Phase and Amplitude Synchronization in Power-Grid Frequency Fluctuations in the Nordic Grid

Abstract

Monitoring and modelling the power grid frequency is key to ensuring stability in the electrical power system. Many tools exist to investigate the detailed deterministic dynamics and especially the bulk behaviour of the frequency. However, far less attention has been paid to its stochastic properties, and there is a need for a cohesive framework that couples both short-time scale fluctuations and bulk behaviour. Moreover, commonly assumed uncorrelated stochastic noise is predominantly employed in modelling in energy systems. In this publication, we examine the stochastic properties of the Nordic Grid, focusing on the increments of the frequency recordings. We show that these increments follow non-Gaussian statistics and display spatial and temporal correlations. Furthermore, we report two different physical synchronisation phenomena: a very short timescale phase synchronisation (< 2 s) followed by a slightly larger timescale amplitude synchronisation (2 s-5 s). Overall, these results show that modelling of fluctuations in power systems should not be restricted to Gaussian white noise.INDEX TERMS Power-grid frequency, power-grid frequency fluctuations, phase synchronisation, amplitude synchronisation.

Microscopic Fluctuations in Power-Grid Frequency Recordings at the Subsecond Scale

“…Note that superstatistics has been discussed on power-grid frequency recordings before [11], and there are further hints that the dynamics of power-grid recordings get more complex on shorter time scales. In fact, if we consider the temporal scales wherein we observe the strongest evidence of multifractality, i.e., for t < 4 s, this agrees well with previous results [27,28], wherein powergrid frequency increments are shown to be well described by a convolution of Gaussian statistics with a parametric function of varying variance. All of this points to even more research is necessary to understand the complexity of powergrid frequency time series on this short time scale.…”

“…Meanwhile, time series with the higher temporal resolution is not easy to obtain. Still, this higher temporal resolution is critical to uncover key properties of the underlying system, see e.g., [27,28] and Figure 1: representative frequency trajectories on 1 s and on 100 ms (0.1 s) resolutions clearly display diferent behavior, with notable fuctuations and high volatility on the short time scale.…”

“…We notice the spatial dependency in the spectrum as diferent locations show diferent magnitudes and positions (in terms of time) of these peaks. Tis is explained by the fact that, e.g., north-south and east-west oscillations have different frequency; see also [15,27,35] for a more detailed discussion of this phenomenon.…”

Multiple satellite and ground clock sources‐based high‐precision time synchronization and lossless switching for distribution power system

“…wileyonlinelibrary.com/iet-com 2041 research on high-precision time synchronization of distribution power system based on multiple clock sources still faces several challenges. First, time synchronization error and time synchronization delay are coupled with each other [11,12]. Selecting a clock source with small time synchronization error may lead to large time synchronization delay due to poor channel condition between the selected source and the gateway, and vice versa.…”

“…First, time synchronization error and time synchronization delay are coupled with each other [11, 12]. Selecting a clock source with small time synchronization error may lead to large time synchronization delay due to poor channel condition between the selected source and the gateway, and vice versa.…”