Théorie des perturbations | EPFL Graph Search

La théorie des perturbations est un domaine des mathématiques, qui consiste à étudier les contextes où il est possible de trouver une solution approchée à une équation en partant de la solution d'un problème plus simple. Plus précisément, on cherche une solution approchée à une équation (E) (dépendante d'un paramètre λ), sachant que la solution de l'équation (E) (correspondant à la valeur λ=0) est connue exactement. L'équation mathématique (E) peut être par exemple une équation algébrique ou une équation différentielle. La méthode consiste à chercher la solution approchée de l'équation (E) sous la forme d'un développement en série des puissances du paramètre λ, cette solution approchée étant supposée être une approximation d'autant meilleure de la solution exacte, mais inconnue, que la valeur absolue du paramètre λ est plus « petite ». Généralités Histoire Dès le début du , la théorie des perturbations a été utilisée par les astronomes pour les besoins de la méc

Phonon Lifetimes Throughout the Brillouin Zone at Elevated Temperatures from Experiment and ab initio

Albert Johann Glensk

We obtain phonon lifetimes in aluminium by inelastic neutron scattering experiments, by ab initio molecular dynamics, and by perturbation theory. At elevated temperatures significant discrepancies are found between experiment and perturbation theory, which disappear when using molecular dynamics due to the inclusion of full anharmonicity and the correct treatment of the multiphonon background. We show that multiple-site interactions are small and that local pairwise anharmonicity dominates phonon-phonon interactions, which permits an efficient computation of phonon lifetimes.

2019

Aspects of the energy transition and their effects on power systems

Laurent Vincent Pagnier

Most European countries are committed to an energy transition which consists in the substitution of conventional CO2 emitting energy sources by new renewable energy sources (RES), in particular wind and solar power. As opposed to conventional energy sources, new RES are distributed, non-dispatchable, fluctuating and inertialess and have negligible marginal costs. In this thesis, we investigate the impact of the energy transition on the electricity sector in Europe. In the first part of this thesis, we investigate the future electricity production and prices in Europe. We develop a dispatch algorithm on an aggregated model of the pan-European power grid with which we study the future European productions. We show that, as the penetration of new RES increases, the transmission grids are more strongly used and that more flexibility is required from conventional generators. The existing infrastructures seem to able to absorb, through increased international power exchanges and usage of the existing pumped-storage hydroelectricity, the variations of new RES productions even for high penetrations. Then we investigate the effects of new RES on electricity prices. We explain why, due to their negligible marginal cost and their lack of dispatchability, they tend to drag electricity prices down and can be considered as a reduction of the load in the electricity pricing. In particular, photovoltaics decreases the volatility of electricity prices. We show that, in most European countries, the day-ahead electricity price is strongly correlated with the residual load, which is obtained by subtracting the non-dispatchable productions, in particular those of the new RES, from the load. From this observation, we build an effective price model based solely on the residual load with which the revenues of different electricity producers are evaluated. The second part of this thesis deals with disturbances in large transmission grids. The substitution of conventional generators by inertialess RES reduces the amount of inertia connected to power systems which might affect their reliability. To examine the propagation of disturbances in large transmission grids, we develop a dynamical model of the continental European transmission grid. We observe that the magnitude of the disturbance following a power loss depends on the fault location. We show that when inertia and primary control are uniformly distributed, the faults exciting the slowest eigenmodes of the network Laplacian are followed by the strongest disturbances. Reducing inertia on those eigenmodes, which are mostly located in the periphery of the grid, affects more its resilience than when the reduction occurs in its center. Finally, we use perturbation theory to derive algorithms for optimal placement of inertia and primary control when some mild inhomogeneities are present in their distributions. We show that,when the vulnerability of the whole grid is taken into account, a uniform distribution of inertia is optimal and the primary control is best placed in the periphery of the grid.

EPFL2019

Aspects of the energy transition and their effects on power systems

Laurent Vincent Pagnier

EPFL2019