  Mitigating climate change requires a transition away from fossil fuels
towards renewable energy. As a result, power generation becomes more volatile
and options for microgrids and islanded power-grid operation are being broadly
discussed. Therefore, studying the power grids of physical islands, as a model
for islanded microgrids, is of particular interest when it comes to enhancing
our understanding of power-grid stability. In the present paper, we investigate
the statistical properties of the power-grid frequency of three island systems:
Iceland, Ireland, and the Balearic Islands. We utilise a Fokker-Planck approach
to construct stochastic differential equations that describe market activities,
control, and noise acting on power-grid dynamics. Using the obtained parameters
we create synthetic time series of the frequency dynamics. Our main
contribution is to propose two extensions of stochastic power-grid frequency
models and showcase the applicability of these new models to non-Gaussian
statistics, as encountered in islands.
