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In this paper, we formulate the Load Flow (LF) problem in radial electricitydistribution networks as an unconstrained Riemannian optimization problem,consisting of two manifolds, and we consider alternative retractions andinitialization options. Our contribution is a novel LF solution method, whichwe show belongs to the family of Riemannian approximate Newton methodsguaranteeing monotonic descent and local superlinear convergence rate. To thebest of our knowledge, this is the first exact LF solution method employingRiemannian optimization. Extensive numerical comparisons on several testnetworks illustrate that the proposed method outperforms other Riemannianoptimization methods (Gradient Descent, Newton's), and achieves comparableperformance with the traditional Newton-Raphson method, albeit besting it by aguarantee to convergence. We also consider an approximate LF solution obtainedby the first iteration of the proposed method, and we show that itsignificantly outperforms other approximants in the LF literature. Lastly, wederive an interesting comparison with the well-known Backward-Forward Sweepmethod.

A Novel Riemannian Optimization Approach to the Radial Distribution Network Load Flow Problem