The application of Carson's equation to the steady-state analysis of distribution feeders

One of the primary purposes of performing the steady-state analysis of a distribution feeder is to determine the voltages at every node. Because these voltages are a function of the line voltage drops it is critical that the line impedances used are as exact as possible. In 1926 John Carson developed equations that would determine the self and mutual impedances of any number of overhead or underground conductors taking into account the effect of ground [1]. In recent years the application of Carson's equation has become the standard for the computation of line impedances. Because Carson's equation results in an infinite series, approximations have been made to ease in the computation of the impedances. The purpose of this paper is to investigate some of the more common approximations and determine what, if any, errors are made.