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

Abstract

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.

Design and applications of Rogowski coil sensors for power system measurements: A review

“…The RC is an electromagnetic induction sensor that works on the principle of Faraday's law [14]. When a time varying magnetic flux (𝛷) is linked up with a coil winding, the relationship between the magnetic flux and electromotive force (emf e) induced in a loop can be described by Faraday's law as:…”

“…Further, the sensitivity of the coil can be increased without increasing the number of turns of the coil winding. A rectangular RC is developed by combining 4 straight coils of circular cross-section [44]. This structure can be useful in the case a larger cross section (dc) of the core and smaller mean diameter (dm) of the coil is required.…”

Simplifying Rogowski Coil Modeling: Simulation and Experimental Verification

“…In [21], the authors design a Rogowski coil from scratch for three-phase current measurement in electric motors. A highly detailed model is presented in [22], relying on equations that require the complete geometry of the device and the space in which it is installed. A four-layer PCB-based Rogowski coil is designed in [23].…”

Using a Current Shunt for the Purpose of High-Current Pulse Measurement

“…There are many different works about Rogowski coils. Current measurements of them can be influenced by many factors ranging from their construction, the shape of the coil loop, and the location of the measured circuit in the coil loop [ 13 , 14 , 15 ]. Accurate calibration methods have been developed for Rogowski coils dedicated to pulsed power systems [ 16 , 17 ].…”