Modeling and optimization of gaseous helium (GHe) cooled high temperature superconducting (HTS) DC cables for high power density transmission

Highlights: • We introduce an HTS DC cable and cryostat transient mathematical model. • HTS DC cable and cryostat transient temperature distribution is assessed. • Model adjustment and experimental validation are conducted. • Total power consumption is estimated based on thermodynamic losses. • The model allows for system design, control and optimization. Superconducting cables are considered a viable technology to meet the increasing global demand of electricity transmission and distribution. This paper presents a transient mathematical model to predict the thermal response of a superconducting cable contained in a flexible cryostat. The model was conceived to be computationally fast so that system response according to variations of physical properties of the materials, and operating and design parameters could be assessed for optimization purposes. A volume element method (VEM) was utilized, which resulted in a system of ordinary differential equations with time as the independent variable. The model is also space dependent, through the establishment of a mesh with a known three-dimensional distribution of the volume elements in the computational domain. Pressure drop in the gas channels and the temperature gradient with respect to space in the flow direction were taken into account. The numerically calculated DC cable heat leak rate under different environmental conditions was initially adjusted and then experimentally validated by direct comparison to actual experimental data. The final part of the study consisted of using the experimentally validated model to perform the DC cable design and operating parameters optimization in order to obtain minimum heat leak rate and pumping power (or total consumed power). By adopting a fixed cable cross sectional area constraint (or total volume for a given length), an optimized helium channels geometry is also found that shows significant improvement in system performance in comparison to an existing system geometry. For example, for a GHe mass flow rate of 3.8 g s⁻¹, the cryostat with the original geometry is shown to consume 20.5% more power than with the optimized geometry. As a result, it is reasonable to state that the combination of accuracy and low computational time allow for the future utilization of the model as a reliable tool for HTS DC cable & cryostat simulation, control, design and optimization purposes.