ECE320, Spring 2006, Exam 2a 24th February, 2006

Name
PID Number
Problem / MaxPoints / Points
1 / 40
2 / 40
3 / 20
Total / 100

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)

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)

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)