Abstract Body

In a linear machine the DC HTS superconducting coils, placed in the stator, can be subjected to a spatially non-uniform and time-varying external magnetic field originating from the AC coils in the mover, while carrying a transport current. Under these conditions, AC losses are generated in the superconducting coils.

In this paper, a new two dimensional analytical approach is proposed by authors to calculate the above mentioned AC losses.

The two-dimensional configuration analyzed in this study contains HTS-taped coils with multiple turns positioned in the stator, and three-phase AC commutated coils are placed in the mover.

The developed analytical methodology combines two existing analytical approaches: the Harmonic Modeling Technique [1] for the analysis of the magnetic field produced by the coils in the mover and the Integral Method [2, 3] for the analysis of the AC losses in the superconductive coils in the stator. The Harmonic Modelling Technique is based on the Fourier analysis where the total geometry is divided into different periodic orthogonal regions. For each region the field solution is obtained by solving the Maxwell equations in terms of the magnetic vector potential A_z and offers an accurate and fast modeling of the electromagnetic phenomena.The Harmonic Modeling Technique is used to predict the spatially non-uniform and time-varying external magnetic field generated by the coils in the mover within the superconducting region, without considering the HTS tapes. As illustrated in Fig.1, initially the region above the moving coils, where the HTS coils are supposed to be, is treated as an air for the analysis of the magnetic vector potential A_z and its derivative in time. The simulation considers multiple time steps (N = 100) to observe the variation in time of the vector magnetic field.

The Integral Method is then used to calculate the AC losses induced in the multiple superconducting tapes in the air by the external magnetic field, which is predicted by means of the Harmonic Modeling Technique. Each tape can be discretized into one-dimensional element with no width. In this analysis the electric field E is a function of the current density J according to the non-linear E-J Power Law, where the critical current density J_c is taken as constant.

The developed analytical method is validated by COMSOL FEM software with the T-A formulation, using the same configuration of the 2D linear motor structure shown in Fig.1, where the superconducting coils are placed in the Region Under Investigation.

The composition of both semi-analytical models developed for superconducting linear machine significantly reduces the simulation time due to their efficient computational performance in comparison with numerical simulations.

References

[1] B. L. J. Gysen, “Generalized harmonic modeling technique for 2D electromagnetic problems: applied to the design of a direct-drive active suspension system”, PhD thesis, Eindhoven University of Technology (2011).
[2] C. Chow and K. T. Chau, “Numerical modelling of HTS tapes under arbitrary external field and transport current via integral method: review and application to electrical machines”, Superconductor Science and Technology, Vol. 36 (2023).
[3] S. Otten and F. Grilli, “Simple and Fast Method for Computing Induced Currents in Superconductors Using Freely Available Solvers for Ordinary Differential Equations”, IEEE Transactions on Applied Superconductivity, vol. 29, pp. 1-8 (2019).

Acknowledgment

This research is carried out under project number T21018 in the framework of the Research Program of the Materials innovation institute (M2i) (www.m2i.nl ) supported by the Dutch government.

Figure 1. Analytical method based on the Harmonic Modelling Technique and the Integral Method. Representation of all the time steps: (a) the Magnetic Vector Potential, (b) its derivative in time.

Keywords: AC Losses Analysis, Integral Method, Harmonic Modeling Technique, Superconducting Linear Motor.