Analysis of the Mutual Inductance in Current Transformers Taking Primary Conductors Eccentricity Into Account

In this work a current transformer (CT) with toroidal core is analyzed from the viewpoint of the eccentricity of the primary circuit where one conductor goes through the core's window and the other is outside the core. The research is focused on the influence of the position of the primary circuit conductors on the evaluation of the mutual inductance between the primary circuit and the secondary winding—an influential factor on the CT's amplitude error. Purely analytical results and closed-form expressions for the mutual inductance are obtained when the core is made of a nonmagnetic material. A finite-element method is also utilized for the numerical computation of the mutual inductance, for nonmagnetic and ferromagnetic cores. Results are cross-validated using both methods. Results are presented and discussed taking into account the system geometry and the number of turns of the secondary winding. This novel contribution shows that the response of nonmagnetic-core current transformers can be significantly affected by the positional eccentricity of the primary circuit, especially when the secondary winding does not possess a large number of turns.