This thesis introduces a comprehensive methodology to improve electromagnetic transient (EMT) modelling of power cables systems. Several improved modelling and validation techniques are proposed at the parameter estimation, time domain simulation and validation stages of the EMT modelling of transmission lines. A novel approach is developed to model sector-shaped cables in electromagnetic transient type programs. First, the applicability of elemental sub-conductor technique is extended to accurately calculate the frequency dependent impedances of sector-shaped cables. The derived admittance and propagation characteristics of the sector-shaped cable are fitted with rational functions using the method of vector fitting in an EMT-type program. The time domain simulations are validated with the numerical inverse Laplace transform method. A novel frequency domain approach is presented to model cascaded transmission systems. The procedure is based on obtaining four composite propagation functions representing the cascaded system. The performance of the technique does not diminish with increased number of cascaded segments and it preserves the intrinsic details of each line segment. This method is capable of modelling cascaded overhead lines or cables with different characteristic admittances and line lengths. This method can be used to validate EMT models of cascaded transmission systems. An improved generalized transmission line model is introduced which is capable of accommodating time steps greater than the travel time of the line. The time step of the conventional EMT models of transmission lines is constrained by the smallest travel time of the line. When the high frequency transients at the line terminations are not of interest, inaccurate nominal π equivalents are used with large time steps to reduce the computational burden. The proposed model not only is more accurate than the π equivalents, but also degenerates to the conventional frequency dependent EMT model when used with time steps smaller than the travel time. Therefore, the proposed model is highly convenient as it can be used for all types of EMT simulations without resorting to nominal π equivalents when the large simulation time steps must be used to reduce computational burden. / February 2017

On étudie dans le cadre de la thèse une famille de schémas numériques permettant de résoudre les équations de Saint-Venant. Ces schémas utilisent une décomposition d'opérateur de type Lagrange-projection afin de séparer les ondes de gravité et les ondes de transport. Un traitement implicite du système acoustique (relié aux ondes de gravité) permet aux schémas de rester stable avec de grands pas de temps. La correction des flux de pression rend possible l'obtention d'une solution approchée précise quel que soit le régime d'écoulement vis-à-vis du nombre de Froude. Une attention toute particulière est portée sur le traitement du terme source qui permet la prise en compte de l'influence de la topographie. On obtient notamment la propriété dite équilibre permettant de conserver exactement certains états stationnaires, appelés état du "lac au repos". Des versions 1D et 2D sur maillages non-structurés de ces méthodes ont été étudiées et implémentées dans un cadre volumes finis. Enfin, une extension vers des méthodes ordres élevés Galerkin discontinue a été proposée en 1D avec des limiteurs classiques ainsi que combinée avec une boucle MOOD de limitation a posteriori. / In this thesis we study a family of numerical schemes solving the shallow water equations system. These schemes use a Lagrange-projection like splitting operator technique in order to separate the gravity waves and the transport waves. An implicit-explicit treatment of the acoustic system (linked to the gravity waves) allows the schemes to stay stable with large time step. The correction of the pressure fluxes enables the obtain of a precise approximation solution whatever the regime flow is with respect to the Froude number. A particular attention has been paid over the source term treatment which permits to take the topography into account. We especially obtain the so-called well-balanced property giving the exact conservation of some steady states, namely the "lake at rest" state. 1D and 2D versions of this methods have been studied and implemented in the finite volumes framework. Finally, a high order discontinuous Galerkin extension has been proposed in 1D with classical limiters along with a combined MOOD loop a posteriori limiting strategy.