Modeling Transmission Lines Using a Hybrid Knowledge-Based and Data-Driven Approach

This article presents a novel hybrid knowledge-based and data-driven scheme to determine the governing partial differential equation (PDE) for the transmission line (TL). The two-dimensional (2-D) current and voltage distributions along the TL are used as the input data. The hypothetical functions, including the candidate terms that may appear in the telegraphic equations, are built based on prior knowledge of the TL system of interest. Through the spatial and temporal derivatives performed on 2-D current and voltage data, the governing PDEs of TLs are solely represented by the linear algebraic equations. The ridge regression is employed to ascertain the actual PDEs of TLs via extracting the active terms from hypothetical functions. The accuracy and effectiveness of this approach are demonstrated through three benchmarked examples, including the lossy, nonuniform, and nonlinear TLs. The results verify that the proposed scheme can inverse the per-unit-length (p.-u.-l.) parameters and identify the governing PDEs. Our work offers a helpful technique to establish connections between observation and the theoretical TL model.