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Questions and Answers of Electrical Engineering

The half-wave, phase-controlled rectifier system of Problem 10.9 and Figure is to be replaced by the full-wave, phase-controlled system of Figure. SCR T1 will be triggered ON at time td (0 td ?/w),
The full-wave, phase-controlled rectifier of Figure is supplying a highly inductive load such that the load current can be assumed to be purely dc, as represented by the current source Idc in the
A full-wave diode rectifier is fed from a 50-Hz, 220-V rms source whose series inductance is 12 mH. It drives a load with a resistance 8.4Ω which is sufficiently inductive that the load current can
A 1-kW, 85-V, permanent-magnet dc motor is to be driven from a full-wave, phase-controlled bridge such as is shown in Figure. When operating at its rated voltage, the dc-motor has a no load speed of
Consider the dc-motor drive system of Problem 10.13. To limit the starting current of the dc motor to twice its rated value, a controller will be used to adjust the initial firing-delay angle of the
A three-phase diode bridge is supplied by a three-phase autotransformer such that the line-to line input voltage to the bridge can be varied from zero to 230 V. The output of the bridge is connected
A dc-motor shunt field winding of resistance 210Ω is to be supplied from a 220-V rms, 50-Hz, three-phase source through a three-phase, phase controlled rectifier. Calculate the delay angle αd which
A superconducting magnet has an inductance of 4.9 H, a resistance of 3.6 mΩ, and a rated operating current of 80 A. It will be supplied from a 15-V rms, three-phase source through a three phase,
A voltage-source H-bridge inverter is used to produce the stepped waveform v (t) shown in Figure. For V0 = 50 V, T = 10 msec and D = 0.3: a. Using Fourier analysis, find the amplitude of the
Consider the stepped voltage waveform of Problem 10.18 and Figure. a. Using Fourier analysis, find the value of D (0 D 0.5) such that the amplitude of the third harmonic component of the voltage
Consider Example 10.12 in which a current-source inverter is driving a load consisting of a sinusoidal voltage. The inverter is controlled to produce the stepped current waveform shown in Figure. a.
A PWM inverter such as that of Figure is operating from a dc voltage of 75 V and driving a load with L = 53 mH and R = 1.7?. For a switching frequency of 1500 Hz, calculate the average load current,
The rotor of a six-pole synchronous generator is rotating at a mechanical speed of 1200 r/min.a. Express this mechanical speed in radians per second.b. What is the frequency of the generated voltage
The voltage generated in one phase of an unloaded three-phase synchronous generator is of the form v(t) = Vo cos cot. Write expressions for the voltage in the remaining two phases.
A three-phase motor is used to drive a pump. It is observed (by the use of a stroboscope) that the motor speed decreases from 898r/min when the pump is unloaded to 830 r/min as the pump is loaded.a.
The object of this problem is to illustrate how the armature windings of certain machines, i.e., dc machines, can be approximately represented by uniform current sheets, the degree of correspondence
A three-phase Y-connected ac machine is initially operating under balanced three-phase conditions when one of the phase windings becomes open-circuited. Because there is no neutral connection on the
What is the effect on the rotating mmf and flux waves of a three-phase winding produced by balanced-three-phase currents if two of the phase connections are interchanges?
In a balanced two-phase machine, the two windings are displaced 90 electrical degrees in space, and the currents in the two windings are phase-displaced 90 electrical degrees in time. For such a
This problem investigates the advantages of short-pitching the stator coils of an ac machine. Figure shows a single full-pitch coil in a two-pole machine. Figure b shows a fractional-pitch coil for
A six-pole, 60-Hz synchronous machine has a rotor winding with a total of 138 series turns and a winding factor kr = 0.935. The rotor length is 1.97 m, the rotor radius is 58 cm, and the air-gap
Assume that a phase winding of the synchronous machine of Problem 4.9 consists of one full-pitch, 11-turn coil per pole pair, with the coils connected in series to form the phase winding. If the
The synchronous machine of Problem 4.9 has a three-phase winding with 45 series turns per phase and a winding factor kw = 0.928. For the flux condition and rated speed of Problem 4.9, calculate the
The three-phase synchronous machine of Problem 4.9 is to be moved to an application which requires that its operating frequency be reduced from 60 to 50 Hz. This application requires that, for the
Figure shows a two-pole rotor revolving inside a smooth stator which carries a coil of 110 turns. The rotor produces a sinusoidal space distribution of flux at the stator surface; the peak value of
A three-phase two-pole winding is excited by balanced three-phase 60-Hz currents as described by Eqs. 4.23 to 4.25. Although the winding distribution has been designed to minimize harmonics, there
The nameplate of a dc generator indicates that it will produce an output voltage of 24 V dc when operated at a speed of 1200 r/min. By what factor must the number of armature turns be changed such
The armature of a two-pole dc generator has a total of 320 series turns. When operated at a speed of 1800r/min, the open-circuit generated voltage is 240 V. Calculate Фp, the air-gap flux per pole.
The design of a four-pole, three-phase, 230-V, 60-Hz induction motor is to be based on a stator core of length 21 cm and inner diameter 9.52 cm. The stator winding distribution which has been
A two-pole, 60-Hz three-phase laboratory-size synchronous generator has a rotor radius of 5.71 cm, a rotor length of 18.0 cm, and an air-gap length of 0.25 mm. The rotor field winding consists of 264
A four-pole, 60-Hz synchronous generator has a rotor length of 5.2 m, diameter of 1.24 m, and air-gap length of 5.9 cm. The rotor winding consists of a series connection of 63 turns per pole with a
Thermal considerations limit the field-current of the laboratory-size synchronous generator of Problem 4.18 to a maximum value of 2.4 A. If the peak fundamental air-gap flux density is limited to a
Figure shows in cross section a machine having a rotor winding f and two identical stator windings a and b whose axes are in quadrature. The self-inductance of each stator winding is Laa and of the
Consider the two-phase synchronous machine of Problem 4.22. Derive an expression for the torque acting on the rotor if the rotor is rotating at constant angular velocity, such that θ0 = wt + δ, and
Figure shows in schematic cross section a salient-pole synchronous machine having two identical stator windings a and b on a laminated steel core. The salient-pole rotor is made of steel and carries
A three-phase linear ac motor has an armature winding of wavelength 25 cm. A three-phase balanced set of currents at a frequency of 100 Hz is applied to the armature.a. Calculate the linear velocity
The linear-motor armature of Problem 4.25 has a total active length of 7 wavelengths, with a total of 280 turns per phase with a winding factor kw = 0.91. For an air-gap length of 0.93 cm, calculate
A two-phase linear permanent-magnet synchronous motor has an air-gap of length 1.0 mm, a wavelength of 12 cm, and a pole width of 4 cm. The rotor is 5 wavelengths in length. The permanent magnets on
The full-load torque angle of a synchronous motor at rated voltage and frequency is 35 electrical degrees. Neglect the effects of armature resistance and leakage reactance. If the field current is
The armature phase windings of a two-phase synchronous machine are displaced by 90 electrical degrees in space.a. What is the mutual inductance between these two windings?b. Repeat the derivation
Design calculations show the following parameters for a three-phase, cylindrical-rotor synchronous generator: Phase-a self-inductance Laa = 4.83mH. Armature leakage inductance Lal = 0.33mH. Calculate
The open-circuit terminal voltage of a three-phase, 60-Hz synchronous generator is found to be 15.4 kV rms line-to-line when the field current is 420 A.a. Calculate the stator-to-rotor mutual
A 460-V, 50-kW, 60-Hz, three-phase synchronous motor has a synchronous reactance of Xs = 4.15 Ω and an armature-to-field mutual inductance, Laf = 83 mH. The motor is operating at rated terminal
The motor of Problem 5.5 is supplied from a 460-V, three-phase source through a feeder whose impedance is Zf = 0.084 + j0.82Ω. Assuming the system (as measured at the source) to be operating at an
A 50-Hz, two-pole, 750 kVA, 2300 V, three-phase synchronous machine has a synchronous reactance of 7.75 Ω and achieves rated open-circuit terminal voltage at a field current of 120 A.a. Calculate
The manufacturer's data sheet for a 26-kV, 750-MVA 60-Hz three-phase synchronous generator indicates that it has a synchronous reactance Xs = 2.04 and a leakage reactance Xal = 0.18, both in per unit
The following readings are taken from the results of an open- and a short-circuit test on an 800-MVA, three-phase, Y-connected, 26-kV, two-pole, 60-Hz turbine generator driven at synchronous speed:
The following readings are taken from the results of an open- and a short-circuit test on a 5000-kW, 4160-V, three-phase, four-pole, 1800-rpm synchronous motor driven at rated speed: The armature
Consider the motor of Problem 5.10.a. Compute the field current required when the motor is operating at rated voltage, 4200 kW input power at 0.87 power factor leading. Account for saturation under
Using MATLAB, plot the field current required to achieve unity-power-factor operation for the motor of Problem 5.10 as the motor load varies from zero to full load. Assume the motor to be operating
Loss data for the motor of Problem 5.10 are as follows: Open-circuit core loss at 4160 V = 37 kW. Friction and windage loss = 46 kW. Field-winding resistance at 75°C = 0.279Ω. Compute the output
The following data are obtained from tests on a 145-MVA, 13.8-kV, three phase, 60-Hz, 72-pole hydroelectric generator. Open-circuit characteristic: Short-circuit test: If = 710 A, Ia = 6070 Aa. Draw
What is the maximum per-unit reactive power that can be supplied by a synchronous machine operating at its rated terminal voltage whose synchronous reactance is 1.6 per unit and whose maximum field
A 25-MVA, 11.5 kV synchronous machines is operating as a synchronous condenser, as discussed in Appendix D (section D.4.1). The generator short-circuit ratio is 1.68 and the field current at rated
The synchronous condenser of Problem 5.17 is connected to a 11.5 kV system through a feeder whose series reactance is 0.12 per unit on the machine base. Using MATLAB, plot the voltage (kV) at the
A synchronous machine with a synchronous reactance of 1.28 per unit is operating as a generator at a real power loading of 0.6 per unit connected to a system with a series reactance of 0.07 per unit.
Superconducting synchronous machines are designed with superconducting fields windings which can support large current densities and create large magnetic flux densities. Since typical operating
For a synchronous machine with constant synchronous reactance Xs operating at a constant terminal voltage Vt and a constant excitation voltage Eaf, show that the locus of the tip of the
A four-pole, 60-Hz, 24-kV, 650-MVA synchronous generator with a synchronous reactance of 1.82 per unit is operating on a power system which can be represented by a 24-kV infinite bus in series with a
The generator of Problem 5.22 achieves rated open-circuit armature voltage at a field current of 850 A. It is operating on the system of Problem 5.22 with its voltage regulator set to maintain the
The 145 MW hydroelectric generator of Problem 5.15 is operating on a 13.8-kV power system. Under normal operating procedures, the generator is operated under automatic voltage regulation set to
Repeat Example 5.9 assuming the generator is operating at one-half of its rated kVA at a lagging power factor of 0.8 and rated terminal voltage.
Repeat Problem 5.24 assuming that the saturated direct-axis synchronous inductance Xd is equal to that found in Problem 5.15 and that the saturated quadrature-axis synchronous reactance Xq is equal
Write a MATLAB script to plot a set of per-unit power-angle curves for a salient-pole synchronous generator connected to an infinite bus (V bus = 1.0 per unit). The generator reactances are Xd = 1.27
Draw the steady-state, direct- and quadrature-axis phasor diagram for a salient-pole synchronous motor with reactances Xd and Xq and armature resistance Ra. From this phasor diagram, show that the
Repeat Problem 5.28 for synchronous generator operation, in which case the equation for δ becomes
What maximum percentage of its rated output power will a salient-pole motor deliver without loss of synchronism when operating at its rated terminal voltage with zero field excitation (Eaf = 0) if Xd
If the synchronous motor of Problem 5.30 is now operated as a synchronous generator connected to an infinite bus of rated voltage, find the minimum per-unit field excitation (where 1.0 per unit is
A salient-pole synchronous generator with saturated synchronous reactances Xd = 1.57 per unit and Xq = 1.34 per unit is connected to an infinite bus of rated voltage through an external impedance X
A salient-pole synchronous generator with saturated synchronous reactances Xd = 0.78 per unit and Xq = 0.63 per unit is connected to a rated-voltage infinite bus through an external impedance X bus =
A two-phase permanent-magnet ac motor has a rated speed of 3000 r/min and a six-pole rotor. Calculate the frequency (in Hz) of the armature voltage required to operate at this speed.
A 5-kW, three-phase, permanent-magnet synchronous generator produces an open-circuit voltage of 208 V line-to-line, 60-Hz, when driven at a speed of 1800 r/min. When operating at rated speed and
Small single-phase permanent-magnet ac generators are frequently used to generate the power for lights on bicycles. For this application, these generators are typically designed with a significant
a. Calculate the field current required to achieve operation at 15.2 N · m torque and 1800 r/min. Calculate the corresponding PWM duty cycle D.b. Calculate the field current required to achieve
The dc motor of Problem 11.1 has a field-winding inductance Lf = 3.7 H and a moment of inertia J = 0.081 kg · m2. The motor is operating at rated terminal voltage and an initial speed of 1300
A shunt-connected 240-V, 15-kW, 3000 r/min dc motor has the following parameters Field resistance: R f = 132Ω, Armature resistance: Ra = 0.168Ω, Geometric constant: Kf = 0.422 V/ (A· rad/sec) When
The data sheet for a small permanent-magnet dc motor provides the following parameters" Rated voltage: Vrated = 3 V, Rated output power: Prated = 0.28 W, No-load speed: nnl = 12,400 r/min, Torque
The data sheet for a 350-W permanent-magnet dc motor provides the following parameters: Rated voltage: Vrated = 24 V, Armature resistance: Ra = 97 m?, No-load speed: nnl = 3580 r/min, No-load
The motor of Problem 11.5 has a moment of inertia of 6.4 x 10-7 oz · in · sec2. Assuming it is unloaded and neglecting any effects of rotational loss, calculate the time required to achieve a speed
An 1100-W, 150-V, 3000-r/min permanent-magnet dc motor is to be operated from a current source inverter so as to provide direct control of the motor torque. The motor torque constant is Km = 0.465 V/
The permanent-magnet dc motor of Problem 11.8 is operating at its rated speed of 3000 r/min and no load. If rated current is suddenly applied to the motor armature in such a direction as to slow the
A 1100-kVA, 4600-V, 60-Hz, three-phase, four-pole synchronous motor is to be driven from a variable-frequency, three-phase, constant V/Hz inverter rated at 1250-kVA. The synchronous motor has a
Consider a three-phase synchronous motor for which you are given the following data: Rated line-to-line voltage (V), Rated volt-amperes (VA), Rated frequency (Hz) and speed (r/min), Synchronous
For the purposes of performing field-oriented control calculations on non-salient synchronous motors, write a MATLAB script that will calculate the synchronous inductance Ls and armature-to field
A 100-kW, 460-V, 60-Hz, four-pole, three-phase synchronous machine is to be operated as a synchronous motor under field-oriented torque control using a system such as that shown in Figure a. The
The synchronous motor of Problem 11.13 is operating under field-oriented torque control such that iD = 0. With the field current set equal to 14.5 A and with the torque reference set equal to 0.75 of
Consider the case in which the load on the synchronous motor in the field oriented torque-control system of Problem 11.13 is increased, and the motor begins to slow down. Based upon some knowledge of
Consider a 500-kW, 2300-V, 50-Hz, eight-pole synchronous motor with a synchronous reactance of 1.18 per unit and AFNL = 94 A. It is to be operated under field-oriented torque control using the
A 2-kVA, 230-V, two-pole, three-phase permanent magnet synchronous motor achieves rated open-circuit voltage at a speed of 3500 r/min. Its synchronous inductance is 17.2 mH.a. Calculate APM for this
Field-oriented torque control is to be applied to the permanent-magnet synchronous motor of Problem 11.18. If the motor is to be operated at 4000 r/min at rated terminal voltage, calculate the
A 15-kVA, 230-V, two-pole, three-phase permanent-magnet synchronous motor has a maximum speed of 10,000 r/min and produces rated open-circuit voltage at a speed of 7620 r/min. It has a synchronous
The permanent magnet motor of Problem 11.17 is to be operated under vector control using the following algorithm. Terminal voltage not to exceed rated value, Terminal current not to exceed rated
Consider a 460-V, 25-kW, four-pole, 60-Hz induction motor which has the following equivalent-circuit parameters in ohms per phase referred to the stator: R1 = 0.103 R2 = 0.225 X1 = 1.10 X2 = 1.13 Xm
Consider the 460-V, 250-kW, four-pole induction motor and drive system of Problem 11.21.a. Write a MATLAB script to plot the speed-torque characteristic of the motor at drive frequencies of 20, 40,
A 550-kW, 2400-V, six-pole, 60-Hz three-phase induction motor has the following equivalent circuit parameters in ohms-per-phase-Y referred to the stator: R1 = 0.108 R2 = 0.296 X1 = 1.18 X2 = 1.32 Xm
A 150-kW, 60-Hz, six-pole, 460-V three-phase wound-rotor induction motor develops full load torque at a speed of 1157 r/min with the rotor short circuited. An external non-inductive resistance of 870
The wound rotor of Problem 11.24 will be used to drive a constant-torque load equal to the rated full-load torque of the motor. Using the results of Problem 11.24, calculate the external rotor
A 75-kW, 460-V, three-phase, four-pole, 60-Hz, wound-rotor induction motor develops a maximum internal torque of 212 percent at a slip of 16.5 percent when operated at rated voltage and frequency
A 35-kW, three-phase, 440-V, six-pole wound-rotor induction motor develops its rated full load output at a speed of 1169 r/min when operated at rated voltage and frequency with its slip rings
a. The value of the peak direct- and quadrature-axis components of the armature currents iD and iQ.b. The rms armature current under this operating condition.c. The electrical frequency of the drive

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