Modeling and Analyzing the Mutual Inductance of Rogowski Coils of Arbitrary Skeleton

There are Rogowski coils of various shapes in the on-site measurement, and it is difficult to calculate the electrical quantities of Rogowski coils of curved skeleton and circular cross-section by simulation software. This paper proposes a theoretical derivation to calculate the mutual inductance between the conductors of any shape and Rogowski coils with skeletons of any shape. Based on the derivation, the influence of four skeleton shapes of Rogowski coils and four shapes of the primary conductors on the mutual inductance of Rogowski coils are studied by the comparison between the ideal cases and some non-ideal ones. The gap and gap compensation of the openable Rogowski coils are also considered. Experiments verify the numerical results according to the derivation. It is shown that to reduce the errors of the measurement the circular skeleton deformation should be avoided, the coil's skeleton should be with curved angle, the primary conductor should be as straight as possible and should go through the center of the skeletons vertically. Furthermore, for the Rogowski coils of the rectangular skeleton, we propose a new skeleton structure to reduce the deviation influence of the primary conductors.