Characteristic Impedance of Power Lines with Ground Wires

In power lines, shield wires are passive wires which are periodically grounded, and their main role is to intercept direct lightning strokes which could cause overvoltages higher than the line lightning withstand level. They are installed above the phase conductors, and, if properly placed, assure lightning protection. It must be noted that this direct protection is successful on power transmission lines, which are usually characterized by values of critical impulse flashover voltage (CFO) much higher compared to distribution lines. The direct stroke performance of distribution lines is practically unaffected by the presence of shield wires, since, in case of a direct strike, a backflashover will occur in most of the cases due to the ground potential rise. In distribution lines shield wires can still play a role since, thanks to their coupling with phase conductors, can reduce the induced voltages produced by indirect lightning. Many studies have dealt with the effectiveness of shield wires on medium and low voltage overhead distribution lines (e.g., in (1)-(7)) and the reduction in terms of induced overvoltages, compared to the results obtained for unshielded lines (e.g. (8)-(10)), is significant; the authors too have deeply investigated the problem of lightning induced overvoltages on unshielded lines (11)-(16). In order to evaluate the induced overvoltages on shielded lines, and to estimate the role of the periodical grounding in the overvoltage mitigation, an important step is the evaluation of the characteristic impedance of the power line. Although periodical grounding of shield wires significantly modifies the characteristic impedance, this aspect is usually underestimated or neglected. In this paper, by making use of the transmission line (TL) approximation (17), we examine the problem of a multiconductor transmission line (MTL), with one conductor periodically grounded, as shown in Fig. 1, and we will show two ways to compute the characteristic impedance. The examined MTL has m-1 non- grounded wires, the m-th wire is the grounded one. The paper is organized as follows: we will first formulate the problem in terms of a Riccati equation, then two different solution methods will be shown along with some numerical results, finally conclusions will be presented.