Abstract
The Second Order Cone Programming (SOCP) relaxation of the branch flow model has been widely applied to solve the Optimal Power Flow (OPF) problem in radial distribution networks. However, the SOCP relaxation does not guarantee solution exactness, unless several conditions are met, thereby occasionally yielding solutions that are not physically feasible. In this paper, we exploit the geometrical properties of the branch flow equations and formulate the OPF problem as a Riemannian optimization problem with inequality constraints. We present a Riemannian Augmented Lagrangian Method consisting of smooth Riemannian optimization subproblems, which ensures the physical feasibility of the solution. Computational experiments on several distribution networks provide encouraging results in terms of solution quality and speed.
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