In order to achieve net zero emissions from the electricity sector, the proportion of renewable energy sources connected to the electrical grid needs to be increased significantly in the coming years. Established renewable energy sources, such as wind power and solar power, will certainly be crucial in achieving this. However, marine energy sources, like marine current power and wave power, have the potential to significantly contribute to the increase of electricity from renewable energy. An important area of study to enable the use of marine energy sources is how to construct electrical systems for offshore renewable energy. Therefore, this thesis addresses some challenges regarding the grid connection of offshore renewable energy. Two important questions for offshore renewable energy are how the offshore electrical grid is constructed and how the power is transmitted to the shore. In the thesis, a review of AC and DC collection grid topologies is presented. Furthermore, HVAC and HVDC transmission for offshore applications are compared in a literature review. It is concluded that for transmission distances longer than 50 km to 100 km, the preferred technology appears to be HVDC. Regardless of how the offshore collection grid is constructed, the energy converters need to be connected to the collection grid and the distribution grid. Uppsala University has deployed a marine current energy converter in the river Dalälven in Söderfors, Sweden. The electrical grid connection system at the test site is based on a B2B converter technology. In the thesis, a simulation model of the grid connection system of the energy converter is presented. The grid connection system at the Söderfors test site includes an LC-filter connected to a power transformer. A novel transfer function is derived for this system and the transfer function is verified with simulations and experimental investigations. It is shown that the derived transfer function is able to capture the frequency response of the experimental system.