# Comprehensive Modeling of Three-Phase Distribution Systems via the Bus Admittance Matrix

arXiv: https://arxiv.org/abs/1705.06782 · HTML: https://mlsanity.com/paper/1705.06782/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2017.

## Built on by (most cited first, 3 of 3)

- [GradMAP: Gradient-Based Multi-Agent Proximal Learning for Grid-Edge Flexibility](https://mlsanity.com/paper/2604.24549/) (2026)
- [Scalable Self-Supervised Learning for Multiphase AC-OPF in Distribution Systems with Topology Reconfiguration](https://mlsanity.com/paper/2608.25095/) (2026)
- [Finite-Sample Probabilistic Safety Certification for AI-Based Grid-Edge Coordination](https://mlsanity.com/paper/2609.28182/) (2026)

## Abstract (arXiv)

The theme of this paper is three-phase distribution system modeling suitable for the Z-Bus load-flow. Detailed models of wye and delta constant-power, constant-current, and constant-impedance loads are presented. Models of transmission lines, voltage regulators, and transformers that build the bus admittance matrix (Y-Bus) are laid out. The Z-Bus load-flow is then reviewed and the singularity of the Y-Bus in case of certain transformer connections is rigorously discussed. Based on realistic assumptions and conventional modifications, the invertibility of the Y-Bus is proved. Last but not least, the MATLAB scripts that construct the detailed component models for the IEEE 37-bus, IEEE 123-bus, and 8500-node feeders as well as the European 906-bus low-voltage feeder are provided.