Centro de Electrónica Industrial (CEI) | Universidad Politécnica de Madrid | cei@upm.es | www.cei.upm.es

In magnetic components for power electronics applications the utilization of high accuracy models for losses estimation is desirable. Usually high accuracy models take a considerable calculation time which difficult their use on early stages of design, such as an optimization process, where a high number of solutions must be considered in relatively short time.To compensate this situation this work aims to develop new simple and high accuracy models to estimate losses that can be easily integrated on magnetic components design and optimization tools without penalizing the calculation time required.

BRIEF INTRODUCTION

WINDING LOSSESFor accurate calculation of losses in magnetic components for power electronics, the effects of the frequency over the component need to be considered. However, the evaluation of these effects will increase the complexity of the model and the required calculation time, as a result, an optimization process where such models have been integrated could be time consuming. Therefor, is necessary to define simple and high accuracy analytical models ,either for core and windings losses, that allow the evaluation of a high number of solutions in short time (being this the main goal of this work).

To overcome the errors in the results of losses estimation in magnetic components, and oriented to the integration on design and optimization tools, different approaches are been studied.

• A simple model for estimate the equivalent winding resistance of magnetic components is proposed. The model is based on information extracted from 2D and 3D FEA simulations and has shown to have very good accuracy. So far, the model had only been applied in core-less components but, since it is based on geometrical and magnetic field parameters, it is valid for any component.

• Different models for precise core losses estimation are being studied to consider their potential integration on design tools.

CONCLUSIONS

Project sponsored by

Losses Calculations in Magnetic Components

F. Holguín

𝑅𝑎𝑐=𝑅𝑑𝑐𝑋2 [ h𝑠𝑖𝑛 𝑋+𝑠𝑖𝑛 𝑋

h𝑐𝑜𝑠 𝑋 −𝑐𝑜𝑠 𝑋 +𝐹 (𝑚) h𝑠𝑖𝑛 𝑋 −𝑠𝑖𝑛 𝑋h𝑐𝑜𝑠 𝑋+𝑐𝑜𝑠 𝑋 ]

Skin effect Proximity effect

Simple solution Based on modifying the Dowell´s equation.

Replacing F(m) by Fx(m) =

𝑎 (𝑚 )=𝑎1𝑚+𝑎0𝑏 (𝑚 )=𝑏2𝑚2+𝑏1𝑚+𝑏0

WINDING RESISTANCE

Where X = , being d = , is the skin depth and F(m) =

𝑅𝑎𝑐=𝑅𝑑𝑐𝑋2 [ h𝑠𝑖𝑛 𝑋+𝑠𝑖𝑛 𝑋

h𝑐𝑜𝑠 𝑋 −𝑐𝑜𝑠 𝑋 +𝑎 (𝑚 ) 𝑋𝑏(𝑚) h𝑠𝑖𝑛 𝑋−𝑠𝑖𝑛 𝑋h𝑐𝑜𝑠 𝑋+𝑐𝑜𝑠 𝑋 ]

The coefficients of and are based on geometrical parameters and local magnetic field, H, therefore gap and edge effects could be integrated on the

expression!!

Case ACase C

Case D

In all cases the results are within 2% of error respect

of measurements !!

RESULTS

Case B

Analytical approach for the calculation of winding losses in core-less magnetic components