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Transcript
EEL4205 Fall 2013 Exam 2
Name:_________________________________________
Problem 1. (50 points)
A non-ideal three-phase Y- transformer is rated 7.2 kV: 110 V (line to line voltage), 10 MVA.
An open-circuit test is conducted from the high-voltage side (or: the low voltage terminals are
O.C.) and the corresponding instrument readings (rms values) are 7.2 kV (line to line), 16A (line)
and 72 kW (total power of all three phases). Similarly, a short circuit test from the high-voltage
side (or: the low voltage terminals are S.C.) gives the 13.2 kV (line to line), 52.5 A (line) and 81
kW (total power of all three phases). The equivalent circuit for each single transformer is
shown in the figure.
(1) Find the turns ratio n for each transformer; (10 points)
(2) Calculate Req, Leq, Rc and Lm in the equivalent circuit; (40 points)
High voltage side
Low voltage side
Answer:
(1) n =
(2) Req =
,
Leq =
,
Rc =
, Lm =
Problem 2. (50 points, 5 points for each question)
For a 3 phase, 2 pole, 24 slot synchronous motor with 5/6 fractional pitch double layer lap
winding on stator, the motor supplies 12 N.m torque to its load at steady state speed of 8000 rpm.
The stator has 1 slot skew. The stator inner diameter D  30 mm and the length of the machine
l  28 mm . The airgap g  1 mm . The Carter’s coefficient for the stator and rotor are is 1.02
and 1.06, respectively. The peak magnetic field intensity in the airgap is 0.65 T. There are 4 turns
per coil on stator. All the stator windings are connected in series (C=1). The three phase stator
windings are connected in Y. The rotor has 18 slots with concentric winding. Assume N1  4 ,
N 2  3 , N 3  2 , N 4  2 , and N5  1 . The rotor slot pitch  r  20 .
Find:
(1)
(2)
(3)
(4)
the tip speed of the rotor;
the force applied to the rotor;
the mechanical power supplied to the load;
k p , k d , ks and the winding factor k w for the fundamental harmonic of stator winding;
(5) the effective number of series turns Nˆ a on stator;
(6) the stator self inductance LA and mutual inductance M s ;
(7) rms phase voltage and terminal voltage of the machine;
(8) the winding factor k w for the fundamental harmonic of rotor winding;
(9) the effective number of series turns Nˆ f on rotor;
(10)
the rotor self inductance Lmf and the mutual inductance Laf between stator and rotor
windings.
Answer:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)