I. Introduction
Today's electric power systems are very large and complex interconnected networks. It has been recognized that they are one of the most critical infrastructures, whose performance has tremendous effects on many aspects of our daily lives in today's society. This key role of the electric power grid poses difficult requirements of meeting acceptable security and reliability levels even during highly abnormal conditions. Such conditions may occur with very low probability but potentially have high impact, and the system must be sufficiently adaptive to minimize the adverse effects on equipment safety and to maintain the continuity of electricity service. It is practically impossible to design the system for serving customers in an uninterrupted way during any combination of extreme conditions, such as those created by the hard-to-predict large equipment failures or by the intended disabling of the key equipment. Because of this, various procedures are put in place to adjust the system when these events happen and to disconnect the service only where it is essential to do so to preserve the service to the rest of the customers. These procedures are currently a combination of system operator's actions, automated control, and automated system protection. This paper concerns, in particular, the problem of protection for transmission lines.