Vulnerability analysis in power systems is a key issue in modern society and many efforts have contributed to the analysis. Recently, complex networks metrics, applied to assess the topological vulnerability of networked systems, have been used in power grids, such as the betweenness centrality. These metrics may be useful for analyzing the topological vulnerability of power systems because of a close link between their topological structure and physical behavior. However, a pure topological approach fails to capture the electrical specificity of power grids. For this reason, an extended topological method has been proposed by incorporating several electrical features, such as electrical distance, power transfer distribution, and line flow limits, into the pure topological metrics. Starting from the purely topological concept of complex networks, this paper defines an extended betweenness centrality which considers the characteristics of power grids and can measure the local importance of the elements in power grids. The line extended betweenness is compared with the topological betweenness and with the averaged power flow on each line over various operational states in the Italian power grid. The results show that the extended betweenness is superior to topological betweenness in the identification of critical components in power grids and at the same time could be a complementary tool to efficiently enhance vulnerability analysis based on electrical engineering methods.