  Distribution power systems (DPSs) are mostly unbalanced, and their loads may
have notable static voltage characteristics (ZIP loads). Hence, despite
abundant papers on linear single-phase power flow models, it is still necessary
to study linear three-phase distribution power flow models. To this end, this
paper proposes a physics-based and data-driven linear three-phase power flow
model for DPSs. We first formulate how to amalgamate data-driven techniques
into a physics-based power flow model to obtain our linear model. This
amalgamation makes our linear model independent of the assumptions commonly
used in the literature (e.g., nodal voltages are nearly 1.0 p.u.) and thus have
a relatively high accuracy generally - even when those assumptions become
invalid. We then reveal how to apply our model to the DPSs with ZIP loads. We
also show that with the Huber penalty function employed, the adverse impact of
bad data on our model's accuracy is significantly reduced, rendering our model
robust against poor data quality. Case studies have demonstrated that our model
generally has 2 to over 10-fold smaller average errors than other linear power
flow models, enjoys a satisfying accuracy against bad data, and facilitates a
faster solution to DPS analysis and optimization problems.
