Dynamical stability of the synchronous regime remains a challenging problem for secure functioning of power grids. Based on the symmetric circular model [Hellmann et al., Nat. Commun. 11, 592 (2020)], we demonstrate that the grid stability can be destroyed by elementary violations (motifs) of the network architecture, such as cutting a connection between any two nodes or removing a generator or a consumer. We describe the mechanism for the cascading failure in each of the damaging case and show that the desynchronization starts with the frequency deviation of the neighboring grid elements followed by the cascading splitting of the others, distant elements, and ending eventually in the bi-modal or a partially desynchronized state. Our findings reveal that symmetric topology underlines stability of the power grids, while local damaging can cause a fatal blackout.
REFERENCES
1.
G.
Filatrella
, A. H.
Nielsen
, and N. F.
Pedersen
, “Analysis of a power grid using a Kuramoto-like model
,” Eur. Phys. J. B
61
, 485
–491
(2008
). 2.
F.
Dörfler
and F.
Bullo
, “Synchronization and transient stability in power networks and nonuniform Kuramoto oscillators
,” SIAM J. Control Optim.
50
, 1616
–1642
(2012
). 3.
M.
Rohden
, A.
Sorge
, M.
Timme
, and D.
Witthaut
, “Self-organized synchronization in decentralized power grids
,” Phys. Rev. Lett.
109
, 064101
(2012
). 4.
A. E.
Motter
, S. A.
Myers
, M.
Angel
, and T.
Nishikawa
, “Spontaneous synchrony in power-grid networks
,” Nat. Phys.
9
, 191
(2013
). 5.
M.
Rohden
, A.
Sorge
, D.
Witthaut
, and M.
Timme
, “Impact of network topology on synchrony of oscillatory power grids
,” Chaos
24
, 013123
(2014
). 6.
J.
Schiffer
, R.
Ortega
, A.
Astolfi
, J.
Raisch
, and T.
Sezi
, “Conditions for stability of droop-controlled inverter-based microgrids
,” Automatica
50
, 2457
–2469
(2014
). 7.
J.
Schiffer
, D.
Zonetti
, R.
Ortega
, A. M.
Stanković
, T.
Sezi
, and J.
Raisch
, “A survey on modeling of microgrids—From fundamental physics to phasors and voltage sources
,” Automatica
74
, 135
–150
(2016
). 8.
S.
Auer
, K.
Kleis
, P.
Schultz
, J.
Kurths
, and F.
Hellmann
, “The impact of model detail on power grid resilience measures
,” Eur. Phys. J. Spec. Top.
225
(3
), 609
–625
(2016
). 9.
H.
Taher
, S.
Olmi
, and E.
Schöll
, “Enhancing power grid synchronization and stability through time-delayed feedback control
,” Phys. Rev. E
100
, 062306
(2019
). 10.
C. H.
Totz
, S.
Olmi
, and E.
Schöll
, “Control of synchronization in two-layer power grids
,” Phys. Rev. E
102
(2
), 022311
(2020
). 11.
F.
Hellmann
, P.
Schultz
, P.
Jaros
, R.
Levchenko
, T.
Kapitaniak
, J.
Kurths
, and Y.
Maistrenko
, “Network-induced multistability through lossy coupling and exotic solitary states
,” Nat. Commun.
11
, 592
(2020
). 12.
L.
Halekotte
, A.
Vanselow
, and U.
Feudel
, “Transient chaos enforces uncertainty in the British power grid
,” J. Phys.: Complex.
2
(3
), 035015
(2021
). 13.
D.
Witthaut
, F.
Hellmann
, J.
Kurths
, S.
Kettemann
, H.
Meyer-Ortmanns
, and M.
Timme
, “Collective nonlinear dynamics and self-organization in decentralized power grids
,” Rev. Mod. Phys.
94
, 015005
(2022
). 14.
C.
Nauck
, M.
Lindner
, K.
Schürholt
, H.
Zhang
, P.
Schultz
, J.
Kurths
, I.
Isenhardt
, and F.
Hellmann
, “Predicting basin stability of power grids using graph neural networks
,” New J. Phys.
24
(4
), 043041
(2022
). 15.
R.
Kogler
, A.
Plietzsch
, P.
Schultz
, and F.
Hellmann
, “Normal form for grid-forming power grid actors
,” PRX Energy
1
(1
), 013008
(2022
). 16.
A.
Buttner
, J.
Kurths
, and F.
Hellmann
, “Ambient forcing: Sampling local perturbations in constrained phase spaces
,” New J. Phys.
24
(5
), 053019
(2022
). 17.
Y.
Maistrenko
, B.
Penkovsky
, and M.
Rosenblum
, “Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions
,” Phys. Rev. E
89
, 060901
(2014
). 18.
P.
Jaros
, Y.
Maistrenko
, and T.
Kapitaniak
, “Chimera states on the route from coherence to rotating waves
,” Phys. Rev. E
91
, 022907
(2015
). 19.
P.
Jaros
, S.
Brezetsky
, R.
Levchenko
, D.
Dudkowski
, T.
Kapitaniak
, and Y.
Maistrenko
, “Solitary states for coupled oscillators with inertia
,” Chaos
28
, 011103
(2018
). 20.
R.
Berner
, A.
Polanska
, E.
Schöll
, and S.
Yanchuk
, “Solitary states in adaptive nonlocal oscillator networks
,” Eur. Phys. J. Spec. Top.
229
, 2183
(2020
). 21.
V.
Maistrenko
, O.
Sudakov
, and Y.
Maistrenko
, “Spiral wave chimeras for coupled oscillators with inertia
,” Eur. Phys. J. Spec. Top.
229
, 2327
–2340
(2020
). 22.
N.
Kruk
, Y.
Maistrenko
, and H.
Koeppl
, “Solitary states in the mean-field limit
,” Chaos
30
, 111104
(2020
). 23.
L.
Schülen
, D.
Janzen
, E.
Medeiros
, and A.
Zakharova
, “Solitary states in multiplex neural networks: Onset and vulnerability
,” Chaos, Solitons Fractals
145
, 110670
(2021
). 24.
V. O.
Munyayev
, M. I.
Bolotov
, L. A.
Smirnov
, G. V.
Osipov
, and I. V.
Belykh
, “Stability of rotatory solitary states in Kuramoto networks with inertia
,” Phys. Rev. E
105
(2
), 024203
(2022
). 25.
See https://www.energy.gov/ne/articles/department-energy-report-explores-us-advanced-small-modular-reactors-boost-grid for Department of Energy Report Explores U.S. Advanced Small Modular Reactors to Boost Grid Resiliency.
26.
See https://news.energysage.com/how-much-do-power-outages-cost/ for “How Much Do Power Outages Cost?”
27.
See https://eepublicdownloads.entsoe.eu/clean-documents/pre2015/publications/ce/otherreports/Final-Report-20070130.pdf for “System Disturbance on 4 November 2006,” Final report, Union for the Coordination of Transmission of Electricity (UCTE).
28.
See https://ec.europa.eu/commission/presscorner/detail/en/IP_07_110 for Press Corner—Press Material from the Commission Spokesperson’s Service.
29.
A. N.
Pisarchik
and U.
Feudel
, “Control of multistability
,” Phys. Rep.
540
(4
), 167
–218
(2014
). 30.
P.
Jaros
, P.
Perlikowski
, and T.
Kapitaniak
, “Synchronization and multistability in the ring of modified Rössler oscillators
,” Eur. Phys. J. Spec. Top.
224
(8
), 1541
–1552
(2015
). 31.
P.
Jaros
, T.
Kapitaniak
, and P.
Perlikowski
, “Multistability in nonlinearly coupled ring of Duffing systems
,” Eur. Phys. J. Spec. Top.
225
(13
), 2623
–2634
(2016
). 32.
D.
Lindley
, “Smart grids: The energy storage problem
,” Nature
463
, 18
–20
(2010
). 33.
X.
Fang
, S.
Misra
, G.
Xue
, and D.
Yang
, “Smart grid—The new and improved power grid: A survey
,” IEEE Commun. Surv. Tutor.
14
(4
), 944
–980
(2011
). 34.
F.
Dörfler
, M.
Chertkov
, and F.
Bullo
, “Synchronization in complex oscillator networks and smart grids
,” Proc. Natl. Acad. Sci. U.S.A.
110
, 2005
–2010
(2013
). 35.
S.
Lozano
, L.
Buzna
, and A.
Daz-Guilera
, “Role of network topology in the synchronization of power systems
,” Eur. Phys. J. B
85
, 231
(2012
). 36.
P. J.
Menck
, J.
Heitzig
, J.
Kurths
, and H.
Joachim Schellnhuber
, “How dead ends undermine power grid stability
,” Nat. Commun.
5
(1
), 3969
(2014
). 37.
P.
Schultz
, J.
Heitzig
, and J.
Kurths
, “A random growth model for power grids and other spatially embedded infrastructure networks
,” Eur. Phys. J. Spec. Top.
223
(12
), 2593
–2610
(2014
). 38.
T.
Coletta
and P.
Jacquod
, “Linear stability and the Braess paradox in coupled-oscillator networks and electric power grids
,” Phys. Rev. E
93
(3
), 032222
(2016
). 39.
J. C.
Lacerda
, F.
Celso
, and E. E. N.
Macau
, “Elementary changes in topology and power transmission capacity can induce failures in power grids
,” Phys. A
590
, 126704
(2022
). 40.
M.
Frasca
and L. V.
Gambuzza
, “Control of cascading failures in dynamical models of power grids
,” Chaos, Solitons Fractals
153
, 111460
(2021
). 41.
F.
Molnar
, T.
Nishikawa
, and A. E.
Motter
, “Asymmetry underlies stability in power grids
,” Nat. Commun.
12
, 1457
(2021
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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