Impedance and Admittance Formulas for a Multistair Model of Transmission Towers

This article discusses formulas for the surge/ characteristic impedance of vertical conductors. Calculated results of the surge impedance are compared with measured results on vertical conductors and transmission towers. The accuracy of the available time-domain formulas is not satisfactory except for Hara’s formulas, while the frequency-domain formulas show satisfactory accuracy. A two-stair model representing a nonuniform transmission tower is investigated based on ABCD parameters, and an approximate characteristic impedance of the nonuniform tower is derived. The circuit-theory approach and finite-difference time-domain (FDTD) computed results using the two-stair model are shown to give better agreement with measured results on UHV and 500-kV towers than those obtained using a single-conductor approximation (uniform line). The FDTD computed results clearly show the position-dependence of line parameters. Existing timedomain formulas describe only the surge impedance seen from the tower top or from the tower base, and thus, are not applicable to a lightning shielding failure studies involving back-flashover, which require the knowledge of the surge impedances of the upper, middle, and lower parts of the tower.