Fast calculation of spatial potentials and robust inversion of field sources for overhead transmission lines in complex terrain

To achieve real-time monitoring of spatial potential and field source voltage of overhead lines in complex terrain, this paper proposes a numerical model for fast forward calculation of spatial potential and robust inversion calculation of field source voltage. The main problem addressed is the computational complexity and accuracy issues associated with traditional numerical methods and simplified engineering methods, which often fail to provide real-time and reliable results in complex terrain environments. This study aims to develop a more efficient and accurate numerical model for real-time monitoring. Specifically, a simplified cross-section model based on the constant boundary element method (BEM) and an unstructured discretization method is established. This model allows for faster forward calculations of spatial potential. Additionally, a robust inversion method based on the optimization of the measurement array structure is presented. This method ensures the accuracy and reliability of the inversion of field source voltage. The effectiveness of the proposed method is demonstrated through both 2-D analytical cases and 3-D cases. The forward calculation time is significantly reduced to less than one voltage cycle (50 Hz), which is crucial for real-time monitoring. Furthermore, the inversion uncertainty is <3E-3 pu., and the inversion error is <1.5 %.