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