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Published December 2023 | Published
Conference Paper

Convergence of Backward/Forward Sweep for Power Flow Solution in Radial Networks

  • 1. ROR icon California Institute of Technology


Solving power flow is perhaps the most fundamental calculation related to the steady state behavior of alternating-current (AC) power systems. The normally radial (tree) topology of a distribution network induces a spatially recursive structure in power flow equations, which enables a class of efficient solution methods called backward/forward sweep (BFS). In this paper, we revisit BFS from a new perspective, focusing on its convergence. Specifically, we describe a general formulation of BFS, interpret it as a special Gauss-Seidel algorithm, and then illustrate it in a single-phase power flow model. We prove a sufficient condition under which the BFS is a contraction mapping on a closed set of safe voltages and thus converges geometrically to a unique power flow solution. We verify the convergence condition, as well as the accuracy and computational efficiency of BFS, through numerical experiments in IEEE test systems.

Copyright and License

© 2023 IEEE.


The work of B. Fang and C. Zhao was supported by Hong Kong Research Grants Council through grant GRF 14212822. The work of S. H. Low was supported by US NSF through grants ECCS 1931662, ECCS 1932611, and Caltech’s Resnick Sustainability Institute and S2I grants.

Additional details

February 13, 2024
February 13, 2024