MODELLING OF XLPE NANOCOMPOSITE POWER CABLE USING COMSOL MULTIPHYSICS
NIROSHINI A/P SUKUMARAN
MODELLING OF XLPE NANOCOMPOSITE POWER CABLE USING COMSOL MULTIPHYSICS
NIROSHINI A/P SUKUMARAN
A project report submitted in partial fulfilment of the requirements for the award of the degree of
Master of Engineering (Electrical Power)
Faculty of Electrical Engineering Universiti Teknologi Malaysia
iii
This project report is dedicated to my beloved mother and father. I give my deepest expression of love and appreciation for the encouragement and support
iv
ACKNOWLEDGEMENT
First and foremost, I would like to express my deepest sincere gratitude to my supervisor Dr. Mohd Hafizi Bin Ahmad for his patience in guidance, motivation, encouragement, enthusiasm and his immerse knowledge on master project. To Dr. Zuraimy B. Adzis and Dr. Mona Riza Bt. Mohd Esa, I thank you for your idea and insightful comment during seminar sessions which are useful in improving master project.
A special thanks and gratitude to my superior in YTL Power Services, Mr. Raman Subramaniam for your moral support, advise and intellectual support in my master program.
Finally, and above all, I cannot begin to express my unfailing gratitude and love to close friends and my family especially my parent, R.Sukumaran and B.Kathiyane who has prayed, supported and understood me throughout this process and has constantly encouraged me when the tasks seemed challenging and insuperable.
v
ABSTRAK
Laporan ini membentangkan pemodelan kabel polyethylene (XLPE) bersalut nano terlindung dengan kehadiran lompang menggunakan menggunakan perisian COMSOL Multiphysics. Lompang sama ada dengan medium udara atau air adalah salah satu faktor yang menyebabkan degradasi penebat kabel. Kehadiran lompang di dalam kabel berlaku semasa proses penghubung silang di mana penembusan wap air berlaku. Dengan menggunakan perisian COMSOL Multiphysics mungkin menjadi kaedah terbaik untuk menyiasat taburan medan elektrik dan pengagihan medan potensial lompang dalam kabel. Kaedah elemen terhingga adalah salah satu daripada kaedah berangka terkini yang digunakan untuk menganalisis elektrik dan pengagihan medan potensi lompang dalam kabel kuasa. COMSOL Multiphysics adalah salah satu alat berkuasa yang melaksanakan kaedah unsur terhingga dengan menyelesaikan persamaan Poisson. Dalam laporan ini, perbandingan kedua-dua jenis bahan kabel XLPE seperti kabel XLPE tulen dan kabel bertebat nano yang dibuat dalam penyiasatan elektrik dan pengagihan medan potensi lompang dalam kabel dengan menganalisis dan membandingkan corak graf dihasilkan oleh dua jenis bahan penebat kabel. Keputusan yang diperolehi daripada simulasi COMSOL menunjukkan medan elektrik dipengaruhi oleh jenis lompang, lokasi lompang dan kehadiran zarah nano di dalam penebat XLPE.
vi
ABSTRACT
This report presents modelling of a nano-insulated cross-linked polyethylene (XLPE) cable with the presence of voids using COMSOL Multiphysics software. Void either with the medium of air or water is one of the factor that causes degradation of the power cable insulation. The void that presence in the power cable is occur during cross linking process where the penetration of water steam happened. Using COMSOL Multiphysics software might be the best method in investigating the electric field distribution and potential field distribution of the void in the power cable. Finite element method is one of the latest numerical methods use in analyze the electrical and potential field distribution of the voids in the power cable. COMSOL Multiphysics is one the powerful tools that implement the finite element method by resolving Poisson’s equation. In this report, comparison of both type of the XLPE cable materials such as pure XLPE cable and nano-insulated cable are made in investigating the electrical and potential field distribution of the voids in the cable by analyze and compare the graph pattern generated by two types of the cable insulation material. Simulation results indicate that the electric field distribution is influenced by the type of the void, void position and presence of nanoparticle in the XLPE insulation.
vii
TABLE OF CONTENTS
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRAK v
ABSTRACT vi
TABLE OF CONTENTS vii
LIST OF TABLES xi
LIST OF FIGURES xii
LIST OF ABBREVIATIONS xiv
LIST OF APPENDICES xvi
1 INTRODUCTION 1 1.1 Introduction 1 1.2 Background of Study 2 1.3 Problem Statement 4 1.4 Objectives 5 1.5 Scope of Study 5 1.6 Project Methodology 6
1.7 Project Report Structure 7
2 LITERATURE REVIEW 9
viii modelling of the XLPE power cable
2.1.1 Theoretical Approach 11
2.1.2 Parametric Analysis 11
2.1.3 Finite Element Method (FEM) 16
2.1.3.1 Maxwell Software 16
2.1.3.2 Static Regime Modelling 18
2.1.3.3 COMSOL Multiphysics 20
2.2 Summary of research on techniques used 22
2.3 Direction of further research 23
3 RESEARCH METHODOLOGY 24
3.1 Introduction 24
3.2 General Development and Implementation of 27
Electrostatic Model
3.2.1 Geometrical Parameter of the XLPE 27
Power Cable
3.2.2 XLPE Power Cable Material and 28
Properties
3.2.3 Electrostatic Model 29
3.3 COMSOL Multiphysics Software Flowchart 31
4 RESULTS & DISCUSSION 34
4.1 XLPE power cable without the existence of 35
void
4.1.1 2D Pure XLPE power cable without the 35
presence of void
4.1.2 3D Pure XLPE power cable without the 37
presence of void
4.1.3 2D Nanocomposite XLPE power cable 39
without the presence of void
4.2 XLPE power cable with the existence of air- 41
ix
4.2.1 2D Pure XLPE power cable with the 41
presence of air-filled void
4.2.2 3D Pure XLPE power cable with the 43
presence of air-filled void
4.2.3 Nanocomposite XLPE power cable 45
with the presence of air-filled void
4.3 XLPE power cable with the existence of water- 46 filled void
4.3.1 2D Pure XLPE power cable with the 47
presence of water-filled void
4.3.2 3D Pure XLPE power cable with the 48
presence of water-filled void
4.3.3 Nanocomposite XLPE power cable 50
with the presence of water-filled void
4.4 XLPE power cable with the existence of air-filled 52 void at different location
4.4.1 2D Pure XLPE power cable with the 53
presence of air-filled void located further away from the conductor
4.4.2 3D Pure XLPE power cable with the 54
presence of air-filled void located further away from the conductor
4.4.3 Nanocomposite XLPE power cable with 56
the presence of air-filled void located further away from the conductor
4.5 XLPE power cable with the existence of water 58 filled void at different location
4.5.1 2D Pure XLPE power cable with the 59
presence of air-filled void located further away from the conductor
presence of air-filled void located further away from the conductor
4.5.3 Nanocomposite XLPE power cable with 62
the presence of air-filled void located further away from the conductor
4.6 Summary: Comparison between the pure XLPE 64
power cable and nano-insulated XLPE power cable
4.6.1 Comparison between the pure XLPE 64
power cable and nano-insulated XLPE power cable without the presence of void
4.6.2 Comparison between the pure XLPE 65
power cable and nano-insulated XLPE power cable without the presence of void
5 CONCLUSIONS & RECOMMENDATION 67
5.1 Project Conclusions 67
5.2 Problem encounter 68
5.3 Recommendation for Future Works 69
REFERENCES 70
Appendices A-C 74
xi
LIST OF TABLES
TABLE NO. TITLE PAGE
2.0 Electric field stress on the different type of nano- 21
filler
2.1 Summary of gaps of the technique used 22
3.0 Research Design 26
3.1 Geometrical Parameter of the XLPE Power Cable 28
3.2 XLPE Power Cable Material with Its Respective 28
Properties
4.1 Electric Field Distribution on the XLPE Power Cable 65
without void
4.2 Electric Field Distribution on the XLPE Power Cable 66
with void
xii
LIST OF FIGURES
FIGURE. NO TITLE PAGE
1.0 Development of the cable insulation material 3
over the years
2.0 Techniques of analyzing the electric field and 10
potential field distribution of cavities in the XLPE cable
2.1 Frequency of damage in PE versus electric field 12
based on variation on void height
2.2 Frequency of damage in PE versus electric field 13
based on variation of temperature
2.3 Frequency of damage in PE versus electric field 14
based on variation of conductivity of material
2.4 Frequency of damage in PE versus electric field 15
based on variation of void radius
2.5 Electric field distribution across the cable 17
2.6 Electric field distribution of a different void shape 18
2.7 Overview of the zone that consists of the 19
voids
2.8 Simulation from COMSOL Multiphysics of 21
XLPE with 5% wt of (a)nanoclay
(b)nanosilica, (c) nanocarbonate
3.1 Project methodology flowchart 26
3.3 COMSOL Multiphysics flowchart 32
4.1 Electric field distribution and electric potential 36
in the pure XLPE cable.
4.2 Electric field distribution in the pure XLPE 36
cable
4.3 Electric field distribution and electric 37
potential in the 3D pure XLPE cable.
4.4 Electric field distribution in the 3D pure XLPE 38
cable
4.5 Electric field distribution and electric 40
potential in the 2D nanocomposite XLPE cable.
4.6 Electric field distribution in the 2D 40
nanocomposite XLPE cable
4.7 Electrical field distribution and potential field 42
distribution in the 2D pure XLPE cable with the presence of air-filled void
4.8 Electrical field distribution in the 2D pure 42
XLPE cable with the presence of air-filled void
4.9 Electrical field distribution and potential field 43
distribution in the 3D pure XLPE cable with the presence of air-filled void
4.10 Electrical field distribution in the 3D pure 44
XLPE cable with the presence of air-filled void
4.11 Electrical field distribution and potential field 45
distribution in the nanocomposite XLPE cable with the presence of air-filled void
4.12 Electrical field distribution in the 46
nanocomposite XLPE cable with the presence of air-filled void
4.13 Electrical field distribution and potential field 47 distribution in the 2D pure XLPE cable with
the presence of water- filled void
4.14 Electrical field distribution in the 2D pure 48
XLPE cable with the presence of water-filled void
4.15 Electrical field distribution and potential field 49
distribution in the 3D pure XLPE cable with the presence of water- filled void
4.16 Electrical field distribution in the 3D pure 49
XLPE cable with the presence of water-filled void
4.17 Electrical field distribution and potential field 51
distribution in the nanocomposite XLPE cable with the presence of water- filled void
4.18 Electrical field distribution in the 51
nanocomposite XLPE cable with the presence of water-filled void
4.19 Electrical field distribution and potential field 53
2D pure XLPE cable with the presence of air- filled void further away from conductor
4.20 Electrical field distribution in the 2D XLPE 54
cable with the presence of air-filled void further away from conductor
4.21 Electrical field distribution and potential field 55
distribution in the 3D pure XLPE cable with the presence of air- filled void further away from conductor
4.22 Electrical field distribution in the 3D pure 55
XLPE cable with the presence of air-filled void further away from conductor
4.23 Electrical field distribution and potential field 57
distribution in the nanocomposite XLPE cable with the presence of air- filled void further away from conductor
4.24 Electrical field distribution in the 57
nanocomposite XLPE cable with the
presence of air-filled void further away from conductor
4.25 Electrical field distribution and potential field 59
distribution in the 2D pure XLPE cable with the presence of water- filled void further away from conductor
4.26 Electrical field distribution in the 2D Pure 60
XLPE cable with the presence of water-filled void further away from conductor
4.27 Electrical field distribution and potential field 61
distribution in the 3D pure XLPE cable with the presence of water- filled void further away from conductor
4.28 Electrical field distribution in the 3D pure 61
XLPE cable with the presence of water-filled void further away from conductor
4.29 Electrical field distribution and potential field 63
distribution in the nanocomposite with the presence of water- filled void further away from conductor
4.30 Electrical field distribution in the 63
nanocomposite XLPE Cable with the presence of water-filled void further away from conductor
xiv
LIST OF ABBREVIATIONS
XLPE - Cross-linked Polyethylene
HVDC - High Voltage Direct Current
DC - Direct Current
FEM - Finite Element Method
PVC - Polyvinylchloride
PE - Polyethylene
2D - Two Dimensional
3D - Three Dimensional
m - Meter
V/m - Volt per meter
SiO2 - Silicon Dioxide
E - Electric Field
V - Potential
Ɛ - Relative Permittivity
Ɛr - Relative Permittivity of the Insulating Material
Ɛ0 - Free Space Permittivity
D - Electric Displacement of the Conductor
E - Electric Field of Cavity
r - Radius of the Conductor
rc - Cavity Radius
rz - Radius of the Area Influenced
𝜀 - Permittivity of the Cavity
𝜀 - Permittivity of the XLPE
n - Normal Component
𝜌 - Free Space Charge
xvi
LIST OF APPENDICES
APPENDIX TITLE PAGE
A Project schedule semester 1 74
B Project schedule semester 2 75
CHAPTER 1
INTRODUCTION
1.1 Introduction
Electricity is useful and important for everyone where it used to power up most of the electrical equipment such as mobile phone, computer, lighting, and others essential appliances. Without electricity, it may interrupt and give rise to certain problem such as industry may have stop production, people have to stay in dark and others inconvenience of the lifestyle.
According to the recent development either in technology or lifestyle, the demand of the electricity keeps increasing over the years. The increase in the demand of the electricity have been a huge concern to the energy utilities where they must make sure sufficient of supply is available in the system. Apart from that, energy utilities have to ensure that the electricity supply is always reliable and stable. In order to ensure the stability of the electricity supply to the consumer, power cable is one of the main component in the power system need to be taken care properly. Any damage occurred on the power cable will cause power interruption. Most of the damage occurred on the power cable is due to damage in the power cable insulation.
2 Therefore, good quality of the power cable insulation will ensure the power system in the stable condition. Electric power cable has evolved by time to time to tally with the present technology. Evolvement of power cable from PVC type to the addition of the nano filler in the power cable insulation at current technology.
Addition of nano filler in the power cable have improved the electrical characteristics of the power cable where it reduces the risk of partial discharge [1].
1.2 Background of Study
Power cable is one of the essential component in the power system especially used in the overhead line and underground lines. Most of the power cable expensive to be replaced in term of the installation cost. Therefore, it is important to have a good cable insulation where can be used for many years without cause any power interruption due to failure of the cable. The condition of the insulation system is determining the cable lifetime due to insulation system continuously encounter stresses such as thermal, electrical, mechanical, chemical and environmental stresses. Presence of the voids [2] might cause degradation of the cable insulation which leads the failure of the cable. Cable insulation material is the most important component need to be considered properly in order to ensure no failure happened.
The development of the cable insulation material from the PVC in the year 1913 introduced by Friedrich to present where the nanocomposite XLPE cable introduced by the Lewis in year 1994. For the past few decades since year 1955 introduced by Gilbert, cross-linked polyethylene (XLPE) cable is widely used in the transmission and distribution industry due to its outstanding features such as good dielectric strength, resist to solvent, dielectric permittivity is low and low loss factor as well, good dimensional stability and behavior of the thermo-mechanical.
3 There is drawback in the usage of the XLPE power cable due to the formation of the space charge and treeing which decreases the service time of the power cable. Formation of the space charge [3] due to penetration of the water steam during cross-linking process and wrong extrusion. These leads to the formation of the voids in the power cables which enhance the partial discharge [1] to be occurred.
Figure 1.0 Development of the cable insulation material over the years.
In the year 1994, Lewis had introduced nanometric dielectric which drawn interest to many researchers on this nanocomposite material as this material able to act as barrier in the formation of the space charge and treeing which eventually improve the quality of the cable insulation where the lifetime of the cable can be prolonged. Nano filler [4] that infused in the XLPE cable have excellent characteristics than the pure XLPE cable where it improves breakdown strength and high resistance to the water and electrical trees. Besides that, nanocomposite cable has potential in reducing the space charge formation in the power cable. Improvement in the XLPE cable insulation material able to prevent the failure of the cable where the risk of the partial discharge able to be reduced.
4 1.3 Problem Statement
High voltage power cable is one of the essential component in the power system which continuously exposed to variety of stresses such as thermal stress, electric stress, chemical stress, environmental stress and other stress that act on the cable insulation. These stresses that act on the cable which will eventually degrade the properties of the insulation. The lifetime of the power cable depends on the cable
insulation. It is important to have a good insulation for the cable to avoid any damage occurred which might interrupt the power system.
One of the major problem that causes the degradation of the power cable insulation is the presence of the voids. The voids can have medium of either air or water that can leads to shorten the lifetime of the power cable. Phenomenon that causes the presence of the voids in the power cable is due to penetration of the water steam during process of the cross-link. Besides that, mistake can also happen during operation of the cross link and wrong extrusion. Usually the size of the voids appear in the cable is about 1 μm to 20 μm. Apart than that, the position of the voids exists in the cable also give impact to the lifetime of the power cable as the voids near to the conductor have high electrical field distribution compare to the voids located further away from the conductor which enhance the partial discharge occurred.
Besides that, cable insulation material also play an important role in preventing the presence of the voids in the cable. Over the years, the cable insulation material had been developed from the PVC material to the XLPE material which show significance improvement in the quality of the cable insulation where the cable is long lasting. Depends on the material of the cable insulation, the voids present encounter different temperature and pressure on it. Proper design of the cable insulation material is needed to ensure the cable can be used for many years which is
5 cost efficient for the power utility company. In this project, nano-insulated XLPE
power cable with the presence of the voids with different feature would be analyzed.
1.4 Objectives:
By referring to the problem statement mentioned above, this research was conducted with several meaningful objectives below:
1. To simulate the electric field distribution and potential field distribution in the
nanocomposite XLPE power cable having void using COMSOL Multiphysics.
2. To analyse the simulation result by considering various factors such as void
position, void size and others.
3. To compare the simulation result with the pure XLPE power cable.
1.5 Scope of Study
By referring to the objectives mentioned above, the limitation and assumption applied in this project is clearly elaborated as the followings:
1. This work focused on the XLPE power cable model only. Based on existing
research, the study of the pure XLPE power cable with the presence of voids was investigated for the electrical field distribution and potential field distribution. It is proven that the voids near to the conductor have high electrical field than the voids further away from the conductor.
6
2. The focus of this study was on electrical field distribution and potential field
distribution based on respective void feature only. Void feature considered in this paper is the void position and type of the void in the XLPE power cable.
3. This work also focused on comparison of the results obtained from the pure
XLPE power cable and nano-insulated XLPE power cable by considering the presence of voids with different void feature.
1.6 Project Methodology
By referring to the objectives mentioned earlier, the following work methodologies have been planned:
1. A literature review on the technique used in analyzing the electric field and
potential field distribution in the void presence in the XLPE cable using finite element method was carried out. Topic related article can be extracted from the conference papers, journal papers, online articles and electronic books from internet or digital library in UTM. Suitable application within each reference was gained.
2. A critical and strategic literature review of electric field and potential field
distribution in the void presence in the XLPE cable using finite element method was performed. In order to propose algorithm, the existing flowchart and formulation have been analyzed. By having in depth literature review, it provides a good theoretical understanding about XLPE cable with the presence of void design considerations need to be taken in order to develop the algorithm.
3. A new modelling of a nano-insulated XLPE power cable with the presence of
7
4. Verification of proposed modelling of a nano-insulated XLPE power cable
with the presence of the voids will be performed by comparing the result output against FEMM software output which is available.
1.7 Project Report Structure
Chapter 1 describes the introduction of the XLPE power cable insulation that used in the power system. It includes the problem statement, objectives, the scope of this project work and the methodology used to apply in accomplishing this project report. Briefly explanation on this chapter will gauge the reader have a clearer picture on the overview of the project.
Chapter 2 presents the literature review on the techniques used to investigate the electrical field distribution and potential field distribution of the voids presence in the XLPE power cable. The data of the literature review was collected from the journal which extracted from the UTM digital library such as IEEE, Scopus, science
direct and others relevant journal. All the journal collected based on the project background which is related to the XLPE power cable insulation having cavities.
In Chapter 3, the mathematical modelling of the electrical field and potential field distribution of the XLPE power cable with the presence of the voids is described in detail. First and foremost, it will cover Poisson’s equation in the modelling. In addition, this chapter will also cover the implementation of the mathematical modelling in the COMSOL Multiphysics software.
8 Chapter 4 starts with the validation of result simulated from the pure XLPE power cable containing voids and the simulation result of the nano-insulated XLPE power cable with the presence of voids will be presented and discuss upon.
Chapter 5 draws the conclusions for the work undertaken are presented and few possible suggestions for future work are highlighted as well.
REFERENCES
1. Emna K, Rabah A, Nejib C. Numerical Modeling of the Electric Field and the Potential Distributions in Heterogeneous Cavities inside XLPE Power Cable Insulation.Journal of Electrical and Electronics Engineering. 2016; 9(2): 37-42 2. P. S. Patel, V. S. Chaudhari and H. M. Patel, “Analysis of Electric Stress in High
Voltage Cables,” International Journal of Engineering Research & Technology, vol. 3, no. 3, pp. 1443-1447, 2014.
3. S.Lachini, A.Gholami and M.Mirzaie, "Determining Electric Field Distribution in HIgh Voltage Cable in Presence of Cavity," Proceedings of the Universities Power Engineering Conference, 2010.
4. D. Pitsa, G. E. Vardakis, M. G. Danikas, Y. Chen Electrical tree simulation and breakdown in nanocomposite polymers: The role of nanoparticles” International Conference on Solid Dielectrics, July 4- 9, 2010
5. M.Hadjadj, B.Mokhtari and D.Mahi, "Study of Physical Parameters Change, by Static Regime Modeling, in a Heterogeneous Insulating Meterial XLPE, containing three cavities, of a Medium Voltage Cable," Journal of Electrical Engineering , vol. 14, no. 1, pp. 85-99, 2014.
6. T. Tanaka, G. C. Montanari and R. Mulhaupt, "Polymer nanocomposites as dielectrics and electrical insulation-perspectives for processing technologies, material characterization and future applications," in IEEE Transactions on Dielectrics and Electrical Insulation, vol. 11, no. 5, pp. 763-784, Oct. 2004. 7. M. G. C. F. Mazzanti G., "Model of inception and growth of damage from
microvoids in polyethylene-based materials for HVDC cables part 1: Theoretical approach," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 14, no. 5, pp. 1255-1263, 2007.
8. Li Xiufeng, Liu Xin, Xu Man, Xie Darong, Cao Xiaolong, Wang Xiaoqiang and Liu Huajun, “Influence of Compatibilizers on the Water-tree Property of Montmorillonite/Cross-linked Polyethylene Nanocomposites”, IEEE 10th International Conference on the Properties and Applications of Dielectric Materials,July 24-28, 2012.
71 9. E. Khouildi, R. Attia and N. Chtourou, "Numerical Modeling of the Electric Field and the Potential Distributions in Heterogeneous Cavities inside XLPE Power Cable Insulation," Journal of Electrical and Electronics Engineering, vol. 9, no. 2, pp. 37-42, October 2016.
10. M. G. C. F. Mazzanti G., "Model of inception and growth of damage from microvoids in polyethylene-based materials for HVDC cables part 2: Parametric investigation and data fitting," IEEE Transactions on Dielectrics and Electrical Insulation, vol. 14, no. 5, pp. 1242-1254, 2007.
11. F. Guastavino, A. Dardano, S. Squarcia, P. Tiemblo, J. Guzman, N.Garcia, “An Experimental Study About Electrical Treeing Inside LDPE Nanocomposites”, IEEE International Conference on Solid Dielectric,2010
12. H.N.O.T.R.; Phung, B.T.; Zhang, H.; Khawaja, R.H.; R. H. Khawaja," Investigation of Electric Field Distribution In Power Cables With Voids", 8th International Conference on Properties and applications of Dielectric Materials, pp 637-640, June 2006.
13. Daniela Cfirstea, Ion Cfirstea,"numerical simulation of electric field distribution in cable terminations", 6th International Conference on Telecommunications in Modern Satellite, Cable and Broadcasting Service, 2003. TELSIKS 2003, vol.2, pp. 479- 482 , 1-3 Oct. 2003.
14. H. S. B. Elayyan and M. H. Abderrazzaq, „„Electric Field Computation in Wet Cable Insulation Using Finite Element Approach”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 12, No. 6; December 2005
15. M. Abou-Dakka, A. Bulinski, and S. Bamji, “Space charge development and breakdown in XLPE under DC field,” IEEE Trans. Dielectr. Electr. Insul., vol. 11, no. 1, pp. 41–49, Feb. 2004.
16. Y. Murata, Y. Murakami, M. Nemoto, Y. Sekiguchi, Y. Inoue, M. Kanaoka, N. Hozumi and M. Nagao: "Effects of Nano-sized MgO-filler on Electrical Phenomena under DC Voltage Application in LDPE" CEIDP2005, pp. 158-161, 2005
17. T. Tanaka, "Dielectric nanocomposites with insulating properties," in IEEE Transactions on Dielectrics and Electrical Insulation, vol. 12, no.5,pp.914-928,Oct 2005
18. B. Zazoum, Eric David, and Anh Dung Ngo, "Simulation and modelling of polyethylene/clay nanocomposite for dielectric application", Transactions on Electrical and Electronic Materials vol. 15, No. 4, pp. 175-181, 2014.
19. Hazlee. A, Illias, George Chen, Paul L and Lewin.: Modelling of Temporal Temperature and Pressure Change due to Partial Discharge Events within a Spherical Cavity in a Solid Dielectric Material using Finite Element Analysis, IEEE, October 2010, p. 501- 504
72 20. D. Kavitha, T. K. Sindhu and T. N. P. Nambiar, "Investigation of treeing process in nanofilled epoxy material by Finite Element Method", Journal of Electrical Engineering, vol. 14, Edition 1, pp. 344-349, 2014.
21. F.C. Cheng ,"Electric Field Distribution Distored By Voids Inside Power Cables", Proceedings of the 5th Intedonal Conference on Advances in Power System Control, Operation and Management, APSCOM 2000, Vol.2,PP. 311- 316 , 30 Oct.-1 Nov. 2000.
22. Cristina Stancu, Petru V. Notingher, ,Florin Ciuprina, PetruNotingher, Jr., Jérôme Castellon, Serge Agnel, and Alain Toureille,” Computation of the Electric Field in Cable Insulation in the Presence of Water Trees and Space Charge”, IEEE Transactions on industry applications, vol. 45, no. 1, January/February, 2009
23. T. Mizutani, H. Semi, K. Kaneko, T. Mori, and M. Ishioka, “Space charge and field distributions in low-density polyethylene,” in Proc. IEEE Int. Symp. Electr. Insul., Anaheim, CA, 2000, pp. 493–496.
24. H. S. B. Elayyan and M. H. Abderrazzaq, „„Electric Field Computation in Wet Cable Insulation Using Finite Element Approach”, IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 12, No. 6; December 2005
25. S. S. Bamji, A. T. Bulinski, and K. M. Prasad, “Electric field calculations with the boundary element method,” IEEE Trans. Electr. Insul., vol. 28, no. 3, pp. 420–424, Jun. 1993.
26. J. H. Lee, G. Park, D. Y. Young, S. Kim, S. Hahn and M. Han, "An accurate method for numerical simulation of electrical tree growth process by Finite Element Method", IEEE International Symposium on Electrical Insulation, pp. 70-73, 1992.
27. Ch. Chakradhar Reddy and T. S. Ramu, "Polymer nanocomposites as insulation for hv dc cables – investigations on the thermal breakdown", IEEE Transactions on Dielectrics and Electrical Insulation, vol. 15, No. 1, pp. 221-227, 2008
28. S. M. Helleso, V. C. Henoen and S. Hvidsten, "Simulation of water diffusion in polymeric cables using finite element methods", IEEE International Symposium on Electrical Insulation, pp. 595-598, 2008.
29. S. Grzybowski, J. Fan, "Electrical breakdown test of 5kV XLPE cable with imperfections under combined ac dc voltage", IEEE International Symposium on Electrical Insulation, vol. 2, pp. 616-619, 1996.
30. Mitra, G. and Salvage, B., "Electric stress in a circular cylindrical gaseous cavity in a solid dielectric, the axis of the cylinder being parallel to the field", Proc. IEE, Vol. 113, 1966, pp. 93 1-955.
31. Nosseir, A., "Calculation of discharge inception voltage due to presence of void in power cables", IEEE Trans., Vol. EI-14, No. 2, April 1979, pp 117-120.
73 32. Blackburn TR, Liu Z, Morrow R, Phung BT. Partial discharges development in a void and its effect on the material surface. Proceedings of the 6th International Conference on Properties and Applications of Dielectric Materials. China. 2000; 2: 280-285.
33. AluruDivyaTeja, K. Rajagopala. “Electric field effect in the formation of water treeing in mv power cables,” vol. 03, Issue. 04, 2014.