Mathematical Proof for the Minimized Stray Fields in Transformers Using Auxiliary Windings Based on State Equations for Evaluation of FEM Results

Stray magnetic field is one of the main issues in design of transformers, since it causes non-ideal behavior of transformers. One of the techniques is usually adopted to mitigate the unwanted stray magnetic field is the use of auxiliary windings creating a magnetic field opposite to the incident one giving rise to the reduction of the total magnetic fields. This paper presents a new mathematical proof for optimized parameters such as connection resistance and leakage inductance of the auxiliary windings based on state equations. Some numerical examples for various types of practical transformers are given to demonstrate the validity of the presented mathematical proof and a comparison is made with the results of transformers behavior which is obtained with the help of finite element method. The proposed method is successfully implemented on three different types of transformers: current injection transformer, pulse transformer and superconductor transformers.