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.

翻译：减缓气候变化需要从化石燃料向可再生能源转型。因此，发电波动性增大，微电网和孤岛电网运行方案正受到广泛讨论。研究物理岛屿的电力系统（作为孤岛微电网的模型），对于加深我们对电力系统稳定性的理解具有重要意义。本文研究了三个岛屿系统——冰岛、爱尔兰和巴利阿里群岛——的电力系统频率的统计特性。我们采用福克-普朗克方法构建描述市场行为、控制作用及噪声对电网动态影响的随机微分方程。利用所得参数，我们生成了频率动态的合成时间序列。本文的主要贡献在于提出了两种电力系统频率随机模型的扩展方案，并展示了这些新模型在岛屿场景中非高斯统计特性下的适用性。