Electrical power systems usually cover large geographical areas and transmission facilities, that are incessantly increasing. These power systems when exposed to different environmental conditions may cause severe faults to occur on the existing system. In this paper, the need for transposing the lines for analysing the faults under phase and sequence frame of reference has been described. Currents flowing in any one conductor will induce voltage drops in the other successive conductors and these may be unequal even though the currents are balanced which is highly objectionable. In order to minimize the effect of line unbalance, there is a chance of interchanging the conductor positions at their regular intervals along the line, termed Transposition. The objective of this paper is to show the effect of transpositions in producing equal series self and mutual impedances in the phase and sequence frame of reference for a chosen 400 kV, double circuit, single ground wire tower configuration. It is also shown that, by applying nine transpositions technique, the effect of mutual sequence coupling between the two circuits is eliminated completely and balanced phase impedance matrix of 6X6 is obtained. The calculations of overhead lines for different tower configurations was carried out using digital computer program MATLAB and results obtained conventionally shows an excellent resemblance in obtaining balanced phase and sequence impedance matrices. Thus, the same simulation can be used for any tower configuration.