Calculation of electrical parameters for short and long polyphase transmission lines

A previous paper described the solution of travelling-wave phenomena in polyphase systems by the use of matrix methods, in which the characteristics were defined in terms of generalised matrixes. The present paper shows how the basic matrixes of the conductor system are derived, taking into account the effect of conductor geometry, conductor internal impedance and the earth-return path. These basic matrixes define the parameters of electrically short lines, and it is shown how they may be expressed in symmetrical-component form where conductor asymmetry is neglected. The theory for solving travelling-wave phenomena given in the previous paper is summarised, and it is shown how the general solutions may be manipulated in a form suitable for digital computation. A representative programme is described which can be used to calculate the parameters of both electrically short and long lines. A typical example of the application of the programme is given in which the numerical values for a line are computed, and these are compared with values which had been previously measured and calculated in a simplified form. This comparison shows the closer agreement between measured values and those obtained by the methods described in the paper. The paper concludes by considering the problems involved in taking into account the more complicated conditions of energisation and termination.