For a graph \(G(V,E)\) with size \(n\) , and for any edge \(f \in E\) , a set \({S}{^{\prime}}-E\) is said to be an power edge dominating set of graph \(G\) if each edge \(g \in E-{S}{^{^{\prime}}}\) is dominated by the following rules: (i) an edge \(f\) in \(E\) is in power edge dominating set (in short PEDS), then it dominates itself and dominates all the adjacent edges of \(f\) (ii) an observed edge \(h\) in \(E\) has \(m\) > 1 adjacent edges and if \(m\) – 1 of these edges are observed earlier, then the remaining non- observed edge is also observed by \(h\in E\) . The minimum cardinality of a power edge domination number of \(G\) is denoted by \({\gamma {^{\prime}}}_{ped}\) ( \(G\) ). In this paper we introduce a new concept namely Power Edge Domination and also calculated the power edge domination number of some special graphs and the Shadow graph on certain graphs.