Max Planck Institute for Dynamics and Self-Organization -- Department for Nonlinear Dynamics and Network Dynamics Group
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Dynamics of Modern Power Grids


Dynamics of Modern Power Grids -- Self-Organization, Stability and Optimal Design

Distributed, renewable energy sources will dominate the dynamics of future electric power grids. The ongoing change of our energy supply from large, centralized power plants based on nuclear or fossil fuels to smaller, decentralized sources based on renewable energies poses an enormous challenge for design and stable operation of the grid. At the same time, upgrading the grid constitutes a multi-billion Euro business: it is not only it necessary to connect all the new power generators and to enable large-scale energy storage and transport, e.g. from off-shore wind parks to the consumers in the inland. Finally, the structure of the power grid has to be optimized to increase its stability against fluctuations and robustness against failures. A partial future solution will be provided by transmitting consumer infor- mation over the so-called 'smart grid' and adapt energy production and distribution, thus aiming to control the entire grid. However, large-scale failures, for instance, already today are consequences of the collective dynamics of the power grid and are often caused by nonlocal mechanisms. We thus urgently need to understand the intrinsic network dynamics on the large scale to complement partial solutions of control engineering and to be able to develop efficient strategies for operating the future grid. To date, most research on the collective dynamics of power grids follows one of two distinct approaches: Electrical engineers model the behavior of single units of the power grid, such as generators and motors, in great detail and try to approximate the entire grid using a rough proxy structure of only a few units. At the other extreme, physicists and mathematicians mostly studied abstract transportation or flow networks, disregarding all the details of the generators and transmission lines.

Bridging the gap between these two approaches, we are now aiming to understand power grid dynamics at an intermediate level using simple but dynamic coarse-scale models. This approach captures the essential features of every element, but is still simple enough to analyze the emergent collective dynamics of the entire power grid and to perform simulations of realistic network structures. Our main objectives are centered around the question how smaller, much more distributed, fluctuating and unreliable power sources impact grid dynamics collectively. Our team in the Network Dynamics Group is studying crucial questions about prediction, failure-control and fault-tolerance as well as non-standard inverse problems such as the optimal design and inference given the relation between grid connectivity and grid dynamics.

Results so far: 1) Addition of new transmission lines may *destabilize* power grid operation (via Braess paradox that we identified in oscillator networks). 2) More and smaller but distributed power plants may stabilize grid operation. 3) Coarse-scale modeling of power grids by oscillator networks seems feasible for study of collective, self-organized synchronization dynamics.

Contact:  Marc Timme 

Members working within this Project:

 Debsankha Manik 

Former Members:

 Martin Rohden 
 Benjamin Schäfer 
 Nora Molkenthin 
 Xiaozhu Zhang 
 Andreas Sorge 
 Marc Timme 
 Dirk Witthaut 

Selected Publications:

B. Schäfer, M. Matthiae, X. Zhang, M. Rohden, M. Timme, and D. Witthaut (2017).
Escape routes, weak links, and desynchronization in fluctuation-driven networks
Phys. Rev. E 95(6):060203. download file

D. Manik, M. Rohden, H. Ronellenfitsch, X. Zhang, S. Hallerberg, D. Witthaut, and M. Timme (2017).
Network susceptibilities: Theory and applications
Phys. Rev. E 95(1):012319. download file

D. Manik, M. Timme, and D. Witthaut (2017).
Cycle flows and multistability in oscillatory networks
Chaos 27(8):083123. download file

H. Ronellenfitsch, D. Manik, J. Horsch, T. Brown, and D. Witthaut (2017).
Dual theory of transmission line outages
IEEE Transactions on Power Systems PP(99).

M. Rohden, D. Witthaut, M. Timme, and H. Meyer-Ortmanns (2017).
Curing critical links in oscillator networks as power flow models
New J. Phys. 19(1):013002. download file

M. Schröder, M. Timme, and D. Witthaut (2017).
A universal order parameter for synchrony in networks of limit cycle oscillators
Chaos 27(7):073119. download file

B. Schäfer, C. Grabow, A. Sabine, K. J, D. Witthaut, and M. Timme (2016).
Taming instabilities in power grid networks by decentralized control
Eur. Phys. J. ST 225(3):569. download file

D. Witthaut, M. Rohden, X. Zhang, S. Hallerberg, and M. Timme (2016).
Critical Links and Nonlocal Rerouting in Complex Supply Networks
Phys. Rev. Lett. 116(13):138701. download file

H. Ronellenfitsch, M. Timme, and D. Witthaut (2016).
A Dual Method for Computing Power Transfer Distribution Factors
IEEE Trans. Power Syst. PP(99). download file

B. Schäfer, M. Matthiae, M. Timme, and D. Witthaut (2015).
Decentral Smart Grid Control
New J. Phys. 17(1):015002. download file

D. Witthaut, and M. Timme (2015).
Nonlocal effects and countermeasures in cascading failures
Phys. Rev. E 92(3):032809. download file

M. Timme, L. Kocarev , and D. Witthaut (2015).
Focus on networks, energy and the economy
New J. Phys. 17(11):110201. download file

M. Rohden, A. Sorge, D. Witthaut, and M. Timme (2014).
Impact of network topology on synchrony of oscillatory power grids
Chaos 24: 013123. download file

D. Witthaut, and M. Timme (2012).
Braess's paradox in oscillator networks, desynchronization and power outage
New J. Phys. 14:083036. download file

M. Rohden, A. Sorge, M. Timme, and D. Witthaut (2012).
Self-Organized Synchronization in Decentralized Power Grids
Phys. Rev. Lett. 109:064101. download file