Coupled thermal-hydraulic and electrical modeling for high-voltage DC superconducting cables for power transmission

Activity carried out by: Sofia Viarengo (tutored by Prof. Laura Savoldi) in collaboration with Prof. Fabio Freschi.

The adoption of DC cables using High Temperature Superconductors (HTS), such as rare-earth (BSCCO or YBCO) tapes or MgB2 wires, is attractive for the DC transmission of high power at high voltage (HVDC) on very long distances, connecting for instance the EUMENA regions or within megalopolis. The current technology readiness level of HVDC HTS cables, preventing their strong penetration in the electric grids, is 5, but it should grow to 9 in the next 10 years by means of a dedicated R&D. One point that is actually weak, in the direction of increasing the stability, safety and reliability of such cables, is their numerical modeling, which needs and integrated thermal-hydraulic and electric approach. In the cable, the superconducting (SC) part, suitably stabilized, is actively cooled by N2 or He, and inserted into concentric cryogenic envelopes, which are shielded and insulated from the external ambient according to different alternative designs. Some modeling effort has been already done, for the pure thermal problem, by means of the lumped-parameters Volume Element Method (VEM), borrowed from the electronic device cooling field. A first coupling of the VEM to an electric model has been performed in literature, with some validation against experimental data. The coolant thermal-hydraulic transients in such model is reduced, however, to simple enthalpy balances, which are unsuited to deal with off-normal operating conditions. Dedicated models for the coolant have been developed, but currently only steady state.

Figure 1. View of a possible three-phase concentric HTS cable design [1].

The implementation of a new tool for HVDC HTS cables modeling, firstly, requires a detailed study of the start-of- art of the most advanced numerical models of superconductors. The thermo-hydraulic model will be a comprehensive modelling in transient conditions of different refrigerant fluid  paths envisaged in the most-advanced cables with the possibility to accounts for different coolants that could be present at the same time in different regions of the cable; moreover, the transient heat-conduction equation will consider for each cooled components of the cable (suitably coupled to fluid and solid components that have a thermal contact by conductive, convective or radiative thermal resistances). The magneto-quasi-static meso-scale will describe the current distribution accounting for the transient losses whenever present and the interaction between the different strands or tapes, according to the cable layout; suitable numerical techniques will be exploited to minimized the computational effort and the memory usage. The numerical tool will be integrated, macro-scale speaking, with the connection to the sub-stations for the fluid pumping.

Figure 2. A possible circuit configuration of the HTS cable system [2].

The development of a new numerical tool requires a rigorous validation & verification (V&V) procedure, in order to guarantee the validity and the quality of the outcomes. The purpose is to verify the code and its solution performed by a suitably numerical convergence analysis and manufactured solutions checks and a detailed benchmark against results of other models, mainly based on finite volume methods. The latter will be performed to check the capability of the code to reproduced published results modeling the same cable layout.

After that verifications, the validation against experimental data available from literature or from other laboratory will be also performed whenever possible.

References:

[1] W. T. B. De Sousa, D. Kottonau, J. Bock and M. Noe, "Investigation of a Concentric Three-Phase HTS Cable Connected to a SFCL Device", IEEE Transactions on Applied Superconductivity, vol. 20, n. 20, 2017

[2] S. Lee, H. Sung, M. Park, D. Won, J. Yoo, H. S. Yang, "Analysis of the Temperature Characteristics of Three-Phase Coaxial Superconducting Power Cable according to a Liquid Nitrogen Circulation Method for Real-Grid Application in Korea", Energies, vol. 12, n. 1740, 2019