Generalized Data-driven Power Flow Linearization: Methodologies, Evaluations, and Challenges

Generalized data-driven power flow linearization (DPFL) has gained increased attention with the rise of datacentric methodologies, enabling the identification of linear, piecewise linear, and space-mapped power flow models with high accuracy. However, selecting the most suitable DPFL approach for a given scenario is challenging, owing to: (i) the absence of a unified mathematical reexamination of existing DPFL methods, (ii) the lack of a systematic analysis of their capabilities and limitations, and (iii) the unavailability of a comprehensive comparison across all approaches, as over 95% of DPFL studies do not release open-source codes. This paper addresses these gaps. It classifies DPFL methods into training algorithms and supportive techniques, systematically discussing their mathematical models, capabilities, and limitations. Additionally, it assesses the applicability of 41 DPFL methods and four classic physics-driven approaches. Extensive numerical evaluations among these 45 methods are further conducted across 22 test cases. The analysis reveals not only the superior accuracy of DPFL approaches but also highlights their hidden underperformance, failures, and high computational costs, which leads to nine promising future directions given the challenges identified. Overall, this paper systematically revisits DPFL theories, numerically evaluates their performance, and provides insights for selecting or improving DPFL methods.