Method of Turns Arrangement With Minimized Mutual Inductance Deviation for Discontinuous Rogowski Coils

Rogowski coils are widely used instruments for current measurement. The mutual inductance between a primary conductor and a Rogowski coil varies with the position of the primary conductor. This deviation in mutual inductance may lead to measurement errors. In discontinuous Rogowski coils, which feature a gap in the frame where coil turns cannot be placed, the issue of mutual inductance deviation is particularly pronounced. The current practice of turns arrangement for discontinuous Rogowski coils is predominantly based on empirical methods and lacks a rigorous theoretical foundation. This article proposes a turns arrangement method for discontinuous Rogowski coils. The proposed method is designed to reduce the mutual inductance deviation of discontinuous Rogowski coils, thereby minimizing associated measurement errors. An equivalent relation is established between the mutual inductance of a discontinuous Rogowski coil and the electric potential in a steady-state current field. For a given number of turns, the turns arrangement of the discontinuous Rogowski coil could be obtained by discretizing the calculated current density. The mutual inductance deviations of Rogowski coils designed by using conventional and proposed turns arrangement methods are compared. The effectiveness of the proposed method in reducing the mutual inductance deviation of discontinuous Rogowski coils is demonstrated. The switching current of a SiC MOSFET is measured simultaneously by using a commercial current probe and a discontinuous Rogowski coil. The measurements demonstrate the current measurement accuracy of the discontinuous Rogowski coil designed according to the proposed turns arrangement method. Furthermore, the influence of gap width and the number of turns on the mutual inductance deviation is discussed.