Capacitance of Single Phase Line

Capacitance between the two conductors of a two wire line is the charge on the conductor per unit of potential difference between them. Capacitance of the line per unit length is given by,

                                      C = q/v   F/m

       The capacitance of single phase line is obtained by substituting in above equation v in terms of q.

      
Consider a single phase overhead transmission line consisting of two conductors 'a' and 'b' which are separated by a distance of D in air as shown in the Fig. 1. The charges on each conductors are respectively +q and -q coulombs per meter length.

       The voltage V_ab between the two conductors can be obtained by finding the potential difference between the two conductors of the line. Firstly let us find the voltage drop due to charge q on conductor a and then finding voltage drop due to charge -q on conductor b. Then by using principle of superposition the voltage drop between conductor a and b is obtained by adding the voltage drops caused by each charge alone.

       The voltage drop V_ab is therefore given by,

       The capacitance between the conductors is given by,

        For air ε_r = 1

       If we take        r_a =  r_b  =  r then

       If it is required to find the capacitance between one of the conductors and the neutral point then it is given by,

       The idea of capacitance to neutral is shown in the Fig. 2.

Fig. 2

       The equations derived so far related to the capacitance are based on the assumption of uniform charge distribution over the surface of the conductor. In presence of other charges, the distribution will not be uniform and the equations which are derived will not give accurate results. However the nonuniformity of charge distribution can be neglected in case of overhead lines as only 0.010% of error is caused for a close spacing of ratio of D/r = 50.

        If instead of a solid round conductor, we have a stranded conductor then the above equation will produce error slightly. The error will be small as only the field very close to the surface of the conductor is not the same as the field at the surface of cylindrical conductor. The outside radius of conductor is used for evaluating capacitance.

       If we are having the value of then capacitive reactance can be easily obtained.

       Permittivity of free air taken as unity.

       The above expression gives X_C for 1 m of line since capacitive reactance is in parallel along the line,  X_C is divided by the length of line in meters to obtain the value of X_C in ohms to neutral for entire length of line. Standard tables are available for outside diameters of most widely used sizes of ACSR.