Abstract: In uncertain scenarios, the robust feasible region can provide quantitative output estimation for virtual power plants to participate in transmission level scheduling. Existing research on the robust feasible region of virtual power plants has not addressed the electric hydrogen coupling system. A robust feasible region model and solution method for virtual power plants considering electric hydrogen coupling are proposed. Firstly, analyze the principle of bidirectional electro hydrogen conversion in reversible solid oxide cells and construct a virtual power plant model with electro hydrogen coupling; Secondly, based on the Projection Convex Hull Search Method (PC-SM), a robust feasible region model for a virtual power plant with electric hydrogen coupling is established; Finally, a new C&CG PCSM coupling algorithm is proposed for solving the robust feasible region model of a virtual power plant with electric hydrogen coupling, using the Column and Constraint Generation (C&CG) algorithm to solve the vertex projection set under the convex hull search direction provided by PC-SM. The simulation results show that the proposed model and solution method can provide theoretical support for the quantitative output estimation of virtual power plants with electric hydrogen coupling participating in transmission level scheduling.