Non-linear, bivariate stochastic modelling of power-grid frequency applied to islands

• Published in: arXiv.org
• Main Authors: Oberhofer, Ulrich, Leonardo Rydin Gorjão, Yalcin, G Cigdem, Kamps, Oliver, Veit Hagenmeyer, Schäfer, Benjamin
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 22.09.2023
• Subjects: Bivariate analysis; Computer Science - Systems and Control; Differential equations; Distributed generation; Fossil fuels; Islands; Noise control; Physics - Data Analysis, Statistics and Probability; Statistics - Applications; Stochastic models
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2301.04551

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.