Litz-wire Winding Research Articles

Feasibility of a new ironless-stator axial flux permanent magnet machine for aircraft electric propulsion application

With the development of aviation electrification, higher demands for electrical machines are put forward in aircraft electric propulsion systems. The aircraft electric propulsion requirements and propulsion motor features are analyzed in this paper. Comparing with conventional PM machines, ironless stator axial flux permanent magnet (AFPM) machine topologies with Litz wire windings allow designs with higher compactness, lightness and efficiency, which are suitable for high-frequency and high-power density applications. Based on the motor requirements and constraints of aircraft electric propulsion systems, this paper investigates a high-power 1 MW multi-stack ironless stator AFPM machine, which is composed of four 250kW modular motors by stacking in axial. The design guidelines and special attentions are presented, in term of electromagnetic, thermal, and mechanical performance for the high-frequency coils and Halbach-array PM rotor. Finally, an ironless stator AFPM motor is manufactured, tested and evaluated with the consideration of cost and processing cycle. The results show that the output power is up to 53.8kW with 95% efficiency at 9000r/min at this stage. The proposed ironless stator AFPM machine with oil immersed forced cooling proves to be a favorable candidate for application in electric aircraft as propulsion motors.

General Analytical Model for the Thermal Resistance of Windings Made of Solid or Litz Wire

In this paper, an analytical method to model the thermal resistance of windings made either of solid or litz wire is presented and validated by measurements. In addition, an extended numerical approach for litz wire windings, which also considers the twist pitch, is shown. With the presented model, it is possible to describe the thermal resistance of arbitrary wire arrangements. This approach can be used in straightforward thermal designs of magnetic devices, or it can be integrated in optimization procedures to improve the thermal designs of magnetic components. The analytical models are verified by measurements with nonpotted and epoxy-potted solid wire test setups and test setups for litz wire, which all show a good matching between the calculated and measured values. Besides the models for the thermal resistance between the winding layers, a method to simplify the thermal network of multilayer windings is presented. Finally, a thermal equivalent circuit of a test transformer has been calculated, which shows a good match between the measured and the predicted temperature distribution.

High frequency power loss measurement platform

ABSTRACTSophisticated techniques are required for getting accuracy in high frequency power losses of magnetic. This paper presents a high frequency power loss measurement platform (full bridge) that provides accurate assessing of losses in magnetic components. This is obtained by a construction of a thermal shunt with radiator to measure the losses of the bridge. An aluminium strip is used as a ‘thermal resistor’. Two negative temperature coefficient resistors measure the temperature drop across the aluminium strip. The magnetic device loss equals the DC input power of the platform minus the bridge loss. The copper loss can be estimated while using litz wire. Using litz wire windings with sufficiently low diameter of the strands allows neglecting eddy current losses, thus measuring only DC resistance is enough for calculating of copper losses. It can be checked by an RLC metre if the assumption is reasonable. The proposed approach and platform are verified by realisation and experiments with a full-bridge converter based on SiC switches and operating in frequency range of 50 kHz–1 MHz. The proposed platform can be used for obtaining the frequency dependence of core losses of magnetic materials.

Accurate Calculation of Eddy Current Loss in Litz-Wired High-Frequency Transformer Windings

The winding power loss of a high frequency transformer is strongly influenced by the high frequency eddy current skin and proximity effects. The litz-wire can reduce effectively the eddy current effects. The precise loss calculation method of litz-wire remains however a difficulty. At present, the Dowell model [1] and Ferreira model [2], [3] are two commonly used methods to calculate the winding loss. The Dowell model is originally derived to calculate the eddy current effects in foil conductors and later on extended to packed windings composed of litz-wire by introducing a porosity factor [4]. The accuracy however declines quickly when porosity factor reduces, and the characteristics of eddy current distribution is not adapted to the litz-wire. On the other hand, the magnetic field of round conductors analyzed by Ferreira model is excellent, but the error become significate at high frequency at high porosity factor [5] because it neglects the interaction between conductors in the same layer [6]. In this paper, an improved model is proposed for calculating the eddy current distribution in litz-wire windings due to the skin and proximity effects. This model can have much more accurate prediction of eddy current distributions in the cross-section of a round litz-wire conductor, and can be used for electromagnetic design of high frequency devices.

Winding Resistance and Power Loss of Inductors With Litz and Solid-Round Wires

An analytical model based on the one-dimensional Dowell's equation for computing the ac-to-dc winding resistance ratio of the litz-wire windings independent of the porosity factor is derived. The model takes into account proximity effect within the bundle and between bundle layers, as well as the skin effect in each strand. Three frequency ranges for the winding resistance characteristics are considered: low-, medium-, and high-frequency range. In each range, the behavior of the ac-to-dc winding resistance ratio $F_R$ is different. Moreover, an analytical optimization of the litz-wire winding strand diameter for litz-wire windings conducting sinusoidal and multiharmonic currents independent of the porosity factor is performed.

Analytical optimization of litz-wire windings independent of porosity factor

Purpose – The purpose of this paper is threefold. First, an analytical model based on one-dimensional Dowell’s equation for computing ac-to-dc winding resistance ratio FR of litz wire is presented. The model takes into account proximity effect within the bundle and between bundle layers as well as the skin effect. Second, low- and medium-frequency approximation of Dowell’s equation for the litz-wire winding is derived. Third, a derivation of an analytical equation is given for the optimum strand diameter of the litz-wire winding independent on the porosity factor. Design/methodology/approach – The methodology is as follows. First, the model of the litz-wire bundle is assumed to be a square shape. Than the effective number of layers in the litz wire bundle is derived. Second, the litz-wire winding is presented and an analytical equation for the winding resistance is derived. Third, analytical optimization of the strand diameter in the litz-wire winding is independent on the porosity factor performed, where the strand diameter is independent on the porosity factor. The boundary frequency between the low-frequency and the medium-frequency ranges for both solid-round-wire and litz-wire windings are derived. Hence, useful frequency range of both windings can be determined and compared. Findings – Closed form analytical equations for the optimum strand diameter independent of the porosity factor are derived. It has been shown that the ac-to-dc winding resistance ratio of the litz-wire winding for the optimum strand diameter is equal to 1.5. Moreover, it has been shown that litz-wire winding is better than the solid-round-wire winding only in specific frequency range. At very high frequencies the litz-wire winding ac resistance becomes much greater than the solid-round-wire winding due to proximity effect between the strands in the litz-wire bundle. The accuracy of the derived equations is experimentally verified. Research limitations/implications – Derived equations takes into account the losses due to induced eddy-currents caused by the applied current. Equations does not take into account the losses caused by the fringing flux, curvature, edge and end winding effects. Originality/value – This paper presents derivations of the closed-form analytical equations for the optimum bare strand diameter of the litz-wire winding independent on the porosity factor. Significant advantage of derived equations is their simplicity and easy to use for the inductor designers.

Transformer Analysis for Wireless Power DC-DC Converters

This paper presents the analysis of two different types of transformer structures used in wireless power applications. Conventional litz wire windings are compared to planar windings in terms of AC/DC performance ratio, coupling and inductance. Planar and litz wire transformer arrangements are proposed. A 6W LLC wireless power converter is used to compare the different transfomer structures. Finite element anlysis is used to determine the transformer coupling coefficient and AC/DC ratios. The simulation results are validated by experimental measurements

Analytical Calculation of Copper Losses in Litz-Wire Windings of Gapped Inductors

In this paper, we present an analytical procedure to predict the ac resistance of litz-wire windings considering air gap fringing fields. For this purpose, an equivalent complex permeability model is derived for hexagonally packed wires. We show how the real as well as the imaginary parts of the complex permeability can be determined with the copper filling factor as a parameter. An analytical 2-D model is deduced to describe the air gap fringing fields of gapped inductors. Accordingly, the proximity losses of the litz-wire winding are determined correctly and the ac resistance of practical inductors can be predicted over a wide frequency range with high accuracy. This offers the opportunity to optimize such components. Finally, the influence of various parameters on the copper losses is investigated and verified by means of experimental data drawn from impedance measurements.

Improved Characterization of the Magnetic Properties of Hexagonally Packed Wires

SummaryWhen designing passive magnetic components, calculations of the magnetic field distribution inside the winding window become necessary. Numerical calculations, but also other methods like the modal decomposition of the boundary value problem encounter difficulties, when the influence of a great number of wires (e.g. litz wire strands) has to be taken into account. To avoid discretization of a great number of tiny strands, a global property like an equivalent permeability may be used to characterize the macroscopic magnetic behavior (Fig. 1). If the magnetic field is characterized by complex amplitudes, this permeability also has a complex value. Its imaginary part describes the proximity losses in the winding. A possibility to derive this permeability from the properties of a single strand is presented in [1], however, as already stated there, this formula is not equally suited for all frequencies, permeabilities and various ratios of strand diameter to the total litz diameter. Especially for higher frequencies, as stated in [2], most approximation formulas deviate considerably from simulation data.In this paper, an improved complex permeability model for litz wire windings is derived heuristically from a comparison between simulation results and the standard analytical model. It is valid for all strand diameters, strand distances and frequencies, and may be used for accurate numerical calculations of magnetic fields and losses in magnetic components.

Winding Loss Simulation and Optimal Design of a High Frequency Coaxial Transformer

A high frequency coaxial transformer (HFCT) with a split winding structure and litz wire has been developed for high frequency (HF) and high power DC/DC converter applications. A method combined numerical analysis of magnetic field and analytical calculation of litz wire winding losses, taking into account conduction losses and proximity effect losses, is proposed for the designed HFCT. The experimental results validate the winding loss calculation method. The measured results demonstrate that the voltage ratio has a good agreement with the turn ratio over the frequency range from 0.1MHz to 1MHz, indicating that the high coupling efficiency has been obtained.

Winding resistance of litz-wire and multi-strand inductors

This study presents an approximate model for multi-strand wire winding, including litz-wire winding. The proposed model is evaluated using Dowell's equation. The model takes into account the existence of proximity effect within the litz-wire bundle between the strands and between the bundles, as well the skin effect. The expressions for optimum strand diameter and number of strands at which minimum winding AC resistance is obtained for the litz-wire windings are derived. The boundary frequency between the low-frequency and the medium-frequency ranges are given for both litz-wire and solid-round wire inductors. Hence, the low-frequency ranges of both wire windings are determined. It is shown that litz-wire is better than the solid wire only in specific frequency range. The model has been verified by the measurements, and the theoretical results were in good agreement with those experimentally measured. Comparison of the theoretical predictions of the proposed approximate litz-wire model with models proposed in other publications and with experimental results is given.

An Equivalent Complex Permeability Model for Litz-Wire Windings

Previous methods for calculating power loss in litz-wire windings usually assume very fine strands such that the diameter of strands is much smaller than skin depth. In this paper, we present a method for calculating proximity-effect loss in litz-wire windings. This method uses an equivalent complex permeability model of the winding to describe the proximity effect. We first obtain a permeability model for litz-wire bundles, then use homogenization techniques to find the average permeability of a winding. Permeability models are provided for bundles consisting either rectangularly packed or hexagonally-packed strands. The permeability model enables high-accuracy proximity-effect loss analysis and field analysis for litz-wire windings at high frequencies. It can also be used to find the leakage inductances in magnetic components.

An Ultrahigh-Speed, Low Power Electrical Drive System

New emerging applications in the areas of portable power generation, small turbocompressors and spindles require the development of ultrahigh-speed, low power electrical drives. A 500 000 r/min, 100 W electrical drive system is presented. Because of the ultrahigh-speed requirements, standard machine design and power electronic topology choices no longer apply and the complete drive system has to be considered. A permanent magnet machine with a slotless litz-wire winding is used, which results in a low motor inductance and a high fundamental machine frequency. Three different combinations of power electronic topologies and commutation strategies have been experimentally investigated. A voltage source inverter with block commutation and an additional dc-dc converter is selected as the most optimal choice for the power electronics interface as it results in the lowest volume of the entire drive system due to lower switching losses, no heat sink cooling required, a small number of semiconductor devices, and relatively simple control implementation in a low cost digital signal processor.

Analysis of effective resistance and eddy-current losses in multiturn winding of high-frequency magnetic components

This paper develops a numerical model for calculation of eddy-current losses in a multiturn winding of a high-frequency transformer. The model assumes periodic arrangement of conductors, and uses the repeat elementary cell concept. The paper proposes analytical expressions and graphic dependences to determine effective frequency-dependent resistance of the winding. It computes the leakage field in the transformer window, taking into consideration the effective magnetic permeability of the multiturn winding as a heterogeneous medium. Finally, it analyzes the values of the resistance at various frequencies for two types of winding (solid conductor winding and Litz wire winding) by numerical and experimental methods.

Cost-constrained selection of strand diameter and number in a litz-wire transformer winding

Design of litz-wire windings subject to cost constraints is analyzed. An approximation of normalized cost is combined with analysis of proximity effect losses to find combinations of strand number and diameter that optimally trade off cost and loss. The relationship between wire size, normalized cost, and normalized loss is shown to have a general form that applies to a wide range of designs. A practical design procedure is provided, Applied to an example design, it leads to less than half the original loss at lower than the original cost, or, alternatively, under one fifth the original cost with the same loss as the original design.

Accurate analytical model of winding losses in round Litz wire windings

An accurate analytical model of losses in round Litz wire windings is presented. The model is based on the exact analytical equations for round conductors, and it closely includes the distribution of the leakage field across the winding space. A closed-form formula of the ac resistance of round Litz wire windings is developed from the model. An analytic solution of the optimal value of the ac resistance is derived. The expression of the strand dimension corresponding to the optimal value of the ac resistance is also determined.

Analytical computation of AC resistance of round and rectangular litz wire windings

A new modelling method for computing the AC resistance of litz wire in windings is presented. The method, being analytically based, is not subject to mesh limitations encountered with numerical methods and can handle multiturn windings with an unlimited number of strands. A feature of this approach is that, as analytical equations are used, it requires less computing power and can be implemented on smaller desktop computers. Experimental measurements are presented which support the validity of this method.