Analysis and Optimization of the Stray Capacitance of Rogowski Coils

In this work, the lumped model of Rogowski coils is briefly reviewed to illustrate that the reduction in stray capacitance expands the bandwidth and improves the high-frequency performance. Then, a network model as well as explicit formulas for the stray capacitance of Rogowski coils are established, and the influence of geometrical parameters of the skeletons on the stray capacitance is investigated. It is found that the stray capacitance of Rogowski coils is approximately proportional to the perimeter of the skeleton cross-section. Based on the above discussion, optimization of the shape of the skeleton cross-section, aiming at minimizing the perimeter without affecting the magnetic flux and mutual inductance of the coils, is carried out. The widely adopted circular and rectangular cross-sections are discussed first. Then, the cross-section of an arbitrary smooth and convex shape is optimized by solving a constrained variational problem, leading to an explicit equation for the optimal skeleton cross-section of Rogowski coils. Numerical results demonstrate that, compared with the common circular and rectangular skeleton cross-sections, the proposed optimal cross-section exhibits the shortest perimeter and thus the highest upper cutoff frequency under fixed magnetic flux. The optimization method developed by this work can provide a theoretical basis and guidance for the design of Rogowski coils.