Theory of parallel grounded wires and production of high frequencies in transmission lines

The overhead grounded wire is used for three purposes: lightning protection, mechanical support for towers, and a test circuit. The functions of the grounded wire are subdivided into at least four categories: First, the vertical grounded wire; second, the lightning rod extending above the ground; third the electrostatic induction in the horizontally situated wires, and fourth, electromagnetic induction. The vertical wire prevents splitting of the poles. The lightning rod is of mooted desirability. The electrostatic induction for a given cloud on wires under various conditions is worked out in this paper. There is given also the protective values of overhead grounded wires in different positions and in different numbers. The effects of electromagnetic inductions have been taken into account. Theory is given to show that the grounded wire introduces into the main wave of induced lightning surge a superposed high frequency of electromagnetic induction. The several factors to be taken into account in the process of determining the protective value of a grounded wire are as follows: 1. Strength of electric field in the neighborhood of the line wires. 2. The direction of the gathering charge in the cloud, that is the path of the discharge relative to the line, parallel or perpendicular to the line before it turns vertically downward to the earth. 3. The screening effect obtained by the use of several wires, with and without grounded wires. 4. The initial momentary potential induced on a wire at the instant the cloud discharges to earth. 5. An instant after the lightning discharge has taken place, the sudden increase in capacitance between the power wire and the adjacent parallel grounded wire. 6. The effect of the number and location of parallel grounded wires. 7. The effect of electromagnetic induction between the horizontal part of the grounded wire and the parallel power wires, in which the energy of the lightning charge on the grounded wire is more or less transferred to the power wire, instead of being dissipated in the earth. High frequencies are produced in this transformation. 8. The gradual transference of the charge which travels along the power wire to the successive sections of the grounded wire and its dissipation in the earth. A cloud charge is chosen of such value as to produce corona potential on a No. 000 B. & S. wire, strung at a height of 1000 cm. (33 ft.) above the surface of the earth. This storm cloud is used as a standard in all cases for comparison. The induced voltage on any wire by lightning is directly proportional to the height of the wire above the earth. The induced quantity is not quite proportional due to the variations in the capacitance of the wire at different heights. For heights between 30 and 60 ft. (9.1 and 18.2 m.), however the quantity can be considered as approximately proportional to the height. The quantity induced on the wire is only slightly affected by the diameter of the wire. This leads to the conclusion that a small grounded wire is nearly as effective as a more expensive large one. The theory is given to show that even on a non-grounded circuit a charge can be induced by a cloud and produce practically the same potentials as when the circuit is grounded. The only exception is that of circuits of short length. The instantaneous value of induced potential on a circuit is independent of the number of wires used. Using a greater number of wires reduces the quantity per wire but does not decrease the instantaneous value of the potential at the instant the cloud discharges to earth. Even the grounded wire may take the full potential and give no relief at the first instant. Whether it does or not depends upon how quickly the discharge takes place from cloud to earth, and how frequently along the line the grounded wire is earthed. There is, however, a screening of electrical energy by increasing the number of power wires. In other words, each surge has less energy although it has not initially less potential. There is given a table of the reduction of quantity per wire as the wires increase in number from one to seven. The two factors in the electrostatic protection of the overhead grounded wire are screening and increase of capacitance of line wires. The presence of the grounded wire reduces the quantity induced on each of the power wires and incidentally after the cloud discharges to earth the grounded wire takes over part of the charge from the power wires and in taking it the capacitance of each power wire is increased. Therefore, with the same quantity of electricity the potential is reduced by this increase in capacitance. The protection afforded by one parallel grounded wire can be expressed as a very simple equation. The protection for each power wire can be calculated entirely independent of how many there are. The general equation to express the protection afforded by two parallel grounded wires is more complex but if the two grounded wires are placed far apart their protective values can, with only a small error, be calculated independently. As the charge runs to earth on the grounded wire at the instant the cloud discharges, it induces on the line wire by electromagnetic induction a considerable voltage in the usual conditions of the overhead grounded wire with low resistance in the earth connections and from which part of the protection afforded by the grounded wire is lost by the fact that the energy oscillates in the ground circuit and is transferred to the power wire. The natural frequency of this wave train is found by multiplying 183,000 miles (300,000 km.) per second by the number of earth connections per mile of grounded wire. The frequency is usually over a million cycles per second. Traveling waves are more or less absorbed as they pass each successive loop of the grounded wire, according to the value of the resistance of earth connection. In any case an endeavor should be made to have the resistance in the earth connection somewhere near the critical damping value. This prevents initial oscillations in the ground circuit and also increases the rate of absorption of a traveling wave. A slight amount of high frequency is produced in a circuit by transposition of power wires. This may be of the order of 2 per cent to 5 per cent of the main voltage. The general deductions for practical use taken from the theory given are as follows: From a theoretical standpoint a single grounded wire should be placed as near as practicable to the power wire in order to get the greatest electrostatic protection. The grounded wires are a little more effective when placed above a power wire than when placed below it. In installing overhead grounded wires the greatest advantage can be obtained by keeping the overhead grounded wires as far apart as possible, that is to say, installed, as far as practicable on opposite sides of the power wires. The protective value of the second wire will then have its full maximum possible value. Also from the electromagnetic standpoint, the two wires should be placed, so far as practicable, on opposite sides of a power wire in order to reduce to a minimum the transfer of surge energy to the power wire. The most practicable condition of protection by four grounded wires is to use the four wires in a rectangular formation which gives the widest separation. Naturally two will be above the power wires and the other two will be either below or at each side about on a level with the two lowest power wires. The mechanical conditions of installation will dictate where these wires will be hung and it is necessary to follow the rule to make the distances between the several grounded wires as great as the conditions will permit and still keep the grounded wires as near a power wire as safe mechanical clearance will justify.