A Three-phase Power Flow Model and Balanced Network Analysis

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}.