A Physics-based and Data-driven Linear Three-Phase Power Flow Model for Distribution Power Systems

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.