The determination and online monitoring of key sections in the power grid are of great significance for the safe and stable operation of the power system. In order to more effectively search for key sections, this paper proposes a method for searching key sections based on key branches. Compared with traditional algorithms that search for key branches based on safety margin, this method searches for key branches based on active power abnormal behavior, greatly reducing the algorithm's time complexity. To adapt to engineering practice, traditional cut-set algorithms for searching key sections are improved to accommodate non-connected power networks. At the same time, the searched key sections are graded, and the monitoring range of key sections is flexibly adjusted according to the budget, realizing effective monitoring of the power grid. Simulation results show that the key sections searched by this algorithm not only include the key sections given by experts in power grid operation modes but also discover new key sections.