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

TL;DR

This paper models the complex, non-Gaussian stochastic dynamics of island power-grid frequencies using extended stochastic differential equations, providing insights into microgrid stability amid renewable energy integration.

Contribution

It introduces two novel extensions to existing stochastic models, specifically tailored for non-Gaussian statistics observed in island power grids.

Findings

Successfully modeled frequency dynamics of Iceland, Ireland, and Balearic Islands.

Generated synthetic frequency time series matching real data.

Enhanced understanding of microgrid stability with renewable energy.

Abstract

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.