Chapter 2. Transformer Circuit Models, including Magnetic Core Characteristics, and Applications

Chapter 2. Transformer Circuit Models, including Magnetic Core Characteristics, and Applications

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39 2. TRANSFORMER CIRCUIT MODELS, INCLUDING MAGNETIC CORE CHARACTERISTICS, AND APPLICATIONS Summary The characteristics of transformer cores are discussed in terms of their basic magnetic properties and how these influence transformer design. Special emphasis is placed on silicon steel cores since these are primarily used in power transformers. However, the magnetic concepts discussed are applicable to all types of cores. The magnetic circuit approximation is introduced and its use in obtaining the properties of cores with joints or gaps is discussed. Basic features of the magnetization process are used to explain inrush current and to calculate its magnitude. The inclusion of the transformer core in electrical circuit models is discussed. Although non-linearities in the magnetic characteristics can be included in these models, for inductions well below saturation a linear approximation is adequate. For many purposes, the circuit models can be further approximated by eliminating the core. As an application, an approximate circuit model is used to calculate the voltage regulation of a two winding transformer. 2.1 INTRODUCTION Transformer cores are constructed predominantly of ferromagnetic material. The most common material used is iron, with the addition of small amounts of silicon and other elements which help improve the magnetic properties and/or lower losses. Other materials which find use in electronic transformers are the nickel-iron alloys (permalloys) and the iron-oxides (ferrites). The amorphous metals, generally consisting of iron, boron, and other additions, are also finding use as cores for distribution transformers. These materials are all broadly classified as ferromagnetic and, as such, share many properties in common. Among these are saturation magnetization or induction, hysteresis, and a Curie temperature above which they cease to be ferromagnetic. © 2002 by CRC Press
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TRANSFORMER CIRCUIT MODELS 40 Cores made of silicon steel (~3% Si) are constructed of multiple layers of the material in sheet form. The material is fabricated in rolling mills from hot slabs or ingots. Through a complex process of multiple rolling, annealing, and coating stages, it is formed into thin sheets of from 0.18-0.3 mm (7–11 mil) thickness and up to a meter (39 in) wide. The material has its best magnetic properties along the rolling direction and a well constructed core will take advantage of this. The good rolling direction magnetic properties are due to the underlying crystalline orientation which is called a Goss or cube-on- edge texture as shown in Fig. 2.1. The cubic crystals have the highest permeability along the cube edges. The visible edges pointing along the rolling direction are highlighted in the figure. Modern practice can achieve crystal alignments of >95%. The permeability is much lower along the cube diagonals or cube face diagonals. The latter are pointing in the sheet width direction. Figure 2.1
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Chapter 2. Transformer Circuit Models, including Magnetic Core Characteristics, and Applications

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