A Graph-Theoretic Approach to Assess the Power Grid Vulnerabilities to Transmission Line Outages

The outages and power shortages are common occurrences in today's world and they have a significant economic impact. These failures can be minimized by making the power grid topologically robust. Therefore, the vulnerability assessment in power systems has become a major concern. This paper considers both pure and extended topological method to analyse the vulnerability of the power system to single line failures. The lines are ranked based on four spectral graph metrics: spectral radius, algebraic connectivity, natural connectivity, and effective graph resistance. A correlation is established between all the four metrics. The impact of load uncertainty on the component ranking has been investigated. The vulnerability assessment has been done on IEEE 9-bus system. It is observed that load variation has minor impact on the ranking.