The stochastic nature of power-grid frequency in South Africa

Abstract

In this work, we explore two mechanisms that explain non-Gaussian behaviour of power-grid frequency recordings in the South African grid. We make use of a Fokker-Planck approach to power-grid frequency that yields a direct relation between common model parameters such as inertia, damping, and noise amplitude and non-parametric estimations of the same directly from power-grid frequency recordings. We propose two explanations for the non-Gaussian leptokurtic distributions in South Africa: the first based on multiplicative noise in power-grid frequency recordings, which we observe in South Africa; the second based on the well-known scheduled and unscheduled load shedding and rolling blackouts that beset South Africa. For the first we derive an analytic expression of the effects of multiplicative noise that permits the estimation of all statistical moments—and discuss drawbacks in comparison with the data; for the second we employ a simple numerical analysis with a modular power grid of South Africa. Both options help understand the statistics of power-grid frequency in South Africa—particularly the presence of heavy tails.