With the rapid-growing penetration of sustainable energy and distributed generation, the increased size and complexity has challenged the contingency analysis of the present power system. Meanwhile, the current electric utility operating policies require that each utility's power system must be able to withstand and recover from any "N-1" contingency analysis ("first contingency" or any single failure), and expects the real-time analysis as the key component of the "self-healing grid" of the future. The approach proposed in this dissertation is aiming to improve the computing performance for the dynamic contingency analysis. Firstly, the graph technology is introduced as the model of the power system, thanks to it has widely used in the Internet, social media, network security, traffic control, e-commerce and so on. Then more research is involved in conjugate gradient algorithm and specific preconditioning for the power system.

As a summary, the dissertation contains the following six chapter. In the first chapter, it introduces the contingency analysis, reviews the direct and iterative methods of solving large-scale equations, and points out the shortcomings of current contingency analysis. Secondly, graph model of the power system builds after the essential and related preparation of graph theory, graph database, and graph computing. Furthermore, graph-based power system analysis presented in chapter 3, including graph-based conjugate gradient algorithm for power flow calculation. In chapter 4, along with the procedure of contingency analysis, it proposes graph-based topology analysis for islanding detection, incomplete LU preconditioner for "N-1" contingency analysis, and graph-based conjugate gradient for quick screening. These suggested approaches is verified in chapter 5, tested parallel performance and compares with the existing methods. Finally, it summaries and prospects its potential compatibility with graph visualization by user interface design, economic optimal power flow, and intelligence machine learning from the previous record.