To reduce the outage time, federated maintenance with multiple lines outages is adopted by the power enterprise gradually. The line's condition is the focus, while the total operating status of the grid is ignored when making the maintenance decision. Multiple lines are out of operation successively, and this amplifies the system vulnerability. The interaction between the power cyber physical system (CPS) aggravates the cross-domain propagation of failure. There is the possibility of cascading failure and blackout due to the synergistic destructive effect. A method is proposed to identify the vulnerable correlation among the transmission lines in this scenario. First, the federated maintenance's energy flow and information transmission process are modeled. A database of accident records caused by the federated maintenance is established. Second, the combinations of lines with the vulnerable correlation in the database are mined. The vulnerability correlations are quantified by calculating the contributions to triggering the blackout. Simulation results show that the lines with vulnerable correlation express the synergistic destructive effect both in the physical and the cyber layers. The method proposed can identify and quantify the vulnerable correlations efficiently. It can provide the theoretical guidance for making reasonable maintenance decisions and avoiding blackouts. This work is supported by the Union Funds of the National Natural Science Foundation of China (No. U1966207).