Decay Length Estimation of Single-, Two-, and Three-Wire Systems Above Ground Under Hemp Excitation

Abstract

We analytically model single-, two-, and three-wires above ground to determine the decay lengths of common and differential modes induced by an E1 high-altitude electromagnetic pulse (HEMP) excitation. Decay length information is pivotal to determine whether any two nodes in the power grid may be treated as uncoupled. We employ a frequency-domain method based on transmission line theory named ATLOG-Analytic Transmission Line Over Ground to model infinitely long and finite single wires, as well as solve the eigenvalue problem of a single-, two-, and three-wire system. Our calculations show that a single, semi-infinite power line can be approximated by a 10 km section of line and that the second electrical reflection for all line lengths longer than the decay length are below half the rated operating voltage. Furthermore, our results show that the differential mode propagates longer distances than the common mode in two-and three-wire systems, and this should be taken into account when performing damage assessment from HEMP excitation. This analysis is a significant step toward simplifying the modeling of practical continental grid lengths, yet maintaining accuracy, a result of enormous impact.

Plane Wave Coupling to a Transmission Line Above Ground with Terminating Loads

“…[2,8,9,23] is appropriate for wires near the ground or buried below the ground. However, we have found that plays a negligible role in aerial lines [13] (which is consistent with the broad applicability of the terminating load capacitance). The external source term for plane wave incidence at oblique angle with respect to z is where .…”

“…The case with open circuits at both ends of the line is shown in Figure 2(a). The dotted curves have idealized open circuits at the ends of the transmission line, whereas the solid curves have the preceding terminating capacitive loads in (13). Notice that the phase shift caused by the terminating capacitive loads results in alignment of the curves in phase with the full wave simulations given by the The case with short circuits at both ends of the line is shown in Figure 2(b).…”

“…In this paper we investigate transmission line models for an aerial wire above a conductive half space. Many contributions have modeled such situations [1][2][3][4][5][6][7][8][9] and have provided powerful formulas for the ground impedance and admittance for aerial and buried conductors, as well as multiple-wire modes and high-frequency modes [5,[10][11][12][13].…”

“…For an open circuit termination, since the distributed admittances of the transmission line model for dense lower dielectric half spaces are typically dominated by the air region above the conductive half space (in other words, the ground admittance has negligible effects for aerial lines [13]), the lumped load capacitance and air conductance elements will have reasonably broad applicability. We include an additional term here in the load capacitance [15].…”