Analytical Formulation of Copper Loss of Litz Wire with Multiple Levels of Twisting Using Measurable Parameters

Litz wire has been widely utilized in power transformers and inductors as a wire with low copper loss at high-frequency operation. The Litz wire is commonly made of many thin isolated strands twisted in multiple levels. Due to its complicated structure, the copper loss prediction of the Litz wire has been difficult, hindering the design optimization of the Litz wire structure. To overcome this difficulty, preceding studies have investigated the analytical copper loss models of the constituting elements of the Litz wire, i.e., the strands and the bundles of strands. The purpose of this article is to propose an analytical copper loss model of the Litz wire by utilizing these preceding knowledge. The proposed model is formulated only with parameters that can be measured by basic testing instruments. Besides, the proposed model considers the bundle structure of the Litz wire, which affects the local ac current distribution, and the twisting pitch, which causes the inclination of the Litz wire strands. The proposed model was tested by comparing the analytical prediction and experimental measurements of the ac resistance of commercially available Litz wires. As a result, the predicted ac resistance showed good agreement with the measured ac resistance, suggesting the appropriateness of the proposed model. © 1972-2012 IEEE

Vf-constrained ηρ-pareto optimization of medium frequency transformers in ISOP-DAB converters

This study deals with ηρ (efficiency-power density) pareto optimisation of medium frequency transformers (MFTs) with considerations of voltage and frequency ( Vf) constraints of semiconductors for mega-watt range input-series output-parallel (ISOP) connected dual-active bridges (DABs). A simple design methodology to include the Litz wire configuration in the optimisation process is proposed. Based on the presented design methodology, the effects of the semiconductors blocking voltage and switching frequency on the ηρ -pareto optimisation are evaluated. First, an idealised optimisation is carried out to understand the general behaviour of the optimum point. Second, brute-force optimisation is utilised to find the practical optimum solution based on the market availability of MFT components. Designing MFTs for a 1 MW 10 kV/600 V ISOP-DAB converter is the subject of numerical studies. The best trade-off between ηρandVf is selected as the final optimal solution and its design correctness is validated using three-dimensional finite-element analysis. Experimental tests on a 3 kW downscaled MFT prototype show that the proposed method is valid in practice

Analysis and Application of Transmission Line Conductors

Skin effect is usually a concern reserved for radio frequency design and for high current conductors used in utility power distribution. Proximity effect between adjacent conductors has traditionally been a concern for the design of magnetic windings and other applications involving wire bundles. The rise in the ubiquity of high speed bit streams and other signals of very wide bandwidth has broadened the range of applicable contexts and increased the need to account for such effects. This is especially true for transmission lines used to interconnect critical signal paths in applications ranging from microelectronic devices to the signal integrity of printed circuit traces and implementation of system cabling. Optimal conductor design is obviously fundamental to transmission line performance. Researchers have paid considerable attention to the topic but the results are scattered throughout the literature. This thesis collected information on extant conductor designs, and the theoretical considerations behind each solution. A detailed analysis of current fl‡ow in a conducting half-space was included as a foundation. The conductor types discussed were solid cylindrical, rectangular, ribbonoid, bimetallic, tubular, laminated, litz, and stranded constructions. Discussions of the performance of stranded shields and conductor roughness e¤ects were included for completeness of understanding

Conceptual design of a noncontacting power transfer device for the ASPS Vernier system

The conceptual of electrical power transfer across a magnetically controlled gap as discussed for several years. The design represents the culmination of the first serious attempt to design a very low force, noncontracting power transfer mechanism. The electromagnetic device advanced herein is an ironless, translatable secondary transformer in which one of the two coils is fixed to the entire magnetic core. The second coil is free to move within the core over the full range of motions required. The specific application considered for this design was the Vernier subsystem of the Annular Suspension and Pointing System (ASPS). The development of and rationale for the electromagnetics design is presented. Similar documentation is provided for the Electronics Design. The Appendices detail the results of small scale model tests, disturbance force calculations, the baseline transformer fabrication drawings, the AVS Converter Parts List, and model schematic diagrams

Developments for the high frequency power transformer design and implementation

The thesis considers design and manufacturing of ferrite based high frequency power transformers. The primary aim of the work was to study core and winding losses and in particular thermal modeling of high frequency power transformers and to determine appropriate loss and temperature rise modeling methods for power converter applications. The secondary aim of the work was to study improved, mass manufacturable winding methods for toroidal, tube-type planar and disc-type planar high frequency power transformers. The analytical high frequency power transformer design equations for core and winding losses and transformer temperature rise were reviewed from literature, formulated for spreadsheet type calculations using excitation, material, geometry and winding implementation parameters and validated by in circuit temperature rise comparisons between calculated and measured values using regression analysis. The core and winding loss calculation methods in literature were found to provide appropriate accuracy for the practical design purposes. Thermal test block tests suggested a slight modification for analytical convective heat transfer equation from the literature. The results from in circuit temperature rise comparisons suggest that the transformer total losses can be predicted with the average standard error below 0.2 W with datasheet type information only. Further, if conductive thermal resistance from transformer via printed circuit board substrate to ambient is available the transformer operating temperature could be predicted with appropriate accuracy (5.6 °C) as well. The new manufacturing methods developed for toroidal, tube and disc-type transformer geometries were proved to be suitable for high frequency operation. With a common mode choke with static shield and windings deposited and etched directly on the toroidal NiZn core a transfer loss resonant frequency above 1.2 GHz was achieved. A multilayer foil winding with interleaved primary and secondary layers resulted resulted leakage inductance of 10 % of the value achieved using a wire-wound winding. The new developments for Z-folded inductive components resulted material cost savings, reduction of winding resistance and adjustability of leakage inductance and winding capacitances.reviewe

The application of resonant-mode techniques to off-line converters for the commercial market

This thesis presents the work performed by the author on the application of resonantmode techniques to commercially-orientated off-line converters. An extensive review of resonant-mode topologies leads to the development of a method of categorisation of these topologies which allows a greater comprehension of their properties. The categories of converter thus obtained are the conventional resonant converter, the quasi-resonant converter, and the gap-resonant converter. The gap-resonant converter is selected for further investigation. An analysis reveals the limited load and input voltage capabilities of this converter, and hence leads to the introduction of a pre-regulating converter to improve reliability and commercial viability. High-frequency techniques are explored and reported, and new techniques are developed in several areas in order to extend the concept of the gap-resonant converter to a realworld practical design. Subjects explored include the high speed driving of power MOSFETs, MOSFET and diode switching losses, high frequency magnetic materials and core losses, and skin and proximity effects. The techniques developed are used in the design of a 30OW, off-line converter with an input voltage range of 165V to 380V after rectification, and a ten-to-one output load range

High Voltage DC-biased Oil Type Medium Frequency Transformer; A Green Solution for Series DC Wind Park Concept

The electric energy generated by remote offshore wind parks is transported to the consumers using high voltage submarine cables. On the generation site, such transmissions are realized today by collecting the energy produced by several wind turbines in a bulky and expensive transformer placed on a dedicated platform. An alternative solution has been proposed recently, which allows to reduce the installation and maintenance costs by eliminating such a platform. It is suggested to equip each wind turbine in the wind park by an individual DC/DC converter and connect them in series to reach the DC voltage level required for an efficient HVDC energy transportation to the shore. The DC/DC converter is supposed to be a Dual Active Bridge (DAB) converter, which can be made reasonably small to be placed on the wind turbine tower or even in its nacelle. The key element of the converter defining its size and mass is a special transformer, which operates at voltages comprising a high (switching) frequency component superimposed on a high DC offset voltage. DC insulation design of such a transformer and investigation of the effects of a high DC insulation level on the other electromagnetic properties of the transformer is the subject of the present research.In order to verify the concept a prototype of the transformer was built, and its evaluation presented. The unit has been manufactured for the rated power of 50 kW and rated voltages 0.4/5 kV including DC offset of 125 kV and square-shaped oscillations with the frequency of 5 kHz. The magnetic system was made of ferrite material and consisted of 10 shell-type core segments. The magnetic properties have been verified by measuring magnetization and losses at various frequencies in the range 1-10 kHz to cover the operational range of the DAB. The types and dimensions of the windings and their conductors were chosen to minimize the proximity and eddy current effects at higher frequencies. To reduce the size of the transformer and to allow for its efficient cooling, the active part was immersed in oil and cellulose-based materials (paper and pressboard) were used to build the high voltage insulation system. The principles for dimensioning the insulation of the transformer are discussed. The criteria used for selecting insulating distances were based on the consideration of the electric field strength obtained from FEM simulations and using the non-linear Maxwell-Wagner model accounting for local variations of the electric field caused by accumulation of interfacial charges induced by DC stresses. The properties of the materials needed for the calculations were obtained by measuring their dielectric constants and electric conductivities. The methodology used for the measurements conducted for conventional mineral oil and eco-friendly biodegradable transformer oils and, respectively, for oil-impregnated paper/pressboard, is presented. The methodologies used for obtaining parameters of the built transformer prototype needed for its integration in the power electric circuit of the DAB are introduced. A method developed for accurate calculations of the leakage inductance for the shell-type multi core transformers with circular windings is described. Two innovative methods for evaluations of parasitic capacitances based on high frequency equivalent circuits of the transformer are presented. The results of their verifications against performed Frequency Response Analysis measurements and FEM calculations as well as their accuracy are discussed.Thermal performance of the developed transformer prototype is analysed based on the results of computer simulations of heat transfer in its active part under rated load. Identified hot spots and solutions for their elimination are presented.Finally, the expected dimensions, weight, and efficiency of an actual DC/DC converter with the rated parameters corresponding to a 6 MW, 1.8 kV real wind turbine having a 250 kV offset DC voltage are estimated assuming that the developed transformer prototype is scalable. It is shown that the proposed solution allows for installing the full-scale converter having 2.2 Tons in weight and 1.8 m3 in volume on the bottom of the wind turbine’s tower