On the Implementation of the Fixed Point Iteration Current Injection Method to Solve Four-Wire Unbalanced Power Flow in PowerModelsDistribution.jl

This report serves as a technology description of a Julia-based re-implementation of the fixed-point current injection algorithm, available in PowerModelsDistribution.jl [1]. This report does not describe a novel method for solving unbalanced power flow problems. It merely provides a description of the fixed point iteration variant of the current injection method, inspired by the existing open-source implementation in OpenDSS1 [2]. The current injection method is commonly conceived as a system of nonlinear equalities solved by Newton s method [3, 4]. However, as Roger Dugan points out in the OpenDSS documentation, the fixed point iteration variant commonly outperforms most methods, while supporting meshed topologies from the ground up. We note that the unbalanced power flow algorithm in turn relies on matrix solvers for sparse systems of equations. In the context of circuits and factorizing nodal admittance matrices, the sparsity-exploiting KLU solver [5] has proven to be both reliable and scalable. OpenDSS uses KLU. This report documents work-in-progress, and the authors aim to update it when learnings are obtained or more features are added to the implementation in PowerModelsDistribution.jl. The authors invite collaborators to contribute through pull requests on the repository.