Nonlinear Stochastic Modeling of the South Korean Power Grid Frequency Dynamics

The mitigation of climate change and the associated restructuring of the energy system is one of the most relevant challenges in society at the moment. A key aspect of the transformation of energy systems is the shift from the use of conventional energy sources to renewable ones. This leads to a more economical use of fossil resources and reduces the environmental impact, but also poses challenges. The increasing amount of renewable energy sources in power grids has a major impact on the grid structure and its stability. Ensuring stability under these changing conditions is a challenge, in particular since power grids and their dynamics differ from region to region. While several studies investigated US or European power grids, Asian grids, such as the South Korean power grid, have been less of a focus. In this article, we analyze in particular the nonlinearity and the bimodality of the frequency time series, and perform a correlation analysis. Further, we use stochastic Fokker-Planck models to create synthetic frequency time series both in a linear and nonlinear manner. We examine the synthetic time series modeled in this way and compare their statistical properties with the empirical data. Thereby, we demonstrate how simple stochastic differential equations can provide a simplified model for the grid frequency, and observe that a model with nonlinear dynamics approximates the empirical data better than a purely linear one.