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In gapped inductors, the fringing field of the air gaps causes additional eddy current losses in the windings and an increase of the inductance. Since this impact of the fringing field is very significant, calculating the additional eddy current losses and the inductance increase is important in the design of inductors. This article proposes analytical formulas to accurately calculate the inductance and the additional eddy current losses in gapped inductors with solid round wire and Litz wire windings. The analytical formulas are verified by measurements, showing that the proposed models are accurate over a wide-frequency range. [ABSTRACT FROM AUTHOR]

For comprehensively optimizing high-frequency foil inductors, calculating the increased inductance and the additional eddy current losses due to a two-dimensional magnetic fringing field caused by air gaps in the center leg is mandatory. This article proposes an analytical model that accurately calculates the inductance and the additional eddy current losses in gapped inductors with foil windings. The analytical field expressions are combined into closed-form winding loss and inductance formulas and verified by measurements. Furthermore, the frequency dependency of the inductance due to the shielding effect of the foil conductors is being discussed. [ABSTRACT FROM AUTHOR]

A fast and accurate model of the transformer leakage inductance is crucial for optimization-based design of galvanically isolated converters. Analytical models are fastly executable, and therefore, especially suitable for such optimizations. This article compares several analytical leakage inductance per unit length models with respect to the accuracy and computational effort. The considered models are applicable to E-Core and U-Core transformers. 2D FEM simulations are used as a benchmark to evaluate the model accuracy, whereas the computation time is extracted as an indicator for computational effort. Six different transformer prototypes provide the geometries for the comparison. Based on the conducted comparisons, Roth's model is the most accurate. Rogowski's model is the fastest low-error model. Margueron's model is the most versatile as it takes the finite permeability of the core into account. The conducted comparisons lay the foundation for accurate and fast Double-2D modeling of the transformer leakage inductance as it is executed for the two main cross sections of E-core and U-core transformers: inside the transformer window, and outside the transformer window. This article is accompanied by a supplementary document summarizing the equations of Roth's and Margueron's model. [ABSTRACT FROM AUTHOR]

Due to the increasing integration of renewable energies into the distribution grid, a deterioration of the grid power quality is expected. Consisting of a low-frequency transformer and a fractionally rated power electronic converter, hybrid transformers (HTs) can be applied to ensure a high power quality by controlling voltage, active and reactive power dynamically. For the application in conventional grids, HTs have to withstand considerable overvoltages and overcurrents during voltage surges or short circuits. Although HTs recently gained increasing research interest, protection requirements and protection concepts have not been discussed yet. These aspects are, however, essential to evaluate the practical potential of HTs. In this article, protection requirements are derived and a protection concept is developed and verified by simulations and experiments for a 100-kVA hybrid distribution transformer. Although the protection concept has a considerable impact on the design and performance of the converter, it increases the total losses and volume of the HT only insignificantly. An efficiency of 98.48% is achievable for an HT including protection, which is only slightly lower than the efficiency of 98.64% for a comparable conventional transformer. This renders the HT a promising solution for today's and future ac grids. [ABSTRACT FROM AUTHOR]

In this paper, the design procedure of a 14.4 kV output voltage, 100 kHz transformer with an isolation voltage of 115 kV using Litz wire is presented. All design models, including a generalized magnetic model for the leakage and the loss calculations as well as an electrical model for the parasitic capacitance estimation for the transformer are derived and proven by measurements. For designing the insulation, a comprehensive design method based on an analytical maximum electrical field evaluation and an electrical field conform design is used. The resulting design is verified by long and short term partial discharge measurements on a prototype transformer. [ABSTRACT FROM AUTHOR]