Solving Optimal Hydrogen Flow via an Eigenvalue-based Hidden Convexity Algorithm

Optimal hydrogen flow (OHF) is a critical task in hydrogen system operation. However, the quadratic non-convexity of the steady-state Weymouth equation poses significant challenges to the optimality. To address this issue, an eigenvalue-based hidden convexity (EBHC) algorithm is proposed in this paper. By exploiting the hidden convexity of the OHF, the original non-convex formulation is decomposed into an upper-level second-order cone programming (SOCP) problem and multiple lower-level non-convex quadratically programming with one quadratic constraint (QP1QC) subproblems. Each QP1QC subproblem is further reformulated into a tractable generalized eigenvalue problem (GEP), which can be solved in parallel. An ADMM-inspired iterative scheme is then employed, where lower-level variables are used to successively refine the upper-level SOCP solution until convergence is achieved. Numerical results on various systems demonstrate the effectiveness and computational efficiency of the proposed algorithm.