User:Dsurya1/sandbox

Motivation:
The following is a simplified presentation about the concept of electrical power transmission line parameters and their calculation. I have taught this topic to engineering students pursuing under graduate program in academic institutions and also to practicing engineers in their training, orientation or refresher programs. Nearly all the text books present the topic of inductance and capacitance of transmission lines starting with the definition of flux linkages per unit current and charge per unit potential difference respectively and expressions for the inductance and capacitance formulae are derived. These parameters ultimately depend on the diameter of the conductors and their geometry or how they are arranged and the distance between them. The expressions for inductance and capacitance of transmission lines involve logarithmic terms and vary very slowly when the size of conductor and distances are changed. In transmission lines the size of conductors used and distances between conductors are standardized depending on the voltage. Hence it is quite in order to assume values corresponding to standard distances and conductor sizes and there is no need to calculate these parameters for the actual size and distance between conductors adopted which may vary slightly from the standard values. In this case the actual values will not differ from the standard values and the same can be adopted without any loss of accuracy. Even though the above facts are mentioned in all the books, it is not somehow emphatically brought out with the result ,when the student is asked “On what factors the parameters of transmission line depend?”, The standard reply usually is “Voltage and load or load current”. In fact this is the experience of the author also, and the students are unable to assume suitable values of inductance and capacitance, if not given. This is the motivation for putting on the web for wider dissemination to all concerned.

Introduction:
A transmission line has four parameters. they are resistance, inductance, capacitance and shunt conductance. These are uniformly distributed along the line. Resistance and inductance are in the series path and capacitance and conductance are in shunt path. We assume the three phase system as balanced under normal operating conditions and at generation  transmission and distribution level  this is true and the extent of unbalance never exceeds 5 %. Hence power systems are always represented as equivalent single phase system showing one of the phases and neutral. Since in balanced systems the same current flows in all the three phases and the phase voltages are same, it is enough to show any one phase only. Inductance and inductive reactance:

Inductance is defined as flux linkages per unit current. Flux linkages are defined as flux multiplied by number of turns. The number of turns for transmission and distribution networks is one turn; hence the flux linkages and flux are numerically same even though the units are different. The flux depends on the permeability. Permeability is basically the flux that can be established in any medium for a given current. Generally the permeability of all nonmagnetic materials is very nearly unity. For example for para magnetic materials like aluminum and air etc it is slightly more than unity in the range of 1.0003 to 1.0005.where as for dia magnetic materials like copper etc, it is slightly less than unity in the range of 0.995 to .998. For ferromagnetic materials like iron, cobalt, nickel and their alloys it is in the range of 700 and above upto 1000. In the transmission line work we use copper, aluminum and ACSR. In the ACSR conductors the amount of steel used is very small and can be neglected. The following list summarises the relative permeability of various materials of interest to power engineers, Air                      1.00000037 Copper                   0.999994 Aluminum                 1.000022 Iron                     > 800.

Relative permeability is the ease which magnetic flux can be established for a given current. Alternatively materials with higher relative perm abilities are better ’conductors’ of flux. Otherwise as far as magnetic flux is concerned it does not matter whether it is air, copper aluminum,. Even though resistance of a wire is defined as ratio of voltage to current, it can be deduced to depend upon the conductivity of the material ( ) of the wire and its length (l) and cross section (a) and given by the following expression R =  l /a   ohms. Similarly even though the inductance is defined as flux per unit current (no of turns being one) it finally depends on the permeability of the medium and the geometry i.e. the number and diameter of the conductors and their arrangement. Here the medium in which the flux established is having almost the same value of permeability whether aluminum, copper, or air which is between the conductors. Thus the inductance of the transmission line is independent of the voltage of the line and the current flowing in the line.