Isogeometric Analysis and Harmonic Stator-Rotor Coupling for Simulating Electric Machines

This work proposes Isogeometric Analysis as an alternative to classical finite elements for simulating electric machines. Through the spline-based Isogeometric discretization it is possible to parametrize the circular arcs exactly, thereby avoiding any geometrical error in the representation of the air gap where a high accuracy is mandatory. To increase the generality of the method, and to allow rotation, the rotor and the stator computational domains are constructed independently as multipatch entities. The two subdomains are then coupled using harmonic basis functions at the interface which gives rise to a saddle-point problem. The properties of Isogeometric Analysis combined with harmonic stator-rotor coupling are presented. The results and performance of the new approach are compared to the ones for a classical finite element method using a permanent magnet synchronous machine as an example

Simulation and Robust Optimization for Electric Devices with Uncertainties

This dissertation deals with modeling, simulation and optimization of low-frequency electromagnetic devices and quantification of the impact of uncertainties on these devices. The emphasis of these methods is on their application for electric machines. A Permanent Magnet Synchronous Machine (PMSM) is simulated using Iso-Geometric Analysis (IGA). An efficient modeling procedure has been established by incorporating a harmonic stator-rotor coupling. The procedure is found to be stable. Furthermore, it is found that there is strong reduction in computational time with respect to a classical monolithic finite element method. The properties of the ingredients of IGA, i.e. B-splines and Non-Uniform B-Splines, are exploited to conduct a shape optimization for the example of a Stern-Gerlach magnet. It is shown that the IGA framework is a reliable and promising tool for simulating and optimizing electric devices. Different formulations for robust optimization are recalled. The formulations are tested for the optimization of the size of the permanent magnet in a PMSM. It is shown that under the application of linearization the deterministic and the stochastic formulation are equivalent. An efficient deterministic optimization algorithm is constructed by the implementation of an affine decomposition. It is shown that the deterministic algorithm outperforms the widely used stochastic algorithms for this application. Finally, different models to incorporate uncertainties in the simulation of PMSMs are developed. They incorporate different types of rotor eccentricity, uncertainties in the permanent magnets (geometric and material related) and uncertainties that are introduced by the welding processes during the manufacturing. Their influences are studied using stochastic collocation and using the classical Monte Carlo method. Furthermore, the Multilevel Monte Carlo approach is combined with error estimation and applied to determine high dimensional uncertainties in a PMSM

A multilevel Monte Carlo method for high-dimensional uncertainty quantification of low-frequency electromagnetic devices

This work addresses uncertainty quantification of electromagnetic devices determined by the eddy current problem. The multilevel Monte Carlo (MLMC) method is used for the treatment of uncertain parameters while the devices are discretized in space by the finite element method. Both methods yield numerical approximations such that the total errors is split into stochastic and spatial contributions. We propose a particular implementation where the spatial error is controlled based on a Richardson-extrapolation-based error indicator. The stochastic error in turn is efficiently reduced in the MLMC approach by distributing the samples on multiple grids. The method is applied to a toy problem with closed-form solution and a permanent magnet synchronous machine with uncertainties. The uncertainties under consideration are related to the material properties in the stator and the magnets in the rotor. The examples show that the error indicator works reliably, the meshes used for the different levels do not have to be nested and, most importantly, MLMC reduces the computational cost by at least one order of magnitude compared to standard Monte Carlo

Uncertainty Quantification For A Permanent Magnet Synchronous Machine With Dynamic Rotor Eccentricity

The influence of dynamic eccentricity on the harmonic spectrum of the torque of a permanent magnet synchronous machine is studied. The spectrum is calculated by an energy balance method. Uncertainty quantification is applied by using generalized Polynomial Chaos and Monte Carlo. It is found that the displacement of the rotor impacts the spectrum of the torque the most

Simulation and Robust Optimization for Electric Devices with Uncertainties

This dissertation deals with modeling, simulation and optimization of low-frequency electromagnetic devices and quantification of the impact of uncertainties on these devices. The emphasis of these methods is on their application for electric machines. A Permanent Magnet Synchronous Machine (PMSM) is simulated using Iso-Geometric Analysis (IGA). An efficient modeling procedure has been established by incorporating a harmonic stator-rotor coupling. The procedure is found to be stable. Furthermore, it is found that there is strong reduction in computational time with respect to a classical monolithic finite element method. The properties of the ingredients of IGA, i.e. B-splines and Non-Uniform B-Splines, are exploited to conduct a shape optimization for the example of a Stern-Gerlach magnet. It is shown that the IGA framework is a reliable and promising tool for simulating and optimizing electric devices. Different formulations for robust optimization are recalled. The formulations are tested for the optimization of the size of the permanent magnet in a PMSM. It is shown that under the application of linearization the deterministic and the stochastic formulation are equivalent. An efficient deterministic optimization algorithm is constructed by the implementation of an affine decomposition. It is shown that the deterministic algorithm outperforms the widely used stochastic algorithms for this application. Finally, different models to incorporate uncertainties in the simulation of PMSMs are developed. They incorporate different types of rotor eccentricity, uncertainties in the permanent magnets (geometric and material related) and uncertainties that are introduced by the welding processes during the manufacturing. Their influences are studied using stochastic collocation and using the classical Monte Carlo method. Furthermore, the Multilevel Monte Carlo approach is combined with error estimation and applied to determine high dimensional uncertainties in a PMSM