Models available in circuit simulation and their drawbacks

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Materials used in power electronics

Based on their hysteresis characteristics, soft magnetic materials occupy different applications in the field of power electronics. Depending on their composition and structure soft magnetic materials used in power electronics are classified into 3 main categories having different properties (saturation, coercivity, permeability, and resistivity). These 3 main magnetic core materials are ferrite cores, iron powder cores and nanocrystalline cores [15].

Ferrite cores

Ferrites are chemically inert ceramic materials, having a magnetic cubic structure. They are physically hard, brittle, stable and high resistivity materials. Ferrites are Metallic Oxides with the general structure XFe2O4 where X is one of the transition metals: Fe, Ni, Zn, Mn, Cu, Ba, Co, and Mg. These metals are mixed, milled, shaped and finally pressed to ensure the required grain size and the final shape of magnetic core. Heating up to 1300ºC is required to physically harden the material and ensure desired magnetic properties [16].
The common types of ferrites are Mn-Zn ferrites used for low frequencies applications up to several kHz and Ni-Zn ferrites used for higher frequencies applications up to few MHz [17][18]. They exist in different core shapes including toroid, E, I and U shapes shown in Figure 1-5 [19][20].

Powder cores

A powder core consists of small particles of pure iron and/or metal alloys, coated with a thin insulating layer and pressed with an addition of lubricant to a bulk material at high pressure. The insulating coating reduces eddy currents by increasing the resistivity of bulk material and decreases the permeability by acting as small air gaps inside the core material. During compaction, internal stresses are generated in the material. A heat treatment process is applied to relieve these stresses and increases the strength of the material. Finally powder cores are covered by a protective coating to improve the mechanical strength and provide insulation. Iron powder materials are most often magnetically, thermally and mechanically isotropic in their behavior [22] [23] [24].
Powder cores have a lower value of permeability but a higher saturation flux density, than ferrites. They are used for medium frequencies applications (hundreds of kHz) like chokes, transformers, EMI filters and RF applications. Notable characteristics of powder cores are their low hysteresis and DC losses, stable inductance and slight sensibility to thermal aging. Iron powder cores are made in different shapes and sizes as in Figure 1-6 [23].

Nanocrystalline cores

Nanocrystalline materials are the result of high-tech production process from low cost raw materials like silicon and iron to produce a new generation of magnetic materials with interesting soft magnetic properties [26]. They combine the high flux of Fe-Si with improved high frequency performance of ferrites, namely low losses and wide permeability range. Due to these advantages, in addition to their low weight and volume, nanocrystalline materials are mainly used in EMI filters and other power electronics applications like switched mode power supplies, static converters, and electrical welding sources [27][28].
Magnetic nanocrystalline materials are formed by an assembly of regions of coherent crystalline structure (the grains), having an average grain diameter from 1 to 50 nm, exhibiting magnetic order and embedded in a magnetic or nonmagnetic matrix. Ribbons of nanocrystalline alloys are made by rapid solidification, deposition techniques and solid state reactions where the initial material may be in the amorphous state and subsequently crystallized. The alloy composition, crystal structure, microstructure and morphology determine the material’s magnetic properties like the saturation flux density BS (up to 1.5 T), permeability — (wide range from 200 to 200 000) the coercive field HC (down to 0.5 A/m) and the Curie temperature TC (up to 600 °C). The produced ribbons are then used to form fragile toroidal cores (Figure 1-7) which are annealed under the presence of a magnetic field to form ultrafine crystals [29][30].
In this thesis we study powder and nanocrystalline cores only due to their high performance in our domain of application (DC-DC converters) and frequency range (a few hundred of kHz). Besides, ferrites were extensively studied unlike nanocrystalline and powder materials. In fact powder and nanocrystalline materials have higher saturation flux density, lower hysteresis losses, and lower DC bias effect than ferrites but ferrites have lower cost and losses at very high frequencies due to their high resistivity. Concerning thermal behavior, ferrites have lower operating and Curie temperatures. Temperature effects on magnetic materials are presented in the following section.

Temperature Effects

For all solids, including magnetic materials, a temperature rise increases the thermal vibration of atoms. This vibration tends to randomize the directions of magnetic moments modifying magnetic behavior of materials.

Curie temperature

Ferrimagnetic and ferromagnetic materials show magnetic behavior below a critical temperature called the Curie temperature (Tc). Above this temperature magnetic moments are oriented randomly, resulting in a zero net magnetization [32][33]. In this region the mutual spin coupling forces are completely destroyed and materials become paramagnetic. This temperature depends on the substance thus varies from one material to another, its order of magnitude is for example about 768°C for iron, 1120°C for cobalt, and 335°C for nickel. The approach to ferromagnetism as a function of temperature is described by the Curie-Weiss Law which gives the magnetic susceptibility as a function of temperature shown in equation (1.1).
Equation (1.1) is valid only for temperatures above the Curie temperature (T>Tc) where Ȥ and ȝ are the magnetic susceptibility and relative magnetic permeability of the material respectively. C is a constant characteristic for a given substance and Tc is the Curie temperature.

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Influence of temperature on magnetic properties

Temperature influences the material’s magnetic behavior by modifying its magnetic properties [13][34]. A nonlinear evolution of magnetic parameters (saturation magnetization, relative permeability, coercive field) as function of temperature exists [35][36][37][38][39][40]. Saturation magnetization for both ferri- and ferro- magnetic materials decrease with temperature. The saturation magnetization is a maximum at 0 K, temperature at which the thermal vibrations are minimum [11]. With increasing temperature, the saturation magnetization diminishes gradually and then drops to zero at Tc. As an example the saturation magnetization of Fe and Fe3O4 as function of temperature are represented in Figure 1-8.

Self-heating Measurements

In previous characterization, the magnetic component was under static thermal conditions. The component is placed in an oven/furnace and constant temperatures (between 25°C and 275°C) are imposed during short time measurements. Another important thermal aspect is the self-heating or dynamic thermal condition. When magnetic components operate constantly, iron and copper losses cause self-heating in both core and winding. Both temperatures increase exponentially with time. Dynamic self-heating measurements are necessary for the development of thermal models which is a part of our work. Thermal modeling and magneto-thermal coupling are explained in next chapter. This section is consecrated for self-heating measurements principle and test bench shown in Figure 1-16.
In self-heating measurements, an inductor of same material (N14E1) is fed with a sinusoidal current of 0.6 A at 20 and 40 kHz to insure self-heating. Then core and winding temperatures dynamic evolution is measured by the help of the test bench presented in figure 16. Two N-type thermocouples are placed in contact with the core and winding. A thermocouple data logger is used and connected to a PC to allow dynamic temperature reading and registration. Temperatures are registered for 500 seconds with a time step of 5 seconds. As a result core and winding temperatures (Tcore and Twinding) as function of time are obtained and presented in Figure 1-17. Core Temperatures at 20 kHz and 40 kHz are shown in red while those of winding are shown in blue. We notice that Tcore is higher than Twinding in both cases and that core temperature passes 70 °C on steady state for 40 kHz.

Dynamic magnetic hysteresis models

When magnetic materials are subjected to dynamic magnetic fields, losses due to eddy currents and domain walls movements are induced. These losses increase with frequency and are not taken into account by static magnetic models. Hence dynamic models are needed to represent the materials dynamic magnetic behavior. Concerning dynamic models, there is not a vast choice, due to the fact that magnetic losses are still not completely understood, especially anomalous losses due to domain wall motion. We present here some of these models.

Preisach-Néel dynamic Model

Various works have been published on extending the original Preisach-Néel model to include dynamic effects [24][25][26]. In the extended model, the rate dependent hysteresis was discussed, by introducing the time variation of input field to either the ϕ(α,β,t) operator, or to the distribution function ρ(α,β,t). This extension of the original Preisach-Néel model added new parameters to the static one. Including a time derivative in the distribution function made its numerical implementation even more complicated.

Table of contents :

Chapter 1
1. Magnetic Materials in Power Electronics
1.1 Introduction
1.2 Magnetic materials in power electronics
1.2.1 Materials Classifications and applications
1.2.2 Soft magnetic materials
1.2.3 Materials used in power electronics
1.3 Temperature Effects
1.3.1 Curie temperature
1.3.2 Influence of temperature on magnetic properties
1.4 Magnetic materials characterization
1.4.1 Principle of characterization
1.4.2 Experimental test Bench
1.4.3 Variable Temperature and Frequency Measurements
1.4.4 Self-heating Measurements
1.5 Conclusion
1.6 References
Chapter 2
2. Magnetic and Thermal Modeling
2.1 Introduction
2.2 Magnetic modeling
2.2.1 Static magnetic hysteresis models
2.2.2 Dynamic magnetic hysteresis models
2.2.3 Models available in circuit simulation and their drawbacks
2.2.4 Parameters identification
2.3 Thermal modeling
2.3.1 Heat transfer
2.3.2 Thermal elements
2.3.3 Thermal model
2.3.4 Parameters identification
2.4 Magneto thermal coupling
2.5 Conclusion
2.6 References
List of Figures
Chapter 3
3. Virtual Prototyping and Developed Model
3.1 Introduction
3.2 Magnetic component modeling for circuit simulators
3.2.1 Modeling Theory and Techniques
3.2.2 Multi/Mixed domain modeling
3.2.3 VHDL-AMS modeling language
3.2.4 Circuit simulation software
3.3 Developed Model
3.3.1 Model Structure
3.3.2 Choice of Materials
3.3.3 Choice of static and dynamic laws
3.3.4 Temperature dependence and parameters extraction
3.4 Simulation and Model Validation
3.5 Conclusion
3.6 References
Chapter 4
4. Power Electronics Application
4.1 Introduction
4.2 Buck Converter
4.3 Realized Circuit and Measurements
4.3.1 Buck Converter Circuit
4.3.2 Choice of Inductors and Magnetic Materials Characterization
4.3.3 Core Losses Measurements and Calculation
4.3.4 Copper Losses Measurements and Calculation
4.4 Model Implementation and Simulation Results
4.5 Other Results and Applications
4.5.1 TRACOPWER commercial converter
4.5.2 Single phase transformer
4.6 Conclusion on Application
4.7 References


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