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Electric Machinery Quiz 1 with Four Problems to Solve, Exams of Electric Machines

Quiz 1 with Four Problems to Solve on Electric Machinery | Fall 2013 MIT

Typology: Exams

2019/2020

Uploaded on 04/23/2020

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Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.685 Electric Machinery
Quiz 1 One Crib Sheet Allowed November 6, 2013
There is space for you to write your answers on this quiz.
There are four problems on this quiz. They have equal weight
Problem 1: Induction Motors
The single phase equivalent circuit of a three-phase, four pole induction m otor is shown in
Figure 1. For the purposes of this problem we will assume armature resistance is negligible.
The machine is connected to a three-phase voltage source with line-neutral voltage of 200
volts, RMS (346 volts, line-line) and a frequency of 400 radians/second. The motor reaches
peak torque at a speed of 160 Radians/second (about 1528 RPM).
j 2.5Ω j 2 Ω
Ωj 10 s
200 v
+
R2
Figure 1: Induction Motor Equivalent Circuit
1. What is the value of that peak torque (in N-m)?
2. What is the value of R2? (in Ω)
1
pf3
pf4
pf5

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Massachusetts Institute of Technology

Department of Electrical Engineering and Computer Science 6.685 Electric Machinery

Quiz 1 One Crib Sheet Allowed November 6, 2013

There is space for you to write your answers on this quiz. There are four problems on this quiz. They have equal weight

Problem 1: Induction Motors

The single phase equivalent circuit of a three-phase, four pole induction motor is shown in Figure 1. For the purposes of this problem we will assume armature resistance is negligible. The machine is connected to a three-phase voltage source with line-neutral voltage of 200 volts, RMS (346 volts, line-line) and a frequency of 400 radians/second. The motor reaches peak torque at a speed of 160 Radians/second (about 1528 RPM).

j 2.5 Ω j 2 Ω

j 10 Ω 200 v s

+

R

Figure 1: Induction Motor Equivalent Circuit

  1. What is the value of that peak torque (in N-m)?
  2. What is the value of R 2? (in Ω)

Problem 2 DC Machines

A permanent magnet DC motor is connected to a 250 Volt (DC) source. Running ’light’ (no mechanical load), it draws negligible current and turns at a speed of 200 Radians/second. (about 1910 RPM). The armature circuit of the machine has a resistance of one Ω. Now the machine is loaded so that it is driving a load torque of 100 N-m, still connected to the 250 VDC source.

  1. How much current is it drawing?
  2. How fast is it turning?
  1. Assuming that the cylinder has surface conductivity of 80,000 S (reciprocal ohms), and the coil is driven by a step of 10 A, what is the magnetic field inside of the cylinder, as a function of time?

Problem 4 Synchronous Machine

A three-phase, two pole synchronous machine has the following characteristics: Rated Power PB 3 MVA Rated Voltage VB 1 kV (Peak) Synchronous Inductance La − Lab 2.5 mH Field to Phase Mutual Inductance M 25 mH Synchronous Frequency ω 0 400 Radians/Second Assume that armature resistance is negligible.

  1. On no-load, open-circuit test at rated speed, what field current is required to produce rated voltage?
  2. On short-circuit test, what field current is required to produce rated current?
  3. Running at rated speed, with field current If = 300A and with rated armature terminal voltage (1,000 V, Peak, what is the peak torque the machine can produce?
  4. Running at rated speed with field current If = 300A and with the armature driven by a balanced three-phase current of Ia = 3, 000 A, Peak, what is the maximum peak torque that the machine can produce?