Sparse Tableau Approach for Unbalanced Three-Phase Distribution Network Modeling and Analysis

This paper provides a comprehensive investigation of an alternative formal modeling approach for power flow studies in unbalanced three-phase distribution networks based on the sparse tableau formulation (STF). Leveraging the flexibility of the STF, it details precise and exact models of feeder lines, stepvoltage regulators, and transformers with various connections, all developed in the form of the STF. In particular, the proposed formulation for all network components is derived rigorously from first principles without relying on any approximations and assumptions. Then, the backward-forward sweep (BFS) algorithm tailored to the features of STF for solving the power flow problem is proposed. Beyond the modeling advantages, the computational benefits of the STF-based BFS are validated using the IEEE 37-node, IEEE 123-node, IEEE 8500-node, and European 906-node Low-Voltage test networks showing equally robust but faster convergence compared to existing methods. The proposed model is applicable to analyze both unbalanced radial and meshed systems, offering contributions to potentially advance power system modeling and analysis techniques for the effective management and operation of future complex active distribution networks.