Finite Element Model of Electrical Machines Coupled to the Grid Simulation Software

Using a finite element (FE) model of the electrical machine in a grid solver enables us to take the machine nonlinearities into account with great precision in the simulation of a complete system. Three methods are usually used for linking the grid and FE solver: direct coupling, lumped components, and current or voltage output approach. In this article, the coupling is treated as the resolution of a nonlinear equation system that is solved with the Newton method. The proposed linking scheme has been used to simulate a two phase short circuit on a hydrogenerator. Its results have been validated by running the same simulation with commercially available software.

Finite Element Model of Hydro Generators Coupled to a Grid Simulation Software

Gilles Rosselet

For the simulation of electrical power systems (adjustable speed drives, wind farms, complete grids, etc.) the Kirchhoff's model is used. Each of the components of this model (transmission line, circuit breaker, electrical machines, etc.) is represented by an equivalent circuit. These equivalent circuit models are unable to take precisely into account the non-linearities of the electrical machines. These non-linearities (eddy currents, magnetic saturation of the materials, skin effect) are however accurately predicted by the finite element method. The goal of this thesis is to add a finite element model of an electrical machine, the hydro generator, to a grid solver. The nature of the link between the grid solver and the finite element model is first investigated. Then, a finite element program used solely to the simulation of the hydro generator and to its link with a grid solver is designed. The features required for such a program are mandated by the physic of the device modelled: dealing with non-linear materials, eddy currents and taking the movement of the rotor into account. Furthermore, it is possible to use the symmetries of the studied device to reduce both the calculating time and the necessary memory. All these features were validated individually, before being used together in the simulation of a hydro generator.

EPFL2010

Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

Guillaume Jouvet

We address the free boundary problem that consists in finding the shape of a three dimensional glacier over a given period and under given climatic conditions. Glacier surface moves by sliding, internal shear and external exchange of mass. Ice is modelled as a non Newtonian fluid. Given the shape of the glacier, the velocity of ice is obtained by solving a stationary non-linear Stokes problem with a sliding law along the bedrock-ice interface. The shape of the glacier is updated by computing a Volume Of Fluid (VOF) function, which satisfies a transport equation. Climatic effects (accumulation and ablation of ice) are taken into account in the source term of this equation. A decoupling algorithm with a two-grid method allows the velocity of ice and the VOF to be computed using different numerical techniques, such that a Finite Element Method (FEM) and a characteristics method. On a theoretical level, we prove the well-posedness of the non-linear Stokes problem. A priori estimates for the convergence of the FEM are established by using a quasi-norm technique. Eventually, convergence of the linearisation schemes, such that a fixed point method and a Newton method, is proved. Several applications demonstrate the potential of the numerical method to simulate the motion of a glacier during a long period. The first one consists in the simulation of Rhone et Aletsch glacier from 1880 to 2100 by using climatic data provided by glaciologists. The glacier reconstructions over the last 120 years are validated against measurements. Afterwards, several different climatic scenarios are investigated in order to predict the shape the glaciers until 2100. A dramatic retreat during the 21st century is anticipated for both glaciers. The second application is an inverse problem. It aims to find a climate parametrization allowing a glacier to fit some of its moraines. Two other aspects of glaciology are also addressed in this thesis. The first one consists in modeling and in simulating ice collapse during the calving process. The previous ice flow model is supplemented by a Damage variable which describes the presence of micro crack in ice. An additional numerical scheme allows the Damage field to be solved and a two dimensional simulation of calving to be performed. The second problem aims to prove the existence of stationary ice sheet when considering shallow ice model and a simplified geometry. Numerical investigation confirms the theoretical result and shows physical properties of the solution.

EPFL2010

Fuel Cell Modeling and Simulations

Bernhard Andreaus, Nordahl Autissier, Diego Larrain, François Maréchal, Dimos Poulikakos

Fundamental and phenomenological models for cells, stacks, and complete systems of PEFC and SOFC are reviewed and their predictive power is assessed by comparing model simulations against experiments. Computationally efficient models suited for engineering design include the (1+1) dimensionality approach, which decouples the membrane in-plane and through-plane processes, and the volume-averaged-method (VAM) that considers only the lumped effect of pre-selected system components. The former model was shown to capture the measured lateral current density inhomogeneities in a PEFC and the latter was used for the optimization of commercial SOFC systems. State Space Modeling (SSM) was used to identify the main reaction pathways in SOFC and, in conjunction with the implementation of geometrically well- defined electrodes, has opened a new direction for the understanding of electrochemical reactions. Furthermore, SSM has advanced the understanding of the COpoisoning- induced anode impedance in PEFC. Detailed numerical models such as the Lattice Boltzmann (LB) method for transport in porous media and the full 3-D Computational Fluid Dynamics (CFD) Navier-Stokes simulations are addressed. These models contain all components of the relevant physics and they can improve the understanding of the related phenomena, a necessary condition for the development of both appropriate simplified models as well as reliable technologies. Within the LB framework, a technique for the characterization and computer- reconstruction of the porous electrode structure was developed using advanced pattern recognition algorithms. In CFD modeling, 3-D simulations were used to investigate SOFC with internal methane steam reforming and have exemplified the significance of porous and novel fractal channel distributors for the fuel and oxidant delivery, as well as for the cooling of PEFC. As importantly, the novel concept has been put forth of functionally designed, fractal-shaped fuel cells, showing promise of significant performance improvements over the conventional rectangular shaped units. Thermo-economic modeling for the optimization of PEFC is finally addressed.

2004

Fuel Cell Modeling and Simulations

Bernhard Andreaus, Nordahl Autissier, Diego Larrain, François Maréchal, Dimos Poulikakos

2004

Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

Guillaume Jouvet

EPFL2010