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 .
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.
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.
Our Contribution in Studying theeffect of space charge in Polymeric Insulation Effect of void formation in polymer Simulation of Space charge limited current (SCLC) phenomenon
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.
Treeing phenomenon observed in epoxy resin in presence of void Treeing formation for different location of Void Model for ANSOFT MAXWELL 3D
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.
Case I :No Charge trapped in cavity1.Effect of variation of distance and position between point electrode and air cavity in Epoxy ford=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…..
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.
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.
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.
4. Effect of variation of distance and position between point electrode and air cavity inPolyimide 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.
Case II : Charge trapped in cavity 1. Effect of variation of +ve volume charge density trapped in air cavity on Polyimide for d=2mmElectric field distribution at 10KV for cavity with 1.0mm distance from electrode for polyimide Volume charge density 0 ,20 ,200 and 1000 Cm-3
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.
2. Effect of variation of -ve volume charge density trapped in air cavity on Polyimide for d=2mmElectric 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
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.
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
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).
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.
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
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
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
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
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%.
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.
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.
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