It is an important aspect of power system resilience research to select a minimum backbone grid priority under extreme disaster conditions. How to establish the model of backbone grid search by analytic expression is a challenge. This paper describes the importance of transmission lines by the flow betweenness and establishes a quadratic cone programming model for backbone grid search by weighting and minimizing the objective of transmission lines. The model includes power balance constraints, generator unit commitment constraints, linear current constraints and so on. The highlight feature of the model is that it avoids the circulation in the network through a set of linear constraints, which accord with the actual power system. The test on an IEEE 39-bus system and an IEEE 118-bus system prove that the proposed method has strong robustness and high computational efficiency

mixed integer quadratic cone programming, backbone grid, circulation, flow betweenness, unit commitment