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Due to power system deregulations, transmission expansion not keeping up with the load growth, and higher frequency of natural hazards resulting from climate change, major blackouts are becoming more frequent and are spreading over larger regions, entailing higher losses and costs to the economy and the society of many countries in the world. Large-scale blackouts typically result from cascading failure originating from a local event, as typified by the 2003 U.S.-Canada blackout. Their mitigation in power system planning calls for the development of methods and algorithms that assess the risk of cascading failures due to relay over-tripping, short-circuits induced by overgrown vegetation, voltage sags, line and transformer overloading, transient instabilities, voltage collapse, to cite a few. How to control the economic losses of blackouts is gaining a lot of attention among power researchers. In this research work, we develop new Monte Carlo methods and algorithms that assess and manage the risk of cascading failure in composite reliability of deregulated power systems. To reduce the large computational burden involved by the simulations, we make use of importance sampling techniques utilizing the Weibull distribution when modeling power generator outages. Another computing time reduction is achieved by applying importance sampling together with antithetic variates. It is shown that both methods noticeably reduce the number of samples that need to be investigated while maintaining the accuracy of the results at a desirable level. With the advent of microgrids, the assessment of their benefits in power systems is becoming a prominent research topic. In this research work, we investigate their potential positive impact on power system reliability while performing an optimal coordination among three energy sources within microgrids, namely renewable energy conversion, energy storage and micro-turbine generation. This coordination is modeled when applying sequential Monte Carlo simulations, which seek the best placement and sizing of microgrids in composite reliability of a deregulated power system that minimize the risk of cascading failure leading to blackouts subject to fixed investment budget. The performance of the approach is evaluated on the Roy Billinton Test System (RBTS) and the IEEE Reliability Test System (RTS). Simulation results show that in both power systems, microgrids contribute to the improvement of system reliability and the decrease of the risk of cascading failure. / Ph. D.

Measuring the risk of a credit portfolio is a challenge for financial institutions because of the regulations brought by the Basel Committee. In recent years lots of models and state-of-the-art methods, which utilize Monte Carlo simulation, were proposed to solve this problem. In most of the models factors are used to account for the correlations between obligors. We concentrate on the the normal copula model, which assumes multivariate normality of the factors. Computation of value at risk (VaR) and expected shortfall (ES) for realistic credit portfolio models is subtle, since, (i) there is dependency throughout the portfolio; (ii) an efficient method is required to compute tail loss probabilities and conditional expectations at multiple points simultaneously. This is why Monte Carlo simulation must be improved by variance reduction techniques such as importance sampling (IS). Thus a new method is developed for simulating tail loss probabilities and conditional expectations for a standard credit risk portfolio. The new method is an integration of IS with inner replications using geometric shortcut for dependent obligors in a normal copula framework. Numerical results show that the new method is better than naive simulation for computing tail loss probabilities and conditional expectations at a single x and VaR value. Finally, it is shown that compared to the standard t statistic a skewness-correction method of Peter Hall is a simple and more accurate alternative for constructing confidence intervals. (author´s abstract) / Series: Research Report Series / Department of Statistics and Mathematics

L’optimisation des traitements en radiothérapie vise à améliorer la précision de l’irradiation des cellules cancéreuses pour épargner le plus possible les organes environnants. Or la dose périphérique déposée dans les tissus les plus éloignés de la tumeur n’est actuellement pas calculée par les logiciels de planification de traitement, alors qu’elle peut être responsable de l’induction de cancers secondaires radio-induits. Parmi les différentes composantes, les neutrons produits par processus photo-nucléaires sont les particules secondaires pour lesquelles il y a un manque important de données dosimétriques. Une étude expérimentale et par simulation Monte Carlo de la production des neutrons secondaires en radiothérapie nous a conduit à développer un algorithme qui utilise la précision du calcul Monte Carlo pour l’estimation de la distribution 3D de la dose neutron délivrée au patient. Un tel outil permettra la création de bases de données dosimétriques pouvant être utilisées pour l’amélioration des modèles mathématiques « dose-risque » spécifiques à l’irradiation des organes périphériques à de faibles doses en radiothérapie. / Treatment optimization in radiotherapy aims at increasing the accuracy of cancer cell irradiation while saving the surrounding healthy organs. However, the peripheral dose deposited in healthy tissues far away from the tumour are currently not calculated by the treatment planning systems even if it can be responsible for radiation induced secondary cancers. Among the different components, neutrons produced through photo-nuclear processes are suffering from an important lack of dosimetric data. An experimental and Monte Carlo simulation study of the secondary neutron production in radiotherapy led us to develop an algorithm using the Monte Carlo calculation precision to estimate the 3D neutron dose delivered to the patient. Such a tool will allow the generation of dosimetric data bases ready to be used for the improvement of “dose-risk” mathematical models specific to the low dose irradiation to peripheral organs occurring in radiotherapy.