Hybrid Data-Model Driven Flexible Convex Polyhedron Construction for Solving Optimal Electricity-Heat-Gas Flow

The integration of electricity, heat, and gas networks introduces additional dimensions of flexibility, but the complex network topology makes power dispatch challenging. This paper presents a method for constructing a convex polyhedron to define the dynamic 3D flexible region (FR), which represents all possible power/heat/gas flow injection solutions that simultaneously satisfy operational constraints. First, a modified energy hub framework is proposed, and Monte Carlo simulations are used to sample feasible unit commitment and power dispatch scenarios. The Quick-Hull algorithm is applied to form a polyhedron that encloses all feasible solutions. Second, a point coordinate projection technique is employed to approximate the non-convex optimization problem to a convex one by shaping a projected 2D dispatchable plane. A case study using the modified IEEE33-NGS15-DHS15 and IEEE33-NGS25-DHS28 test systems demonstrates the efficiency and effectiveness of the proposed 3D geometry-based approach in solving joint scheduling problems across electricity, heat, and gas clusters.