Abstract
In this paper, it is shown that Carson's equation can still be applied for the calculation of the series reactance of transmission lines with no ground return current as well as the one with ground return. It is proved in the following method. First two voltage drop equations for three-phase three wire transmission line are derived, one without considering ground return and the other using Carson's equation. The impedance matrix of the two equations are different from each other. But if we put the condition of zero ground current, $I_a+I_b+I_c=0$, those two equations becomes the identical equations. Therefore even a transmission line is not grounded, its line parameters can still be obtained using the Carson's equation. It has been confused whether or not Carson's equation can be used for an ungrounded system. It is because where ever Carson's equation is shown in the book, it also says that the system has ground return current paths as a premise. It is also verified with EMTP studies on the test circuit.
