Extended synchronization on complex networks and dynamic stability in future power grids

• Applicant: Dr. Frank Hellmann
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: from 2019 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 410409736

• Final Report Year: 2023

Final Report Abstract

The power grid is undergoing a fundamental transformation. Big power plants operating on fossil fuels are being replaced by decentral renewable sources, that connect to the grid in a fundamentally different way. As the dynamics of the grid were determined primarily by these big power plants, this transformation will pose challenges to the dynamical stability of the system in the future. A key challenge to studying these problems from a whole system perspective, was that adequate mathematical models for future systems did not exist. The central achievement of this research project was to establish and validate a unified model for the dynamics of current and future actors. This is achieved by focusing on the physics of the power flow and the design desiderata of future actors. Exploiting a novel symmetry identified in the system, we combined these into a normal form for grid actors that is well suited to describing real systems as well as for theoretical analysis. We then showed that this formulation allows identifying general properties of grid forming actors that enhance the overall systems’ stability. In the second phase of the project, various aspects of the power grid networks were identified that can hinder or help resilience. A novel mechanism that amplifies fluctuations was discovered and mathematically described. Further, a method to discover lines that are critical to the resilience of the system in the face of extreme events was introduced. Using the example of Hurricanes hitting the Texas power grid, it was shown that protecting a few critical lines identified by our method can dramatically increase the resilience of the system.

Publications

• An Open Source Software Stack for Tuning the Dynamical Behavior of Complex Power Systems. 2022 Open Source Modelling and Simulation of Energy Systems (OSMSES), 1-6. IEEE.
  Buttner, Anna; Wurfel, Hans; Plietzsch, Anton; Lindner, Michael & Hellmann, Frank
  
• Linear response theory for renewable fluctuations in power grids with transmission losses. Chaos: An Interdisciplinary Journal of Nonlinear Science, 32(11).
  Plietzsch, Anton; Auer, Sabine; Kurths, Jürgen & Hellmann, Frank
  
• PowerDynamics.jl—An experimentally validated open-source package for the dynamical analysis of power grids. SoftwareX, 17, 100861.
  Plietzsch, Anton; Kogler, Raphael; Auer, Sabine; Merino, Julia; Gil-de-Muro, Asier; Liße, Jan; Vogel, Christina & Hellmann, Frank
  
• “Normal form for grid-forming power grid actors”. In: PRX Energy 1.1 (2022), p. 013008
  Raphael Kogler; Anton Plietzsch; Paul Schultz & Frank Hellmann
  
• A framework for synthetic power system dynamics. Chaos: An Interdisciplinary Journal of Nonlinear Science, 33(8).
  Büttner, Anna; Plietzsch, Anton; Anvari, Mehrnaz & Hellmann, Frank
  
• “Exploring the stable parameter regions of the normal form for grid forming inverters using numerical simulations”. MA thesis. Berlin: Technische Universität Berlin, 2023
  Marvyn Bornemann
  
• “Protecting the Texas power grid from tropical cyclones: Increasing resilience by protecting critical lines”. In: Accepted Nature Energy (2023).
  Julian Stürmer; Anton Plietzsch; Thomas Vogt; Frank Hellmann; Jürgen Kurths; Christian Otto; Katja Frieler & Mehrnaz Anvari