Despite the spectacular development of numerical methods, the use of analytical formulas to solve electromagnetism problems in multilayered complex structures still remains attractive due to their much shorter computation time. One of the most essential computations is a calculation on the proximity effects observed in a wire that is immersed in an external harmonic electromagnetic field. The mathematical model of this problem is known and contains Bessel functions, which are numerically unstable for very low and high arguments. In this article, a novel numerically stable algorithm for the computation of proximity effects and power induced in a multilayered cylindrical structure is presented.

Nowadays, as an alternative to conventional mineral oils used for cooling in distribution transformers, environment-friendly ester oils are getting more attention. For this reason, the main objective of this work was to compare the cooling efficiency of both types of coolants in the medium-power distribution transformer under different ambient conditions. It was conducted by the development of a validated coupled numerical model that included all thermal, flow and electromagnetic phenomena. Moreover, all the calculations were carried out for mineral, synthetic and natural ester oils. As a result, the coupled CFD model determined the hot-spot temperature within the transformer tank at three ambient temperatures on the basis of the local distribution of the power losses in windigns and core that were delivered from the electromagnetic submodel. The investigated ambient temperatures of -10, 20 and 30°C represented summertime and wintertime for two climate conditions. The numerical results also showed a satisfactory agreement with the measured temperature values recorded in the analysed distribution transformer with mineral oil. In addition, it was presented that the highest hot-spot temperature of 94.6°C was reached for the case of natural ester oil at 30°C of the ambient temperature representing maximum monthly averaged Argentinian climate conditions. In these conditions, the hot-spot temperature transformer with mineral oil was only 1.6 K lower. Furthermore, one of the investigated synthetic ester oil allowed to reach even better cooling effectiveness than in the case of mineral oil. Therefore, more effective cooling connected with environment-friendly characteristics encourages to use biodegradable oils for distribution transformers.

This paper presents a fast and computationally stable analytical algorithm used to perform the characteristic impedance of cylindrical multilayer waveguides used in high-precision sensors and apparatuses. Most of the algorithms used for the calculation of the characteristic impedance of those waveguides are based on approximations. Their application is limited to waveguides with a certain (usually small) number of layers. There may be insufficient layers, especially when coaxial waveguides are part of a precise measurement device. This article presents a numerically stable analytical algorithm using modified scaled Bessel functions to perform the characteristic impedance and the components of cylindrical coaxial multilayer waveguides. The results achieved by the extracted algorithm were compared to the results obtained by simulation using finite element method (FEM) software and the current method, whose main drawback is the fictive sublayers, which significantly increase the computation time. The excellent agreement between the results confirmed the precision of the algorithm and the time required for the calculation was reduced several times.