This dissertation addresses mathematical modelling applied to power system analysis within an international perspective. It consists of two parts: one of practical model development and one of theoretical model studies. The power systems to be analysed are more specifically those found in the Baltic Sea Region. They are characterised by having a mix of hydroelectric and thermal based production units, where the latter type includes the combined heat and power (CHP) plants that are widely used in e.g. Denmark and Finland. Focus is on the medium- to long-term perspective, i.e. within a time horizon of about 1 to 30 years. A main topic in the dissertation is the Balmorel model. Apart from the actual model, analyses of how to represent different elements appropriately in the model are presented. Most emphasis is on the representation of time and the modelling of various production units. Also, it has been analysed how the Balmorel model can be used to create inputs related to transmissions and/or prices to a more detailed production scheduling model covering a subsystem of the one represented in the Balmorel model. As an example of application of the Balmorel model, the dissertation presents results of an environmental policy analysis concerning the possible reduction of CO2, the promotion of renewable energy, and the costs associated with these aspects. Another topic is stochastic programming. A multistage stochastic model has been formulated of the Nordic power system. This allows analyses to be performed where the uncertainty of the inflow to the hydro reservoirs is handled endogenously. In this model snow reservoirs have been added in addition to the hydro reservoirs. Using this new approach allows sampling based decomposition algorithms to be used, which have proved to be efficient in solving multistage stochastic programming problems. For solving the stochastic model a new sampling based method was developed that performed as least as good as existing methods. Stopping criteria for use in this kind of algorithms are also addressed and a new one suggested, which ensures the quality of the solution with a user-specified probability.