The topic of grid-forming inverters (GFM) has been trending in power system research for some time, as it unlocks new opportunities in the renewable transition. One example of this is the power system in Suðuroy, Faroe Islands, which frequently runs on 100\% wind power production, with the help of a GFM battery system (6.3 MW/7.5 MWh) and a synchronous condenser (8 MVA), both installed in 2022. The island has an installed wind power capacity of 6.3 MW and an average demand of 4 MW; hence the wind power penetration is frequently high. The battery system was designed to stabilize the frequency in the island and to be able to manage power quality of the island by rapidly injecting or absorbing power in case of a sudden change in wind power production, while the synchronous condenser was sized to deliver the same amount of short circuit power as the existing thermal power plant, i.e. the short circuit power contribution from the GFM battery system was not considered. This paper aims to assess the contribution from the GFM battery system to system disturbances. This study is based on EMT simulation studies, which have to be verified through field testing in future works.