Complex network study pointed out that, between the macro level and the micro level, there still exist abundant various dimensions addressed as subgraph, including motifs, cliques, cores... The structural property of these subgraphs plays an import role for the robustness in the function of the system. In this paper, the network motif existing in different IEEE test systems and real power grids are identified, and the consistency between the structural feature of motif and power system design for reliable power supply is revealed. By incorporating the transmission line margin into the procedure of finding significant motifs, the risk of cascading overloads due to insufficient transmission capacity and the decrease of connectivity of the power network is reflected by the occurrence of certain motifs in the power network. Through the simulation of cascading failures along the continuous increase of load demand and random line failures, different phases in the evolution of cascading failures are defined, and the patterns in the occurrence of motifs corresponded to different phases are identified. The performance of network motifs as a warning signal for higher risk of large outages is also tested under continuous line/node removal scenario. Test results show that the occurrence of motifs can be a good supplement to the EENS to describe the risk of outages.