Susceptibility of power grids to input fluctuations

With the increasing inclusion of regenerative resources in the energy mix, their intermittent character challenges power grid stability. Hence it is essential to determine which input fluctuations power grids are particularly vulnerable to. Focusing on angular stability in transmission grids, we propose a linear-response approach that yields a frequency-resolved measure of a grid's susceptibility to temporal input fluctuations. This approach can be applied to arbitrary transmission grid topologies as well as other settings described by oscillator networks.

[1]  A. Campa,et al.  Kuramoto model of synchronization: equilibrium and nonequilibrium aspects , 2014, 1403.2083.

[2]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[3]  Adilson E Motter,et al.  Cascade-based attacks on complex networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Gouhei Tanaka,et al.  Node-wise robustness against fluctuations of power consumption in power grids , 2014 .

[5]  V. E. Lynch,et al.  Critical points and transitions in an electric power transmission model for cascading failure blackouts. , 2002, Chaos.

[6]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[7]  Hervé Bercegol,et al.  Mean-field approach for frequency synchronization in complex networks of two oscillator types. , 2017, Physical review. E.

[8]  M. Bandi.  Spectrum of Wind Power Fluctuations. , 2016, Physical review letters.

[9]  E. Lorenz,et al.  Short term fluctuations of wind and solar power systems , 2016, 1606.03426.

[10]  Marc Timme,et al.  Network susceptibilities: Theory and applications. , 2016, Physical review. E.

[11]  Florian Dörfler,et al.  Synchronization in complex networks of phase oscillators: A survey , 2014, Autom..

[12]  Joachim Peinke,et al.  On the stability and quality of power grids subjected to intermittent feed-in , 2016 .

[13]  Thomas K. D. M. Peron,et al.  The Kuramoto model in complex networks , 2015, 1511.07139.

[14]  Dirk Helbing,et al.  Transient dynamics increasing network vulnerability to cascading failures. , 2007, Physical review letters.

[15]  Joachim Peinke,et al.  Self-organized synchronization and voltage stability in networks of synchronous machines , 2013, ArXiv.

[16]  Arindam Ghosh,et al.  Renewable energy sources and frequency regulation : survey and new perspectives , 2010 .

[17]  Jürgen Kurths,et al.  Basin stability of the Kuramoto-like model in small networks , 2014 .

[18]  Adilson E. Motter,et al.  Comparative analysis of existing models for power-grid synchronization , 2015, 1501.06926.

[19]  J. Kurths,et al.  Multiple-node basin stability in complex dynamical networks. , 2016, Physical review. E.

[20]  R. Spigler,et al.  The Kuramoto model: A simple paradigm for synchronization phenomena , 2005 .

[21]  G. Filatrella,et al.  Analysis of a power grid using a Kuramoto-like model , 2007, 0705.1305.