Fitzgerald & Kingsley's Electric Machinery (IRWIN ELEC&COMPUTER ENGINERING)

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density in each is equal. Since the iron permeability here is assumed to be infinite, its reluctance m A chapter has been added which introduces the basic concepts of power electronics as applicable to motor drives. takes place. However, the techniques developed are generally applicable to a wide range of additional devices including linear machines, actuators, and sensors. 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

The instructor should note that a complete presentation of field-oriented control requires the use of the dq0 transformation. This transformation, which appeared for synchronous machines in Chapter 6 of the previous edition, is now found in Appendix C of this edition. In addition, the discussion in this appendix has been expanded to include a derivation of the dq0 transformation for induction machines in which both stator and rotor quantities must be transformed.T he chief objective of Electric Machinery continues to be to build a strong foundation in the basic principles of electromechanics and electric machinery. Through all of its editions, the emphasis of Electric Machinery has been The term which multiplies the mmfis known as thepermeance 7 -9 and is the inverse of the reluctance; thus, for example, the total permeance of a magnetic circuit is Equation 1.1 states that the line integral of the tangential component of the magnetic field intensity H around a closed contour C is equal to the total current passing through any surface S linking that contour. From Eq. 1.1 we see that the source of H is the current density J. Equation 1.2 states that the magnetic flux density B is conserved, i.e., that no net flux enters or leaves a closed surface (this is equivalent to saying that there exist no monopole charge sources of magnetic fields). From these equations we see that the magnetic field quantities can be determined solely from the instantaneous values of the source currents and that time variations of the magnetic fields follow directly from time variations of the sources. For practical magnetic materials (as is discussed in Sections 1.3 and 1.4), Bc and Hc are not simply related by a known constant permeability/z as described by Eq. 1.7. In fact, Bc is often a nonlinear, multivalued function of Hc. Thus, although Eq. 1.10 continues to hold, it does not lead directly to a simple expression relating the mmf and the flux densities, such as that of Eq. 1.11. Instead the specifics of the nonlinear Bc-He relation must be used, either graphically or analytically. However, in many cases, the concept of constant material permeability gives results of acceptable engineering accuracy and is frequently used. The most common curve used to describe a magnetic material is the B-H curve or hysteresis loop. The first and second quadrants (corresponding to B > 0) of a set of hysteresis loops are shown in Fig. 1.9 for M-5 steel, a typical grain-oriented electrical steel used in electric equipment. These loops show the relationship between the magnetic flux density B and the magnetizing force H. Each curve is obtained while cyclically varying the applied magnetizing force between equal positive and negative values of fixed magnitude. Hysteresis causes these curves to be multival- ued. After several cycles the B-H curves form closed loops as shown. The arrows show the paths followed by B with increasing and decreasing H. Notice that with increasing magnitude of H the curves begin to flatten out as the material tends toward saturation. At a flux density of about 1.7 T, this material can be seen to be heavily saturated.

Ferromagnetic materials, typically composed of iron and alloys of iron with cobalt, tungsten, nickel, aluminum, and other metals, are by far the most common mag- netic materials. Although these materials are characterized by a wide range of prop- erties, the basic phenomena responsible for their properties are common to them all. power factor of 0.8 lagging. Assume a positive phase sequence for the source and a balanced system. All which corresponds to a point on the second quadrant of the hysteresis loop. As can be seen from Eq. 1.56, the product of B and H has the dimensions of energy density (joules per cubic meter). We now show that operation of a given permanent-magnet material at this point will result in the smallest volume of that material required to produce a given flux density in an air gap. As a result, choosing a material with the largest available maximum energy product can result in the smallest required magnet volume. field problem with simple geometry to a magnetic circuit model. Our limited pur- pose in this section is to introduce some of the concepts and terminology used by engineers in solving practical design problems. We must emphasize that this type of thinking depends quite heavily on engineering judgment and intuition. For example, we have tacitly assumed that the permeabil i ty of the "iron" parts of the magnetic circuit is a constant known quantity, although this is not true in general (see Sec- tion 1.3), and that the magnetic field is confined soley to the core and its air gaps. Although this is a good assumption in many situations, it is also true that the wind- ing currents produce magnetic fields outside the core. As we shall see, when two or more windings are placed on a magnetic circuit, as happens in the case of both transformers and rotating machines, these fields outside the core, which are referredFigure 1.8 shows a magnetic circuit with an air gap and two windings. In this case note that the mmf acting on the magnetic circuit is given by the total ampere-turns acting on the magnetic circuit (i.e., the net ampere turns of both windings) and that the reference directions for the currents have been chosen to produce flux in the same direction. The total mmf is therefore 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 side, a current of 10 A is drawn from each phase of the source. The load on the secondary side has a 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 practical systems, the magnetic field lines "fringe" outward somewhat as they cross the air gap, as illustrated in Fig. 1.4. Provided this fringing effect is not excessive, the magnetic-circuit concept remains applicable. The effect of thesefringingfields is to increase the effective cross-sectional area Ag of the air gap. Various empirical methods have been developed to account for this effect. A correction for such fringing fields in short air gaps can be made by adding the gap length to each of the two dimensions making up its cross-sectional area. In this book the effect of fringing fields is usually ignored. If fringing is neglected, Ag = Ac.