Synchronization and Criticality in the Stability of Power Grids

The integration of renewable energy sources into electricity systems brings clear benefits in sustainability, efficiency, and reduced emissions. Yet, their intermittency introduces new forms of dynamical instability. Fluctuations in renewable generation act as external perturbations that may trigger congestion, frequency deviations, voltage imbalances, and even large-scale blackouts, as observed in Spain in April 2025. Ensuring grid stability thus requires predictive frameworks capable of anticipating such vulnerabilities.

From a physics standpoint, power grids can be seen as large-scale networks of coupled oscillators, where synchronization is essential for reliable operation. Disturbances in this synchronization can propagate through the system, producing cascading failures. These networks represent paradigmatic complex systems, displaying features familiar from nonlinear dynamics and statistical physics: synchronization transitions, phase coherence, and critical fluctuations. The Kuramoto model and its generalizations provide a natural framework to study the onset and loss of synchronization under perturbations, while also offering insights into universal mechanisms that connect microscopic fluctuations with macroscopic instabilities. In this sense, power grids serve as a unique laboratory to explore fundamental questions of collective dynamics with direct societal impact.

The main objective of this PhD project is to explore how variability in renewable production affects synchronization in power grids and how such perturbations can induce transitions to unstable states. By extending models of collective dynamics, the project aims to identify the fundamental mechanisms behind network fragility and propose strategies to enhance resilience.

The PhD workplan involves (i) reviewing previous research on synchronization phenomena in networks of coupled oscillators, (ii) identifying and characterizing the main external drivers shaping variability in energy production and consumption, and (iii) developing computational models to analyze the emergent collective dynamics and stability of power grids under such perturbations.

Candidates should have:

• Background in Statistical Physics and Complex Systems, including familiarity with models such as Kuramoto, Ising, spin-glass models or population dynamics.
• Knowledge of probability, statistics, and stochastic processes.
• Programming skills (Python, R, C++, parallel computing, or similar).
• Interest in applying physics-based approaches to the study of complex systems and collective dynamics.

The group in Stochastic Processes in Biological and Social Systems (Daniel Campos and Javier Cristin) has expertise in areas such as collective dynamics, stochastic phenomena, random walks, and search and exploration patterns. It is part of the SGR Ecoevolutionary responses of animals to climate change, focused on understanding the collective response of populations to external forcing from a statistical physics perspective.

The Theoretical Physics Group (Pere Masjuan) specializes in Particle Physics, from the Standard Model (SM) to Beyond the SM, as well as Astroparticles and Cosmology. Their work includes refining SM parameters with Effective Field Theories, exploring anomalies in the flavor sector, and studying the role of particle physics in the early universe through gravitational waves and dark matter.

Both groups share an interest in the collective behavior of interacting systems and their responses to perturbations, though at different spatial and temporal scales. They plan to combine tools and methodologies to complement their approaches.