The energy transition will significantly impact distribution transformers as they will have to deal with more load on them, which is also more variable due to renewable energy sources. However, currently, these transformers are often not monitored with sensors. Therefore, the Dutch network operator Stedin asked to investigate the possibilities of a digital twin for distribution transformers without many sensors. This thesis presents two ways to do so: the currently most used but more empirical loading guide and a more analytical method where we solve Maxwell's equations using the finite element method (FEM). Furthermore, the transition to more renewable energy sources and sources that draw instant power from the grid causes the current to get distorted. This distortion can be mathematically analyzed using harmonic functions, and we will consider the impact of these harmonics in both the loading guide and the FEM model.

The loading guide is a method written in slightly different ways in the IEEE and IEC standards that takes the load on a transformer and the ambient temperature around the transformer to determine the hot spot temperature inside the transformer. By saying that the hot spot temperature is the warmest point inside the transformer, we can determine the percentage of loss of life of a transformer for a particular loading pattern. However, the loading guide only considers one set of parameter values for distribution transformers, which can vary widely in rating, location and ventilation household, leading to an over-or underestimation of the temperature, which in both cases can lead to extra costs. Additionally, the impact of harmonics is an empirical addition to the loading guide and only considers the effect on temperature rise and not the losses.

Therefore, we consider the transformer in a finite element approach. We solve Maxwell's equation on a transformer cross-section with the FEM, resulting in a 2D model that can calculate the losses for a particular geometry. This model is made using COMSOL Multiphysics. Furthermore, we calculate the core and winding losses under a harmonic load, resulting in considerably higher losses than without harmonics.

As the FEM model is quick and straightforward to run, it can serve as a first step towards developing a digital twin of distribution transformer, giving a way to determine the losses analytically. With future development, the model can provide better insight into the temperature distribution in the transformer.

In this thesis Bayesian Networks are used to predict European football matches between the years 2008 and 2016. The goal of this research is to see how the structures learned by different Bayesian Network learning algorithms influences the predictions. First the data is explored and modified to be used for Bayesian Networks and secondly the theory is explained using examples. Finally the theory is applied on the data and the structures are learned with the help of a bootstrap method and the predictions are validated using 5-fold cross validation. We can conclude that the networks learned by the algorithms and with the help of an expert give a good representation of the underlying relationships, but are not very good in prediction the end result.