AC Winding Loss Research Articles

Design Consideration of Rectangular Conductors and Slot Wedge for AC Winding Loss Reduction in High Speed Train Traction Motor

Design Consideration of Rectangular Conductors and Slot Wedge for AC Winding Loss Reduction in High Speed Train Traction Motor

Analytical Models for Solid & Litz Wire AC Winding Loss in Toroidal Inductors

Analytical Models for Solid & Litz Wire AC Winding Loss in Toroidal Inductors

Modeling and Design of High-Power, High-Current-Ripple Planar Inductors

This article is focused on modeling and design optimization of high-current-ripple planar inductors in liquid-cooled high-power applications, such as electric-vehicle drivetrain systems, where efficiency and power density are the key performance metrics. The planar-inductor optimization is facilitated by innovations in computationally efficient and accurate models of ac winding loss and thermal management. A novel approximate analytical model for the ac winding loss takes into account effects of inside-the-core versus outside-the-core winding geometry as well as the air-gap fringing effect. Furthermore, thermal management strategies are introduced to enhance the vertical thermal flow from the core and the windings to the cold plate, leading to 2.5–3 times higher peak power capability compared with standard solutions. The developed modeling and optimization techniques are applied to planar inductor design in a 16.5-kW-rated SiC-based zero-voltage-switching quasi-square-wave boost converter, and the insights of selecting the core dimensions, number of turns and inductance are discussed in detail. The designed ELP 43-based planar inductor achieves a power density of 175.7 kW/L, and is experimentally validated on the converter prototype, achieving 98.8% efficiency at the typical 9.45-kW point, and less than 60 °C of worst-case temperature rise with a winding loss of 68 W in full power operation.

A Fourier-Based Semi-Analytical Model for Foil-Wound Solid-State Transformers

A mesh-free semi-analytical Fourier-based method is presented to evaluate the frequency-dependent losses in the windings of solid-state transformers (SSTs) with foil-wound transformers. In the employed diffusion equation, which accounts for induced eddy currents, the imposed current density and conductivity in the transformer window area are represented using spatial Fourier series and method of images. As a result, induced current density distribution in foil conductors and ac loss in medium frequency transformers (MFTs) is calculated using the semi-analytical method. The proposed method is verified using the finite element method (FEM). It is observed that with the considered approach one can estimate the ac winding loss in the frequency range of 5–25 kHz, with 2.7% maximum absolute error and approximately 2.5 times less number of degrees-of-freedom compared to FEM computations.

Computationally Efficient Stator AC Winding Loss Analysis Model for Traction Motors Used in High-Speed Railway Electric Multiple Unit

The aim of this proposed work is to develop a computationally efficient and accurate AC winding loss analysis model for the traction motors for use in high-speed railways (HSRs). The goal of the model is to be able to study AC winding loss under both sinusoidal and pulse width modulated (PWM) inverter voltage sources. The traction motor model considered for the proposed study is a form wound winding permanent magnet (PM) assisted synchronous reluctance motor (PMaSynRM). The traction motor uses an open slot with two-layer winding. First, a flux linkage table is built using finite element analysis (FEA) with sinusoidal current as the input. The machine model then includes the effect of the PWM inverter voltage source with the current controller. For the AC winding loss analysis, the fundamental component and the harmonics due to PWM are considered separately. To find the loss due to the fundamental component only, the vector potential of the slot region is mapped to the subconductors of the form wound winding and the eddy current distribution and the AC winding loss are calculated. The effect of the harmonics due to the PWM switching is then added in the post-processing stage by analytically evaluating the individual harmonic effect. The whole AC loss analysis model proposed in this work is computationally more efficient than the conventional FEA because the transient state of the system is removed. Moroover, the PWM voltage source effect is divided into the effects of the fundamental component and switching harmonics by combining the vector potentia mapping and post-processing analytical calculation.

Thin Film Magnetic Core Microinductor With Stacked Windings

In this work a stacked winding thin film magnetic core microinductor is proposed to improve the ratio of inductance to dc resistance (DCR). This article also describes an improved ac winding loss model accounting for the asymmetric 2-D magnetic fields present within the device. Two six-turn single layer and stacked winding devices are fabricated, and small signal measurements are presented with dc inductance of 150 nH and DCR of 0.35 Ω for the stacked winding inductor, and with DCR of 0.47 Ω for the single winding inductor. In this case, the total DCR of stacked winding inductor is reduced by approximately 25% compared with the corresponding single layer structure with an equivalent inductance and device area.

Modeling, Investigation, and Minimization of AC Winding Loss in Slotless PM Machines

The AC winding loss can be the primary source of losses in slotless permanent magnet (PM) machines. This paper presents the simplified model, investigation, and reduction method of the AC winding loss in slotless radial flux PM machines. Preferentially, the open-circuit AC winding loss is calculated in the rotor reference frame based on the resistance limited. Subsequently, a fast optimization model, including the AC winding loss, is developed by solving the field equations only once for a specific geometry. As a result, the influence of the design parameters on the AC winding loss can be investigated by taking advantage of the fast computational model. It shows that the concentrated winding with multiples of 2-pole/3-coil is the best selection to achieve the low AC winding loss due to the possibility of using multiple parallel paths. Finally, the finite element (FE) and experimental results demonstrate the validity of the proposed analysis.

An Overview of Methods and a New Three-Dimensional FEA and Analytical Hybrid Technique for Calculating AC Winding Losses in PM Machines

This article proposes a new hybrid analytical and numerical finite element (FE) based method for calculating ac eddy current losses in wire windings and demonstrates its applicability for axial flux permanent magnet electric machines. The method takes into account three-dimensional (3-D) field effects in order to achieve accurate results and yet greatly reduce computational efforts. The new 3-D FE-based method is advantageous as it employs minimum simplifications and considers the end turns in the eddy current path, the magnetic flux density variation along the effective length of coils, and the field fringing and leakage, which ultimately increases the accuracy of simulations. This study is one of the first ones to compare meticulous 3-D finite element analysis (FEA) models with more approximate, but faster solution methods, which can be employed in the optimization process. The accuracy of the 3-D FEA calculations has been confirmed through tests on a prototype axial flux permanent magnet machine. The proposed method is applicable for cases with majority of ac copper losses induced due to external magnetic flux sources, such as permanent magnets. Examples of such machines designs are coreless or open slot PM machines with conductors sizes smaller than skin depth.

Cauer-Equivalent Circuit for Inductors Considering Hysteresis Magnetic Properties for SPICE Simulation

This article presents a new method to synthesize the Cauer-equivalent circuit for inductors that can represent the hysteresis, eddy current, anomalous core losses, dc and ac winding losses as well as inductance. Only the measurement of inductor loss under the sinusoidal excitation is required to synthesize the SPICE loss model. The proposed circuit model can be used to evaluate the loss under arbitrary voltage/current excitations. In the proposed approach, the measured loss is subdivided into the ac and hysteresis losses. Then, the Cauer-equivalent circuit for SPICE simulation is synthesized from the loss model. It is shown that the losses evaluated by the proposed model are in good agreement with the measured results under the condition of the sinusoidal and triangular cases with and without dc bias current.

Reduction of AC Winding Losses Due to Fringing-Field Effects in High-Frequency Inductors With Orthogonal Air Gaps

In high-frequency inductors, ac winding losses are affected by skin and proximity effects, including uneven current distribution due to fringing magnetic fields around air gaps. It is well known that fringing effects can be mitigated using distributed air gaps. This article is focused on an orthogonal air-gap approach, which is a distributed air-gap technique where gaps are placed in core segments parallel with the windings and in core segments perpendicular to the windings. The orthogonal air-gap approach is developed using a one-dimensional analytical framework and validated by two-dimensional and three-dimensional finite-element simulations. Analytical guidelines are presented to optimize the air-gap distribution to achieve minimum ac resistance. As a case study, a planar inductor is designed for an 8-kW SiC-based buck converter operating at 250 kHz. It is shown how the orthogonal air gaps result in approximately 50% reduction in ac resistance and substantially reduced inductor losses compared to the design using standard air gaps. Experimental validation includes measurements of losses on the converter prototype as well as quality factor measurements in a resonant-circuit test setup.

Computationally Efficient Strand Eddy Current Loss Calculation in Electric Machines

A fast finite element (FE) based method for the calculation of eddy current losses in the stator windings of randomly wound electric machines is presented in this paper. The method is particularly suitable for implementation in large-scale design optimization algorithms where a qualitative characterization of such losses at higher speeds is most beneficial for identification of the design solutions that exhibit the lowest overall losses including the ac losses in the stator windings. Unlike the common practice of assuming a constant slot fill factor s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> for all the design variations, the maximum s <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</sub> in the developed method is determined based on the individual slot structure/dimensions and strand wire specifications. Furthermore, in lieu of detailed modeling of the conductor strands in the initial FE model, which significantly adds to the complexity of the problem, an alternative rectangular coil modeling subject to a subsequent flux mapping technique for determination of the impinging flux on each individual strand is pursued. Rather than pursuing the precise estimation of ac conductor losses, the research focus of this paper is placed on the development of a computationally efficient technique for the derivation of strand eddy current losses applicable in design optimization, especially where both the electromagnetic and thermal machine behavior are accounted for. A fractional-slot concentrated winding permanent magnet synchronous machine is used for the purpose of this study due to the higher slot leakage flux and slot opening fringing flux of such machines, which are the major contributors to strand eddy current losses in the windings. The analysis is supplemented with an investigation on the influence of the electrical loading on ac winding loss effects for this machine design, a subject that has received less attention in the literature. Experimental ac loss measurements on a 12-slot 10-pole stator assembly will be discussed to verify the existing trends in the simulation results.

Two-Dimensional Gapping to Reduce Light-Load Loss of Point-of-Load Inductor

Point-of-load converter at light load has low efficiency owing to the “fixed losses” such as core loss and ac winding loss. This paper focuses on two-dimensional (2-D) gapping of a ferrite core to shape inductance versus load current to reduce inductor loss at light load. Since the maximum inductance of conventional stepped gap is limited by the cross-sectional area of the thin gap, a 2-D gap is formed by joining two orthogonal gaps to gain flexibility. Higher inductance is achieved at light load compared with uniform-gap and stepped-gap geometries having the same volume and dc resistance. AC resistance is reduced at light load thanks to a magnetic path that steers ac flux away from the winding. Two C-cores with 2-D gap were fabricated and tested on a buck converter with 50% reduced total inductor loss at 10% load current.

AC Winding Loss of Phase-Shifted Coupled Windings

In circuits where there is an inherent phase shift angle between coupled winding currents such as in coupled inductors, it is important to accurately calculate the ac winding loss at the correct phase shift and frequency. Phase shift between winding currents can cause the ac winding loss to vary significantly due to changes in the magnetic field distribution. This paper presents an analysis of winding loss for the general case of coupled windings with arbitrary phase-shifted currents and its effect in a number of practical devices. A detailed approach to analytically calculate ac winding loss in microfabricated-coupled stripline inductors is presented along with a derivation of the resistance matrix for the device. The analysis and methodology are then validated using finite element analysis and experimental results.

Simplified Analytical Model and Investigation of Open-Circuit AC Winding Loss of Permanent-Magnet Machines

This paper presents a simplified analytical model based on one slot per pole for predicting the open-circuit AC winding loss of surface-mounted permanent-magnet machines accounting for the influence of tooth-tips but neglecting the redistribution effect of eddy currents. The comparison between the analytical models and finite-element results shows that the simplified analytical model has similar accuracy as the analytical model accounting for all slots together. The influence of various design parameters, such as conductor layout, slot width, slot opening width, tooth-tip height, magnet pole-arc to pole-pitch ratio, and gap between tooth-tips and conductors, on the open-circuit AC winding loss is investigated. It shows that the open-circuit AC winding loss gradually decreases with the number of radial conductor layers if the number of circumferential layers is larger than 1, although the radial segmentation is ineffective when there is no circumferential segmentation. The loss decreases greatly when the number of circumferential layers changes from 1 to 2, but reduces slowly when the conductors are further circumferentially segmented.

Derivation and Scaling of AC Copper Loss in Thermal Modeling of Electrical Machines

Accurate prediction of temperature-dependent ac winding loss effects is crucial in the design of electrical machinery. Average ac winding loss as a function of operating frequency is commonly characterized by the ratio of the equivalent ac and dc resistances (Rac/Rdc). However, as the ac and dc components of the winding loss scale differently with temperature, a single value of Rac/Rdc derived for one temperature can be inadequate when used in thermal modeling. In this paper, methods of deriving the Rac/Rdc ratio, together with scaling techniques of the ac winding loss accounting for thermal effects, are discussed. As an alternative to computationally intensive 3-D finite-element analysis, an experimental approach based on tests on full-scale stator assemblies is proposed. A previously proposed scaling technique of the ac winding loss is discussed and developed further. The proposed techniques of deriving the ac winding loss accounting for temperature variation are illustrated using both theoretical analysis and experimental data.

Comparison of Realization Techniques for PFC Inductor Operating in Discontinuous Conduction Mode

Several design techniques are compared for producing a power factor correction (PFC) boost inductor operating in discontinuous conduction mode. In this application, fringing fields associated with high frequency current pulses cause problems of winding loss in the vicinity of an air gap, in particular with planar core shapes. For this reason, a planar inductor in which a lumped gap is replaced by a distributed air gap material is described and investigated. The consequences of lumped versus distributed air gap for the losses of the boost inductor are investigated. A significant reduction in AC winding loss of the planar structure with the composite core is demonstrated. However, the trade-off between reduced winding loss and increased core loss for this technique has to be considered along with the selection of proper winding technology. Four boost inductor design realizations are built and compared. Presented winding loss models are verified with measurements on prototypes operating in an 80 W PFC converter.