Important questions to enable the use of marine current energy are how the electrical system is designed, how multiple energy converters are interconnected offshore and how the power is transmitted to the shore. The Division of Electricity at Uppsala University have constructed and deployed a marine current energy converter in the river Daläven in Söderfors, Sweden. In the study presented in this article, a model of a near-shore low-voltage AC collection grid and a near-shore low-voltage DC collection grid is presented for the technology at the Söderfors test site. The models are implemented in MATLAB/Simulink. For collection grids of five turbines, it is shown that the proposed control schemes are able to deliver power to the distribution grid. The controllers are able to achieve this even when one turbine is suddenly disconnected from the grid. Furthermore, it is shown that the conduction losses of the DC system are higher than the losses of the AC system for nominal and high water speeds. However, in a qualitative comparison between the systems it is concluded that despite the higher losses, the DC system can be an interesting option. This is because fewer components need to be placed in the turbine, which is beneficial in offshore systems where space is a limiting factor. Furthermore, a DC system can be less expensive since fewer cables are needed.