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Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems
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  • Ignacio Losada Carreño ,
  • Shammya Saha ,
  • Anna Scaglione ,
  • Daniel Arnold ,
  • Ngo Sy-Toan ,
  • Ciaran Roberts
Ignacio Losada Carreño
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Shammya Saha
Arizona State University

Corresponding Author:[email protected]

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Anna Scaglione
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Daniel Arnold
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Ngo Sy-Toan
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Ciaran Roberts
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Abstract

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. Log(v) 3LPF uses a logarithmic transform of the voltage phasor to linearize the AC power flow equations around the balanced case. We incorporate the modeling of ZIP loads, transformers, capacitor banks, switches and their corresponding controls and express the network equations in matrix-vector form. With scalability in mind, special attention is given to the computation of the inverse of the system admittance matrix, Ybus. We use the Sherman-Morrison-Woodbury identity for an efficient computation of the inverse of a rank-k corrected matrix and compare the performance of this method with traditional LU decomposition methods in terms of FLOPS. We showcase the solver for a variety of network sizes, ranging from tens to thousands of nodes, and compare the Log(v) 3LPF with commercial-grade software, such as OpenDSS.
Jan 2023Published in IEEE Transactions on Power Systems volume 38 issue 1 on pages 100-113. 10.1109/TPWRS.2022.3166725