A simplified approach to choosing number and diameter of strands in litz wire is presented. Compared to previous analyses, the method is easier to use. The parameters needed are only the skin depth at the frequency of operation, the number of turns, the breadth of the core window, and a constant from a table provided in the paper. In addition, guidance is provided on litz wire construction - how many strands or sub-bundles to combine at each twisting operation. The maximum number of strands to combine in the first twisting operation is given by a simple formula requiring only the skin depth and strand diameter. Different constructions are compared experimentally.

https://thayer.dartmouth.edu/inductor/papers/SimpLitz.pdf

Simplified design method for litz wire

Besides product differentiation, cost is a key parameter for market success and sustainable competitive advantage of industrial companies. Academic research in the field of power electronics, however, is often confined to the search for technical innovations or optimizations with focus on pure physical performance indices while the cost dimension is neglected. An explanation for the lack of such cost considerations is the generally poor availability of cost data in academia. This paper discusses the necessity of an increased awareness and sensitivity towards costs and the related opportunities for academic research. Furthermore, cost models for the power semiconductors, the passive components, the cooling systems and the printed circuit boards of switched-mode power converters with an approximate rated power between 5 and 50kW are derived. Based on manufacturer prices for large ordering quantities, numerical values for the cost model parameters are proposed. An example of a multi-objective comparison of different power converter topologies for photovoltaic applications regarding efficiency, volume and total semiconductor chip area is extended by the cost dimension to demonstrate the benefits of employing the developed cost models.

Component cost models for multi-objective optimizations of switched-mode power converters

High-flux-density materials, such as iron-based amorphous metal and 6.5% silicon steel for gapped inductors, and powdered alloys for gapless inductors, are very competitive for high-power-density inductors. The high-flux-density materials lead to low weight/volume solutions for high-power dc-dc converters used in hybrid-electric and electric vehicles. In this paper, the analytical selection of the magnetic materials is investigated, and modified performance factors are introduced for convection- and conduction-cooled magnetic components. The practical effects of frequency, dc bias, flux-density derating, duty cycle, airgap fringing on the core loss, and thermal configuration based on lamination direction are investigated for iron-based amorphous metal, 6.5% silicon steel, and iron-based powdered alloy material. A 2.5-kW converter is built to verify the optimum material selection and thermal configuration. Analytical, simulation, and experimental results are presented.

Revised Magnetics Performance Factors and Experimental Comparison of High-Flux Materials for High-Current DC–DC Inductors

In this paper, a 2.5-kW 330–410-V/14-V, 250-kHz dc/dc converter prototype is developed targeted for electric vehicle/hybrid vehicle applications. Benefiting from numerous advantages brought by the LLC resonant topology, this converter is able to perform high efficiency, high power density, and low EMI. To arrange high-output current, this paper proposes a parallel-connected LLC structure with developed novel double-loop control to realize an equal current distribution and an overall efficiency improvement. Considering the LLC cell's dimensioning, this paper establishes a more precise model by taking the secondary leakage inductance into consideration. System amelioration and design considerations of the developed LLC are also presented in this paper. A special transformer is presented, and various types of power losses are quantified to improve its efficiency. This converter also implements synchronous rectification, power semiconductor module, and an air-cooling system. The power conversion performance of this prototype is measured and the developed prototype attains a peak efficiency of 95% and efficiency is higher than 94% from 500 W to 2 kW, with a power density of 1 W/cm3. Finally, the EMC results of this prototype are also measured and presented.

https://hal.archives-ouvertes.fr/hal-01102420/document

Double-Phase High-Efficiency, Wide Load Range High- Voltage/Low-Voltage LLC DC/DC Converter for Electric/Hybrid Vehicles

Proximity effects caused by uneven distribution of current among the insulated wire strands of stator multi-strand windings can contribute significant bundle-level proximity losses in permanent magnet (PM) machines operating at high speeds. Three-dimensional finite element analysis is used to investigate the effects of transposition of the insulated strands in stator winding bundles on the copper losses in high-speed machines. The investigation confirms that the bundle proximity losses must be considered in the design of stator windings for high-speed machines, and the amplitude of these losses decreases monotonically as the level of transposition is increased from untransposed to fully-transposed (360°) wire bundles. Analytical models are introduced to estimate the currents in strands in a slot for a high-speed machine.

Transposition effects on bundle proximity losses in high-speed PM machines

Numerical techniques are used to find the inductor core dimensional ratios that minimize winding loss. It is shown that common core shapes result in significant excess losses, even if the shape of the wire winding is optimized. A design example demonstrates the practical implications of this technique for choosing cores-a standard core with dimensional ratios close to optimum provides a 32 % savings in power loss compared to another popular core shape. Further improvements in power loss could be achieved by using optimized core shapes. Improvements to software for shape-optimization of windings are described, including accounting for different turn lengths at different radii, the ability to select gaps in different core legs, and better approximations of three-dimensional field geometry.

/pdf/optimal-core-dimensional-ratios-for-minimizing-winding-loss-41sy7ow4mj.pdf

Optimal core dimensional ratios for minimizing winding loss in high-frequency gapped-inductor windings

Litz-wire windings for gapped inductors are optimized for minimum cost within a loss constraint or vice-versa. Optimal winding shapes and the strand diameter and number for each shape are found through simultaneous consideration of two-dimensional field effects and of cost and AC-loss implications of litz stranding.

/pdf/analysis-of-minimum-cost-in-shape-optimized-litz-wire-eaktkwl5vv.pdf

R.A. Jensen

Papers

Optimal core dimensional ratios for minimizing winding loss in high-frequency gapped-inductor windings

Analysis of minimum cost in shape-optimized Litz-wire inductor windings