A Riemannian optimization approach to the radial distribution network load flow problem

The Load Flow (LF) equations in power networks are the foundation of several applications on active and reactive power flow control, distributed and real-time control and optimization. In this paper, we formulate the LF problem in radial electricity distribution networks as an unconstrained Riemannian optimization problem, consisting of two manifolds, and we consider alternative retractions and initialization options. We introduce a Riemannian approximate Newton method tailored to the LF problem, as an exact solution method guaranteeing monotonic descent and local superlinear convergence rate. Extensive numerical comparisons on several test networks illustrate that the proposed method outperforms standard Riemannian optimization methods (Gradient Descent, Newton's), and achieves comparable performance with the traditional Newton-Raphson method (in Euclidean coordinates), albeit besting it by a guarantee to convergence. We also consider an approximate LF solution obtained by the first iteration of the proposed method, and we show that it significantly outperforms other approximants in the LF literature. Lastly, we derive an interesting analogy with the well-known Backward-Forward Sweep (BFS) method showing that BFS iterations move on the power flow manifold, and highlighting the advantage of our method in converging under high constant impedance loading conditions, whereas BFS may diverge. (C) 2021 Elsevier Ltd. All rights reserved.