The ADI Method for Simulations of SFCL

Abstract

In spite of the recent advances achieved with superconducting fault current limiters, modeling and simulation of such devices are still important issues. Different approaches have been used to model the transient behavior of such devices when submitted to fault currents. In this paper, the alternating direction implicit method is used to numerically solve the thermal equations discretized by the finite-difference method (FDM). That is a fast method to solve the system of differential equations resultant from the FDM discretization. It also allows the insertion of inhomogeneities of the superconducting tapes in the simulation and the study of its influence on fault limitation. The results of simulations models were compared with experimental data. A good agreement between simulated current and voltages with tests has been found in the present work. In addition, the temperature increase and the electrical field in the tapes during the fault time is shown.Index Terms-Alternating direction implicit (ADI), superconducting fault current limiter (SFCL), transient simulations.

Understanding the impact of failure modes of cables for the design of turbo-electric distributed propulsion electrical power systems

“…A number of complex methods for modelling superconducting cables and materials have been presented in the literature. For example, the Finite Element Method (FEM) and Finite Difference Method (FDM) can be used to calculate the complex heat sharing between different layers of the material [15]. These are not well suited to dynamic system studies due to their computational intensity.…”

“…These are not well suited to dynamic system studies due to their computational intensity. Therefore in order to model the transient behavior within a system, this paper models the cable as a non-linear resistance that varies according to the E-J power law (1); an approach demonstrated for developing dynamic models of resistive fault current limiters [15,16].…”

“…In addition, the critical current density, Jc, is dependent on operating temperature of the superconductor: where Tr is the temperature at the reference critical current density [15][16].…”

A wide range E − J constitutive law for simulating REBCO tapes above their critical current

“…when the current is above the critical current I c ) of the superconducting material, and other models remain empirical [7][8][9][10][11][12]: for instance, they use a piecewise power-law in which the overcritical current regime is modeled as the flux creep region, but with a lower n-value [13]. Accurate knowledge of the E − J relation can help improve the reliability of the models, and thus, the performance of the simulated devices working in the overcritical current regime or where the electro-magnetothermal aspects must be studied carefully, for instance a hotspot scenario [14][15][16], a non-insulated coil [17,18] or a superconducting dynamo [19].…”

An open-source 2D finite difference based transient electro-thermal simulation model for three-phase concentric superconducting power cables

“…For those reasons, in this manuscript we deploy the ADI routine for the solution of the discretized equations originated from the FDM scheme. The ADI routine has been recently successfully used for simulations of superconducting fault current limiters [33][34][35] This paper is organized as follows: section 2 presents the main designs concepts and parameters of the cable under study. A brief discussion about pressure drop in the cable during transient regimes in the cable is made in this section.…”