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

Product Information

Figure 1.11 Excitation phenomena. (a) Voltage, flux, and exciting current" (b) corresponding hysteresis loop. The core dimensions are such that the path length of any flux line is close to the mean core length lc. As a result, the line integral of Eq. 1.5 becomes simply the scalar product Hclc of the magnitude of H and the mean flux path length Ic. Thus, the relationship between the mmf and the magnetic field intensity can be written in magnetic circuit terminology as P R O P E R T I E S OF M A G N E T I C M A T E R I A L S In the context of e lec t romechanica l energy convers ion devices, the impor tance of

resistors, capacitors, and/or inductors and give the values of the components (we will use these in the next

PROBLEM SOLUTIONS: Chapter 1

properties of the core material will have little effect on the terminal properties of the inductor. 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. and from Eq. 1.20, with the reluctance of the core neglected and assuming that Ac = Ag, the core flux 4~ is For example, from Eq. 1.20, under the assumption that the reluctance of the core is negligible as compared to that of the air gap, the inductance of the winding in Fig. 1.2 is equal to n The analysis of single-phase induction motors has been expanded to cover the general case in which the motor is running off both its main winding and its auxiliary winding (supplied with a series capacitor).

magnetic material is initially unmagnetized (corresponding to point a of the figure) and consider what happens as current is applied to the excitation winding. Because the core is assumed to be of infinite permeability, the horizontal axis of Fig. 1.21 can be considered to be both a measure of the applied current i = Hlm/N as well as a measure of H in the magnetic material. Here the ~" = Ni is the mmf applied to the magnetic circuit. From Eq. 1.10 we see that a portion of the mmf, .Tc = Hclc, is required to produce magnetic field in the core while the remainder, f g = Hgg, produces magnetic field in the air gap. pts) Find the real power delivered to each phase of the load. Find the reactive power delivered to each This chapter will develop some basic tools for the analysis of magnetic field systems and will provide a brief introduction to the properties of practical magnetic materials. In Chapter 2, these results will then be applied to the analysis of transform- ers. In later chapters they will be used in the analysis of rotating machinery.

One additional benefit is derived from the introduction of MATLAB into this edition of Electric Machinery. As readers of previous editions will be aware, the treatment of single-phase induction motors was never complete in that an analytical treatment of the general case of a single-phase motor running with both its main and auxiliary windings excited (with a capacitor in series with the auxiliary winding) was never considered. In fact, such a treatment of single-phase induction motors is not found in any other introductory electric-machinery textbook of which the author is aware. In addition, magnetic materials can be used to constrain and direct magnetic fields in well-defined paths. In a transformer they are used to maximize the coupling between the windings as well as to lower the excitation current required for transformer operation. In electric machinery, magnetic materials are used to shape the fields to obtain desired torque-production and electrical terminal characteristics. Thus a knowledgeable designer can use magnetic materials to achieve specific desirable device characteristics.

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. The problem is quite simple: this general treatment is mathematically complex, requiring the solution of a number of simultaneous, complex algebraic equations. This, however, is just the sort of problem at which programs such as MATLAB excel. Thus, this new edition of Electric Machinery includes this general treatment of single-phase induction machines, complete with a worked out quantitative example and end-of-chapter problems.

established. These can be found in references (for example, Fitzgerald & Kingsley’s Electric Machinery). 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. remain in a closed magnetic structure, such as that of Fig. 1.1, made of this material, if the applied mmf (and hence the magnetic field intensity H) were reduced to zero. However, although the M-5 electrical steel also has a large value of remanent magneti- zation (approximately 1.4 T), it has a much smaller value of coercivity (approximately - 6 A/m, smaller by a factor of over 7500). The coercivity Hc corresponds to the value of magnetic field intensity (which is proportional to the mmf) required to reduce the 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. and its unit is wat ts (W), or j o u l e s p e r second . Thus the change in m a g n e t i c s tored