This paper reviews the modeling of high-temperature superconductors (HTS) using the finiteelement method (FEM) based on the H-formulation of Maxwell's equations. This formulation has become the most popular numerical modeling method for simulating the electromagnetic behavior of HTS, especially thanks to the easiness of implementation in the commercial finite-element program COMSOL Multiphysics. Numerous studies prove that the H-formulation is able to simulate a wide scope of HTS topologies, from simple geometries such as HTS tapes and coils, to more complex HTS devices, up to large superconducting magnets. In this paper, we review the basics of the H-formulation, its evolution from 2D to 3D, its application for calculating critical currents and AC losses as well as magnetization of HTS bulks and tape stacks. We also review the use of the H-formulation for large-scale HTS applications, its use to solve multi-physics problems involving electromagnetic-thermal and electromagnetic-mechanical couplings, and its application to study the dynamic resistance of superconductors and flux pumps.

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Overview of H -Formulation: A Versatile Tool for Modeling Electromagnetics in High-Temperature Superconductor Applications

This work covers the high-temperature superconducting (HTS) technologies based on the highlights in recent achievements in the applied HTS field in China. Its comprehensive coverage includes practical HTS material manufacturing and characterization, large-scale applications, and electronic applications. The applied HTS technologies have been well enabled to build applicable devices, and their characteristics have been well verified in the HTS devices developed to be industrialized for practical applications. The highlighted HTS devices and their performance details reveal the trend and the necessary improvement required to reach the goal of industrial applications of HTS technologies.

Enabling High-Temperature Superconducting Technologies Toward Practical Applications

High-temperature superconductors (HTSs) including HTS bulks and tapes have potential applications in linear motion drive and magnetic levitation/suspension systems generating substantial advantages over conventional ones. When an HTS linear motor is integrated with an HTS magnetic suspension subsystem, it can inherit both merits of HTS linear motion drive and HTS magnetic suspension simultaneously and can be applied into various fields, such as the maglev and electromagnetic aircraft launch systems (EMALSs). Based on different HTS aspects and arrangements, three modes of HTS linear synchronous motor (HTSLSM) integrated with HTS magnetic suspension subsystems have been proposed in this paper. To verify the modes for the design of a practical HTSLSM, the structural features of these systems are described, the magnetization characteristics to obtain HTS bulk magnets, the trapped-field attenuation characteristics of the HTS bulk magnet exposed to external traveling field, and the magnetic field distribution characteristics for different permanent-magnet guideways have been studied with experimental verification. Based on the study, a demonstration prototype of a single-sided HTSLSM integrated with HTS magnetic suspension subsystems has been developed. Its performance and thrust characteristics have been obtained by experimental measurements and compared with theoretical results. With regard to practical applications, two modes of double-sided HTSLSM integrated with HTS magnetic suspension subsystems have been designed for the maglev and EMALS, respectively, and then, the 2-D finite-element-analysis models for the HTSLSMs were built to analyze their performance characteristics. The comprehensive simulations and experimental results constitute a framework for the structural and electromagnetic design of the HTSLSM integrated with HTS magnetic suspension for practical applications.

High-Temperature Superconducting Linear Synchronous Motors Integrated With HTS Magnetic Levitation Components

The superconductive fault current limiter (SFCL) is one of the most ideal solutions to limit the dc fault current in the voltage source converter (VSC)-based dc system. With regard to the application of SFCLs in dc systems, not only the dc-side fault current but also the currents at the ac side and in the converter itself should be limited during a dc fault. Considering the whole-system current-limiting capability, this paper analyzes the applicability of different SFCLs in the VSC-based dc system according to transient characteristics of the dc fault. It is concluded that the resistive SFCL has better current-limiting capability than others. Meanwhile, the technical requirements and parameter influence for designing a resistive SFCL are discussed. Simulation tests based on MATLAB/Simulink are carried out to verify the correctness of the theoretical analysis.

Studies on the Application of R-SFCL in the VSC-Based DC Distribution System

We developed a saturated iron-core type 35 kV/90 MVA superconductive fault current limiter and installed the device in a transmission network at Puji substation of China Southern Power Grid for live-grid operation. Innovative design in the iron-core configuration ensures that the device has low impedance in normal power transmission and sufficiently high impedance for a fault current limiting action. A magnetization control circuit allows the iron-core to be saturated or de-saturated depending upon the functional requirements. An energy release and voltage-surge protection unit can promptly discharge the magnetic energy accumulated in the iron-core and suppress the induced and surge voltages of the dc circuit in a current limiting event. This device has been designed to reduce the magnitude of a fault current by about 50%, which will prevent the breaking capacity of the existing circuit breakers in the transmission network from being exceeded in the predictable future. This article presents structural and functional specifications and reports up-to-date live-grid operation data of the device.

Manufacturing and Test of a 35 kV/90 MVA Saturated Iron-Core Type Superconductive Fault Current Limiter for Live-Grid Operation

We have been carrying out a saturable iron core reactive type superconducting fault current limiter (SFCL) development program since 2002. The major two disadvantages that people used to be foretold for a saturable iron core reactive type SFCL are the massive use of iron (resulting in large size, heavy weight, and high cost) and the high induced voltage hazard to the dc superconducting coil (this may damage the current supply of the dc bias) as a fault takes place. We have found the ways to deal with these two problems, making such kind of equipment reliable and cost effective. In this paper, we will report the technical data and testing results of a 3 phase lab testing model. Some key design parameters of the 35 kV/100 MVA prototype will also be presented.

Development of Saturated Iron Core HTS Fault Current Limiters

A dc magnetization system, comprises a HTS dc bias coil, a current source, a high-speed switch, and an energy release circuit, was built for a 35 kV/90 MVA saturated iron-core fault current limiter to enhance its functional capability and reliability and to reduce its size and weight. The dc bias coil is made of high temperature superconducting silver sheathed Bi-2223 tapes with a magnetization capacity of 141,000 ampere ldr turns. The current source is able to supply a maximum of 350 A constant current. The energy release circuit was designed to quickly discharge the magnetic energy of the saturated iron cores and to suppress the voltage surge across the dc coil when the magnetization circuit was switched to open in a short-circuit event. This controllable magnetization system enables the fault current limiter to respond to a short-circuit fault in one millisecond, to reach full current limiting function in 5 milliseconds, and to re-saturate the iron cores in 800 milliseconds after the clearance of a fault. In this paper, we introduce the configuration and specifications of the system. Some experimental results are also reported.

DC Magnetization System for a 35 kV/90 MVA Superconducting Saturated Iron-Core Fault Current Limiter

The current limiter includes following parts: iron core set including two or more paired identical i«„…i» shaped iron cores prepared by piling silicon steel sheets; AC winding sheathed outside core leg, all AC windings in each phase cascaded are connected to AC power network in series; superconductive DC winding encircling all core legs inside iron core, and connected to constant DC power source; short circuit auxiliary winding placed at inside or outside superconductive DC winding, matched to superconductive DC winding in shape; induction breaker connected to DC loop of superconductive DC winding; Dewar is as a low temperature container, and the said all superconductive DC windings are put its vacuum cavity. The disclosed current limiter possesses features of fast response, quick speed for restricting short circuit current, simple structure, safe and reliable operation.

Quick current limiting type superconductive short circuit fault

The present invention relates to a compact iron core structure of a saturated core type superconductivity current limiter, which comprises two to six mouth-shaped iron cores, wherein, each mouth-shaped iron core comprises an intermediate iron core column, a side column, an upper yoke iron and a lower yoke iron. Each side column is sleeved with an alternating current winding, the cross-section shape of the intermediate iron core column is different from that of the side column, two to six of the intermediate iron core columns are compactly combined and assembled into a combined intermediate column which has an angle of 360 DEG around the center, an assembled insulating partition is arranged between each two intermediate iron core columns, the outline of a cross-section rim of the combined intermediate column is of a circle, and one direct current winding is sleeved outside the combined intermediate column. The iron core structure effectively utilizes space to ensure that the iron core structure is more reasonable, reduces the whole volume of a saturable core superconducting fault current limiter and a saturable reactor and so on, strengthens the excitation degree of the direct current winding to the iron cores, decreases the magnetic leakage, reduces manufacturing cost, and contributes to industrialized application.

Compact type core construction of iron saturation superconducting current limiter

The invention discloses a parallel superconducting fault current limiter, which comprises a reactance system, a direct current control system and a low-temperature system, wherein each phase of the reactance system consists of an iron core, two alternating current windings and a direct current exciting winding; and the two alternating windings are connected to a grid in parallel, and the two alternating current windings are the same. The ratio of the cross section of a direct current iron core column of the direct current exciting winding and the cross section of the alternating current iron core columns of the alternating windings is 1.01:10. Compared with serial superconducting fault current limiter, the novel superconducting fault current limiter has advantages in many aspects and thus represents a substantial progress in the industrialization process of the superconducting fault current limiter. The superconducting fault current limiter is expected to provide a breach to the further industrialization of the superconducting fault current limiter.

Yang Wang

Papers

Development of Saturated Iron Core HTS Fault Current Limiters

DC Magnetization System for a 35 kV/90 MVA Superconducting Saturated Iron-Core Fault Current Limiter

Quick current limiting type superconductive short circuit fault

Compact type core construction of iron saturation superconducting current limiter

Parallel superconducting fault current limiter