Log(v) 3LPF: A Linear Power Flow Formulation for Unbalanced Three-Phase Distribution Systems

In this work, we introduce Log(v) 3LPF, a linear power flow solver for unbalanced three-phase distribution systems. 3LPF uses logarithmic transform of the voltage phasor to linearize AC equations around balanced case. We incorporate modeling ZIP loads, transformers, capacitor banks, switches and their corresponding controls express network in matrix-vector form. With scalability mind, special attention is given computation inverse system admittance matrix, Ybus. use Sherman-Morrison-Woodbury identity an efficient rank-k corrected matrix compare performance method with traditional LU decomposition methods using Big- $\mathcal {O}$ notation. showcase variety sizes, ranging from tens thousands nodes, commercial-grade software, such as OpenDSS.