Mathematical Model of Ice Melting on Transmission Lines

Abstract

During ice storms, ice forms on high voltage electrical lines. This ice formation often results in downed lines and has been responsible for considerable damage to life and property as was evidenced in the catastrophic ice storm of Quebec recently. There are two main aspects, viz., the formation of ice and its timely mitigation. In this paper, we mathematically model the melting of ice due to a higher current applied to the transmission wire. The two dimensional cross-section contains four layers consisting of the transmission wire, water due to melting of ice, ice, and the atmosphere. The model includes heat equations for the various regions with suitable boundary conditions. Heat propagation and ice melting are expressed as a Stefan-like problem for the moving boundary between the layers of ice and water. The model takes into account gravity which leads to downward motion of ice and to forced convection of heat in the water layer. In this paper, the results are applied to the case when the cross-sections are concentric circles to yield melting times for ice dependent on the increase in intensity of the electrical flow in the line.