase spectra over

the frequency range from 1MHz to 100MHz for cables with global thermal aging to

simulate 20 years of service at various temperatures

1

2

3

0.01

0.02

0.03

0.04

0.05

γ

i

(ω) γ

r

(ω)

2x107 6x107 1x108

ω (Hz)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A 

B 

C 

A 

B 

C 

2x107 6x107 1x108

ω (Hz)

Figure B-2 Imaginary and real components of the propagation function over the

frequency range from 1MHz to 100MHz for cables with global thermal aging to simulate

20 years of service at various temperatures 
210

3.9x107

50

100

150

60

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

4.5x107 4.3x107 4.1x107

3.9x107

 4.5x107 4.3x107 4.1x107

40

20

-20

-40

-60

A 

A 

B 

B 

C 

C 

Figure B-3 Impedance magnitude per unit length and phase spectra over the frequency

range from 39MHz to 45 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity

0.06

0.07

1

2

3

0.01

0.02

0.03

0.04

0.05

γ

i

(ω) γ

r

(ω)

2x107 6x107 1x108

A 

B 

C 

A 

B 

C 

2x107 6x107 8x107 4x107

ω (Hz)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

ω (Hz)

Figure B-4 Imaginary and real components of the propagation function over the

frequency range from 1MHz to 100MHz for cables with global thermal aging to simulate

40 years of service at various temperatures 
211

98

100

102

104

106

108

0.3

0.4

0.5

2x107 6x107

 1x108

Ψ(ω)

50 oC (122 oF) 

C 

60 oC (140 oF) 

70 oC (158 oF) 

A 

B 

A 

B 

C 

A 

B 

C 

2x107 6x107

 1x108

|Z0(T)|/l [S/m] 

ω (Hz) ω (Hz)

Figure B-5 Characteristic impedance magnitude per unit length and phase spectra over

the frequency range from 1MHz to 100MHz for cables with global thermal aging to

simulate 40 years of service at various temperatures

1.4x107

200

400

600

80

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

1.8x107 2.2x107

1.4x107 1.8x107 2.2x107

A 

A 

B 

B 

C 

C 

60

40

20

-20

-40

-60

Figure B-6 Impedance magnitude per unit length and phase spectra over the frequency

range from 14MHz to 22 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots of different

severity
212

1.4x107

600

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs]

ω [Hzs] 

A 

A B 

B 

C 

C 

400

200

80

60

40

20

-20

-40

1.8x107

 2.2x107

1.4x107

 1.8x107 2.2x107

Figure B-7 Impedance magnitude per unit length and phase spectra over the

frequency range from 14MHz to 22 MHz for cables with global thermal aging to

simulate 20 years of service at 50oC, plus additional thermal aging to simulate hot

spots of different size

4.12x107

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

A 

A 

B B 

C 

C 

40

30

20

10

-10

-20

36

34

32

30

28

4.16x107

 4.20x107

4.12x107

 4.16x107 4.20x107

Figure B-8 Impedance magnitude per unit length and phase spectra over the

frequency range from 41MHz to 42 MHz for cables with global thermal aging to

simulate 20 years of service at 50oC, plus additional thermal aging to simulate hot

spots of different size
213

3.9x107

150

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (158 oF) Hot Spot at 1.0m-2.0m from POM 

70 oC (158 oF) Hot Spot at 8.0m-9.0m from POM 

A 

B 

ω [Hzs] 

ω [Hzs] 

A 

A 

B 

B 

C 

C 

100

50

4.1x107

 4.3x107

60

40

20

-20

-40

-60 4.5x107

3.9x107

 4.1x107 4.3x107 4.5x107

Figure B-9 Impedance magnitude per unit length and phase spectra over the frequency

range from 39MHz to 45 MHz for cables with global thermal aging to simulate 20 years

of service at 50oC, plus additional thermal aging to simulate hot spots at different

locations

1.4x107

600

80

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

ω [Hzs] 

ω [Hzs] 

A A 

B 

B 

C 

C 400

200

1.8x107

 2.2x107

1.4x107

 1.8x107 2.2x107

60

40

20

-20

-40

-60

No Hot Spot 

C 

70 oC (158 oF) Hot Spot at 1.0m-2.0m from POM 

70 oC (158 oF) Hot Spot at 8.0m-9.0m from POM 

A 

B 

Figure B-10 Impedance magnitude per unit length and phase spectra over the

frequency range from 14MHz to 22 MHz for cables with global thermal aging to simulate

20 years of service at 50oC, plus additional thermal aging to simulate hot spots at

different locations
214

175

-60

-40

-20

20

40

60

3.9x107

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs]

ω [Hzs] 

4.1x107 4.3x107

A 

B B 

C 

C 

150

125

100

75

50

4.5x107

3.9x107 4.1x107 4.3x107 4.5x107

A 

Figure B-11 Impedance magnitude per unit length and phase spectra over the

frequency range from 39MHz to 45 MHz for cables with global thermal aging to

simulate 40 years of service at 50oC, plus additional thermal aging to simulate hot

spots of different severity

1.4x107

200

300

400

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

60 oC (140 oF) 1.0m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

1.8x107 2.2x107

1.4x107

 1.8x107 2.2x107

A A 

B 

B 

C C 

60

40

20

-40

-60

100

Figure B-12 Impedance magnitude per unit length and phase spectra over the

frequency range from 14MHz to 22 MHz for cables with global thermal aging to simulate

40 years of service at 50oC, plus additional thermal aging to simulate hot spots of

different severity
215

1.4x107

200 

300 

400

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (140 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

1.8x107 2.2x107

A 

A 

B 

B 

C 

C 

60

40

20

-40

-60

100

500

1.4x107 1.8x107

 2.2x107

Figure B-13 Impedance magnitude per unit length and phase spectra over the

frequency range from 14MHz to 22 MHz for cables with global thermal aging to

simulate 40 years of service at 50oC, plus additional thermal aging to simulate

hot spots of different size

-60

-40

-20

20

40

60 175

3.9x107

|Z(ω)|/l [S/m] 

Φ(ω) [Degrees] 

No Hot Spot 

C 

70 oC (140 oF) 0.5m Hot Spot 

70 oC (158 oF) 1.0m Hot Spot 

A 

B 

ω [Hzs] 

ω [Hzs] 

4.1x107 4.3x107

A 

B C B 150

125

100

75

50

4.5x107

A 

3.9x107 4.1x107 4.3x107 4.5x107

C 

Figure B-14 Impedance magnitude per unit length and phase spectra over the

frequency range from 41MHz to 42 MHz for cables with global thermal aging to simulate

40 years of service at 50oC, plus additional thermal aging to simulate hot spots of

different size
216

175

3.9x107

|Z(ω)|/l [S/m] Φ(ω) [Degrees] 

No Hot Spot 

C 

1.0m Hot Spot 1-2m from POM 

1.0m Hot Spot 8-9m from POM 

A 

B 

ω [Hzs] 

ω [Hzs] 

4.1x107 4.3x107

B A 

B 

C 

150

125

100

75

50

4.5x107

A 

3.9x107 4.1x107 4.3x107 4.5x107

C 

60

40

20

-40

-60

Figure B-15 Impedance magnitude per unit length and phase spectra over the

frequency range from 39MHz to 45 MHz for cables with global thermal aging to simulate

40 years of service at 50oC, plus additional thermal aging to simulate hot spots at

different locations