1 UNSW, Australia School of Electrical Engineering & Telecommunications FINAL EXAMINATION Session 1, 2015 ELEC3115 Electromagnetic Engineering TIME ALLOWED: 3 hours TOTAL MARKS: 100 TOTAL NUMBER OF QUESTIONS: 5 THIS EXAM CONTRIBUTES 60% OF THE TOTAL COURSE ASSESSMENT. Reading Time: 10 minutes. This paper contains 9 pages, including a formulae sheet which can be found on page 8 and 9. Candidates must answer ALL 5 questions: THREE from Part A and TWO from Part B. Answer each question in a separate answer book. Marks for each question are indicated beside the question. This paper MAY NOT be retained by the candidate. Authorised examination materials: Drawing instruments may be brought into the examination room. Candidates should use their own UNSW-approved electronic calculators. This is a closed book examination. Assumptions made in answering the questions should be stated explicitly. All answers must be written in ink. Except where they are expressly required, pencils may only be used for drawing, sketching or graphical work. 2 PART A QUESTION 1 [20 marks] An insulated power cable with inner conductor diameter of 16 mm has two insulating layers: XLPE (cross-linked polyethylene) with relative dielectric constant, r1 2.8 , and EPR (Ethylene Polypropylene Rubber) with relative dielectric constant, r2 2 . The dielectric breakdown strengths (Emax) of these two materials are: XLPE : Emax = 20MV/m EPR Emax = 15 MV/m (i) Show that E field variation with radial distance around a long, isolated, cylindrical charged conductor such as the power cable is LrE a 2 r where r is the radial distance from the axis of the conductor L is the line charge density of the conductor = o r, is the total permittivity of the dielectric material; ( o = 8.854 10 12 F/m), where r is the relative permittivity of the material. [3 marks] (ii) Which dielectric material should form the inner layer Discuss the reasons behind your selection using boundary conditions for the normal components of the E fields between material boundaries. [2 marks] (iii) Assume that the outside of the cable insulation is conducting ground and hence is at zero potential. Find the minimum thicknesses of each insulation layer for operation of the cable at 132kV, if the maximum E fields within both dielectric materials are not to exceed 50% of their respective breakdown strengths (Emax). [10 marks] Question 1 continues in the next page 3 (iv) Sketch neatly the maximum allowable E field variations with radial distance in the inner and outer layers of insulation, indicating for each dielectric material the maximum and minimum E field that will occur. Do not ignore the
boundary condition between the outer layer insulator and surrounding air. [5 marks] QUESTION
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[20 marks] A power transmission line consists of two bare copper conductors of circular cross-section, each having a radius a = 12 mm, and they are spaced D = 1.2 m apart. The space between the conductors is air with a dielectric strength of 3 MV/m. (i) Assuming uniformly distributed charge on the conductor, show that the capacitance per unit length of the line is ln C D a a . [5 marks] (ii) Using the express of (i), calculate the capacitance/m of the line. [2 marks] (iii) Calculate the leakage resistance of the line (i.e. the resistance between the conductors) per unit length, assuming that the conductivity of air is 5 10-10 S/m and that of copper is 5.8 107 S/m. [3 marks] (iv) Taking help of expression of (i) and method of images, develop an expression for capacitance between a bare copper conductor of the transmission line and ground which is assumed to be a perfect conducting body. If the height h of the conductor above the ground is 10m, calculate the value of this leakage capacitance/m. [5 marks] (v) A line trap is an air core coil used on high voltage power transmission lines to assist in directing high frequency signals coupled to the line for communication purposes. A typical coil has the following characteristics: Question 2 continues in the next page 4 Rated current, I = 400 A (this is the normal operating current) Number of turns, n = 33 Rated voltage, V = 132,000 Volts (the device must be insulated from earth) Maximum fault current = 10,000 A for 3 seconds Radius of the coil, a = 17.5 cm Length of the coil, l = 40 cm The inductance of the coil is given by 2 2 on aL K l (K = constant 0.7) Determine the radial forces acting on the coil when the maximum allowable fault current of 10,000 Amps flows through the winding. [5 marks] QUESTION 3 [20 marks] A toroidal core with a mean diameter of 250 mm and a cross-sectional area of 1000 mm2 has an air gap of length 1.25 mm cut in it. Fringing and leakage of flux around the air gap may be neglected. (i) Determine the current required in a coil of 1500 turns to produce a flux density of 1 T. The relative permeability r of the core material (iron) may be assumed to be 3000 for this level of flux density. [Permeability H/m70 r 0, 4 10 ]. [5 marks] (ii) The above coil is the primary of a single-phase ideal transformer. The AC supply voltage to the primary winding is sinusoidal at 50 Hz. What is the highest RMS AC supply voltage that can be applied to the coil, so the maximum flux density in the core does not exceed 1 T