AC E X C I T A T I O N In ac power systems, the waveforms of voltage and flux closely approximate sinusoidal functions of time. This section describes the excitation characteristics and losses associated with steady-state ac operation of magnetic materials under such operating conditions. We use as our model a closed-core magnetic circuit, i.e., with no air gap, such as that shown in Fig. 1.1 or the transformer of Fig. 2.4. The magnetic path length is lc, and the cross-sectional area is Ac throughout the length of the core. We further assume a sinusoidal variation of the core flux ~o(t); thus Because of the high permeability of the magnetic core, an exact solution would show that the magnetic flux is confined almost entirely to the core, the field lines follow the path defined by the core, and the flux density is essentially uniform over a cross section because the cross-sectional area is uniform. The magnetic field can be visualized in terms of flux lines which form closed loops interlinked with the winding. The power at the terminals of a winding on a magnetic circuit is a measure of the rate of energy flow into the circuit through that particular winding. The power, p, is determined from the product of the voltage and the current

McGraw-Hill has set up a website, www.mhhe.com/umans, to support this new edition of Electric Machinery. The website will include a downloadable version of the solutions manual (for instructors only) as well as PowerPoint slides of figures from the book. This being a new feature of Electric Machinery, we are, to a great extent, starting with a blank slate and will be exploring different options for supplementing and enhancing the text. For example, in recognition of the fact that instructors are always looking for new examples and problems, we will set up a mechanism so that instructors can submit examples and problems for publication on the website (with credit given to their authors) which then can be shared with other instructors. From which we see that the inductance of a winding in a magnetic circuit is propor- tional to the square of the turns and inversely proportional to the reluctance of the magnetic circuit associated with that winding. The magnetic circuit of Fig. 1.6a consists of an N-turn winding on a magnetic core of infinite permeability with two parallel air gaps of lengths g~ and g2 and areas A~ and A2, respectively. Many motor-drive systems are based upon the technique of field-oriented con- trol (also known as vector control). A significant addition to this new edition is the discussion of field-oriented control which now appears in Chapter 11. This is some- what advanced material which is not typically found in introductory presentations of electric machinery. As a result, the chapter is structured so that this material can be omitted or included at the discretion of the instructor. It first appears in the section on torque control of synchronous motors, in which the basic equations are derived and the analogy with the control of dc machines is discussed. It appears again in its most commonly used form in the section on the torque control of induction motors. I N T R O D U C T I O N TO M A G N E T I C C I R C U I T S The complete, detailed solution for magnetic fields in most situations of practical engineering interest involves the solution of Maxwell 's equations along with various constitutive relationships which describe material properties. Although in practice exact solutions are often unattainable, various simplifying assumptions permit the attainment of useful engineering solutions. 1

PROBLEM SOLUTIONS: Chapter 1

The next five chapters provide a more in-depth discussion of the various machine types: synchronous machines in Chapter 5, induction machines in Chapter 6, dc machines in Chapter 7, variable-reluctance machines in Chapter 8, and single/two- phase machines in Chapter 9. Since the chapters are pretty much independent (with the exception of the material in Chapter 9 which builds upon the polyphase-induction- motor discussion of Chapter 6), the order of these chapters can be changed and/or an instructor can choose to focus on one or two machine types and not to cover the material in all five of these chapters. want to submit their suggestions and experiences to share with other users. In this con- text, the website would appear again to be an ideal resource for enhancing interaction between instructors. secondary voltages/currents for transformers that transition between wye- and Δ-connections are well Notice that as H is decreased from its maximum value to zero, the flux density decreases but not to zero. This is the result of the relaxation of the orientation of the magnetic moments of the domains as described above. The result is that there remains a remanant magnetization when H is zero.

This seventh edition of Fitzgerald and Kingsley’s Electric Machinery by Stephen Umans was developed recognizing the strength of this classic text since its first edition has been the emphasis on building an understanding of the fundamental physical principles underlying the performance of electric machines. As applied to the magnetic circuit of Fig. 1.1, the source of the magnetic field in the core is the ampere-turn product N i. In magnetic circuit terminology N i is the magnetomotive force (mmf) .T" acting on the magnetic circuit. Although Fig. 1.1 shows only a single coil, transformers and most rotating machines have at least two windings, and N i must be replaced by the algebraic sum of the ampere-turns of all the windings.Professor Kingsley first asked this author to participate in the fourth edition of Electric Machinery; the professor was actively involved in that edition. He participated in an advisory capacity for the fifth edition. Unfortunately, Professor Kingsley passed away since the publication of the fifth edition and did not live to see the start of the work on this edition. He was a fine gentleman, a valued teacher and friend, and he is missed.

In Example 1.9, we found an expression for the flux density in the air gap of the magnetic circuit of Fig. 1.17: for a magnetic circuit with a single winding. For a static magnetic circuit, the induc- tance is fixed (assuming that material nonlinearities do not cause the inductance to vary), and this equation reduces to the familiar circuit-theory form

Drive-systems based upon power electronics permit a great deal of flexibility in the control of electric machines. This is especially true in the case of ac machines which used to be found almost exclusively in applications where they were supplied from the fixed-frequency, fixed-voltage power system. Thus, the introduction to power electronics in Chapter 10 is followed by a chapter on the control of electric machines.