Mutual Inductance of Rogowski Coil: Absolutely Convergent Perturbation Series in Small Eccentricity of Primary Conductor

Double series expansion for mutual inductance between Rogowski coil with rectangular cross section and finite straight primary conductor is obtained by applying free-space Green function expansion in Bessel functions. The system of Rogowski coil and primary conductor with imperfections caused by eccentricity of primary conductor and non-uniformity of wire turns on air-core of Rogowski coil is considered. Exact analytical calculation yielded double series expansion containing associated Legendre polynomials and it turns out to be absolutely convergent perturbation series in powers of eccentricity of primary conductor. Double series is truncated and as such is applied for calculation of mutual inductance. Seventeen test cases were constructed to examine accuracy and speed of convergence of double series. The results obtained by truncating double series coincide with the reference value of mutual inductance in at least 10 significant digits for every test case. Presented test cases are divided in three groups with intention that each group reveal how variation of exactly one parameter of the eccentricity, non-uniformity of wire turns and length of primary conductor affects mutual inductance. It was observed that variation of eccentricity and length of primary conductor have significant influence on mutual inductance, while no significant effects on mutual inductance were observed due to variation of parameter describing non-uniformity of wire turns.