A Three-phase Power Flow Model and Balanced Network Analysis

TL;DR

This paper introduces a novel approach to formulate unbalanced three-phase power flow problems by separating device and network models, and extends it to balanced networks with formal proof of validity.

Contribution

It presents a new modeling framework that explicitly separates device and network models and applies spectral analysis to validate per-phase analysis in balanced networks.

Findings

New formulation for unbalanced three-phase power flow problems.

Validation of per-phase analysis for balanced networks.

Spectral property of the conversion matrix ensures model accuracy.

Abstract

First we present an approach to formulate unbalanced three-phase power flow problems for general networks that explicitly separates device models and network models. A device model consists of (i) an internal model and (ii) a conversion rule. The conversion rule relates the internal variables (voltage, current, and power) of a device to its terminal variables through a conversion matrix {\Gamma} and these terminal variables are related by network equations. Second we apply this approach to balanced three-phase networks to formalize per-phase analysis and prove its validity for general networks using the spectral property of the conversion matrix {\Gamma}.