A Robust Estimation Method for the Coupling Matrix in Non-Contact Measurement of Switching Transient Voltages in 500 kV Transmission Lines

Determining the coupling matrix is crucial for reconstructing transient voltages on overhead transmission lines using non-contact measurement techniques. However, existing methods often fail to account for the effects of asymmetrical sensor placement and the presence of multiple adjacent conductors in substations. This paper proposes an optimization-based approach to estimate the coupling matrix elements, aiming to minimize the transient voltage reconstruction error, with the measured power frequency voltage imposed as a constraint. The influence of adjacent conductors on the measured electric field is assumed to have a waveform similar to that of the measured conductors, as ensured by the electrically small condition during switching transients. The method is applied to reconstruct the closing and opening transient voltage waveforms of a 500 kV overhead transmission line. The estimated coupling matrix coefficients exhibit consistent performance across 11 tests, with maximum estimation errors of 6.2% and 2.5% for the opening and closing transient voltages, respectively. Moreover, the results indicate that the low-frequency response characteristics of capacitive voltage transformers (CVTs) are insufficient for capturing the opening transient voltages on transmission lines. By leveraging the full waveform of the measured transient electric field signal, the proposed method eliminates the need for symmetrical sensors and ensures robust field performance.