In this paper, design formulas for the calculation of the leakage inductance of toroidal transformers are presented. The formulas are obtained from the analytical integration of the stored energy. The formulas are sufficiently simple and accurate to be introduced in the loop of a design program avoiding expensive finite element simulations. It is found that toroidal transformers naturally produce the minimum leakage inductance possible for medium-voltage power transformers. To limit the short-circuit currents in power and distribution systems, a larger than the minimum leakage inductance is often required. This paper presents two methodologies to increase the leakage inductance of toroidal distribution transformers: selectively enlarging the inter-winding spacing and inserting a piece of ferromagnetic material in the leakage flux region between the windings. Extensive validation with 2D and 3D finite element simulations is performed. Additionally, experimental verification of both formulas and numerical simulations was carried out comparing the calculations against measurements on prototypes.

When a transformer is subjected to very fast front transients, the penetration of the magnetic flux into the core becomes, in general, negligible. To represent this phenomenon, it is common practice to compute the winding inductance matrix (turn-to-turn) at very high frequencies using the expressions for air-core inductors. However, since the core becomes a magnetic insulating wall at very high frequencies (MHz), the distribution of the magnetic field is altered because the field cannot enter the region occupied by the core. Therefore, the air-core approximation formulae overestimate the inductance at high frequencies. This is especially true in the region inside the core window. Large errors are found when the inductances are computed with the air-core approximation. This paper presents a technique, based on the application of a multilayer method of images, to take the presence of the core into consideration. The final expressions are very simple, yet they give remarkably accurate results. Comparisons with finite-element analyses prove the excellent accuracy of the technique.

In this work two stress grading options for 115 kV non-ceramic suspension insulators are analyzed by means of 2D and 3D simulations. Both options were optimized in order to compare the maximum reduction that can be obtained on the electric field at the surface of the insulator. In the first option the shape and permittivity value of the housing material next to the energized end were the optimized parameters. For the second option, the installation of a corona ring, the position and dimensions of the ring were optimized. Electric field simulations were performed with the finite element method (FEM) while for the optimization process different functions of the MATLAB optimization toolbox were used. The optimization was performed with 2D FEM simulations and the optimal designs were then used on 3D models, in order to verify that these designs remain as the best option. According to the results, it was found that the use of a corona ring in 115 kV lines produces the maximum reduction of electric field as long as it is installed in the optimal position. A modification of the housing profile next to the energized end will also produce a significant reduction on the maximum electric field on 115 kV non-ceramic insulators.

Modern power systems face several problems at frequencies above the range of traditional stability studies due to the increasing penetration of power electronic devices. This phenomenon has been recently referred to as electromagnetic transient stability and is a common issue in systems with power electronic converters at any power and voltage level, such as FACTS, HVDC, power electronic interfaces for grid connection of renewable energies, custom power devices for power quality enhancement, among others. The study of power systems stability is usually carried out by simulation tools that represent the power system through phasor models. However, due to the faster dynamics of modern systems, the harmonic interaction among the controllers, the converters, and the electric power components, recent research results suggest that some stability analysis should be conducted with models suitable for wider frequency ranges, e.g., electromagnetic transient models. This paper reviews the use of frequency domain methods to analyze the influence of the modeling approach of passive power components on the results of electromagnetic transient stability studies.