Abstract
The energy system is rapidly changing to accommodate the increasing number of renewable generators and the general transition towards a more sustainable future. Simultaneously, business models and market designs evolve, affecting power-grid operation and power-grid frequency. Problems raised by this ongoing transition are increasingly addressed by transdisciplinary research approaches, ranging from purely mathematical modelling to applied case studies. These approaches require a stochastic description of consumer behaviour, fluctuations by renewables, market rules, and how they influence the stability of the power-grid frequency. Here, we introduce an easy-to-use, data-driven, stochastic model for the power-grid frequency and demonstrate how it reproduces key characteristics of the observed statistics of the Continental European and British power grids. We offer executable code and guidelines on how to use the model on any power grid for various mathematical or engineering applications.
Highlights
The energy system is currently undergoing a rapid transition towards a more sustainable future
New policies, technologies, and market structures are being implemented in various regions in the energy systems [2]
Regardless of the specific aspect of the energy system, one element remains unchanged: The electrical power system and the stability of its frequency are critical for a stable operation of our society [7]
Summary
The energy system is currently undergoing a rapid transition towards a more sustainable future. Drift terms describe the deterministic behaviour of the full stochastic system, e.g. the movement of a particle within a potential or in our case the control and damping forces acting within the power grid, causes a ‘‘drift’’ towards the stable state. From a data-driven perspective, we can recover the drift D(1) and diffusion D(2) coefficients strictly from the data by employing a histogram regression or a Nadaraya–Watson kernel estimator This approach is useful when the fundamental equations of motion are not known but we use it here to approximate the functional form of the Fokker–Planck equation and recover the primary control c1 and noise amplitude , as given by (3) and (4), respectively. In panel (b) the subtraction of the detrending on the data yields the purely stochastic process governing the power-grid frequency dynamics without deterministic or slow time scale influences. A single measurement of 60 minutes of data already entails a good ground for estimation but naturally employing as much data as possible yields more reliable parameter estimations, as well as the possibility of error estimation in an efficient way
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