Establishment of the Inductance Matrix of Uninsulated Superconducting Windings With Different Shapes and the Treatment of Their Singular Value Problems

In order to accurately and efficiently study the transient process of quenching in non-insulated superconducting windings, the Partial Element Equivalent Circuit (PEEC) model is employed. This model regards the superconducting winding as being composed of multiple independent segments. To establish the model parameter matrix, it is necessary to calculate the resistance and inductance parameters for each independent segment. Among these, the inductance parameters can be derived from the relationship between the magnetic vector potential A and the current density J. However, during the derivation process, when calculating the self-inductance of each segment, a singularity problem may arise. This issue can be resolved through the method of partial integration. This paper will elaborate on the derivation process of the inductance matrix for circular windings, straight laminations, and D-shaped windings, with a focus on the solution to the self-inductance singularity problem.