A fixed-point current injection power flow for electric distribution systems using Laurent series

Juan S. Giraldo*, Oscar Danilo Montoya, Pedro P. Vergara, Federico Milano

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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This paper proposes a new power flow (PF) formulation for electrical distribution systems using the current injection method and applying the Laurent series expansion. Two solution algorithms are proposed: a Newton-like iterative procedure and a fixed-point iteration based on the successive approximation method (SAM). The convergence analysis of the SAM is proven via the Banach fixed-point theorem, ensuring numerical stability, the uniqueness of the solution, and independence on the initializing point. Numerical results are obtained for both proposed algorithms and compared to well-known PF formulations considering their rate of convergence, computational time, and numerical stability. Tests are performed for different branch R/X ratios, loading conditions, and initialization points in balanced and unbalanced networks with radial and weakly-meshed topologies. Results show that the SAM is computationally more efficient than the compared PFs, being more than ten times faster than the backward–forward sweep algorithm.

Original languageEnglish
Article number108326
JournalElectric power systems research
Early online date13 Jul 2022
Publication statusPublished - 1 Oct 2022


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