SKIN EFFECT – BASIC DEFINITION AND TUTORIALS

What is skin effect?

Real, or ohmic, resistance is the resistance offered by the conductor to the passage of electricity. Although the specific resistance is the same for either alternating or continuous current, the total resistance of a wire is greater for alternating than for continuous current.

This is due to the fact that there are induced emfs in a conductor in which there is alternating flux. These emfs are greater at the center than at the circumference, so the potential difference tends to establish currents that oppose the current at the center and assist it at the circumference.

The current is thus forced to the outside of the conductor, reducing the effective area of the conductor. This phenomenon is called skin effect.

Skin-Effect Resistance Ratio. The ratio of the A.C. resistance to the D.C. resistance is a function of the cross-sectional shape of the conductor and its magnetic and electrical properties as well as of the frequency.

For cylindrical cross sections with presumed constant values of relative permeability and resistivity, the function that determines the skin-effect ratio is

where r is the radius of the conductor and f is the frequency of the alternating current. The ratio of R, the A.C. resistance, to R0, the D.C. Resistance.

Skin Effect On Steel Wires and Cables.

The skin effect of steel wires and cables cannot be calculated accurately by assuming a constant value of the permeability, which varies throughout a large range during every cycle. Therefore, curves of measured characteristics should be used. See Electrical Transmission and Distribution Reference Book, 4th ed., 1950.

Skin Effect of Tubular Conductors.

Cables of large size are often made so as to be, in effect, round, tubular conductors. Their effective resistance due to skin effect may be taken from the curves of Sec. 4. The skin-effect ratio of square, tubular bus bars may be obtained from semiempirical formulas in the paper “A-C Resistance of Hollow, Square Conductors,” by A. H. M. Arnold, J. IEE (London), 1938, vol. 82, p. 537.

These formulas have been compared with tests. The resistance ratio of square tubes is somewhat larger than that of round tubes. Values may be read from the curves of Fig. 4, Chap. 25, of Electrical Coils and Conductors.

THE TRANSMISSION AND DISTRIBUTION SYSTEM BASIC AND TUTORIALS

Like any other industry, the electric power system may be thought of as consisting of three main divisions:

1. manufacture, production or generation, cogeneration,
2. delivery or transmission and distribution,
3. consumption.

The figure below show a typical transmission and distribution system in both pictorial and block diagram forms. Although geographical difficulties, demand variances, and other reasons may make for minor differences in some transmission and distribution systems, the voltages chosen here are pretty typical.

This is what happens to electricity between the generator and a home, office, store, or factory. There are many definitions of transmission lines, distribution circuits, and substations specifying distinctions between them.

However, none of these definitions is universally applicable. To give some idea of where one ends and the other begins: Transmission may be compared to bulk delivery of a commodity from factory to regional depots; subtransmission from the depot to central area warehouses; primary distribution from area warehouse to local wholesale vendors; secondary distribution from the vendors to local stores; services from store to consumer.

In the pictorial rendition, note that the generator produces 20,000 volts. This, however, is raised to 138,000 volts for the long transmission journey. This power is conducted over 138,000-volt (138 kV) transmission lines to switching stations located in the important load area served.

These steel tower or wood frame lines, which constitute the backbone of the transmission system, span fields and rivers in direct cross country routes. When the power reaches the switching stations, it is stepped down to 69,000 volts (69 kV) for transmission in smaller quantities to the substations in the local load areas. (In some cases it might be stepped down to 13,800 volts [13.8 kV] for direct distribution to local areas.)

Transmission circuits of such voltages usually consist of open wires on wood or steel poles and structures in outlying zones (along highways, for example) where this type of construction is practicable.

Other transmission-line installations can provide an interchange of power between two or more utility companies to their mutual advantage. Sometimes, in more densely populated areas, portions of these transmission lines may consist of high-voltage underground systems operating at 69,000, 138,000, 220,000, 345,000, 500,000, and 750,000 volts.

At the substations, the incoming power is lowered in voltage for distribution over the local area. Each substation feeds its local load area by means of primary distribution feeders, some operating at 2400 volts and others at 4160 volts and 13,800 volts or higher.

Ordinarily, primary feeders are one to five miles in length; in rural sections where demands for electricity are relatively light and scattered, they are sometimes as long as 10 or 12 miles. These circuits are usually carried on poles; but in the more densely built-up sections, underground conduits convey the cables, or the cable may be buried directly in the ground.

Distribution transformers connect to the primary distribution lines. These transformers step down the primary voltage from 2400 volts, 4160 volts, or 13,800 volts, as the case may be, to approximately 120 volts or 240 volts for distribution over secondary mains to the consumer’s service.

The lines which carry the energy at utilization voltage from the transformer to consumer’s services are called secondary distribution mains and may be found overhead or underground. In the case of transformers supplying large amounts of electrical energy to individual consumers, no secondary mains are required.

Such consumers are railroads, large stores, and factories. The service wires or cables are connected directly to these transformers. Transformers may also serve a number of consumers and secondary mains; they are located in practically every street in the area served by utility companies.

Services and meters link the distribution system and the consumer’s wiring. Energy is tapped from the secondary mains at the nearest location and carried by the service wires to the consumer’s building.

As it passes on to operate the lights, motors, and various appliances supplied by the house wiring, it is measured by a highly accurate device known as the watt-hour meter. The watt-hour meter represents the cash register of the utility company.