Re: Breakdown voltage in HV transmission lines (was: this was..)

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Original poster: "Dr. Resonance" <resonance-at-jvlnet-dot-com> 


Thanks for the data Antonio.  Very interesting.

Dr. Resonance


 >
 > Tesla list wrote:
 >  >
 >  > Original poster: "Dr. Resonance" <resonance-at-jvlnet-dot-com>
 >  >
 >  > Ed:
 >  >
 >  > I have always wondered how these long distance EHV lines avoid
producing
 >  > excessive corona.
 >  >
 >  > The cables do not appear to be very large in diameter --- perhaps an
inch or
 >  > two at best.  With that small radius and diameter, why don't they emit
 >  > tremendous corona?
 >  >
 >  > With corona inception potential around 67 kV per inch (30 kV/cm) they
should
 >  > be glowing a lot with their small diameters.  Especially in rainy
weather.
 >
 > The fundamental reason is because the wires are essentially straight.
 > Cylindric conductors donīt follow the same rule of spheres, where 30 kV
 > per cm of radius is enough to create corona.
 >
 > If you try to calculate the electric field at the surface of a long
 > wire that is at a given potential, the result is that that if the wire
 > has infinite length and is really straight, the breakdown voltage is
 > infinite. But real wires are always somewhat curved by gravity.
 >
 > I can use the field of a toroid implemented in the Inca program to have
 > an idea of what happens. Consider a ring of wire, with wire diameter of
 > 1 cm and varying major diameter. I list below the breakdown voltages
 > calculated by the program:
 >
 > Major diameter:
 > 1 cm:  15.0 kV (a ball with 1 cm of diameter)
 > 2 cm:  22.6 kV
 > 4 cm:  32.9 kV
 > 10 cm: 50.0 kV
 > 1 m:   95.2 kV
 > 10 m: 133.8 kV
 > 100 m: 169.8 kV
 > 1000 m: 203.9 kV
 >
 > The breakdown goes slowly to infinity as the radius of curvature
 > (half of the major diameter of the toroid) of the wire decreases.
 >
 > A bunch of wires results in a larger effective diameter of the wire,
 > and in greater breakdown voltage. I can still use the program to
 > evaluate this case.
 > Consider 4 wires with 1 cm of diameter disposed as a square with
 > distance between the centers of the wires of 4 cm.
 > A ring of this "wire" with distance from the center to the center
 > of the inner wires of 10 cm is described in the program as:
 >
 > * Toroidal conductor with 4 wires
 > C1 wire 50 0.1 0.02 0.005 0 360
 > C2 wire 50 0.1 -0.02 0.005 0 360
 > C3 wire 50 0.14 0.02 0.005 0 360
 > C4 wire 50 0.14 -0.02 0.005 0 360
 >
 > The breakdown voltage for this case results as 112.4 kV
 > For larger rings (also changing the distance from the center to the
 > center of the inner wires, that is approximately the radius of
 > curvature of the composite wire):
 > 0.5 m: 181 kV (compare with 95.2 kV with 1 wire)
 > 5 m:   288 kV (compare with 133.8 kV)
 > 50 m:  385 kV (compare with 169.8 kV)
 > 500 m: 478 kV (compare with 203.9 kV)
 >
 > So, it's not difficult to keep transmission lines at very high
 > potentials
 > without excessive corona at the wires. The most problematic areas are
 > the middle points between towers, where the radius of curvature is
 > maximum, and the suspension devices in the towers, where it's common to
 > see corona rings.
 >
 > Antonio Carlos M. de Queiroz
 >
 >
 >