The current capacity of high-temperature superconductors (HTS) has encouraged several applications of these materials in electric power systems. These applications in electrical machines represent a promising solution for more compact and efficient designs. Despite no measurable resistance in the superconducting state, HTS could experience losses under time changing transport current or magnetic field. Therefore, loss estimation is a key input for the design. Maxwell's equations in the T-A formulation form can be used to model and estimate losses in the superconducting tapes of an electrical machine. This formulation requires the current as a function of time in each superconducting tape as an input. A methodology to calculate this current distribution is presented in this article. The procedure introduces a previous step in the building model process and allows a better connection of the machine design with the estimation of losses in the superconductor in order to get a more efficient machine. The approach is applied to a 10 MW superconducting generator, where over one thousand tapes cross-sections are modelled in 2D. The superconductor's non-linear behaviour and critical current density anisotropy are considered. Losses are estimated for different designs and a sensitivity analysis is presented for different temperatures and frequencies, in addition to other alternatives to reduce losses. INDEX TERMS AC Losses, superconducting generator, high-temperature superconductors, T-A formulation.

The modeling and analysis of superconducting coils is an essential task in the design stage of most devices based on high-temperature superconductors (HTS). These calculations allow verifying basic estimations and assumptions, proposing improvements, and computing quantities that are not easy to calculate with an analytical approach. For instance, the estimation of losses in HTS is fundamental during the design stage since losses can strongly influence the cooling system requirements and operating temperature. Typically, 2D finite element analysis is used to calculate AC losses in HTS, due to the lack of analytical solutions that can accurately represent complex operating conditions such as AC transport current and AC external applied magnetic field in coils. These 2D models are usually a representation of an infinitely long arrangement. Therefore, they cannot be used to analyze end effects and complex 3D configurations. In this publication, we use the homogenization of the T-A formulation in 3D for the analysis of superconducting coils with complex geometries where a 2D approach can not provide accurate analyses and verification of assumptions. The modeling methodology allows an easier implementation in commercial software (COMSOL Multiphysics) in comparison with the currently available 3D H homogenization, despite the complexity of the geometry. This methodology is first validated with a racetrack coil (benchmark case) by comparing the results with the well-established H formulation. Then, the electromagnetic behavior of coils with more complex geometries is analyzed.

Hysteretic losses in MgB 2 wound superconducting coils of a 500 kW synchronous hybrid generator were estimated as part of the European project SUPRAPOWER led by the Spanish company Tecnalia Research and Innovation. Particular interest was given to the losses found in tapes in the superconducting rotor caused by the magnetic flux ripples originating from the conventional stator during nominal operation. To compute the losses, a 2D Finite Element Method was applied to solve the H-formulation of Maxwell's equations considering the nonlinear properties of both the superconducting material and its surrounding Ni matrix. To be able to model all the different turns composing the winding of the superconducting rotor coils, three geometrical models of single tape cross section of decreasing complexity were studied: 1) the first model reproduced closely the actual cross section obtained from micrographs, 2) the second model was obtained from the computed elastoplastic deformation of a round Ni wire, 3) the last model was based on a simplified elliptic cross section. The last geometry allowed validating the modeling technique by comparing numerical losses with results from well-established analytical expressions. Additionally, the following cases of filament transpositions were studied: no, partial and full transposition. Finally, choosing the right level of geometrical details to predict the expected behavior of individual superconducting tapes in the rotor, the following operational regimes were studied: Bias-DC current, ramping current under ramping background field, and magnetic flux ripples under DC background current and field.

One of the main tasks during the design of a superconducting electrical machine is the estimation of losses in the superconducting coils. These losses can be decisive in such applications since they influence the cooling power requirements and the overall efficiency of the machine. In this publication, we focus on the dissipation in the stator superconducting coils of a synchronous machine for a wind turbine application. The T-A formulation of Maxwell's equations is used in a 2D finite element model to analyse the behaviour of the magnetic field around the coils and calculate losses. Particular attention is given to the position of the coils inside a slot and several coil configurations are presented. It is shown that certain coil arrangements lead to a significantly lower total loss, a more uniform loss distribution, which ultimately leads to the possibility of increasing the operating temperature.

In order to reliably make use of superconductors in wind generators, a double-stator superconducting flux modulation generator is proposed here to avoid rotation of field coils and armature windings. The superconducting field coils are located in the inner stator while the armature windings are placed in the outer stator. In this way, the stationary-rotatory couplings of current and cryogenic coolants for superconducting field coils and/or armature windings are removed. Because of the modulation effect of the reluctance rotor between the two stators and the armature reaction field, moving AC magnetic fields are acted on superconducting coils in the inner stator. These moving AC magnetic fields are called magnetic field harmonics in the flux modulation generators. The frequencies of these harmonics are multiples of rotor mechanical frequency. Compared to synchronous superconducting generators, the amplitudes of the harmonics are higher. Even though methods to reduce the amplitudes of harmonics have been studied, the level of the AC loss in the superconducting field coils is still unknown. In this paper, numerical simulations based on the T–A formulation are used to estimate the AC loss of the superconducting field coils in a 10 MW double-stator superconducting flux modulation generator. It is found that by choosing a suitable working temperature, the AC loss of the superconducting field coils without any harmonic reduction methods is not very high, but eddy current loss of copper thermal shield inside the cryostat is significantly higher.