Download ECE320-Exam2

ECE320, Spring 2006, Exam 2a
24th February, 2006
Name
PID Number
Problem
1
2
3
Total
Max Points
40
40
20
100
Points
Instructions:

Closed book, but you are allowed to have one-page single-sided handwritten notes and
your exam_1 notes.

You can have 3 pages of blank papers for calculation purpose.

Write your solutions and steps neatly and orderly. No credits for random side
writings.

Box your answers.
Problem 1. (40 points) In the magnetic circuit below, the air-gap is g = 5 mm, i = 40 A, N =
250 turns, cross section of the iron everywhere A = 40 mm*50 mm.
a) Draw an analog electric schematic for the magnetic circuit for both cases of iron core’s µ =
∞ and µ ≠ ∞. (10 points)
Assuming that the iron core has an infinite permeability, solve the following problems:
b) Calculate the flux density in the air-gaps. (10 points)
100 mm
c) What would be flux density in the air gaps
if the current is i = 40 sin (377 t) A. (10 points)
d) For the above (c), what would be the voltage induced
in the coil? (10 points)
g
iron
i
110 mm
Problem 2. (40 points) A 50 kVA, 10kV/250 V, 60Hz, single-phase transformer has the
following test results: Open-circuit test (open the high voltage side): 250V, 5A, and 250 watts
measured on the low voltage side and Short-circuit test (short the low voltage side): 300V,
rated current, and 500 watts measured on the high voltage side.
a) Draw the simplified high-voltage side referred equivalent circuit in actual values. (8 points)
b) Calculate the winding resistance in actual values. (8 points)
c) Draw the simplified equivalent circuit in pu values. (8 points)
d) Calculate the leakage reactance in pu values. (8 points)
e) A load is connected to the low voltage side, drawing 50 kVA with pf =.866 lagging at 250 V.
Using per-unit values to calculate the high-voltage side voltage. (8 points)
Problem 3. (20 points)
A three-phase transformer is made from three single-phase ones, each single-phase transformer is
rated at 10 kVA, 20kV/200V; rated winding losses 100 W, core losses 50 W. The three-phase
transformer is connected in delta on the high voltage side and in star on the low voltage side.
(a) What are the voltage ratings, current ratings, core loss (at the rated voltage), winding loss (at the
rated current) for the 3-phase transformer? (10 points)
(b) Draw the schematic connection of the 3-phase transformer and a phasor diagram to express the
phase relationship between the high-voltage side and low-voltage side line-to-line voltages
assuming the transformer is ideal. (10 points)