Analytical AC Loss Comparison Between REBCO, MgB$_{2}$, Copper, and Aluminum Litz Wires for Cryogenic Electrical Machines

Cryogenic electrical machines can have high power densities because conductors can carry large current densities at low temperatures. This article compares four types of conductors: copper Litz wire, aluminum Litz wire, MgB<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula> multifilamentary wire, and REBCO tape, and one set of material parameters are used for each conductor for case studies in this article. Based on analytical loss formulas from the literature, the conductors' loss at different engineering current densities, temperatures, and external magnetic fields are compared. The effect of striating REBCO tapes is also investigated. On an individual conductor level, under simultaneous transport ac with external ac field of amplitude 0.4 T, both at 150 Hz, we find that when MgB<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{2}$</tex-math></inline-formula> and REBCO carry ac close to their critical current densities, their losses are lower than the losses of the Litz wires at the same current densities. Further, we consider 3 MW, 4500 rev/min, 150 Hz machines with magnetic loading of 0.4 T when the armature is made of the different conductors. As the current density in armature conductors increases, the machine volume decreases. At 77.5 K, machines with copper and aluminum Litz wires have lower losses than machines with REBCO for the same machine volumes. At 20 K, for small machine volumes, machines with aluminum Litz wire armatures have the lowest losses.