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.

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

This paper proposes and develops a circuit-based model aiming to simulate variable magnetic power elements in power electronic converters. The derived model represents the magnetic element by a reluctance-based equivalent circuit. The model takes into consideration device core losses, with the main emphasis given to hysteresis losses, which are modeled using the Jiles-Atherton model. The core loss model is further validated on different ferromagnetic materials to prove its range of applicability. The winding losses of the magnetic device are also taken into consideration, which are obtained using Dowell empirical formulas. In addition, the frequency dependence of the device losses is also considered. The proposed modeling procedure has been applied to study and characterize a double E-core variable power inductor structure in a 1 kW SiC full bridge DC-DC converter. The procedure has been verified by comparing the simulation results to the experimental measurements, confirming the validity and accuracy of the full circuit-based model.

Modeling of magnetic elements including losses-application to variable inductor

The resistance of the electric machine’s windings is an important parameter when analyzing the machine’s performance, as conduction losses in the winding are often the largest loss component. However, this resistance changes with frequency due to the skin and proximity effects, making it challenging to accurately estimate these losses. In this article, a computationally efficient, general method of calculating the ac resistance of an electric machine winding with rectangular conductors is presented. The method uses a 1-D magnetoquasi-static model of the stator slot region to develop boundary transfer relations between individual turns. These relations are then used to create an impedance matrix from which the ac resistance can be calculated. This technique is more flexible than previous solutions since it can accommodate different winding configurations such as fractional-pitch windings. It is shown that a fractional-pitch winding has a lower ac resistance than a full-pitch winding. Finite-element analysis simulations and experimental results are used to validate the proposed method.

Computationally Efficient AC Resistance Model for Stator Winding With Rectangular Conductors

This article studies design guidelines to optimize the inductive coils for electric vehicles by replacing the standard compact ferrite core with a compound of polymers, nanoparticles, and tile-links of ferrite and by reviewing different aspects of the winding to improve mechanical behavior and efficiency. A system composed of the studied vehicle assembly and ground assembly from the society of automotive engineers’ recommended practice is defined. Fast three-dimensional (3-D) finite element simulations are performed by evaluating different geometric aspects of the vehicle assembly. In doing so, the variation of coupling factor and inductance related to the geometry can be observed and compared in order to analyze the performance when the amount of compact ferrite is reduced. The polymer bonded magnetic is, then, incorporated to improve the decreased magnetic behavior due to the reduction in ferrite. In previous works, the modeling of the litz-wire and polymer bonded magnetic were developed to accelerate the simulations. In this article, we include the modeling of the compact ferrite tile-links to further reduce the time consumption of these simulations. Moreover, simple two-dimensional simulations are described to study the windings’ parasitic capacitances. The design guidelines, based on fast 3-D simulations, are detailed and validated with particular prototypes.

Design Guidelines of Inductive Coils Using a Polymer Bonded Magnetic Composite for Inductive Power Transfer Systems in Electric Vehicles

This paper introduces a new two-dimensional (2D) modeling approach for the fast calculation of inductor and transformer foil winding losses. The proposed modeling procedure is derived from the Partial Element Equivalent Circuit (PEEC) method, which is originally a full three-dimensional (3D) electromagnetic solution technique. With the presented modifications, the PEEC method can take into account the influence of an air gap fringing field and core material boundaries as well as skin- and proximity effect. A comparison to 2D Finite Element Method (FEM) simulations shows that the developed PEEC-based approach exhibits similar accuracy but shorter calculation times than the classical FEM modeling techniques typically employed for the calculation of non-uniform current distribution within foil windings. The new modeling approach is experimentally verified by calorimetric loss measurements of a gapped foil winding E-core inductor. Due to the fast calculation speed of the new approach, optimizations of inductive components with foil windings over a wide design space are finally possible.

A fast method for the calculation of foil winding losses

The Dowell expression is the most commonly used method for the analytic calculation of the equivalent resistance in windings of magnetic components. Although this method represents a fast and useful tool to calculate the equivalent resistance of windings, it cannot be applied to components that do not fit with classical 1D assumption, which is the case of gapped magnetic components. These structures can be accurately analyzed using finite-element analysis (FEA) with the time cost that this represents. Modifying the Dowells equation, and taking advantage of the orthogonality between skin and proximity effects, a simple solution that allows its application in gapped magnetic components is proposed in this work, which results shows a very good accuracy compared with experimental measurements.

/pdf/simple-analytical-approach-for-the-calculation-of-winding-14nc07roqa.pdf

Simple analytical approach for the calculation of winding resistance in gapped magnetic components

An improved 2-D equivalent (i2D) analytical calculation method to estimate conductive losses in gapped magnetic components in a wide range of frequencies is presented In the previous work, which is based on the superposition of losses mechanisms (skin, gap and proximity) in the winding of the component, several expressions to separately evaluate all components of losses were used and the total winding loss could be obtained by the addition of the calculated values Although the obtained results were in good agreement with finite element analysis (FEA) and measurements this method is limited to conductors with smaller radius than the skin depth at the considered frequency In this paper the dependence of the wire diameter is eliminated by means of the inclusion of the proximity magnetic field in the calculations while the number of required equations is reduced The method is used to evaluate conduction losses in inductors for switched mode power supplies (SMPS) and the results are compared with FEA simulations

/pdf/power-losses-calculations-in-windings-of-gapped-magnetic-6r4jo83gkb.pdf

Power losses calculations in windings of gapped magnetic components: The extended 2-D method

A model is proposed for the calculation of the winding losses at the beginning of the design process of high frequency transformers and inductors. Although this kind of losses have been subject of investigation for years, their analytical calculation in gapped components is still limited, and the use of numerical analysis tools, such as finite elements analysis (FEA) tools, are commonly needed for winding characterization. A general 2-D equivalent analytical model for windings losses calculation in gapped magnetic components that shows very good results compared with FEA calculation is presented. The model can be integrated in design and optimization tools in order to evaluate the influence of the gap on the windings at the very early stages of the design process.

/pdf/power-losses-calculations-in-windings-of-gapped-magnetic-5367t610dr.pdf

Power losses calculations in windings of gapped magnetic components

The improved 2-D equivalent analytical calculation method to estimate conductive losses in gapped magnetic components in a wide range of frequencies is extended to the calculations of conduction losses in flyback transformers. The i2D method, that is applicable to power inductor, is extended is extended to the winding loss calculation in gapped transformers, such as flyback transformers, by means of harmonic decomposition of the current though the windings that allows the proximity field calculation and, afterward, the estimation of the losses in the windings. The method is used to evaluate conduction losses in flyback transformers for switched mode power supplies (SMPS) and the results are compared with finite element analysis (FEA) and measurements.

/pdf/power-losses-calculations-in-windings-of-gapped-magnetic-1pbrfub026.pdf

Power losses calculations in windings of gapped magnetic components: The i2D method applied to flyback transformers

A simplified capacitive model for transformers with center-tapped windings has been developed. A Finite Element Analysis (FEA) tool is used to compute the electric energy in the windings of the transformer in order to obtain the required parameters of the model. Due to its reduced number of elements it can be easily used to model the capacitive effects in symmetrical (center-tapped) multi-winding magnetic components such as transformers for Push-Pull (PP), Half-Bridge (HB) and Full-Bridge (FB) applications. Some experimental results are compared with simulations.

/pdf/a-simplified-capacitive-model-for-center-tapped-multi-2mwlicjk00.pdf

A simplified capacitive model for center-tapped multi-windings transformers

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