Abstract Body

Force-balanced coils (FBCs) can balance the electromagnetic forces through a helically wound configuration and minimize the required mass of structures for energy storage based on the virial theorem [1]. Figure 1(a) shows a schematic illustration of the FBC windings. The darker hatch indicates one complete helical winding. The FBCs in Fig. 1(a) consist of six helical coils with six poloidal turns per toroidal turn.

High-temperature superconductors are expected to reduce refrigerator energy consumption for superconducting coils. The author conducted a design study of a 360-MWh SMES for daily load leveling using 15-kA REBCO conductors [2]. The 360-MWh SMES consists of 4000 superconducting coils with the FBC configuration. The energy cycle efficiency is estimated at least 70% with a cooling temperature of 20 K.

The FBCs can also reduce the vertical magnetic field that penetrates the helical windings by modulating the pitch of the winding. Figure 1(b) shows a schematic illustration of an ideal magnetic field distribution of the FBCs. One poloidal magnetic surface matches up with the coil surface to reduce the vertical magnetic field. By the effect of the modulated winding pitch, the FBCs can be expected to reduce the degradation of the critical current caused by the vertical magnetic field that penetrates REBCO conductors. However, three-dimensional complex shapes of the FBC helical windings may lower the critical current of REBCO conductors. In particular, the in-plane curvature of the FBC applies the edgewise strains to REBCO conductors. A geodesic trajectory of the FBC windings becomes one of the feasible solutions to minimize the in-plane curvature variations of the helical windings, effectively leading to minimizing the edgewise strains in REBCO conductors. The pitch modulation of the helical windings can also achieve the geodesic trajectory. To establish the winding technique of helical coils without a decrease in the critical current of REBCO conductors, the author’s research group develops a prototype of a winding machine for the FBC and designs a 1-T class small model coil using REBCO conductors [3].

This work discusses the design considerations of the FBC windings for SMES using high-temperature superconductors. First, the author summarizes the design conditions of the FBC windings and introduces the progress of the FBC research. Second, the author investigates the magnetic field distribution of the FBC windings and evaluates the feasibility of preventing the critical current degradation of high-temperature superconductors due to the vertical magnetic field. Figure 1(c) compares the pitch modulations between the magnetic surface pitch (minimization of the vertical magnetic field) and the geodesic pitch. Although the geodesic pitch will have almost the same trajectory as the magnetic surface pitch, a detailed evaluation of the vertical magnetic field is required. Finally, based on the scaling law, the author estimates the theoretical energy cycle efficiency determined by the mass of structures, the ampere-meters of high-temperature superconductors, and heat loads and explores the potentiality of the FBCs as SMES coils using high-temperature superconductors.

References

[1] S. Nomura and H. Tsutsui, “Structural limitations of energy storage systems based on the virial theorem,” IEEE Trans. Appl. Supercond., vol. 27, no. 4, Jun. 2017, Art. No. 5700106.

[2] S. Nomura, H. Chikaraishi, H. Tsutsui, and R. Shimada, “Feasibility study on large scale SMES for daily load levelling using force-balanced helical coils,” IEEE Trans. Appl. Supercond., vol. 23, no. 3, Jun. 2013, Art. No. 5700904.

[3] H. Kamada, A. Ninomiya, S. Nomura, T. Yagai, T. Nakamura, and H. Chikaraishi, “Development of 1-T class force-balanced helical coils using REBCO tapes,” IEEE Trans. Appl. Supercond., vol. 30, no. 4, Jun. 2020, Art. No. 4600905.

Figure 1. Schematic illustration of the FBC windings (a), the magnetic field distribution (b), and an example of the FBC winding trajectories depending on the difference of the pitch modulations (c).

Keywords: Electromagnetic force, helical coil, high-temperature superconductor, SMES