On the flat voltage profile of a transmission line

It is a well known idea as well as practice to install capacitor switching stations at proper points in an electrical grid to support the voltage. This idea is further exploited in respect of obtaining a flat voltage profile over a transmission line for specified terminal conditions. This paper aims to establish a mathematical formalism in designing the capacity of switching stations and the number of switching stations needed. The equations for the “voltage-sag” are originally derived for the general case of (n-1) number of capacitor switching stations causing `n´ sections of the transmission line, for any arbitrary terminal voltage conditions. A flatness index (FI) is defined and shown to be zero for the uncompensated line and unity for the ideally compensated line