Numerical analysis of electromagnetic fields by Proper Generalized Decomposition in electrical machines
Final Report Abstract
The numerical simulation of electrical machines, holding large DOF, represent a major computational effort which can be avoided by using model order reduction techniques. The Proper Generalized Decomposition (PGD) shows particular advantages in terms of flexibility and computational savings. In this project, the PGD is employed to a wide variety of electromagnetic field problems occurring in the analysis of electrical machines. The PGD is combined with the magnetic vector potential formulation and the magneto-dynamic 𝑇 − Ω − formulation. The feasibility is underlined by accurate results in three-dimensional simulations. A comparison with the Proper Orthogonal Decomposition, which is a widely established MOR-technique, shows that the PGD comes with a similar accuracy without the requirement of previously computed solutions. Consecutively, a combination of the singular value decomposition and the mathematical residual is presented to cope with the restriction to a-posteriori error criteria which is contradictory to an a-priori reduction method. After the general appropriability for linear time dependent problems has been shown, the Discrete Empirical Interpolation Method (DEIM) is combined with the PGD and by implementing an optimized greedy algorithm in the DEIM, the stability is improved. The simulations of different machines indicate the feasibility and the reduction in terms of DOF is greatly improved. In a final step, the parametric extension of the PGD to different machine parameters copes with the large computational effort related to parameter studies, while ensuring technical relevant accuracy. An in-depth study of different domain-coupling methods in combination with the PGD to reduce the computational effort depicted that for linear simulations inhomogeneous Dirichlet boundary conditions are a useful tool, however, in nonlinear simulations it is not generally feasible. To extend the PGD to non- conforming domains, a combination with Lagrange Multipliers is presented, which enables to combine a coarse mesh in the complementary region with a fine mesh in the subdomain of particular interest.
Publications
- "Measurement and Simulation of a Rotational Single Sheet Tester," in Archives of Electrical Engineering, vol. 1, no. 68, pp. 173-183, 2019
F. Müller, G. Bavendiek, B. Schauerte and K. Hameyer
(See online at https://doi.org/10.24425/aee.2019.125988) - "Error Estimators for Proper Generalized Decomposition in Time-Dependent Electromagnetic Field Problems," in IEEE Transaction on Magnetics, vol. 56, no. 1, pp. 1-4, Jan. 2020
F. Müller, T. Henneron, S. Clénet and K. Hameyer
(See online at https://doi.org/10.1109/tmag.2019.2949094) - "Model Order Reduction Techniques Applied to Magnetodynamic T-Ω-Formulation," in COMPEL – The international journal for computation and mathematics in electrical and electronic engineering, vol. 39, no. 5, pp. 1057-1069, May 2020
F. Müller, L. Crampen, T. Henneron, S. Clénet and K. Hameyer
(See online at https://doi.org/10.1108/compel-01-2020-0025) - "Efficient Estimation of Electrical Machine Behavior by Model Order Reduction," in IEEE Transaction on Magnetics, vol. 57, no. 6, pp. 1-4, Jun. 2021
F. Müller, A. Siokos, J. Kolb, M. Nell and K. Hameyer
(See online at https://doi.org/10.1109/tmag.2021.3070183) - "Remanence Deviations in Permanent Magnet Synchronous Machines Evaluated Using a Model Order Reduction Approach," in EMF 2021 – The 12th International Symposium on Electric and Magnetic Fields, Marseille, France, July, 2021
J. Kolb, F. Müller and K. Hameyer
- „Nonlinear Parametric Simulation by Proper Generalized Decomposition on the Example of a Synchronous Machine,” in ISEF 2021 - 20th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering, Cracow, Poland, September, 2021
F. Müller, P. Baumanns, M. Nell and K. Hameyer
- “Consideration of Rotational Motion in the Proper Generalized Decomposition by a Sliding Interface Technique,” COMPUMAG 2021 - 23rd International Conference on the Computation of Electromagnetic Fields, Cancun, Mexico, January, 2022
F. Müller and K. Hameyer
(See online at https://doi.org/10.1109/tmag.2022.3159093)
