Litz-wire Winding Research Articles

A Homogenized FEM Data-Driven Model for Calculating Leakage Inductance of High-Frequency Transformer With Litz-Wire Winding

A Homogenized FEM Data-Driven Model for Calculating Leakage Inductance of High-Frequency Transformer With Litz-Wire Winding

Litz-Wire Winding Loss Calculation Method for Optimal Design of High-Frequency Transformers

Litz-Wire Winding Loss Calculation Method for Optimal Design of High-Frequency Transformers

AC-Winding-Resistance Calculation of Toroidal Inductors with Solid-Round-Wire and Litz-Wire Winding Based on Complex Permeability Modeling

This paper has investigated a method for calculating the frequency-dependent winding resistance of toroidal inductor windings with Litz-wire as well as solid-round wire. The modified Dowell’s model is employed to address the effectiveness for inductor windings with the low and high filling factors. To overcome the limitation of this model, especially for a winding densely wound around the core, an alternative approach based on the complex permeability and iterative calculations is proposed. For the calculated AC-resistance factor of five inductors with different numbers of turns, layers with the same wire diameters are compared with that of FEA, and the three air-core toroidal windings are manufactured and tested within the frequency where the self-resonance can be neglected. The proposed model demonstrates the versality of the AC-resistance calculation of both solid- and Litz-wire windings within an error of 15% across a wide range of frequencies up to 1 MHz, compared with FEA.

Modeling of Litz Wire Winding AC Resistance Based on Improved Segmented Equivalent Circuit

Modeling of Litz Wire Winding AC Resistance Based on Improved Segmented Equivalent Circuit

Analytical Double-2D Frequency-Dependent Leakage Inductance Model for Litz-Wired High-Frequency Transformer

Accurate and fast calculation of frequency-dependent leakage inductance is critical for the optimization of the high-frequency transformer with Litz wire winding. The analytical method is widely used due to its high computation speed. However, its computation accuracy is limited due to the following factors. i) One-dimensional (1D) or two-dimensional magnetic field model (2D) has unsatisfying accuracy for the transformer with a rotationally asymmetric structure. ii) The skin and proximity effect factors based on the multilayer foil winding are inaccurate for the Litz wire winding in the calculation of frequency-dependent magnetic energy. This paper proposes a double-2D frequency-dependent leakage inductance model for the transformer with Litz wire winding. It uses the image method to calculate the 2D leakage magnetic field inside and outside the core window, respectively, which considers the rotationally asymmetric structure in leakage inductance calculation. The round conductor model is proposed for the frequency-dependent magnetic energy calculation. The single strand in a Litz wire is taken as the basic modeling object of the round conductor model, which is more detailed than the multilayer foil winding model for the Litz wire winding. The comparison between the experiment, FEM, state-of-the-art models and the proposed model is conducted for eight transformers with E-core, U-core, round or rectangular Litz wire winding. The proposed model shows satisfying computation accuracy in the whole frequency band. And the computational speed of the proposed model is 100 times that of the FEM.

Current Displacement Effects on Copper Losses in PWM Supplied Electrical Machines

This document provides a comparison of hairpin winding, pull-in winding and litz wire winding technology on the ac copper losses of a permanent magnet (PM) excited electrical machine. Current displacement effects under pure sinusoidal current and pulse width modulated (PWM) voltage supply are studied based on Finite Element Analysis (FEA). The resulting additional ac copper losses are analyzed for three winding technologies.

Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer

Semi-Analytical AC Resistance Prediction Model for Litz Wire Winding in High-Frequency Transformer

An Accurate Calculation Method of Leakage Inductance of High-Frequency Transformer With Litz Wire Winding Considering Irregular Region

The leakage inductance of a high-frequency transformer affects the operating mode and performance in dc/dc converters, so it is necessary to calculate the leakage inductance accurately. In the existing analytical calculation methods of leakage inductance of high-frequency transformers with Litz wire winding, the nonarea-equivalent high-frequency analytical method is applied to calculate leakage inductance. However, the calculated leakage inductance value is lower than its actual value due to the neglect of the irregular region between turns. In order to improve the calculation accuracy, this article proposes an analytical calculation method of leakage inductance for the high-frequency transformer with Litz wire winding, which considers the irregular region between turns. The 2-D magnetic field distribution in the transformer window and attenuation caused by high-frequency effects on magnetic field energy are analyzed and applied in this proposed method, to take the energy stored in the irregular region between turns into account indirectly. Thus, the proposed analytical expression for leakage inductance is derived correspondingly. Finally, the accuracy of the proposed method is verified by simulations and experiments. The results indicate that the relative error of calculating leakage inductance can be reduced from 16.25% to 3.79% by the proposed method within a certain range of wire densities.

Analytical Winding Loss and Inductance Models for Gapped Inductors With Litz or Solid Wires

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.

High Voltage Winding Internal Electric Field Shielding Structure for Medium Voltage High Frequency Transformers

In this letter, an internal electric field shielding layer for high voltage winding of medium voltage high frequency transformer used in a modular cascaded medium voltage solid state transformer is proposed. Without breaking the litz wire insulation layer, the high electric field is effectively shielded by a semiconducting layer and an unclosed copper foil spiral, which are electrically connected together. Not only the electric field in the main wall insulation is uniformed but also the peak value of the internal field is greatly reduced, which will help to achieve lower partial discharge and higher insulation reliability. With this structure, the difficulties of pouring process and electric field estimation for the litz wire winding are both avoid. Finally, a no partial discharge 100 kW medium voltage high frequency transformer prototype with 75 kV base insulation level is built and verified with the insulation tests.

Inductor Design for Nonisolated Critical Soft Switching Converters Using Solid and Litz PCB and Wire Windings Leveraging Neural Network Model

High frequency and high efficiency inductor design method is proposed for the application of critical soft switching with large current ripple to improve the power density and efficiency of electrified energy conversion systems. Firstly for the theoretical design section, the core/coil size, number of turns, airgap, inductance are optimized to minimize the inductor losses. Secondly for the structural design section of coil, a 3D routing method of litz PCB winding is developed to reduce the AC copper losses. The strand number, trace width, thickness and layout of litz PCB are analyzed in detail. Different types of coil, including solid/litz types of PCB/wire windings, are compared and analyzed based on the high frequency copper loss reduction and space utilization. For the structural design section of core, E and I cores are optimized to reduce the volume and core losses. Specifically, E-E, E-I, I-I and E-Air types of core structures are designed and compared considering the core loss, volume reduction and airgap limitation for the stack of turns. Ten derived prototypes are built to benchmark with the commercial inductors. Power losses, temperature rise and cost are reduced by a factor of 10, 2.5 and 3 with the proposed core and coil structures.

Common Mode Noise Analysis for Inductive Power Transfer System Based on Distributed Stray Capacitance Model

This article reveals the significant stray capacitances in inductive power transfer (IPT) coil, and offers two methods for modeling the stray capacitance effect: concentrated model and distributed model. Both analytic formulas and FEM simulation are introduced to estimate the value of parasitic capacitances, and experimental measurements on an 11 kW IPT coil prototype are conducted to verify the correctness of both methods. The common-mode noise propagation circuit of the IPT system is derived and simulated based on these two models. The results show that parasitic capacitance between Litz wire winding and shielding metal on the transmitter side plays a dominant role in CM noise propagation and the distributed model has higher fidelity because of its asymmetric structure. Besides, to mitigate conductive CM noise, an EMI filter, and HF isolation transformer are introduced. Finally, the conductive EMI tests are performed in an 11kW IPT prototype. The experimental results validate the accuracy of the proposed CM noise model with stray capacitances of the IPT coil. And the combination of EMI filter and HF isolation transformer can suppress CM noise greatly and render the CM noise spectrum below the CISPR 32 Class-B limit.

Modelling and optimization of winding resistance for litz wire inductors

Optimization of winding resistance for litz wire inductors is essential to reduce losses and improve energy transfer efficiency in electrical power systems. In this study, an approximate model for the optimization of winding resistance in litz wire inductors based on Dowell's equation is developed in three frequency ranges. The proximity and skin effects are analysed separately and subsequently combined to obtain an approximation with minimum theoretical error. Two error functions are defined to determine the frequency ranges for which the approximation is valid. Based on this Dowell's model approximation, it is found that, with the other parameters of the inductors fixed, both the porosity factor and conductivity have an optimal value that minimizes AC resistance for the litz wire windings. Thus, expressions for the optimum porosity factor and conductivity are derived, the optimization schemes under different practical engineering conditions are also given. The theoretical results are in good agreement with the experimental measurements, which indicates that the proposed model is valid for three frequency ranges, and the proposed optimization method is practical and suitable.

Closed‐form complex permeability expression for proximity‐effect homogenisation of litz‐wire windings

The eddy-current losses in litz-wire windings are mostly due to the proximity effect, which can be macroscopically modelled via a complex frequency-dependent permeability. In this study, the authors propose a new closed-form expression for this complex permeability. Results are compared with approximations found in the literature in a wide-frequency range. For the sake of validation, a two-dimensional)-axisymmetric gapped transformer with litz-wire primary and secondary coils is studied.

An Analytical Loss Model of Litz-Wire Windings for Transformers Excited by Converters With Winding Configurations Considered

An accurate analytical model for litz-wire (LW) winding loss calculation of power electronic transformers (PETs) was deduced. First, the skin effect and proximity effect losses at bundle levels of a single straight LW were introduced. Then, the proximity loss of an air-core LW winding was studied by adopting the coordinate transformation technique (CTT) considering helical winding (HW) configurations and twisting configurations (TCs). Last, a 2-D analytical model for LW windings considering magnetic materials, LW configurations, and winding configurations (WCs) was proposed with the help of CTT, Dowell method, and Roth’s method. This model is helpful for the design of LW windings considering more details such as the choices of WCs and LW configurations.

Accurate Calculation and Sensitivity Analysis of Leakage Inductance of High-Frequency Transformer With Litz Wire Winding

Leakage inductance is an important parameter in a high-frequency transformer for its influence on power transmission performance and the soft switching of converters. Nowadays, Litz wire is widely used to control winding loss and reach high efficiency. However, it is not an easy task to accurately calculate its leakage inductance. This article presents a detailed model of leakage energy in Litz wire, and proposes an accurate closed-form expression for calculating the leakage inductance in a high-frequency transformer. The skin effect and the proximity effect of Litz wire are taken into account in two-dimensional polar coordinates, and the filling factor of Litz wire is also considered. A global sensitivity analysis is performed to assess the influence of each parameter on the overall leakage inductance. Finally, two transformer prototypes are made to verify the accuracy of the proposed analytical expression.

Experimental Extraction of Winding Resistance in Litz-Wire Transformers—Influence of Winding Mutual Resistance

The extraction of winding resistance from impedance measurements needs a compensation of undesirable effects, e.g., core loss and distributed winding capacitance. This paper rigorously shows that the core loss (or core-loss resistance) measured with the two-winding method always includes the effect of the winding mutual resistance. At high frequencies, this effect becomes more prominent and can cause an overestimation of the measured core-loss resistance. As a result, the compensated winding resistances can be significantly underestimated. To mitigate this effect, this paper proposes to measure the core-loss resistance on an auxiliary 1:1 transformer with single-turn windings. Consequently, it is scaled to obtain the actual core loss. The proposed analysis and method is applicable to multiwinding systems. For validation, this paper considers a gapped transformer with litz-wire winding for high-frequency operations. The experimental results are validated against the results from its three-dimensional finite-element (FE) model. The litz-wire winding is considered in the FE model by means of a homogenization approach. With the method proposed in this paper, the experimentally extracted winding resistances become more accurate and are in good agreement with the FE results.

Derivation of The Planar Square Coil Litz-Wire Winding Resistance for Sinusoidal Currents

Derivation of The Planar Square Coil Litz-Wire Winding Resistance for Sinusoidal Currents

Thermal Modeling of Inductor and Transformer Windings Including Litz Wire

Design optimization of magnetic components, which considers both electrical and thermal performance, can help in designing power converters with a high power density. This paper proposes an approximate analytical model for thermal resistance of inductor and transformer windings, including litz wire, which only requires knowledge of thermal properties of constituent materials and geometric dimensions. The model is based on regular square and hexagonal packing of insulated wires and is derived by integration of infinitesimal thermal resistances along a specified heat flow path. The model closely agrees with finite-element analysis (FEA) and can be used in place of time-consuming FEA as part of larger thermal network models for magnetic components. The model is also experimentally validated using a toroidal inductor with a litz-wire winding; the model has less than 12% error compared to the experimental measurement. Application of the model for practical windings, including litz-wire windings, is also discussed. The model can be used during the design process of magnetic components of a switching power converter to evaluate the temperature and potential hot spots. The model provides closed-form results, hence fast computation times, and so can be used in design optimization procedures.

Eddy Current Losses Analysis and Optimization Design of Litz-Wire Windings for Air-Core Compulsators

Compulsators are popular choices for high-end railgun power supplies. In order to increase the power density, air-core compulsators are proposed by using composite materials instead of ferromagnetic materials. Compared with the conventional iron-core machines, armature conductors of the air-core machines are not surrounded by the ferromagnetic teeth, resulting in the conductors been exposed to highly dense revolving magnetic field, which causes eddy current losses in the conductor strands. On the other hand, high-frequency currents flow through the armature winding during the self-excitation and discharge process, which also causes skin effect and proximity effect losses. Therefore, an effective winding design is essential to ensure proper current density distribution and eddy current losses of armature conductors to avoid local overheating. This paper deduced the calculation model of eddy current losses of a single conductor under alternating magnetic fields and then established the eddy losses calculation model of the air-core compulsator’s armature winding. The expression indicates that the eddy current losses of a conductor are determined by both the radial and tangential components of the flux density, which can be obtained by finite-element analysis. Based on the calculation model, the performance of two particular armature designs (a solid conductor and a compacted type-8 litz wire with the same area) are analyzed and discussed. The conductor eddy current losses are estimated and compared for both designs. Finally, an optimization study is carried out to find the best choice of strand diameter to minimize the total losses.