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EE311 ELECTRONIC AND ELECTRICAL PRINCIPLES 3

Date: xx May 2017

PART A

Attempt the following compulsory question

(c)      Sketch the typical architecture for a rural power distribution network, and explain what changes might be made in order to improve its reliability of supply. 2 marks

(d)       A three phase delta connected, 460V, 945rpm, 50Hz, 6-pole wound rotor induction motor, with the rotor windings short-circuited, find the start-up current when starting at full voltage. R1 = 0.20 R2 = 0.20 X1 = X2 = 0.95 . 2 marks

(e)       A full loaded transformer has a copper loss of 440W and iron loss of 350W. Determine the total loss when the transformer is half loaded. . 2 marks

[Total: 10 marks]

Attempt ONE further optional question from this part.

Q2 (a) Considering a single phase load and supply, it can be shown from simple circuit analysis that the cable voltage drop is given by:

ΔV = VSupply  − VlOad  = 2IZ

where Z represents the impedance of each cable conductor.

For the three phase case shown in Figure Q2a, perform a similar analysis and prove that for the balanced three phase case,

(b)       For  the  THREE  phase  system  and  loads  shown  in  Figure  Q2b,

determine  suitable  cable  sizes  such that the voltage  at  each  load remains within statutory limits. Use the cables sizes and parameters given in Table Q2. 12 marks

(c)       Describe what you understand are the key characteristics of a typical transmission network, and explain how you expect such networks to change in the future. 4 marks

[Total: 20 marks]

Q3. A small part of a three-phase network supplying a number of loads is shown

in Figure Q3. The grid infeed fault level is 950MVA.

(a)       Using a common base of 50MVA, determine the resulting per unit

values for the network components shown in Figure Q3. Show these on a sketch of the single line diagram. 5 marks

(b)       Calculate the steady state fault level at busbar D in the network shown

in Figure Q3 under the following two conditions:

(i)   the generator at D and the motor at B are disconnected (ii)  the generator at D and the motor at B are all connected 12 marks

(c)       Without calculation, describe how the fault level at busbar D would be  affected  if  an  additional  line  was  built  connecting  busbars B and C. Clearly explain your reasoning. 3 marks

[Total: 20 marks]

PART B

Attempt the following compulsory question

2 marks

[Total: 10 marks]

Attempt ONE further optional question from this part.

Q4. (a)        Find      the      phasor      of     the      following      time      functions i(t) = 2cos(Ot + 3/4). 2 marks

(b) Using phasor domain representation, write Maxwell’s equations for the isotropic and homogeneous medium characterized by c, μ, . 4 marks

(c) The magnetic field of the plane wave traveling in a medium with cr    =   9    made    of   nonmagnetic,    nonconducting    material    is H = 2cos (2 109 t -  ky), (A/m) (see coordinates in Figure Q5c):

(i)   Find the phase velocity u, wave number k, angular frequency O, and medium impedance  n for this medium;

(ii)  Find wave’s direction of travel;

(iii) Find the corresponding vector E;

(iv) Find the corresponding vector S; what is vector S called and what its meaning is?

(v)  Consider xyz coordinates shown in Figure Q5c and indicate the orientation of vectors E, H, S, and ^;

(vi) What is the average power density SAV of this wave?

14 marks

[Total: 20 marks]

Q6. (a)       Show  that  the  input  impedance  of  a  transmission  line   (with

characteristic impedance ZO and which is terminated with a load ZL) is equal to ZO when ZL = ZO . 4 marks

(b)       A distortionless line satisfies the condition R’C’ = L’G’ .  If such a

transmission line has R’ = 2 Ω/m; L’ = 200 nH/m; G’ = 800 µS/m; and C’ = 80 pF/m, determine:

(i)   The characteristic impedance, ZO, of the line

(ii)  The attenuation constant, α, of the line (you may assume that R’ = α ZO )

(iii) The propagation velocity of a signal if the dielectric medium of the line has a relative permittivity of 2.5 12 marks

(c)     If a 10 V pulse (with a pulse width of 10 μs) were to be injected into the  above-mentioned  transmission  line  that  is  100  m  long  and terminated in its characteristic impedance, write down the expression you would use to predict the magnitude of the pulse at the end of the line.  Hence, evaluate this magnitude. 4 marks

[Total: 20 marks]