Presentation on theme: "S High Voltage Engineering S Suurjännitetekniikka"— Presentation transcript:
1 S-18.3150 High Voltage Engineering S-18.3146 Suurjännitetekniikka Exercise 2S High Voltage EngineeringS Suurjännitetekniikka
2 Question 1The figure depicts average breakdown voltage (U50) as function of gas pressure (p) for a coaxial SF6 insulator. The structure was originally designed for 6 bar. However, it became apparent that it wasn’t economically efficient to design the system for such high pressures. For this reason, pressure was decreased to 4 bar. Design the structure again so that the breakdown voltage and the ratio D/d remains the same. What are the new D and d parameters?5010015020025030035040045012345678p [bar]U50 [kV]dDd=20 mmD=54 mm
3 Average breakdown voltage: 450Average breakdown voltage:400350(original)300250U50 [kV]200(reduced)150100We want to increase this to equal original Ub(6bar) by altering dimensions5012345678p [bar]Coaxial Geometry:dDd=20 mmD=54 mm
4 Denote d´= new inner conductor diameter Breakdown field strength, p = 4 bar:Denote d´= new inner conductor diameterWe want the same breakdown voltage at 4 bar as with original 6 barD/d ratio remains same (can use original dimensions)
5 Fixed ratio: New outer diameter: 6 bar: D = 54 mm d = 20 mm ∆ = 34 mm Although, the ratio D/d remains the same, distance between electrodes has increased.Originally, breakdown at 4 bar would have occurred at 280 kV. With the new increased distance, voltage has to increase to 370 kV for breakdown to occurBreakdown voltage level is maintained the same with new dimensions and reduced pressure.
6 Question 2Calculate the onset of partial discharge for the resin test object when breakdown voltage in the cavity obeys Paschen’s law. Pressure in the cavity is 1013 mbar and its dimensions are 1 mm x 5 mm (h x w). Both cavity and the test object are cylindrical. Calculate the apparent charge and consumed energy of the discharge.0,11101000,0010,01pd [bar∙mm]U50 [kV]
7 Three-Capacitance Model: ha3 mm4=ref = 30 mmf = 5 mmhcCbCcCaVoltage is distributed inversely proportional in relation to capacitance:
8 Paschen’s Law: Ub = f(pd) 0,11101000,0010,01pd [bar∙mm]U50 [kV]Paschen’s Law: Ub = f(pd)p =1013 mbar, d =1 mm Inception voltage of discharge in cavity uci = 4.5 kVInception voltage (applied voltage required to ignite discharge in cavity) ui = 1.5∙ uci = 6.75 kV ≈ 6.8 kV
9 Calculating apparent charge: Discharge is much faster than the feeding circuit (external circuit is too slow to react to discharge circuit can be removed)During discharge, from the point of view of Cc representing the capacitance in the void, the rapid change in voltage is distributed between the series connection of Cb and Ca which are now in parallel with Cc~CbC´aCc∆ ucCalculating apparent charge:Extinction voltage = 0 VAssumingApparent charge:
10 Consumed energy during discharge: Calculating energy:where q = 1.6 nC and u = ui = 6.8 kVConsumed energy during discharge:
11 Question 3The system in question 2 has 50 Hz alternating voltage of kVRMS. Pressure in the cavity is 1013 mbar. Breakdown voltage in the cavity obeys Paschen’s law and the extinction voltage is 0.5 kV. Draw the voltage waveform and calculate the steady state partial discharge frequency.
12 Applied voltagewhere U = 6 kVVoltage over cavity:Inception voltage:Extinction voltage:
13 Number of discharges per period · 50 Hz 8u(t)uc(t)6+uci42+uce-uce-2-uci-4-6Discharge frequencyNumber of discharges per period · 50 Hz== 4 · 50 Hz = Hz-8
14 Question 4The figure shows a bushing (feed-through insulator). Cylinder 1 is the bushing conductor. Insulation layers 2, 3, and 4 have thin metal sheets between them to improve dielectric strength. Design lengths l2 and l3 so that maximum field strength in both sheets is of the same magnitude. What is this maximum field strength value?l4321DD1 = 20 mm D2 = 34 mmD3 = 48 mm D4 = 62 mmL4 = 140 mm U14 = 30 kV
15 Electric field for a cylinder: UlElectric field for a cylinder:Design lengths l2 and l3 so that maximum field strength in both sheets is of the same magnitudel4321D1Dl4 and D1…4 are given: