Assignment Task

Question 1

A 3-phase, 8-pole induction motor is connected to a 60 Hz AC source.

• What is the synchronous speed?
• Calculate the full-load torque value when the slip is 4% and the motor nominal power is 25 kW.

Question 2

A 3-phase industrial motor is designed for heavy-duty applications. It operates at the following parameters:

• Horsepower: 400 hp
• Frequency: 60 Hz
• Voltage: 2300 V
• Full-load speed: 1750 rpm
• Efficiency: 88%
• Power factor: 85%

Using the given specifications, solve the following tasks:

• Determine the motor`s line current.
• Calculate the mechanical torque exerted by the motor, considering typical total windage and friction losses in a 3-phase induction motor.
• Estimate the heat loss generated in the rotor during operation.
• Analyze the total iron and copper loss incurred in the motor.
• Explore the impact of a 10% terminal voltage drop on the motor`s speed, assuming the torque remains constant.
• Assess the change in shaft output power when the motor is supplied with the 10% reduced voltage, assuming the torque remains constant.

Question 3

A single-phase, capacitor-start, capacitor-run motor, NEMA F class, manufactured by Baldor Electric Company has the following datasheet.

Calculate the following using the above information:

a. Find per-unit values of the rotor quantities. b. Find the value of the full-load input active power. c. Find the value of the full-load input reactive power.

Question 4

In a practical electrical engineering scenario, consider a 3-phase synchronous generator with the following parameters:

• Synchronous reactance: 5 Ω per phase
• Resistive load: 15 Ω per phase
• Excitation voltage per phase: 14 kV

Solve the following tasks based on the given parameters:

• Depict the equivalent electrical circuit of the generator, illustrating its components and connections.
• Compute the equivalent impedance of the circuit, detailing both its amplitude and phase.
• Determine the line current flowing through the circuit.
• Calculate the generator`s line-to-neutral terminal voltage.
• Assess the voltage drop experienced across the synchronous reactance during operation.
• Illustrate the voltage phasor diagram of the generator, representing its electrical characteristics.
• Analyze and determine the torque angle associated with the generator`s operation.

Question 5

A 3-phase, 10 hp, 900 V, 4-pole, 60 Hz, star-connected synchronous motor has a synchronous reactance of 12 Ω and negligible resistance. The motor operates on a 900 V∠0° busbar voltage. With a shaft load of 10 hp and rotational losses of 640 W, the excitation emf is adjusted to 600 V (line).

• Determine the torque angle of the motor.
• Calculate the armature current flowing through the motor.
• Determine the power factor of the motor.
• Assess whether the motor is under-excited or over-excited.
• Calculate the apparent power consumed by the motor.
• Determine the total reactive power exchanged between the motor and the electrical supply.
• Calculate the developed mechanical torque of the motor.
• Calculate the shaft torque produced by the motor.

Question 6

A 3-phase, 6-pulse converter shown below is supplying power to a separately excited DC motor. The converter is connected to a 460 V, 60 Hz power supply. The motor has a rated armature current of 25 A, an armature resistance of 0.4 Ω, and operates at a rated speed of 1600 rpm. The delay angle of the converter is set to 30°.

Calculate the following:

• Determine the rated voltage of the motor.
• Calculate the reactive power absorbed by the converter.
• If the motor can start with a lower voltage and the starting current is 150 A, calculate the required delay angle of the converter.
• Calculate the required delay angle needed to achieve a speed of 1800 rpm.

Question 7

The 3-phase, 60 Hz, 12-pole motor depicted in the figure below is a synchronous motor connected to a cycloconverter. The nominal ratings of the motor are provided in the table below. The cycloconverter is supplied by a 3-phase, 60 Hz, 415 V source. If a desired speed of 385 rpm at full load is required, calculate:

• The frequency to be applied to the motor stator windings.
• The voltage to be applied to the motor stator windings.