Eigenvalue-Based Hidden Convexity Algorithm for Radial Distribution Network Optimization with Non-convex Power Flow Equations

Distribution network optimization is represented by non-convex power flow equations, where traditional convex relaxation methods may lead to inaccurate or infeasible solutions. To effectively solve the non-convex optimization problem, an eigenvalue-based hidden convexity (EBHC) algorithm is proposed for radial distribution network optimization with continuous variables and separable objectives. Specifically, the original nonconvex problem is reformulated within a standard ADMM framework by separating the convex and non-convex components of the quadratic equality constraints. The convex component is represented as a centralized second-order cone programming (SOCP) problem that can be efficiently solved, while the non-convex component is decomposed into multiple sub-problems, each taking the form of a quadratic program with a single quadratic constraint. Each sub-problem exhibits a special mathematical structure, enabling parallel solution via multiple generalized eigenvalue problems (GEPs). The theoretical guarantees of the algorithm rely on the assumption that Slater's condition holds and that the network is radial. Through iterative coordination between the convex and non-convex components, the non-convex quadratic equality constraints are strictly satisfied. Numerical experiment results demonstrate the effectiveness and accuracy of the proposed algorithm.