The document discusses space charge and its effects on cable insulation failures. Space charge forms due to inhomogeneous resistivity, ionization within dielectrics, charge injection from electrodes, and polarization. Its presence distorts electric fields inside dielectrics, potentially leading to localized breakdown. Simulation results show how voids and trapped charge can enhance electric field stresses. The document also examines space charge limited current in cable insulation and simulates the relationship between current density and voltage for parallel plate electrodes, finding good agreement with analytical solutions. Future work is proposed to further study space charge effects in cables and insulation materials.

1. Supervisor Submitted by:
Mr.J.C.Pandey Chandan Kumar 07000420
Assistant Professor Prem Krishn 07000460
Electrical Engineering
IT BHU

2. Significance of the topic
 Researchers unable to explain failure of cables at operating stress much lesser than
their rated stress.
 The cable which have passed all the test for cable like mechanical test, dielectric
power test, PD test etc. are also failing in the use.
 Earlier the reason was found to be partial discharges, but, later it was found that
space charge is the main reason behind PD phenomenon in cables.
 HVDC transmission systems are becoming popular due to their inherent advantages
over HVAC system.
 HVDC cable insulation is more prone to threat from failure.
 Important factor in life estimation of insulator .

3. Space charge
 What it is ?
Space charge is a concept in which electric charge is treated as a continuum of
charge distributed over a region of space rather than distinct point-like charges.
(charge is not considered as point charge but as charge distributed over a volume
inside the dielectric)
 How it is formed:
 Spatial Inhomogeneous resistivity.
 Ionization of species within the dielectric to form hetero-charge.
 Charge injection from electrodes (trapping).
 Polarization in structures such as water trees.

4. Effect of Space Charge
 Field inside a dielectric gets modified in
presence of space charge, which may lead
to high field intensity at certain locations
causing localised breakdown and formation
of voids in case of solid dielectrics.
 These voids can again lead to increase in
Electric field of nearby regions leading to
treeing phenomenon and finally complete
breakdown of the material.

5. Our Contribution in Studying the
effect of space charge in Polymeric
Insulation
 Effect of void formation in polymer
 Simulation of Space charge limited current (SCLC)
phenomenon

6. Challenges faced
 Measurement and simulation of effect of space charge on polymeric
insulation electric field stresses is very difficult to simulate as we don’t
know the exact distribution of charge in the space.
 Problem more intensified in case of opaque insulations, as we can’t use
techniques like EL easily in that case.
 The distribution changes considerably with the properties of the medium
(dielectric):
e.g. charge can easily get stuck in the medium if the dielectric has:
1.solid defects.
2.electronegative atoms.

7. Treeing phenomenon observed in epoxy resin in
presence of void
Treeing formation for different location of Void
Model for ANSOFT MAXWELL 3D

8. Maxwell Simulation
Effect of Cavity formed as a result of space charge on Electric field in different
dielectrics for a Point Plane geometry Configuration
• Effect of variation of distance between point and plane electrode (d) in Epoxy with no cavity
(a) (b) (c)
Electric field distribution at 10KV (a) for d=2 mm (b) for d=5mm (c) for d=10mm
•As the distance between plane point electrode increases the electric field inside the
dielectric decreases.
•The smaller the distance more will the stress exerted on the surface near to plane electrode.

9. Case I :No Charge trapped in cavity
1.Effect of variation of distance and position between point electrode and air cavity in Epoxy for
d=2mm
(a) (b)
(c) (d)
(e) (f )
Electric field distribution at 10KV for d=2mm (a) Right of Electrode by 0.4mm (b) Right of Electrode by 0.5mm
(c) Right of Electrode by 1.0mm (d) Right of Electrode by 2.0mm (e)Below electrode by 0.4mm (f) Below electrode by 1.0 mm
continued…..

10.  The Electrical Field Intensity has increased with the appearance of void as
compared to the case where void was absent.
 The field distortion depends upon the position of the cavity, geometry of insulation.
When cavity is very near to Point electrode the field is non uniform and distributed
as U shaped cup.
 The Curvature of U shaped cup first decreases and then increases as seen .So the
electric field stress in region surrounding the electrode is more when void is near to
the electrode and is less when it is far away from the electrode.
 The electric field pattern also indicates that there is an optimal distance for which
the stress in the region is maximum. This distance depends on radius of
probe, cavity diameter, electrical voltage, electrode material and dielectric constant
of insulator.
 When the cavity is just below electrode then its position determines the field
distribution. When it is near to the Point electrode the curvature of U cup is large
and it decreases with increase in distance between cavity and electrode. So field
stress is more with increase in distance from the electrode.

11. 2. Effect of variation of distance and position between point electrode and two air cavity in Epoxy for
d=2mm
(a) (b)
Electric field distribution at 10KV (a) for distance 0.5mm (b) for distance 1.0mm
The above simulation depicts that the cavity will distort the electric field and the stress on
insulator is more as compared to single cavity. Also the field near the probe is increased by
large amount as shown by the numerical figure by a factor of 10.

12. 3. Effect of variation of distance and position between point electrode and water cavity in Epoxy
for d=2mm.
(a) (b)
Electric field distribution at 10KV for water filled cavity (a) for distance 0.5mm (b) for distance 1.0mm
From here it can be concluded that liquid cavity posses lesser threat to the
insulator compared to the solid cavity. The above statement is can also be
theoretically verified from the relationship for breakdown for internal discharges.

13. 4. Effect of variation of distance and position between point electrode and air cavity in
Polyimide for d=2mm
(a) (b)
Electric field distribution at 10KV for cavity with 1.0mm distance from electrode for polyimide (a) air filled
cavity (b) water filled cavity
•It can be concluded that the electric field gets reduced by a factor of 6-15 for different regions
of the insulator which is due to higher dielectric constant of the polyimide compared to epoxy.
•Here also effect of water cavity is less severe than the effect of air cavity. The field gets highly
distorted at the surface of the cavity.

14. Case II : Charge trapped in cavity
1. Effect of variation of +ve volume charge density trapped in air cavity on
Polyimide for d=2mm
Electric field distribution at 10KV for cavity with 1.0mm distance from electrode for polyimide Volume charge density 0 ,20 ,200 and 1000
Cm-3

15.  Increase in the charge of the same polarity as the voltage applied on
electrode the electric field in the region in between point electrode and
void increases.
 electric field around the point electrode decreases first and then
increase as the charges first oppose the applied electric field then
overcome it and electric field increases due to their own field.
 So breakdown chances will decrease at lower charge density but will be
more due to localized enhancement of electric field at higher charge
density.

16. 2. Effect of variation of -ve volume charge density trapped in air
cavity on Polyimide for d=2mm
Electric field distribution at 10KV for cavity with 1.0mm distance from electrode for polyimide with Volume charge density
0 -20 ,-100 and -1000 Cm-3

17.  If the charge inside the void is of opposite polarity than that of voltage applied
to the electrode then the electric field in the insulator is increased.
 It is observed that the electric field in envelope surrounding the point electrode
and cavity is increased and with rise in charge density .This envelope starts
growing in size with maximum electric field around the void which is 10-1000
times more than the electric field in reference case.
 This shows that the breakdown will be more rapid in case the opposite polarity
charge is trapped in the void. So opposite charge trapping is more severe.
 So, electrical engineer need to find a solution to minimize the effect of such
void in insulation.

18. SPACE CHARGE LIMITED CURRENT
(SCLC)
 At lower voltages, the current density is given by the Ohmic current
J=neμE
 As the applied voltage is increased, the charges tend to accumulate in
the region between the electrodes and the electric field due to the
accumulated charge influences the conduction current.
 This mechanism is usually referred to as SPACE CHARGE LIMITED
CURRENT (SCLC).
and is given by
2
J = 9 ϵ μ V / 8d3

19. Simulation
(plate-plate electrode case)
 Importance of simulation:
- Establish a relationship between current density
and Voltage between the electrodes.
- Find the space charge distribution, E and V formed
in region between the electrodes (life estimation).

20. Geometry:
Plates are 2cm thick and 20 cm in length. Distance between plates is 10 cm.
Air dielectric is used as insulation between the electrodes. Computational
domain taken for the simulation is 200 cm long and 200 cm wide.

21. Boundary conditions :
 The electrodes are ohmic and electrons are supplied at the rate of their removal.
 The current is function of number and drift velocity of electrons and not dependent
on the position in the sample, z measured from the positive electrode
i.e. J = n(z) e μ E(z)
 There is no discontinuity in Electric field within the dielectric. i.e.
intgr(E(z) d(z))=V.
Assumptions :
 There are no traps present in the dielectric.
 The charge is distributed uniformly within the polymer.
 There is only one type of charge carrier.
Equations used :
 Poisson’s Equation : d2V/dz2 = e n(z)/ϵ
 Current continuity equation : J = n(z) e μ E(z) – eDdn/dz + ϵ dE/dt
Platform Used : Comsol Multiphysics

22. Electric field variation
700000
600000
500000
Electric Field in V/m
400000 V=1KV
V=7KV
300000 V=15KV
V=33KV
200000
100000
0
0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02 1.00E-01 1.20E-01
distance from positive electrode in metres

23. Potential variation
35000
30000
25000
Electric Potential in V/m
20000
V=1KV
15000
V=15KV
33 KV
10000
V= 7KV
5000
0
-2.00E-02 0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02 1.00E-01 1.20E-01
distance from positive electrode in metres

24. Variation of space charge density

25. Calculations :
V(electrode) in E in V/m ρ*μ J(C/m2 s)
KV
1 10630.7805 1878.21e-13 1.9966e-6
3 32036.0379 5634.63e-13 1.8051e-5
5 52742.9312 9391.05e-13 4.9531e-5
7 74301.0616 13147.47e-13 9.7687e-5
9 95462.722 16903.89e-13 1.6136e-4
11 1.1668e5 20660.31e-13 2.4106e-4
13 1.3789e5 24416.73e-13 3.3668e-4
15 1.591e5 28173.15e-13 4.4823e-4
17 1.8033e5 31929.57e-13 5.7578e-4
19 2.0152e5 35685.99e-13 7.1914e-4
21 2.2274e5 39442.41e-13 8.7854e-4

26. Simulation Result : Plot of J vs. V
 General model Power:
 J= f(x) = a*Vb
 Coefficients (with 95%
confidence bounds):
 a = 1.996e-006
(1.991e-006, 2.002e-
006)
 b = 1.999 (1.998,
2)
 Goodness of fit:
 SSE: 1.455e-013
 R-square: 1
 Adjusted R-square: 1
 RMSE: 1.271e-007

27.  Result expected from Analytical Solution of the
problem geometry:
 Value of under experimental conditions: 1.992e-
006

 Error in value (simulation):
 a: (1.996e-006 - 1.992e-006)/ 1.992e-006 = 2.008e-3
 i.e. 0.2%
 b: (2-1.99)/2=5e-3
 i.e. 0.5 %
 Therefore, Maximum overall error = (2e-3 + 0.035) = 0.037
= 3.7%.

28. Conclusion:
 In the first part of the project the Effect of void formation inside a polymer
was discussed. Based on the simulated model on ANSOFT Maxwell it was
shown how the treeing phenomenon is affected by the presence of cavity.
Also the variation of electric field with different parameters was shown. At
last the effect of cavity filled with trapped charge was discussed. Polarity
was found to have large significance there.
 In the second part, the SCLC theory was discussed. Simulation was done in
case of parallel plate electrodes with air as the insulating medium.
Simulation was carried out for a range of applied DC voltages. A
relationship between current density and applied voltage was established
using the simulation results and was compared with the analytical solution.

29. Future work:
 The simulation of the model for effect of void in polymer was performed only
for plane-point electrode geometry for DC Voltage case. The model can also be
simulated for AC voltage.
 Other modeling like modeling of actual 3 core coaxial cable can be done to
study the effect of void further. Fractal modeling of tree phenomenon can also
be simulated which can give insight to the stochastic modeling of treeing in
polymer.
 The SCLC model can be applied for other cases like point-plane electrodes, as
in case of corona wire and for polymeric dielectrics like epoxy, polyimide.
Moreover, experimental determination of space charge density can be done
using known methods like PEA. This will provide further ease in modeling the
phenomena accurately. Life of insulation materials under various voltage
stresses can also be predicted using space charge density obtained from SCLC
model.

30. Bibliography :
 [1] Kothari D.P., Nagrath I.J., “Power System Engineering”, second Edition, published by the Tata
McGraw Hill Education Pvt. Ltd.,pp.872-873.
 [2] Naidu M.S., Kamaraju V., “High Voltage Engineering”, third Edition, published by the Tata
McGraw Hill Education Pvt. Ltd.,pp.95-98,pp.407-412.
 [3] Niemeyer L., Pietronero L., Wiesmann H., “Fractal dimension of dielectric breakdown”, Phys. Rev.
Lett., vol. 52, pp. 1033.1036, 1984.
 [4] Vardakis G.E., Danikas M.G., “Simulation of electrical tree propagation in solid insulating material
containing spherical insulating particle of a different permittivity with the aid of cellular
automata”,Elec.Energ.Vol. 17, December 2004, pp.377-389
 [5] Fukuma M., Itoga T., Fujikawa S., “Numerical analysis of PEA signal in line –plate electrode
system”, Properties and applications of Dielectric Materials, 2006. 8th International Conference
proceeding ,pp. 88-87.
 [6] Bamji S. S., Bulinski A. T., Abou-Dakka M., “Luminescence and Space Charge in Polymeric
Dielectrics”, IEEE Transactions on Dielectrics and Electrical Insulation Vol. 16, No. 5; October
2009, pp.1376-1392.
 [7] Koppisetty K, Serkan M., Kirkici H., “Image Analysis: A Tool for Optical-Emission Characterization
of Partial-Vacuum Breakdown”, IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 37, NO.
1, JANUARY 2009, pp.153-158.
 [8] Wu X.,Chen G., Davies A. E., “Space Charge Measurements in Polymeric HV Insulation
Materials”, IEEE Transactions on Dielectrics and Electrical Insulation vol. 8 No. 4,pp.725-730

31.  [9] Mazzanati G,Montanari G.C.,Dissado L.A,“Electrical Aging and Life Models: The Role of Space Charge” IEEE
 [10] G.Jiang, J.Kuang, S.boggs, “Critical parameters for electrical tree formationin XLPE”,IEEE trans. Power”, Del., Vol.
13, pp.292-296, 1988.
 [11] A. Many and G.Rakavy, “Theory of transient space-charge-limited-currentin solids in the presence of
trapping”, Phys. rev., Vol. 126, pp.1980-1988, 1962.
 [12] H.R.Zeller, W. Schneider, “Electrofracture mechanics of dielectric aging”, J.Appl.Phys., Vol.56,pp. 455-459,1984.
 [13] Tanaka T., “Space charge injected via interfaces and tree initiation in polymers”,2001 Annual report,CEIDP,pp 1-15.
 [14] Sergey Karpov and Igor Krichtafovitch, “Electrohydrodynamic flow modeling using FEMLAB”, Proceedings of the
COMSOL Multiphysics User’s Conference 2005 Boston.
 [15] Thomas Christen and Martin Seeger, “Simulation of unipolar space charge controlled electric fields”, ABB Achweiz
AG, Corporate Research, Im Segelhof, CH-5405 Baden-Dattwil, Switzerland.
 [16] Mahajan A., Seralathan K. E., Gupta N., “Modeling of electrical tree propagation in the presence of voids in epoxy
resin”,2007 International Conference on Solid Dielectrics, Winchester, U.K, July 8-13,2007,PP 138-141
 [17] Dissado L.A., Fothergill J.C., “Electrical degradation and breakdown in Polymers”, Peter Peregrinus
Ltd., London, U.K

32. Thank you