INDUCTANCE OF THREE PHASE TRANSMISSION LINES

Inductance is the property in an electric circuit where a change in the electric current through that circuit induces an electromotive force(Emf) that opposes the change in current

In electrical circuits, any electric current, i, produces a magnetic field and hence generates a total magnetic flux Φ, acting on the circuit. This magnetic flux, due to Lenz's law tends to act to oppose changes in the flux by generating a voltage (a back EMF) in the circuit that counters or tends to reduce the rate of change in the current. The ratio of the magnetic flux to the current is called the self-inductance, which is usually simply referred to as the inductance of the circuit. To add inductance to a circuit, electronic component called inductors are used, which consist of coils of wire to concentrate the magnetic field.

The term 'inductance' was coined by Oliver Heaviside in February 1886. It is customary to use the symbol L for inductance, possibly in honour of the physicist Heinrich Lenz

The unit of inductance is the henry (H), named after American scientist and magnetic researcher Joseph Henry 1 H = 1Wb/A.

Definitions

The quantitative definition of the (self-) inductance of a wire loop in SI units ( webers per ampere known as henries is

where L is the inductance, Φ denotes the magnetic flux through the area spanned by the loop, Ni is the current in amperes. The flux linkage thus is is the number of wire turns, and

Properties of inductance

Taking the time derivative of both sides of the equation NΦ = Li yields:

In most physical cases, the inductance is constant with time and so

By Faraday's law of Induction we have:

where is the Electromotive force (emf) and v is the induced voltage. Note that the emf is opposite to the induced voltage. Thus:

or

Bundled conductors

At extra-high (EHV), that is, voltages above 230 kV, corona with its resultant power loss and particularly its interference with communications is excessive if the circuit has only one conductor per phase. The high-voltage gradient at the conductor in the EHV range is reduced considerably by having two or more conductors per phase in close proximity copared with the spacing between phases. Such a line is said to be composed of bundled conductors. The bundle consists of two, three or four conductors. The three conductor bundle usually has the conductors at the vertices of an equilateral triangle, and the four conductor bundle usually has its conductors at the corners of a square. The current will not devide exactly between the conductors of the bundle unless there is a transposition of the conductors within the bundles, but the difference is of no practical imporatnce, and the GMD method is accurate for caculations.

Reduced reactance is the equally important advantage of bundling. Increacing the number of conductors in the bundle reduces the effects of corona and reduces the reactance. The reduction of reactance results from the increased GMR of the bundle. The calculation of GMR is, of course, exactly the same as that of a stranded conductor. Each conductor of a two-conductor bundle, for instance, is treated as one strand of a two-strand conductor. If we let indicate the GMR of a bundle conductor and the GMR of the individual conductors composing the bundle.

For a two-strand bundle

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For a three-strand bundle

=

For a four-strand bundle