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

## TL;DR

This paper develops detailed three-phase distribution system models for the Z-Bus load-flow method, including components like loads, lines, and transformers, and proves the invertibility of the bus admittance matrix under realistic assumptions.

## Contribution

It introduces comprehensive models for various distribution system components and rigorously proves the invertibility of the Y-Bus matrix, facilitating accurate load-flow analysis.

## Key findings

- Detailed component models for loads, lines, and transformers
- Proof of Y-Bus invertibility under realistic conditions
- MATLAB scripts for multiple benchmark feeders

## Abstract

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.