Applications of graph theory in the energy sector, demonstrated with feature selection in electricity price forecasting

Sammanfattning: Graph theory is a mathematical study of objects and their pairwise relations, known as nodes and edges respectively. The birth of graph theory is often considered to take place in 1736 when the Swiss mathematician Leonhard Euler tried to solve a routing problem involving seven bridges of Königsberg in Prussia. In more recent times, graph theory has caught the attention of companies from all types of industries due to its power of modelling and analysing exceptionally large networks. This thesis investigates the usage of graph theory in the energy sector for a utility company, in particular Fortum whose activities consist of, but not limited to, production and distribution of electricity and heat. The output of the thesis is a wide overview of graph-theoretic concepts and their practical applications, as well as a study of a use-case where some concepts are put into deeper analysis. The chosen use-case within the scope of this thesis is feature selection - a process for reducing the number of features, also known as input variables, typically before a regression model is built to avoid overfitting and increase model interpretability. Five graph-based feature selection methods with different points of view are studied. Experiments are conducted on realistic data sets with many features to verify the legitimacy of the methods. One of the data sets is owned by Fortum and used for forecasting the electricity price, among other important quantities. The obtained results look promising according to several evaluation metrics and can be used by Fortum as a support tool to develop prediction models. In general, a utility company can likely take advantage graph theory in many ways and add value to their business with enriched mathematical knowledge.