Electric machinery and power system fundamentals chapman pdf download

The other dimensions of the core are as shown in the figure. Find the value of the current that will produce a flux of 0. With this current, what is the flux density at the top of the core? What is the flux density at the right side of the core?

Assume that the relative permeability of the core is The top and bottom form one region, the left side forms a second region, and the right side forms a third region. The reluctances of these regions are: l l 0. A ferromagnetic core with a relative permeability of is shown in Figure P The dimensions are as shown in the diagram, and the depth of the core is 7 cm.

The air gaps on the left and right sides of the core are 0. Because of fringing effects, the effective area of the air gaps is 5 percent larger than their physical size. If there are turns in the coil wrapped around the center leg of the core and if the current in the coil is 1. What is the flux density in each air gap? Let R1 be the reluctance of the left-hand portion of the core, R2 be the reluctance of the left-hand air gap, R3 be the reluctance of the right-hand portion of the core, R4 be the reluctance of the right-hand air gap, and R5 be the reluctance of the center leg of the core.

A two-legged core is shown in Figure P The winding on the left leg of the core N1 has turns, and the winding on the right N2 has turns. The coils are wound in the directions shown in the figure. A core with three legs is shown in Figure P Its depth is 5 cm, and there are turns on the leftmost leg. The relative permeability of the core can be assumed to be and constant. What flux exists in each of the three legs of the core? What is the flux density in each of the legs?

Let R1 be the reluctance of the left-hand portion of the core, R2 be the reluctance of the center leg of the core, R3 be the reluctance of the center air gap, and R4 be the reluctance of the right-hand portion of the core. R4 A wire is shown in Figure P which is carrying 5. Calculate the magnitude and direction of the force induced on the wire. The wire is shown in Figure P is moving in the presence of a magnetic field.

With the information given in the figure, determine the magnitude and direction of the induced voltage in the wire. Repeat Problem for the wire in Figure P The core shown in Figure P is made of a steel whose magnetization curve is shown in Figure P How much flux is produced in the core by the currents specified? What is the relative permeability of this core under these conditions? Was the assumption in Problem that the relative permeability was equal to a good assumption for these conditions?

Is it a good assumption in general? It is not very good in general. Its depth is 8 cm, and there are turns on the center leg. Skip to main content. By using our site, you agree to our collection of information through the use of cookies. To learn more, view our Privacy Policy. Log In Sign Up. Download Free PDF. Danish Razzak. Solution Manual of Electric Machinery Fundamentals by. File sharing network. File upload progressor. Fast download. Wednesday, September 6, Add Comment The books related to electric machinery is studied worldwide are by a famous electrical engineer Stephen J.

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This book presents a thorough analysis of newly available sinusoidal three-phase windings in electrical machines, which provide many benefits over traditional windings, including energy savings, noise and vibration reduction, and reduced need for non-ferrous metals. What is the starting torque of this motor? A V four-pole hp Hz Y-connected three-phase induction motor develops its full-load induced torque at 3.

At full load, the output power of this motor is 75 hp and its slip is 1. The two curves are plotted below. As you can see, only the 0. The Thevenin equivalent of the input circuit was calculated in part a. The easiest way to find the line current or armature current at starting is to get the equivalent impedance Z F of the rotor circuit in parallel with jX M at starting conditions, and then calculate the starting current as the phase voltage divided by the sum of the series impedances, as shown below.

Answer the following questions about the motor in Problem What will the voltage be at the motor end of the transmission line during starting?

Note that the terminal voltage sagged by about 9. The referred impedances are R1c a 2 R1 1. Note that this voltage sagged by 6. In this chapter, we learned that a step-down autotransformer could be used to reduce the starting current drawn by an induction motor.

While this technique works, an autotransformer is relatively expensive. A much less expensive way to reduce the starting current is to use a device called Y-' starter described earlier in this chapter. Answer the following questions about this type of starter. However, since the line current for the original delta connection was 3 times the phase current, while the line current for the Y starter connection is equal to its phase current, the line current is reduced by a factor of 3 in a Y-' starter.

A V hp six-pole '-connected Hz three-phase induction motor has a full-load slip of 4 percent, an efficiency of 91 percent, and a power factor of 0. At start-up, the motor develops 1. This motor is to be started with an autotransformer reduced voltage starter. A wound-rotor induction motor is operating at rated voltage and frequency with its slip rings shorted and with a load of about 25 percent of the rated value for the machine.

For most loads, the induced torque will decrease. This reduces the phase current and line current in the motor and on the secondary side of the transformer by a factor of 0. However, the current on the primary of the autotransformer will be reduced by another factor of 0.

When it is necessary to stop an induction motor very rapidly, many induction motor controllers reverse the direction of rotation of the magnetic fields by switching any two stator leads. When the direction of rotation of the magnetic fields is reversed, the motor develops an induced torque opposite to the current direction of rotation, so it quickly stops and tries to start turning in the opposite direction. If power is removed from the stator circuit at the moment when the rotor speed goes through zero, then the motor has been stopped very rapidly.

This technique for rapidly stopping an induction motor is called plugging. The motor of Problem is running at rated conditions and is to be stopped by plugging. Calculate the torque-speed characteristic for this induction motor, and compare it to the torque- speed characteristic for the single-cage design in Problem How do the curves differ? Explain the differences. As a result, the impedance of the rotor is calculated as the parallel combination of these two current paths. Also, recall that rotor reactance varies with rotor frequency.

The rotor reactance is given by the equation X sX o where s is the slip and X o is the rotor reactance at locked-rotor conditions. We must apply this equation to calculate the rotor impedance at any slip, and then divide the resulting reactance by the slip to get to the equivalent impedance at locked-rotor conditions the reactance at locked-rotor conditions is the term that goes into the torque equation. The following information is given about the simple rotating loop shown in Figure B 0.

What is the power flowing into or out of the machine? When the loop goes beyond the pole faces, eind will momentarily fall to 0 V, and the current flow will momentarily reverse. Therefore, the average current flow over a complete cycle will be somewhat less than 5. Refer to the simple two-pole eight-coil machine shown in Figure P The following information is given about this machine: Figure P B Consider the internal resistance of the machine in determining the current flow.

The voltage produced by this machine can be found from Equations and ZvBl ZrZ Bl EA a a where Z is the number of conductors under the pole faces, since the ones between the poles have no voltage in them. There are 16 conductors in this machine, and about 12 of them are under the pole faces at any given time.

Therefore, the current flowing in the machine will be EA A dc machine has 8 poles and a rated current of A. How much current will flow in each path at rated conditions if the armature is a simplex lap-wound, b duplex lap-wound, c simplex wave-wound? How many parallel current paths will there be in the armature of an pole machine if the armature is a simplex lap-wound, b duplex wave-wound, c triplex lap-wound, d quadruplex wave-wound?

An eight-pole, kW, V dc generator has a duplex lap-wound armature which has 64 coils with 10 turns per coil. How wide must each one be? Since it is duplex-wound, each brush must be wide enough to stretch across 2 complete commutator segments. Since there are 16 parallel paths through the machine, the armature resistance of the generator is 0. Figure P shows a small two-pole dc motor with eight rotor coils and 10 turns per coil. The flux per pole in this machine is 0.

Ignore any internal resistance in the motor. If K is known, then the speed of the motor can be found. Refer to the machine winding shown in Figure P How wide should they be? At the time shown, those windings are 1, 2, 9, and Each brush should be two commutator segments wide, since this is a duplex winding.

Of that number, an average of 14 of them would be under the pole faces at any one time. Therefore, there are 28 conductors divided among 4 parallel paths, which produces 7 conductors per path. Therefore, E A 7e VT for no-load conditions. Describe in detail the winding of the machine shown in Figure P If a positive voltage is applied to the brush under the north pole face, which way will this motor rotate?

If a positive voltage is applied to the brush under the North pole face, the rotor will rotate in a counterclockwise direction. Column 1 contains field current in amps, and column 2 contains the internal generated voltage EA in volts. In Problems through , assume that the motor described above can be connected in shunt. The equivalent circuit of the shunt motor is shown in Figure P If the resistor Radj is adjusted to : what is the rotational speed of the motor at no-load conditions?

Assuming no armature reaction, what is the speed of the motor at full load? What is the speed regulation of the motor? If the motor is operating at full load and if its variable resistance Radj is increased to :, what is the new speed of the motor? Assume no armature reaction, as in the previous problem. Assume that the motor is operating at full load and that the variable resistor Radj is again :.

How does it compare to the result for Problem ? If Radj can be adjusted from to :, what are the maximum and minimum no-load speeds possible with this motor? What is the starting current of this machine if it is started by connecting it directly to the power supply VT? How does this starting current compare to the full-load current of the motor?

This much current is extremely likely to damage the motor. Assume that the armature reaction increases linearly with increases in armature current. For the separately excited motor of Problem a What is the maximum no-load speed attainable by varying both V A and Radj? Neglect armature effects in this problem. Both curves are plotted on the same scale to facilitate comparison. The motor is connected cumulatively compounded and is operating at full load.

What will the new speed of the motor be if Radj is increased to :? How does the new speed compared to the full-load speed calculated in Problem ? For Problem , the motor is now connected differentially compounded as shown in Figure P The motor is now connected differentially compounded.

Its magnetization curve is shown in Figure P The core losses are W, and the mechanical losses are W at full load. Assume that the mechanical losses vary as the cube of the speed of the motor and that the core losses are constant. Its armature resistance is 0. Neglect rotational losses. Column 1 contains magnetomotive force in ampere-turns, and column 2 contains the internal generated voltage EA in volts.

Therefore the speed of the motor at these conditions is EA The motor described above is connected in shunt. Note that is curve is plotted on the same scale as the shunt motor in Problem Derive the shape of its torque- speed characteristic. A series motor is now constructed from this machine by leaving the shunt field out entirely. Derive the torque-speed characteristic of the resulting motor.

To make a practical series motor out of this machine, it would be necessary to include 20 to 30 series turns instead of An automatic starter circuit is to be designed for a shunt motor rated at 20 hp, V, and 75 A. The armature resistance of the motor is 0.

The motor is to start with no more than percent of its rated armature current, and as soon as the current falls to rated value, a starting resistor stage is to be cut out. How many stages of starting resistance are needed, and how big should each one be?

The maximum desired starting current is 2. The three stages of starting resistance can be found from the resistance in the circuit at each state during starting. The adjustable resistance in the field circuit Radj may be varied over the range from 0 to : and is currently set to :. Armature reaction may be ignored in this machine. What is the output torque of the motor? What would happen to the motor if its field circuit were to open?

Ignoring armature reaction, what would the final steady-state speed of the motor be under those conditions? The magnetization curve for a separately excited dc generator is shown in Figure P Its field circuit is rated at 5A. The following data are known about the machine: R A 0.

The machine in Problem is reconnected as a shunt generator and is shown in Figure P SOLUTION a The total field resistance of this generator is 30 :, and the no-load terminal voltage can be found from the intersection of the resistance line with the magnetization curve for this generator. The magnetization curve and the field resistance line are plotted below. As you can see, they intersect at a terminal voltage of V. As shown in the figure below, there is a difference of 3.

This program created the plot shown above. Note that there are actually two places where the difference between the E A and VT lines is 3.

The code shown in bold face below prevents the program from reporting that first unstable point. Tell user. As shown in the figure below, there is a difference of 7. The program to create this plot is identical to the one shown above, except that the gap between E A and VT is 7. The resulting terminal voltage is about V. Note that the armature reaction reduces the terminal voltage for any given load current relative to a generator without armature reaction. If the field resistor decreases to 5 : while the armature current remains 25 A, what will the new terminal voltage be?

Assume no armature reaction. The point where the distance between the E A and VT curves is exactly 4. The new point where the distance between the E A and VT curves is exactly 4. Note that decreasing the field resistance of the shunt generator increases the terminal voltage. Its equivalent circuit is shown in Figure P Answer the following questions about this machine, assuming no armature reaction.

Compare it to the terminal characteristics of the shunt dc generators in Problem d. If the machine described in Problem is reconnected as a differentially compounded dc generator, what will its terminal characteristic look like? Derive it in the same fashion as in Problem Compare it to the terminal characteristics of the cumulatively compounded dc generator in Problem and the shunt dc generators in Problem d. A cumulatively compounded dc generator is operating properly as a flat-compounded dc generator.

The machine is then shut down, and its shunt field connections are reversed. SOLUTION a The output voltage will not build up, because the residual flux now induces a voltage in the opposite direction, which causes a field current to flow that tends to further reduce the residual flux.

A three-phase synchronous machine is mechanically connected to a shunt dc machine, forming a motor- generator set, as shown in Figure P The dc machine is connected to a dc power system supplying a constant V, and the ac machine is connected to a V Hz infinite bus.

The dc machine has four poles and is rated at 50 kW and V. It has a per-unit armature resistance of 0. The ac machine has four poles and is Y-connected. It is rated at 50 kVA, V, and 0. Assume that the magnetization curves of both machines are linear. How much power is being supplied to the dc motor from the dc power system? How large is the internal generated voltage E A of the dc machine?

How large is the internal generated voltage E A of the ac machine? What effect does this change have on the real power supplied by the motor-generator set? On the reactive power supplied by the motor- generator set? Calculate the real and reactive power supplied or consumed by the ac machine under these conditions. On the reactive power supplied by the motor-generator set?

How can the real power flow through an ac-dc motor-generator set be controlled? How can the reactive power supplied or consumed by the ac machine be controlled without affecting the real power flow?

This is also the power converted from electrical to mechanical form in the dc machine, since all other losses are neglected. Therefore, the power into the dc machine is VT I A The internal generated voltage E A of the dc machine is This fact is true because P WZ , and the speed is constant since the MG set is tied to an infinite bus.

The phasor diagram illustrating this change is shown below. The internal generated voltage in the dc machine is given by the equation E A KIZ , and Z is held constant by the infinite bus attached to the ac machine. Therefore, E A on the dc machine will decrease to 0. This is also the output power of the dc machine, the input power of the ac machine, and the output power of the ac machine, since losses are being neglected.

Note that changes in power flow also have some effect on the reactive power of the ac machine: in this problem, Q dropped from This adjustment has basically no effect on the real power flow through the MG set. The rotational losses may be assumed constant over the normal operating range of the motor.

If the slip is 0. R2 Reverse 0. Repeat Problem for a rotor slip of 0. How much induced torque will the motor be able to produce on its main winding alone? Assuming that the rotational losses are still 51 W, will this motor continue accelerating or will it slow down again? The motor will continue to speed up. Note that this program shows the torque-speed curve for both positive and negative directions of rotation.

Also, note that we had to avoid calculating the slip at exactly 0 or 2, since those numbers would produce divide-by-zero errors in Z F and Z B respectively. A V 1. Find the induced torque in the motor in Problem if it is operating at 5 percent slip and its terminal voltage is a V, b V, c V. What type of motor would you select to perform each of the following jobs? A reluctance motor would also do nicely. How many poles must it have?

Construct a table showing step size versus number of poles for three-phase and four-phase stepper motors. Figure PA-1 shows a three-phase power system with two loads. The '-connected generator is producing a line voltage of V, and the line impedance is 0. Load 1 is Y-connected, with a phase impedance of 2. SOLUTION To solve this problem, first convert the delta-connected load 2 to an equivalent wye by dividing the impedance by 3 , and get the per-phase equivalent circuit.

Figure PA-2 shows a one-line diagram of a simple power system containing a single V generator and three loads.

Assume that the transmission lines in this power system are lossless, and answer the following questions. What are the phase voltage and currents in that load? If they are not equal, why not? The powers of Loads 1 and 2 have already been calculated. The line currents to each individual load are: P1 kW I L1 These values are not the same, because the three loads have different impedance angles.

Essentially, Load 3 is supplying some of the reactive power being consumed by Loads 1 and 2, so that it does not have to come from the generator. Prove that the line voltage of a Y-connected generator with an acb phase sequence lags the corresponding phase voltage by 30q. Draw a phasor diagram showing the phase and line voltages for this generator. The phasor diagram for this connection is shown below. Find the magnitudes and angles of each line and phase voltage and current on the load shown in Figure P Figure PA-4 shows a small V distribution system.

Assume that the lines in the system have zero impedance. Find the total current supplied to the distribution system by the utility. What happened to the total current supplied? A 2-slot three-phase stator armature is wound for two-pole operation. If fractional-pitch windings are to be used, what is the best possible choice for winding pitch if it is desired to eliminate the fifth-harmonic component of voltage? Derive the relationship for the winding distribution factor k d in Equation B If a line is drawn from the center of a chord to the origin of the circle, it forma a right triangle with the radius at the end of the chord see voltage E A5 above.