AC loss and modelling of superconducting machines for electric aircraft

Abstract

Superconducting machines may be used on electric aircraft because of the high current-carrying capacity of superconductors. After reviewing major superconducting machine topologies and prototypes in the 21st century, the ac loss of superconductors is studied analytically, numerically and experimentally.

Analytically, the ac loss of a multifilament MgB2 wire and a REBCO tape at different engineering current densities, temperatures and external magnetic fields are compared with copper and aluminum Litz wires using existing analytical formulas. Further, the ac losses and volumes of 3 MW, 4,500 rpm, 150 Hz synchronous machines with 0.4 T magnetic loading are compared when the armatures are made of the different conductors. In addition, the magnetic field distribution over time in partially and fully superconducting machines with MgB2 armature are modelled analytically. This information is used to calculate the ac loss of MgB2 wires using formulas developed in this thesis that calculate the loss of a multifilament wire under time-varying magnetic field that has two orthogonal components transverse to the wire’s longitudinal axis. The fast analytical programme developed is used to evaluate the mass and efficiency of many partially and fully superconducting machines rated at 3 MW, 4,500 rpm (32,400 geometries tested for each type).

Numerically, the integral method from the literature is used to calculate ac loss in superconducting tapes in an air-cored machine in a two-stage process: the magnetic field in the tape area is first calculated in a COMSOL model of the machine without the tapes, and then exported as the “external field” into the integral method model that consists of the tapes only. The time taken by the integral method is only 2% of the time taken by the T-A formulation in COMSOL for the full machine. The with-iron version of the integral method from the literature is applied in a similar manner to a machine with iron cores, but good agreement with COMSOL requires adjustment of the element size of the iron boundary by trial-and-error. Moreover, this thesis extends the integral method to model racetrack coils in which the cable is made of tapes that are coupled-at-ends (coupled at the terminals of the cable) and fully coupled (electrically connected along the whole cable length).

Experiments are performed on a novel experimental platform in which a superconducting coil wound from coupled tapes is cooled by circulating gaseous helium. Transport ac loss of the coil at approximately 35–45 K is measured using electrical methods: the method based on multiplying rms values of compensated voltage and current signals is compared with the method based on integrating the product of voltage and current signals. Regarding calorimetric methods, experimental results suggest that ac loss cannot be inferred from the difference between helium temperatures at the inlet and outlet of the sample chamber, but there is a clear and linear correlation between rise in temperature close to the sample and ac loss caused by transport ac at a given frequency.