Electric Machinery. Sixth Edition. A. E. Fitzgerald. Late Vice President for Academic Affairs and Dean of the Faculty. Northeastern University. Charles Kingsley, Jr. Arthur E. Fitzgerald, Charles Kingsley, Jr., and Stephen D. Umans, Electric Machinery, Sixth Edition, McGraw-Hill, 1. (Three-Phase Circuits) 2. ( Magnetic. Stephen J. Electric machinery fundamentals / Stephen Chapman. - 4th ed. p. em. Includes index. ISBN I. E lectric machinery. I. T itle. T K
|Language:||English, Spanish, Arabic|
|Genre:||Business & Career|
|Distribution:||Free* [*Registration needed]|
Stephen J. Chapman received a B.S. in Electrical Engineering from Louisiana. State University () and an M.S.E. in Electrical Engineering from the Univer-. Electric Machinery Fitzgerald 7th Edition PDF Electric Machinery Fitzgerald 7th Edition Book PDF Extra Link Book Description: This seventh edition of Fitzgerald . Electric machinery. 2. Power electronics. I. Title. TKS44 '— dc Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1.
Unlike static PDF Electric Machinery Fundamentals solution manuals or printed answer keys, our experts show you how to solve each problem step-by-step. No need to wait for office hours or assignments to be graded to find out where you took a wrong turn.
You can check your reasoning as you tackle a problem using our interactive solutions viewer. Plus, we regularly update and improve textbook solutions based on student ratings and feedback, so you can be sure you're getting the latest information available. How is Chegg Study better than a printed Electric Machinery Fundamentals student solution manual from the bookstore? Our interactive player makes it easy to find solutions to Electric Machinery Fundamentals problems you're working on - just go to the chapter for your book.
Hit a particularly tricky question? Systems with more than two electrical terminals are handled in analogous fashion. In rotating machines, voltages are generated in windings or groups of coils by rotating these windings mechanically through a magnetic field, by mechanically rotating a magnetic field past the winding, or by designing the magnetic circuit so that the reluctance varies with rotation of the rotor.
The flux linking a specific coil is changed cyclically, and a time-varying voltage is generated. Electromagnetic energy conversion occurs when changes in the flux linkage result from mechanical motion. A set of such coils connected together is typically referred to as an armature winding, a winding or a set of windings carrying ac currents. In ac machines such as synchronous or induction machines, the armature winding is typically on the stator.
In dc machines, the field winding is found on the stator. In synchronous machines, the field winding is found on the rotor. Permanent magnets can be used in the place of field windings. In most rotating machines, the stator and rotor are made of electrical steel, and the windings are installed in slots on these structures. The stator and rotor structures are typically built from thin laminations of electrical steel, insulated from each other, to reduce eddy-current losses.
In synchronous machines, rotor-winding currents are supplied directly from the stationary frame through a rotating contact. In induction machines, rotor currents are induced in the rotor windings by a combination of the time-variation of the stator currents and the motion of the rotor relative to the stator. Synchronous Machines Fig. The armature winding is on the stator, and the field winding is on the rotor.
The field winding is excited by direct current conducted to it by means of stationary carbon brushes that contact rotating slip rings or collector rings. It is advantages to have the single, low-power field winding on the rotor while having the high-power, typically multiple-phase, armature winding on the stator.
Conductors forming these coil sides are connected in series by end connections. The rotor is turned at a constant speed by a source of mechanical power connected to its shaft.
Flux paths are shown schematically by dashed lines. Assume a sinusoidal distribution of magnetic flux in the air gap of the machine in Fig. The radial distribution of air-gap flux density B is shown in Fig. As the rotor rotates, the flux —linkages of the armature winding change with time and the resulting coil voltage will be sinusoidal in time as shown in Fig 4.
The frequency in cycles per second Hz is the same as the speed of the rotor in revolutions in second rps. A two-pole synchronous machine must revolve at rpm to produce a Hz voltage. Figure 4. A great many synchronous machines have more than two poles. Fig 4. The field coils are connected so that the poles are of alternate polarity. There are two complete wavelengths, or cycles, in the flux distribution around the periphery, as shown in Fig.
The generated voltage goes through two complete cycles per revolution of the rotor. The frequency in Hz is thus twice the speed in rps. When a machine has more than two poles, it is convenient to concentrate on a single pair of poles and to express angles in electrical degrees or electrical radians rather than in physical units.
One pair of poles equals electrical degrees or 2 electrical radians. The rotors shown in Figs. The field winding is a two-pole distributed winding; the coil sides are distributed in multiple slots around the rotor periphery and arranged to produce an approximately sinusoidal distribution of radial air-gap flux.
Most power systems in the world operate at frequencies of either 50 or 60 Hz. A salient-pole construction is characteristic of hydroelectric generators because hydraulic turbines operate at relatively low speeds, and hence a relatively large number of poles is required to produce the desired frequency.
Steam turbines and gas turbines operate best at relatively high speeds, and turbine- driven alternators or turbine generators are commonly two- or four-pole cylindrical- rotor machines. With very few exceptions, synchronous generators are three-phase machines. A simplified schematic view of a three-phase, two-pole machine with one coil per phase is shown in Fig.
Note that a minimum of two sets of coils must be used. In an elementary multipole machine, the minimum number of coils sets is given by one half the number of poles.
Then the coils of the three phases may then be either Y- or -connected. The electromechanical torque is the mechanism through which a synchronous generator converts mechanical to electric energy. When a synchronous generator supplies electric power to a load, the armature current creates a magnetic flux wave in the air gap that rotates at synchronous speed. This flux reacts with the flux created by the field current, and an electromechanical torque results from the tendency of these two magnetic fields to align.
In a generator this torque opposes rotation, and mechanical torque must be applied from the prime mover to sustain rotation. The counterpart of the synchronous generator is the synchronous motor. Ac current supplied to the armature winding on the stator, and dc excitation is supplied to the field winding on the rotor. The magnetic field produced by the armature currents rotates at synchronous speed.
To produce a steady electromechanical torque, the magnetic fields of the stator and rotor must be constant in amplitude and stationary with respect to each other. In a motor the electromechanical torque is in the direction of rotation and balances the opposing torque required to drive the mechanical load. Note that the flux produced by currents in the armature of a synchronous motor rotates ahead of that produced by the field, thus pulling on the field and hence on the rotor and doing work.
This is the opposite of the situation in a synchronous generator, where the field does work as its flux pulls on that of the armature, which is lagging behind.
Induction Machines Alternating currents are applied directly to the stator windings. Rotors currents are then produced by induction, i.
Alternating currents flow in the rotor windings of an induction machine, in contrast to a synchronous machine in which a field winding on the rotor is excited with dc current.
The induction machine may be regarded as a generalized transformer in which electric power is transformed between rotor and stator together with a change of frequency and a flow of mechanical power. The induction motor is the most common of all motors. The induction machine is seldom used as a generator. In recent years it has been found to be well suited for wind-power applications.
It may also be used as a frequency changer. In the induction motor, the stator windings are essentially the same as those of a synchronous machine. The rotor windings are electrically short-circuited. The rotor windings frequently have no external connections. Currents are induced by transformer action from the stator winding. Squirrel-cage induction motor: The armature flux in the induction motor leads that of the rotor and produces an electromechanical torque.
The rotor does not rotate synchronously. It is the slipping of the rotor with respect to the synchronous armature flux that gives rise to the induced rotor currents and hence the torque.
Induction motors operate at speeds less than the synchronous mechanical speed. A typical speed-torque characteristic for an induction motor is shown in Fig.
The armature winding is on the rotor with current conducted from it by means of carbon brushes. The field winding is on the stator and is excited by direct current. An elementary two-pole dc generator is shown in Fig. The air-gap flux distribution usually approximates a flat-topped wave, rather than the sine wave found in ac machines, and is shown in Fig. Rotation of the coil generates a coil voltage which is a time function having the same waveform as the spatial flux-density distribution.
The voltage induced in an individual armature coil is an alternating voltage and rectification is produced mechanically by means of a commutator. Stationary carbon brushes held against the commutator surface connect the winding to the external armature terminal. The need for commutation is the reason why the armature windings are placed on the rotor.
The commutator provides full-wave rectification, and the voltage waveform between brushes is shown in Fig.
It is the interaction of the two flux distributions created by the direct currents in the field and the armature windings that creates an electromechanical torque. If the machine is acting as a motor, the torque acts in the direction of the rotation.
The individual coils are interconnected so that the result is a magnetic field having the same number of poles as the field winding. Consider Fig. Full-pitch coil: In the design of ac machines, serious efforts are made to distribute the coils making up the windings so as to minimize the higher-order harmonic components.
The rectangular air-gap mmf wave of the concentrated two-pole, full-pitch coil of Fig. The windings of the three phases are identical and are located with their magnetic axes degrees apart. The winding is arranged in two layers, each full-pitch coil of N c turns having one side in the top of a slot and the other coil side in the bottom of a slot a pole pitch away.
It can be seen that the distributed winding produces a closer approximation to a sinusoidal mmf wave than the concentrated coil of Fig. The modified form of 4. The application of three-phase currents will produce a rotating mmf wave.
Rotor windings are often distributed in slots to reduce the effects of space harmonics. As shown in Fig. The armature coil connections are such that the armature winding produces a magnetic field whose axis is vertical and thus is perpendicular to the axis of the field winding. As the armature rotates, the magnetic field of the armature remains vertical due to commutator action and a continuous unidirectional torque results.
The mmf wave is illustrated and analyzed in Fig. DC machines often have a magnetic structure with more than two poles. The machine is shown in laid-out form in Fig. The investigations of both ac and dc machines are based on the assumption of sinusoidal spatial distribution of mmf. Results from examining a two-pole machine can immediately be extrapolated to a multipole machine. Detailed analysis of the magnetic field distributions requires complete solutions of the field problem.
Field coils excited; no current in armature coils. General Electric Company. Note that from Eq. The air-gap mmf of a single-phase winding exicted by a source of ac current can be resolved into rotating traveling waves. This decomposition is shown graphically in Fig.
In a three-phase machine, the windings of the individual phases are displaced from each other by electrical degrees in space around the air-gap circumference as shown in Fig. Under balanced three-phase conditions, the excitation currents Fig. It is the interaction of this magnetic flux wave with that of the rotor which produces torque. Constant torque is produced when rotor-produced magnetic flux rotates in synchronism with that of the stator. As time passes, the resultant mmf wave retains its sinusoidal form and amplitude but rotates progressively around the air gap.
The net result is an mmf wave of constant amplitude rotating at uniform angular velocity. Practice Problem 4. A synchronous machine is an ac machine whose speed under steady-state conditions is proportional to the frequency of the current in its armature. The rotor, along with the magnetic field created by the dc field current on the rotor, rotates at the same speed as, or in synchronism with, the rotating magnetic field produced by the armature currents, and a steady torque results.
Armature winding: Field winding: Cylindrical rotor: Salient-pole rotor: Acting as a voltage source: Frequency determined by the speed of its mechanical drive or prime mover.
The amplitude of the generated voltage is proportional to the frequency and the field current.
When a synchronous generator is connected to a large interconnected system containing many other synchronous generators, the voltage and frequency at its armature terminals are substantially fixed by the system.
It is often useful, when studying the behavior of an individual generator or group of generators, to represent the remainder of the system as a constant-frequency, constant-voltage source, commonly referred to as an infinite bus. Analysis of a synchronous machine connected to an infinite bus. Torque equation: In a generator, the prime-mover torque acts in the direction of rotation of the rotor, and the electromechanical torque opposes rotation.
The rotor mmf wave leads the resultant air-gap flux. In a motor, the electromechanical torque is in the direction of rotation, in opposition to the retarding torque of the mechanical load on the shaft.
Torque-angle curve: Figure 5. Any further increase in prime-mover torque cannot be balanced by a corresponding increase in synchronous electromechanical torque, with the result that synchronism will no longer be maintained and the rotor will speed up.
Single-phase, line-to-neutral equivalent circuits for a three-phase machine operating under balanced, three-phase conditions. Both the external system and the machine itself can be represented as an impedance in series with a voltage source. Note that E1 and E 2 are the line-to-neutral voltages.
RT Not infrequently the past practice of the individual engineer is the sole reason for a selected procedure. In his latest book Kron sets forth the results of a decade in which he has studied mathematically developed equivalent circuits to uncover their fundamental similarities.
This work has resulted in a non-mathematical representation of models. Although the term "tensor" is not used in this representation, and although there are no matrices of mathematical symbols, the tensor idea is expressed by means of electrical circuit symbols.
Multimesh circuits of electrical impedance combinations are used as models of machines and interconnections of machines. The author shows how currents, fields, and torques can be computed directly by the use of their equivalent models. In preparation for this step the principles are given for determining a representative model and for insuring that true equivalence has been achieved by it.