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

Doubly fed induction generators (DFIGs) have attracted a wide interest for wind power generation, but they suffer from high sensitivity to grid disturbances, particularly grid faults. In this paper, a modified flux-coupling-type superconducting fault current limiter (SFCL) is suggested to improve the fault ride-through (FRT) capability of DFIGs. The SFCL's structure and principle is first presented. Then, considering that the SFCL can be installed at a DFIG's different locations, its influence mechanism to the DFIG's FRT capability is analyzed, and some technical discussions on the design of the SFCL are carried out. Furthermore, the simulation model of a 1.5-MW/690-V DFIG integrated with the SFCL is built, and the performance analysis is conducted. From the results, introducing the SFCL can effectively limit the fault currents across the DFIG's stator and rotor sides, and when the stator side is selected as the installation site, the terminal-voltage sag can be also improved, which helps prevent the disconnection of the DFIG from the power grid.

Fault Ride-Through Capability Enhancement of DFIG-Based Wind Turbine With a Flux-Coupling-Type SFCL Employed at Different Locations

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 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

High reliability is one of the key requirements for a power grid device. The reliability of a superconducting fault current limiter (SFCL) largely depends on the reliability of its cryogenic system. An open cryogenic system was designed and fabricated for a 220 kV/300 MVA saturated iron-core SFCL, which was composed of a Dewar, heat insulation pipelines, a liquid nitrogen tank, a control circuit, and a vacuum pump. In its configuration, a high-temperature superconducting (HTS) dc bias coil is immersed with liquid nitrogen inside the Dewar. The control circuit constantly monitors the liquid nitrogen level and controls the supply of liquid nitrogen in accordance with the liquid nitrogen level. Nitrogen vapor is directly released into the environment. The SFCL including the cryogenic system was installed in the Shigezhuang substation of Tianjin, China. There are three operation modes for the cryogenic system. The first is the ac coil and the HTS coil being loaded with current. The second is the HTS coil being loaded with current, while no current in the ac coil. The last mode is no current loading in both the coils. Operation data of the cryogenic system are analyzed to compare thermal load, pressure, and supply cycle of liquid nitrogen in the three operation modes.

Design, Fabrication, and Operation of the Cryogenic System for a 220 kV/300 MVA Saturated Iron-Core Superconducting Fault Current Limiter

The function of the superconducting bias coil in a saturated iron-core fault current limiter is to magnetize the iron cores. For practical utility devices of HV power grids, the rated capacity is usually 100 MVA or higher. The size and weight of the iron cores of a saturated iron-core fault current limiter with such capacity is quite large, so the bias coil needs to have high magnetization capacity and consequently a large diameter. The stability and safety of the bias coil are of critical importance for the reliability required by power utilities. Experience taught us that great care must be taken in the design, fabrication, testing, and grid operation to avoid potentially fatal risks. In this paper, we will discuss and analyze the possible safety hazards for a large size superconducting bias coil, which may result in mechanical failure and electrical impact, causing significant damage to the coil. Possible causes of the hazards are improper configuration, mismatch of component materials during thermal cycling, manufacturing failures in fabrication, lack of protection in testing and operation, etc. We will also report measures we took to eliminate or reduce these safety hazards.

Safety Considerations in the Design, Fabrication, Testing, and Operation of the DC Bias Coil of a Saturated Iron-Core Superconducting Fault Current Limiter

Bo Tian

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

Design, Fabrication, and Operation of the Cryogenic System for a 220 kV/300 MVA Saturated Iron-Core Superconducting Fault Current Limiter

Safety Considerations in the Design, Fabrication, Testing, and Operation of the DC Bias Coil of a Saturated Iron-Core Superconducting Fault Current Limiter

Dc bias system of a 35 kV/90 MVA saturated iron core SFCL