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Electricity markets are central to the coordination of power generation and demand. The European power system is divided into several bidding zones, each having an individual electricity market price. While individual price time series have been intensively studied in recent years, spatiotemporal aspects have received little attention. This article provides a comprehensive data-centric analysis of the patterns and correlations of the European day-ahead electricity prices between 2019 and 2023, characteristically abnormal due to the energy crisis in Europe. We identify the dominant communities of bidding zones and show that spatial differences can be described with very few principal components. Most bidding zones in Continental Europe were brought together during the energy crisis: Correlations increased, and the number of relevant principal components decreased. Opposite effects occur in the Nordic countries and the Iberian Peninsula where correlations decrease and communities fragment. [ABSTRACT FROM AUTHOR]

During the last glacial interval, the Northern Hemisphere climate was punctuated by a series of abrupt changes between two characteristic climate regimes. The existence of stadial (cold) and interstadial (milder) periods is typically attributed to a hypothesised bistability in the glacial North Atlantic climate system, allowing for rapid transitions from the stadial to the interstadial state – the so-called Dansgaard–Oeschger (DO) events – and more gradual yet still fairly abrupt reverse shifts. The physical mechanisms driving these regime transitions remain debated. DO events are characterised by substantial warming over Greenland and a reorganisation of the Northern Hemisphere atmospheric circulation, which are evident from concomitant shifts in the δ18 O ratios and dust concentration records from Greenland ice cores. Treating the combined δ18 O and dust record obtained by the North Greenland Ice Core Project (NGRIP) as a realisation of a two-dimensional, time-homogeneous, and Markovian stochastic process, we present a reconstruction of its underlying deterministic drift based on the leading-order terms of the Kramers–Moyal equation. The analysis reveals two basins of attraction in the two-dimensional state space that can be identified with the stadial and interstadial regimes. The drift term of the dust exhibits a double-fold bifurcation structure, while – in contrast to prevailing assumptions – the δ18 O component of the drift is clearly mono-stable. This suggests that the last glacial's Greenland temperatures should not be regarded as an intrinsically bistable climate variable. Instead, the two-regime nature of the δ18 O record is apparently inherited from a coupling to another bistable climate process. In contrast, the bistability evidenced in the dust drift points to the presence of two stable circulation regimes of the last glacial's Northern Hemisphere atmosphere. [ABSTRACT FROM AUTHOR]

Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous machines. The results are based on an extensive linear stability analysis of the third-order model for synchronous machines, comprising the classical power-swing equations and the voltage dynamics. The article addresses the impact of Ohmic losses, which are important in distribution and microgrids but often neglected in analytical studies. We compute the shift of the stability boundaries to leading order, and thus provide a detailed qualitative picture of the impact of Ohmic losses. A subsequent numerical study of the criteria is presented, without and with resistive terms, to test how tight the derived analytical results are.

We study numerically the dynamics of a network of all-to-all-coupled, identical sub-networks consisting of diffusively coupled, non-identical FitzHugh-Nagumo oscillators. For a large range of within- and between-network couplings, the network exhibits a variety of dynamical behaviors, previously described for single, uncoupled networks. We identify a region in parameter space in which the interplay of within- and between-network couplings allows for a richer dynamical behavior than can be observed for a single sub-network. Adjoining this atypical region, our network of networks exhibits transitions to multistability. We elucidate bifurcations governing the transitions between the various dynamics when crossing this region and discuss how varying the couplings affects the effective structure of our network of networks. Our findings indicate that reducing a network of networks to a single (but bigger) network might not be accurate enough to properly understand the complexity of its dynamics.

We investigate the interplay of rotor-angle and voltage stability in electric power systems. To this end, we carry out a local stability analysis of the third-order model which entails the classical power-swing equations and the voltage dynamics. We provide necessary and sufficient stability conditions and investigate different routes to instability. For the special case of a two-bus system, we analytically derive a global stability map.