  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}.
