The application of high-temperature superconductors to accelerator magnets for future particle colliders is under study. Numerical methods are crucial for an accurate evaluation of the complex dynamical behavior of the magnets, especially concerning the magnetic field quality and thermal behavior. We present a coupled A-H field formulation for the analysis of magneto-thermal transients in accelerator magnets. The magnetic field strength H accounts for the eddy current problem in the source regions containing the superconducting domains, while the magnetic vector potential A represents the magnetoquasistatic problem in the normal and non-conducting domains. Furthermore, we include a thin shell approximation for the source regions, making the formulation suitable for large scale models composed of thousands of tapes. In this work, the relevant equations are derived and discussed, with emphasis on the coupling conditions. The weak formulation is derived, and numerical results are provided in order to both, verify the formulation and scale it to the size of an accelerator magnet.

The design of an electrical machine can be quantified and evaluated by Key Performance Indicators (KPIs) such as maximum torque, critical field strength, costs of active parts, sound power, etc. Generally, cross-domain tool-chains are used to optimize all the KPIs from different domains (multi-objective optimization) by varying the given input parameters in the largest possible design space. This optimization process involves magneto-static finite element simulation to obtain these decisive KPIs. It makes the whole process a vehemently time-consuming computational task that counts on the availability of resources with the involvement of high computational cost. In this paper, a data-aided, deep learning-based meta-model is employed to predict the KPIs of an electrical machine quickly and with high accuracy to accelerate the full optimization process and reduce its computational costs. The focus is on analyzing various forms of input data that serve as a geometry representation of the machine. Namely, these are the cross-section image of the electrical machine that allows a very general description of the geometry relating to different topologies and the classical way of scalar geometry parameterizations. The impact of the resolution of the image is studied in detail. The results show a high prediction accuracy and proof that deep learning-based meta-models are able to minimize the optimization time. The results also indicate that the prediction quality of an image-based approach can be made comparable to the classical way based on scalar parameters.

In this paper, the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic character due to non-conducting regions. It is shown how the necessary modification can be automatically incorporated by using a suitable time-stepping method. This paper closes with the first demonstration of a simulation of a realistic four-pole induction machine model using Parareal.

Conventional magneto-static finite element (FE) analysis of electrical machine design is time-consuming and computationally expensive. Since each machine topology has a distinct set of parameters, design optimization is commonly performed independently. This article presents a novel method for predicting key performance indicators (KPIs) of differently parameterized electrical machine topologies at the same time by mapping a high-dimensional integrated design parameters in a lower-dimensional latent space using a variational autoencoder (VAE). After training, via a latent space, the decoder and multi-layer neural network will function as meta-models for sampling new designs and predicting associated KPIs, respectively. This enables parameter-based concurrent multi-topology optimization.

This work deals with shape optimization of electric machines using isogeometric analysis. Isogeometric analysis is particularly well suited for shape optimization as it allows to easily modify the geometry without remeshing the domain. A 6-pole interior permanent magnet synchronous machine (IPMSM) is modeled using a multipatch isogeometric approach and rotation of the machine is realized by modeling the stator and rotor domain separately and coupling them at the interface using harmonic basis functions. Shape sensitivity analysis is used to find the shape derivative of the optimization goal functional, i.e., the total harmonic distortion of the electromotive force. This method allows for a freeform shape optimization which is not restricted by a choice of a set of optimization parameters. This freeform shape optimization is applied for the first time to an isogeometric model of an IPMSM minimizing the total harmonic distortion of the electromotive force as a goal functional, where a reduction of 75 % is achieved.