Abstract The electric field in the presence of space charge is governed by Poisson equation and the current continuity equation, so, it is difficult to describe the phenomena precisely by an analytical expression due to the non-uniformity of the electric field. In such cases, we seek to experimental modeling or numerical techniques. One of these numerical techniques is the finite difference method. It based on solving the differential equations by approximating them with difference equations, such that the computational domain is divided into several grid points. In order to increase the accuracy of the finite difference method, finer grids using very small step size w.r.t to the domain dimensions (i.e. excessive grid points) should be used resulting in a very low truncation error which could be neglected. Solving Poisson equation requires finer grids which take a very long computational time, which approximately represents 99% of the total computational time to converge to certain solution for the potential values at the grid points. To achieve fast convergence for the results, several iterative relaxation methods were applied. The high frequency dampening effect of these relaxation methods is an important issue. If the error has a high frequency component, relative to the grid spacing, then the relaxation with Gauss-Seidel will damp it rapidly. For the low frequency errors, Gauss-Seidel will not work efficiently. For finer grids, it is very time consuming to obtain the desired convergence for the solution by Gauss-Seidel iterative method. So the need for a fast iterative solver arises. To minimize the computational time on working on fine computational domains, the multigrid method is introduced in this work as it possesses a significant place as an iterative solver. The multigrid methods accelerate the convergence rate especially on fine grids. It re-defines the problem on a coarser grid, and then Gauss-Seidel relaxation method will be more effective on the high frequency error at the coarse grid spacing. Once the coarse grid solution has been reached, the solution is interpolated to a finer grid. So, by multigrid methods we can use finer grids resulting in negligible truncation error and accurate finite differences approximation without suffering from the high computational time needed. As there have been several reported experimental data in the wire duct precipitators, the reliability of the finite difference method is checked with the multigrid methods. The multigrid method is applied to solve Poisson equation especially on finer grids as a quick convergent iterative solution to the Finite Difference Technique. Two schemes of the multigrid method, mainly the V-cycle and the Full Multigrid Method (FMG), are implemented. The above-mentioned schemes are successfully transcendent due to timing performance as compared to the Gauss-Seidel method. The proposed algorithm allows the use of finer grids to get a more accurate picture of the performance of the precipitators in the design stage without suffering from the excessive computational time. Precise results for the potential and current density computations, closed to the previous published experimental measurements, are obtained for several design parameters of the precipitators compared with earlier numerical techniques. The full multigrid method is implemented to monitor the computational domain's optimum grid size for modeling the corona problem, which in turn helps to reduce the experimental effort. Also, the full multi-grid method is also examined against a successive over-relaxation (SOR) strategy, and the latter is effectively transcendent in terms of performance in timing. Then, the finite difference method integrated with the full multigrid technique is implemented to model the monopolar corona in HVDC transmission line systems. The Full Multigrid (FMG) method is selected as an iterative solver for the finite difference method to solve Poisson equation especially on fine grids. The present analysis does not entail the assumption of constant electric field around the surface of the conductor and that the space charge affects only the magnitude of the electric field not the direction. The proposed method is employed to compute the electric field and the current density on the ground plane without the wind effect. Also, the proposed technique studies the effect of wind in the present analysis, the results verified that the transverse wind affects both the electric field and the current density on the ground plane. The effect of changing the wind speed on the profiles of the electric field and the current density is analyzed. The proposed method is compared with previous experimental results and numerical techniques, and a good agreement is reached. Finally, the proposed technique solves the monopolar corona in bundled HVDC transmission line systems. The present analysis does not approximate the bundle conductor with an equivalent conductor radius. Firstly, the proposed method is compared with previous experimental results. Secondly, a flexible laboratory model for bundled HVDC transmission line is constructed to validate the calculated corona current and the current density distribution on the ground plane for different number of bundles and for different bundle spacing. Bundles one, two, and four are adopted in the experimental setup. For the same applied voltage, the results verified that the corona current decreases as the number of bundles increases or the spacing between bundles decreases. So, the obtained results confirmed that the corona power losses can be minimized, without the need for increasing the conductor radius or its height above the ground. The results by the proposed method agreed well with the present and the previous experimental work.

In order to expand and upgrade the electrical power grid, the performance improvement of power transformers is indispensable. Oil-filled transformers are one of the popular types of power transformers. Transformer oil (Base insulating oil) provides both thermal cooling and electrical insulation functions. So, improving its thermal and dielectric properties affects positively the whole performance of power transformer. Recently, nanotechnology was used as an effective science in the field of transformer oil development to enhance its thermal and dielectric properties under the name of nanofluids. In this thesis, barium titanate nanoparticles were inserted into the base insulating oil by a concentration of 0.005, 0.01, and 0.02 gram per liter as individual nanofluid samples. Some measurements were done for these samples. These measurements are heat transfer coefficient, breakdown voltage, relative permittivity, conductivity, and dielectric dissipation factor. The dispersion of barium titanate nanoparticles into the base insulating oil enhances the thermal properties by more than 20% for all individual nanofluid samples but some dielectric properties were negatively affected by this dispersion. To overcome this problem of dielectric properties degradation, other three hybrid nanofluid samples were prepared using three different types of metal oxide nanoparticles; titania, alumina and silica. These samples were prepared by adding a concentration 0.01 gram per liter of each metal oxide nanoparticles together with 0.005 gram per liter of barium titanate nanoparticles into the base insulating oil. Same measurements were done for these hybrid samples as same as individual samples. The thermal and dielectric properties of hybrid nanofluid samples were examined to study the behavior of nanoparticles hybridization on transformer oil properties. Due to the different surface charging of barium titanate and titania nanoparticles, the best enhancement of breakdown voltage and heat transfer coefficient was achieved. Dynamic light scattering technique was used to evaluate the particle size distribution of nanoparticles into the hybrid samples and to clarify the corresponding physical interpretation behind the obtained enhancement. On the other hand, thermal model of 1 MVA, 50 Hz, 22/0.4 kV stepping down immersed oil distribution transformer was introduced using COMSOL Multiphysics Software. The COMSOL Multiphysics Software is commercial software that resolves the heat transfer in fluids based on the finite element method. The liquid materials that used for the proposed model were the base insulating oil and the best prepared nanofluids sample. Internal heat energy, temperature gradient, and temperature distribution were evaluated using COMSOL Multiphysics Software. The obtained results introduced that; the thermal stress on the base insulating oil inside transformer can be reduced by about 10 oC due to the presence of the hybridization of barium titanate and titania nanoparticles. Based on these results, the filling of distribution transformer by HNFS/TNP oil instead of base insulating oil doubles the lifetime of the oil in the service and improves the performance of the transformer.

Power transformers are one of the most important components of electric power distribution and transmission systems. Therefore their reliable and efficient operation for many years is of basic importance for a reliable electrical energy supply. The reliability of a power transformer is limited by the reliability of the electrical insulation system which also operates additionally as a heat transfer medium. It is very important to check their insulation levels and their oil insulations. The detection of partial discharge (PD) in transformer oils have great significance for the diagnosis and running state assessment of power transformers. In this thesis, a method of detecting transformer oils decomposition components caused by PD is proposed. Accordingly, multi-wall carbon nanotube MWNT) films sensors which are used to detect PD of oils is developed. adopting a kind of chemical modification with concentrated sulfuric and nitric acid, the functional modification to carbon nanotubes CNTs) is realized, as well as transmission electron microscope (TEM) and Fourier transform infrared spectrum analysis (FTIR) of the CNTs before and after the modification. The test is conducted for MWNTs films sensor in the laboratory using oil testing device. Test results show the MWNTs films sensor has many defects and active functional groups and with strong absorption capacity for transformer oils decomposition components; it shows good sensitivity and fast response characteristics.

The main goal of this thesis focuses on the investigation of the electric field distributions inside a typical 500/220 kV open distribution substation under actual loading conditions and during different working conditions, Hot-Stick position and Bare-Hand position. Moreover, the assessment of the human exposure to these fields is investigated by calculating the induced currents and current densities inside the workers body during different working conditions and at different positions inside this substation. This study will serve for planning service works or for inspection of equipment inside high voltage (HV) substations with regarding the safety of workmen. The developed computer model for this substation is based on three dimensional (3D) charge simulation technique (CSM). To validate the electric fields calculated by the computer model, real measurements are performed inside this typical substation. The electric field distribution is investigated also at height levels of 8m, 11m, 14m and 17m above ground to represent the positions of live line maintenance (Bare-Hand position). Moreover these values of electric field are compared to international guidelines for personnel exposure to electric field to stand upon how much of deviation and how much of risk to which the workers are exposed. In the final phase in this thesis, a computer model is developed to simulate the human body in proximity to substation’s equipment. This model is used to calculate the induced current densities and currents inside the different tissues of human body, and compare these values with the recent published standards for electric field exposures to ensure worker safety and to ensure safe operation inside this substation. The human body is allocated in different positions inside this substation and at different working conditions (Hot-Stick positions and Bare-Hand positions) taking into account the different profiles and shapes for human body. This thesis is a preliminary example of the work of engineers. It is the actual application of pure science in the design and construction of a practical system such as design of high voltage substations, transmission system. Implementing the results of this thesis will decrease the impact of high voltage substations on the surrounding environment while maintaining the safety of the workers and the reliability of the equipment.

For the enhancement of insulation reliability and the compact design in gas insulated power equipment, the solid insulators play crucial role of electrical insulation. In order to improve the insulation performance of the solid insulators, we should consider the following two technical points. Firstly, we have to improve the insulation performance of solid dielectrics itself. The second is the control of the electric field distribution in and around the solid insulating spacers. In this paper, we have proposed a new concept for spacer insulation; an application of a functionally graded material (FGM). We investigated the applicability of FGM for reducing the electric stress on triple junction point, which was one of the important factors dominating a long-term insulating property of the solid. Finite Element Method (FEM) has been used throughout this work, for its favorable accuracy, to calculate the electric field distribution inside gas insulated bus duct (GIBD). The electric field distribution around earthed particle contamination which adhered to uniform and FGM of disc-spacer is studied. Electric field relaxation effect (EFGM / Euniform) by introduction of the U-shape FGM spacer is also studied. The breakdown voltage calculations in case of gap with particles contamination are studied. The effect of gas pressure, SF6-gas concentration in various mixtures and the particle dimension (length and hemi-spherical radius) on the breakdown voltage are also studied. Finally, the effect of FGM of spacer on breakdown voltage is also studied

For the enhancement of insulation reliability and the compact design in gas insulated power equipment, the solid insulators play crucial role of electrical insulation. In order to improve the insulation performance of the solid insulators, we should consider the following two technical points. Firstly, we have to improve the insulation performance of solid dielectrics itself. The second is the control of the electric field distribution in and around the solid insulating spacers. In this paper, we have proposed a new concept for spacer insulation; an application of a functionally graded material (FGM). We investigated the applicability of FGM for reducing the electric stress on triple junction point, which was one of the important factors dominating a long-term insulating property of the solid. Finite Element Method (FEM) has been used throughout this work, for its favorable accuracy, to calculate the electric field distribution inside gas insulated bus duct (GIBD). The electric field distribution around earthed particle contamination which adhered to uniform and FGM of disc-spacer is studied. Electric field relaxation effect (EFGM / Euniform) by introduction of the U-shape FGM spacer is also studied. The breakdown voltage calculations in case of gap with particles contamination are studied. The effect of gas pressure, SF6-gas concentration in various mixtures and the particle dimension (length and hemi-spherical radius) on the breakdown voltage are also studied. Finally, the effect of FGM of spacer on breakdown voltage is also studied

Abstract: Gas-insulated systems (GISs) have been widely used in the electric power grid with substantial growth. It is a complete enclosure of all energized parts in a grounded metallic encapsulation insulated with compressed gas. The use of GIS in the power system network has acquired considerable importance because of its compactness, maintenance free, safe and reliable operation. However, the reliability of GIS is adversely affected by the presence of contaminating conducting particles in the insulation structure. The existence of a particle in GIS initiates partial discharge (PD) when the electric field at its tip exceeds the limiting dielectric strength of the gas and may in time initiates the process of breakdown. Therefore, the detection of partial discharge at early stages and the identification of geometry, size and location of a particle contaminant causing the discharge play an important role in evaluating the integrity of equipment insulation and allow the user to predict which equipment of GIS is in need of maintenance. This thesis presents a method for detecting and identifying the geometry of a fixed contaminating metallic particle in GIS. A fixed particle–initiated negative corona in air insulated co-axial cylindrical configuration is investigated at a voltage slightly above the corona onset level. Then, the onset voltage of negative corona is calculated based on the criterion developed for the formation of repetitive negative corona, Trichel pulses. This calls at first for an accurate calculation of the electric field in the vicinity of the particle where avalanches grow. The investigated gap in presence of a particle is a three-dimensional field problem due to the asymmetrical position of a particle inside the gap. The three-dimensional electric field is calculated using the charge simulation technique with a new charge distribution. The characteristics of the initiated Trichel pulses are calculated by mathematical modeling the processes taking place during the discharge of negative corona. The Trichel pulse characteristics are calculated for different particle sizes and shapes at an applied voltage slightly above corona onset voltage level. These data of pulse characteristics and onset voltage level are used as a bias for designing and training the artificial neural network technique (ANN). An experimental set-up has been built up to measure the onset voltage of negative corona initiated by a particle in air insulated co-axial configuration to check the accuracy of the present calculation. The effect of varying field nonuniformity, particle shape, size and position on onset voltage of negative corona is investigated. The calculated onset voltage values agreed well with those measured experimentally. Also, by the same experimental set-up, the Trichel pulse characteristics are measured to check the accuracy of the present calculation. The calculated values of pulse amplitudes and repetition rates agreed well with those measured experimentally. Hence, for identification of particle contamination geometry in GIS, the Trichel pulse characteristics, peak current and repetition rate are measured. These measured values and the applied voltage are given as an input data to the trained ANN to test for the presence of a contaminating particle and reveal its geometry and location.

Nonthermal plasma jets generated in atmospheric pressure discharges represent a rapidly developing technology of great application promises. However, the scope of research is to design an affordable, portable and efficient atmospheric nonthermal plasma jet (ANPJ) device that could be used in many applications. The device is powered by a compact, low-cost and commercially power supply characterized by output of 10 kV, 30 mA and 20 kHz. A device capable of generating a plasma jet was designed, fabricated and operated with Nitrogen gas or Air as carrier gas with different flow rates from 3 to 25 L/min. This design achieves the goals of producing a non-thermal plasma jet under atmospheric pressure and operates with low-cost and available components. The electrical parameters such as discharge voltage using a potential divider with a ratio of 1000:1 and discharge current using the voltage across a 25  resistor were measured and analyzed. The results of these electrical parameters showed that the maximum values of 3.4 kV and 28 mA for N2 gas of flow rate equals 12 L/min respectively and their maximum values equal 3.4 and 33.6 mA for Air at the same discharge conditions. The mean consumed power (P), power efficiency and mean energy were investigated and analyzed. Also Lissajous figure (V-Q curve) was used to calculate the accurate values of the mean power. Results of these parameters showed that maximum values of 29.75 W, 62% and 1.52 mJ/µs for N2 gas and 32.1 W, 67% and 1.68 mJ/µs for Air are obtained at flow rate of 12 L/min respectively. The jet phenomenology was investigated by using a digital camera to detect the jet column length for both carrier gases at different flow rates. ii The results cleared that, a maximum jet column length of 14 mm for N2 gas and 7 mm for Air at flow rate of 12 L/min. The luminous radiation emission intensity was measured by using a photomultiplier tube (PMT) for the same discharge conditions. Also, the spectrum of the jet column produced from the plasma jet device was analyzed by using spectrometer detector for both carrier gases at flow rate of 12 L/min. Results of luminous radiation intensity along the plasma jet column showed that, the maximum luminous radiation intensity is observed at 2 mm axial length from the cathode surface for both carrier gases. Also the maximum luminous radiation is obtained at 12 L/min flow rate for both carrier gases. It was much larger in case of N2 gas than that of Air. The plasma electron excitation temperature was estimated for both carrier gases at different flow rates separately by two methods firstly, by using PMT with two different wavelengths filters, secondly, from the plasma jet spectrum. The gas temperature was measured by using thermocouple thermometer at different axial distances of the plasma jet column at the same discharge conditions mentioned above. Results of these measurements illustrated that, the electron temperature is decreased with increasing the flow rate and it was much larger than the gas temperature. Also the gas temperature was found to be approximately room temperature at the end of the plasma jet column. Three applications were done using the plasma jet device under consideration to detect its capability to cover wide-range of applications. These applications are wettability modification of Mylar substrate, Polyethylene Terephthalate (PET) surface treatment, cleaning and etching of black surface (ink) from printed paper. The surface properties of plasma iii jet treated materials, have been investigated using liquid contact angle (), Fourier Transform InfraRed (FTIR) and Scanning Electron Microscope (SEM). All the above applications were investigated at the optimum condition of N2 gas and Air flow rate. The analysis of these applications showed that, the wettability modification, polymer treatment, cleaning and etching can be done using this plasma jet device.

With the development of cities and electric power industry, the demand of electrical energy, generation, transmission, distribution and the voltage levels have increased considerably. Therefore the power frequency electric field and environmental impact assessment near / under the high voltage overhead busbars, incoming and outgoing feeders inside the high voltage substations (HVS) have caused wide public concern. Nowadays most research on electric field are concerned with calculation the electric field distribution around the transmission lines, insulators and cables but they rarely concerned with its calculation inside HVS. In this paper, a different type of calculation is achieved, the charge simulation method (CSM) is employed to analyze the three dimensional (3-D) electric field distribution near / under the busbars, incoming and outgoing feeders. At last, the effects of changing the level of operating voltage, the space between the phases, the level of calculation inside HVS is demonstrated.

SF6 gas insulated switchgear plays an important role in electric power networks all over the world due to its merits as compared to traditional air insulated switchgear.The mixtures composed of a strongly electronegative gases with high dielectric strength such as SF6 and two ordinary gases such as N2 and Air or CO2 and Air with a various fractional concentrations are used in this paper to reduce the gas price and liquefaction temperature. From this point of view, various types of gas mixtures are used inside gas insulated switchgear (GIS) to give a higher dielectric strength. In this paper, the Finite Elements Method (FEM) is used to evaluate the potential and electric field distributions on and around contaminating filamentary wire particle at two positions, first is resting on the earthed plate and second is hovering inside the gap. The effects of particle dimensions such as (length, radius) and gap spacing on the electric field values are also studied. The breakdown voltage calculations under uniform field in case of clean gap and non-uniform field in case of gap with particle contamination are studied. The effects of gas pressure, SF6 gas concentration in mixture, gap spacing and particle dimensions on the breakdown voltage calculations are also studied.

SF6 gas insulated switchgear plays an important role in electric power networks all over the world due to its merits as compared to traditional air insulated switchgear.The mixtures composed of a strongly electronegative gases with high dielectric strength such as SF6 and two ordinary gases such as N2 and Air or CO2 and Air with a various fractional concentrations are used in this paper to reduce the gas price and liquefaction temperature. From this point of view, various types of gas mixtures are used inside gas insulated switchgear (GIS) to give a higher dielectric strength. In this paper, the Finite Elements Method (FEM) is used to evaluate the potential and electric field distributions on and around contaminating filamentary wire particle at two positions, first is resting on the earthed plate and second is hovering inside the gap. The effects of particle dimensions such as (length, radius) and gap spacing on the electric field values are also studied. The breakdown voltage calculations under uniform field in case of clean gap and non-uniform field in case of gap with particle contamination are studied. The effects of gas pressure, SF6 gas concentration in mixture, gap spacing and particle dimensions on the breakdown voltage calculations are also studied.