AC loss modeling of stacked HTS strips with economic analysis

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Abstract

In order to fabricate high-current superconducting conductors for engineering applications, the configuration of stacked high-temperature superconductor (HTS) strips is one of the most popular choices. AC losses in HTS stacks have been vastly studied, but the economic study towards the AC losses with respect to the capital investment and operating costs of HTS stacks is still missing. First, the modelling strategy using the finite element method (FEM) based on the H-formulation is explained, and the basic AC loss simulation of a single strip is verified by the Norris analytical methods. The HTS stack (16 strips) is used as an example, and the corresponding current distribution and magnetic field are analyzed. The relationship between the AC loss and current-carrying capability is studied for multiple stacks with different numbers of strips. Economic analysis is performed with regard to the relationship between the AC losses and investment/operating costs of multiple stacked HTS strips. In this article, the numerical modeling together with the economic analysis of stacked HTS strips bring new visions, which can be beneficial for the future designs of high-current superconducting conductors and cables.

Introduction

The commercialization of second generation high-temperature superconductor (HTS) strips has brought the large-scale and widespread applications [1], such as nuclear fusion [2], magnetic resonance imaging [3], high-energy accelerators [4], fault current limiters [5,6], power cables [7,8] and superconducting magnetic energy storage [9,10]. In practical engineering applications, multiple superconducting tapes are usually stacked together to improve the capacity of current transmission, and obtain a stronger magnetic field to meet the requirements of actual applications [11]. In order to improve the current-carrying capacity of the second generation ReBCO tape, and develop high-current conductors with robust structures that can be used in high-field applications, several approaches have been proposed to make high-current cables using ReBCO tapes [12], including the conductor on round core (CORC) cable [13], [14], [15], Roebel cable [16], [17], [18], and several versions of twisted [19], [20], [21] and untwisted stacked-tape conductors [22].

As the number of HTS stacks increases, the magnetic field superposition by each HTS strip will cause larger overall AC loss [23]. In order to design efficient and economic superconducting cables, the regularity of AC loss needs to be thoroughly studied using modeling methods [24].

The modeling methods based on the finite element method (FEM) are widely used in the researches of superconductivity [25,26]. FEM analyses have been carried out to model the current density of single/multiple strips and their AC losses [27], [28], [29]. In general, there are several types of finite element methods that have been proposed fully or partly based on the Maxwell equations: T-A formulation [30], A-V formulation [31], T formulation [32,33], and H formulation [34,35]. It is important to accurately model the AC losses of HTS strips, and find out the relationship between the number of strips and the current-carrying capability, in order to optimize the performance of HTS stacks/cables.

Although AC losses in HTS stacks have been extensively investigated [36], [37], [38], the economic analysis on the AC losses regarding the capital investment and operating costs of HTS stacks/cables is still missing. This paper investigates the economic relationship between AC losses and investment/operating costs of multiple stacked HTS strips, and provides a general cost-analysis method which can be suitable for various HTS stacks/cables. Section 2 presents the numerical modeling method of HTS strips in details. Section 3 establishes the basic model of a single strip, and gives the comparison between the AC loss simulation and the AC loss calculation by the Norris analytical models [39]. In section 4, taking 16 stacked strips as an example, the magnetic field distribution and current distribution of HTS strips are analyzed. Section 5 studies the relationship between the AC loss and current-carrying capability of multiple strip stacks. Section 6 analyzes the economic relationship between the investment/operating costs of multiple HTS stacks and their AC losses. By using the numerical model and economic analysis, the stacked HTS strips are studied with respect to the AC loss calculation together with cost-analysis. The technical-economic methodology can be useful for the future designs of high-current superconducting conductors.

Section snippets

H-formulation

Finite-element method (FEM) simulations using the COMSOL Multiphysics [40] have been widely used in recent years to simulate the AC losses and electrodynamics of HTS [41], [42], [43]. For 2D simulations, the edge-element model is employed to calculate the magnetic field H and current density J, based on the following set of equations [44]:(μrμ0H)t+ρ×J=0J=×Hwhere μ0, μr and ρ are the vacuum permeability, relative permeability and resistivity, respectively. For a superconductor, ρ depends on

Single strip

The HTS material used in this work refers to a commercial ReBCO strip manufactured by Shanghai Superconductor Technology Co., Ltd. Its average width and thickness are about 4 mm and 75 μm, respectively. As mentioned above, this study is regarding the HTS strip working at the power frequency (e.g., 50 Hz), so we only focus the most important layer - the superconducting layer. The thickness is 1 μm and the width is 4 mm, which uses the real geometry of the superconducting layer.

Norris analytical

Multiple stacked strips

In order to increase the current-carrying capacity of the superconducting conductors, multiple strips are usually stacked. In this paper, an HTS stack is used as an example to explore the regularity of the AC losses in HTS stacks with multiple strips. In this section, 16 strips are stacked as an example to build a high-current conductor. The total current I in the HTS stack is:I=N×Ia×sin(2πft)

Fig. 4 presents the schematic of an HTS stack of 16 strips (the actual air domain in simulation is over

Strip usage and ac loss

After analyzing the characteristics of AC losses in multiple stacked strips, this section studies the relationship between the usage of strips with different numbers and the AC losses. Fig. 8 shows the strategy of stacking different numbers of HTS strips. Fig. 8(a-e) shows the strategy of 2, 4, 8, 16 and 32 HTS strips, respectively. The gap between each strip is set to be 0.1 mm.

Fig. 9 shows the relationship between the AC losses of multiple HTS stacks and the average current of a single strip.

Economic analysis

The results in Section 5 show that with the same transport current, the higher number of stacked strips is, the smaller the AC loss will be. However, in practical engineering applications, it is necessary to evaluate the static investment cost of stacked strips and the operating cost caused by AC losses. According to the actual operating conditions, the optimal number of stacked strips can be selected to satisfy a certain transport current.

As this is a small-scale study, the processing costs,

Conclusion

This article presents the numerical modeling together with the economic analysis of stacked HTS strips. The modeling uses the H-formulation based on the FEM platform COMSOL. The basic AC loss simulation of a single strip is well verified by the Norris analytical methods. The current density and magnetic field distribution of the HTS stack (16 strips) are further investigated.

The relationship between the AC loss and current-carrying capability is studied. One finding is that for the same

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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