NAME: _________________________________
Department of Electrical and Computer Engineering
SPRING 2015 COMPREHENSIVE/BREADTH EXAM
Questions 2/3/4
TTG Area: Power Systems
ECGR 4143 Electrical Machines
Concept Question [5pts]
a) Why is reluctance analogous to resistance?
b) In magnetic circuits is most of the energy contained in the air region or magnetic material
region? Why? What about the reluctance?
Choose to answer only TWO of the following three questions below.
Problem 1. A Linear Magnetic Circuit Analysis [15 pts]
The magnetic structure shown below is made of cast steel (µr = 1400) and it has two air-gaps in
parallel. Assume no fringing or flux leakage.
a) Draw the magnetic equivalent circuit for this magnetic structure.
b) Find the equivalent reluctance as seen by the winding, neglect the reluctance of the cast steel.
c) Find the flux, , within the central leg if the current in the winding is 1 A. Neglect the
reluctance of the cast steel.
d) If the central leg can carry magnetic flux density B = 1.0 Tesla without saturating, find the
current in the winding for B = 1 T, again, ignore the reluctance of the cast steel.
e) Find the equivalent reluctance as seen by the winding, but this time do not ignoring the cast
steel reluctance.
NAME: _________________________________
Problem 2. Linear Axial Actuator Design [15 pts]
We want to design a coil to be placed on the center leg of the magnetic actuator shown below. The
actuator must be able to provide a total pull force of 60 N on the armature supported by the springs.
The dimensions of the electromagnet are in centimeters. The depth of the sheet steel core and
armature is 5 cm.
5
l
20
5
10
5
5
50
a) Assume that all of the reluctance is in the air gaps. Find the flux in the center leg of the core,
when the gap length l = 1 cm, that will provide a pull force of 60 N.
b) For the conditions described in part (a) what is the MMF (Ni) needed to create 60N of force.
c) Using the flux derived in part (a) calculate the MMF in the center leg,(Hl)center, and the MMF
in the left leg, (Hl)left, of the core using µr = 4775 for sheet steel core.
NAME: _________________________________
Problem 3. Synchronous Generators [15 pts]
A 10kVA, 208Vll, 1200RPM, 3 phase, 60Hz, Y-connected synchronous generator has a fieldwinding resistance of 4Ω. The armature-winding impedance is 0.4+6j Ω per phase. When the
generator is operating at its full load the power factor is 0.8 lagging and the field-winding current
is 6A. The friction and windage loss at full load is 500W.
a) Draw the per-phase equivalent circuit for the synchronous generator
b) Calculate the rated per-phase armature current.
c) Calculate the no load voltage Ea
d) What is the voltage regulation percentage (VR%) at this rated condition.
e) What is the efficiency at this rated condition?