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

Leonardo Rydin Gorjao,Luigi Vanfretti,Benjamin Schafer,Dirk Witthaut,Christian Beck

doi:10.1109/access.2022.3150338

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.

Highlights

T HE power-grid frequency is a key indicator of the stability of electric power systems
Our results further emphasise the outstanding importance of broad availability of highquality data for research on power system operation and energy science in general
Our analysis has shown two essential results: (1) If locations are relatively close electrically, the increments are correlated even at the shortest possible time lag of 0.02 s, indicating that ambient fluctuations of power generation and consumption that drive the frequency dynamics are correlated

Summary

INTRODUCTION

T HE power-grid frequency is a key indicator of the stability of electric power systems. An important practical research topic is the dynamics and design of inverter-based power grids lacking the inertia provided by large synchronous machines [11]–[14] Another key area is the development of detailed simulation models to study frequency dynamics and synchronisation for actual grid layouts and contingency situations [15], [16]. Other works exist highlighting the importance of short-term volatility in renewables [34] and even first spatio-temporal considerations in Continental Europe [35] and general power grid systems [36] Both spatio-temporal or general time series analysis require access to high-quality, spatially distributed frequency recordings with phasor measurement units (PMUs) or PMUlike devices. We firstly observe phase synchronisation propagating linearly through the network (0.5–2 seconds), which contrasts our second finding of a diffusive-like coupling in amplitude synchronisation (2–5 seconds)

SYNCHRONISATION PHENOMENA AND INCREMENT STATISTICS

PHASE AND AMPLITUDE SYNCHRONISATION

INCREMENT STATISTICS

PHASE SYNCHRONISATION

CONCLUSION