Self-organized synchronization and voltage stability in networks of synchronous machines

Abstract

The integration of renewable energy sources in the course of the energy transition is accompanied by grid decentralization and fluctuating power feed-in characteristics. This raises new challenges for power system stability and design. We intend to investigate power system stability from the viewpoint of self-organized synchronization aspects. In this approach, the power grid is represented by a network of synchronous machines. We supplement the classical Kuramoto-like network model, which assumes constant voltages, with dynamical voltage equations, and thus obtain an extended version, that incorporates the coupled categories voltage stability and rotor angle synchronization. We compare disturbance scenarios in small systems simulated on the basis of both classical and extended model and we discuss resultant implications and possible applications to complex modern power grids.

The Kuramoto model in complex networks

“…However, the model is based on simplifying (and unrealistic) assumptions, which makes its applications difficult. In order to fill this gap and further analyze more realistic networks, high-order models have been recently considered [360][361][362]. One of the issues pursued by these approaches is the precise understanding of effects of network structures on the collective behavior of power-grids.…”

“…Effects of temporal energy feed-in fluctuations induced by renewable sources, e.g. solar plants [361], on synchronization and stability remain open. A rewiring algorithm by implementing a simple hill-climb method on switching edges was proposed to enhance synchronization [368].…”

“…Taking into account that the electrodynamical behavior yields a third-order model with voltage dynamics (extended from the classical second-order Kuramoto model (292)), where the third characteristic, voltage, is included besides phase and frequency [361]. In comparison to the second-order Kuramoto model (292), this shows different stability behavior due to the evolution of voltage dynamics and should provide more realistic features of real power grids.…”

Interdisciplinary challenges in the study of power grid resilience and stability and their relation to extreme weather events

“…Focussing on real-time operational decisions in real-world power grids, [20] presents a set of security indices regarding rotor angle, voltage, and frequency stability, damping of power swings, and frequency or voltage excursions across specified thresholds, which are useful for evaluating the severity of several possible contingencies in a power system. Rotor angle and voltage stability are studied more theoretically in [21] by augmenting the widely used simple swing-equation with dynamical voltage equations and assessing basin stability in the resulting model. The work of [22] complements these studies by focussing on collective instabilities that are not related to overloads and might e.g.…”

“…These papers can be roughly grouped into five categories, namely, surveys [1][2][3][4] prediction and volatility of renewable infeed [5][6][7] derivation of requirements for a resilient power grid infrastructure [8][9][10][11][12][13] relationships between grid stability and complex network topology [14][15][16][17] and the analysis of special issues in dynamic stability [20][21][22]. Because of the various overlaps, we still chose to assemble these works in alphabetical order in this volume.…”