Assignment  1

Electric Fields, Dielectrics, Generation and Measurements of HVDC & HVAC

1) For a coaxial cylindrical single-phase cable with an inner cable radius "r', outer grounded sheath radius "R' and an applied cable voltage "V", prove that the optimum value for the Field Efficiency Factor is 0.582

2) Draw a detailed neat sketches for the following;
a. 3-Stages Cascaded Transformer
b. 5-Stages Cockcroft-Walton Voltage Multiplier
c. Van De Graaff Generator
d. Capacitors and nodes no-load building up voltage waveforms for the first 2 stages of n-stages Cockcroft-Walton Voltage Multiplier

3) A dielectric cube of 5 cm edges and a volume and surface resistivity of 5*10³ Ω.m and 10¹³ Ω, respectively, has been placed between two metal electrodes connected to 2 kV DC voltage. Determine the residual leakage current through the cube and the specific power loss in the cube assuming that the surface leakage current flows in through the top surface only.

4) A 10-stages Cockcroft-Walton voltage multiplier is supplied by a single-phase HV transformer operating at 150 Hz with a secondary voltage of 120 kV. All capacitors of the voltage multiplier have equal capacitances of 0.05 μF. If the load current is 6 mA, calculate,
a. The DC output voltage,
b. The percentage voltage regulation
c. The optimum number of stages required to minimize the voltage regulation and calculate the corresponding voltage drop if the capacitance of the first stage of the oscillating column changed to 0.1 μF while other capacitances remains at 0.05 μF.

5) A 2-stages Cockcroft-Walton voltage multiplier is supplied by a single-phase HV transformer operating at 1 kHz with a secondary voltage of 10 kV. If the capacitances of the top stage C₁= C₁' = 0.05 μF while the capacitances of the lower stage C₂ = C'2 = 0.075 pF. If the load current is 10 mA,

a. Draw a neat sketch of the multiplier

b. Calculate the DC output voltage, the total voltage drop, the total ripple voltage and the total percentage voltage regulation

c. Repeat part b if C₁ = C1' = C2 = C2' = 0.05 μF.

6) A HV testing setup, shown in figure, is used to test the flashover and measure the flashover voltage of an insulator. The input voltage "V_s" increased gradually until flashover occurred at V_s= 330 V. The power (testing) transformer has turns (transformation) ratio of 1:100.

a. What are the reading of the voltmeters (assumed uncalibrated) at the instant of flashover it

i The resistance potential divider has R₁= 199 MΩ and R₂ = 1MΩ.

ii The capacitance potential divider has C₁= 1μF and C₂ = 99 μF.

iii The potential transformer has turns ratio of 300:1.

b. What should be the sphere gap separation distance at the instant of flashover if the sphere gap has the following characteristics at N.T.P. conditions

7) A series resonant transformer circuit with a 15 kVA, 230 V/50 kV, 50 Hz feed transformer is used to generate HVAC waveform to test a cable of 5000 pf at 200 kV. The feed transformer has a pu resistance and pu reactance of 2.5% and 6%, respectively. Neglect the dielectric loss of the cable. If the pu reactor's resistance is 2.5%, calculate the required series inductance of the reactor, the quality factor of the reactor, and the primary input voltage of the feed transformer.