Abstract-This paper describes an original approach for determining independent loops needed for mesh-current analysis in order to solve circuit equation system arising in inductive Partial Element Equivalent Circuit (PEEC) approach. Based on the combined used of several simple algorithms, it considerably speed-up the loops search and enables the building of an associated matrix system with an improved condition number. The approach is so well-suited for large degrees of freedom problems, saving significantly memory and decreasing the time of resolution.

High-temperature superconducting materials have remarkable current-carrying capabilities, even when operated under high magnetic fields. Since long rare earth-barium-copper oxide (REBCO)-coated conductors are now available (thanks to improvements in the fabrication process) this material has become an attractive option for high field magnet applications. However, such extreme operating conditions require an efficient quench protection system to prevent the coil from developing damaging hot spots, which greatly depends on the winding used. We focus here on the protection of insulated HTS coils against thermal runaways that can locally destroy the magnet. We developed a transient two-dimensional (2D) axisymmetric model using a volume integral formulation based on generalization of the partial element equivalent circuit method to compute the local current density distribution inside REBCO-insulated coils and account for local performance variations. Indeed, the most interesting property of integral methods is the requirement that only active regions are meshed, which leads to a significant reduction in the size of the problem. The formulation is introduced for general 3D cases and its adaptation to 2D axisymmetric problems is detailed. The formulation has been validated thanks to a bulk magnetization benchmark, the results of which (obtained with the finite element method) were compared with our integral formulation solution. The model has also been compared with experimental data obtained on a double pancake coil. The objective is to study the effects of magnetization on the transient voltage due to dynamic current distribution when ramping up the magnet so as to be able to determine some key parameters associated with coil protection. Such an approach is developed on a small-scale test case and the transient behaviours observed are discussed.

Thanks to their very high current carrying capabilities even under high magnetic field conditions and their outstanding mechanical properties, high temperature superconductors (HTSs) such as REBCO (rare-earth BaCuO) tapes are very attractive for high magnetic field applications. Depending on the magnet design goals and constraints, it can be advantageous in some cases to reduce the electrical margins of the conductor. Considering the uncertainty in locally evaluating the critical current, and the inhomogeneities of present-day REBCO tapes, there is a significant risk of the critical current being overstepped locally, thus triggering local damaging hotspots. Such an event does not have the sudden occurrence and/or fast spreading quality usually associated with the concept of 'quench' and should be simply seen as thermal runaway induced by dissipative zones (DZs). The development of numerical models to evaluate the occurrence and propagation of such zones inside windings is critical in the development of a HTS magnet fully using REBCO tape performance while guaranteeing safe operation conditions. In this work, we have developed a transient electro-thermal model adapted to pancake-based coils. It accounts for both the nonlinear electrical and thermal behavior of the material and considers the local inhomogeneities of the critical current I c along the tape. The electrical part is one-dimensional (1D) and computes the nonlinear dissipation in the conductor depending on the local operation conditions while the thermal part is two-dimensional (2D) to account for the heat propagation along the conductor length and from turn to turn. In order to improve computation efficiency, adaptive time-stepping methods have been introduced with the objective of ensuring good accuracy of simulation results.