Anomalous synchronization stability in power grids
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The document summarizes research on the synchronization stability of power grid networks. It presents analysis of a toy model that shows an anomalous peak in stability during a transition as the transmission capacity increases. Real data is also presented on the Chilean power grid network, which includes information on different power sources. The research aims to better understand stability at both the community and individual node levels between theoretical analysis and real-world applications.
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Anomalous synchronization stability in power grids
- 1. Anomalous behavior of the synchronization stability on power-grid networks Kim Heetae1 , Lee Sang Hoon2 , Son Seung-Woo3 Asia Pacific Center for Theoretical Physics School of Physics, Korea Institute for Advanced Study Department of Applied Physics, Hanyang University 19 Oct. 2016 KPS 2016 Fall meeting, Kimdaejung Convention Center, Gwangju, South Korea
- 2. Anomalous behaviour of the synchronization stability on power-grid networks Kim Heetae1 , Lee Sang Hoon2 , Son Seung-Woo3 Asia Pacific Center for Theoretical Physics School of Physics, Korea Institute for Advanced Study Department of Applied Physics, Hanyang University 19 Oct. 2016 KPS 2016 Fall meeting, Kimdaejung Convention Center, Gwangju, South Korea Anomalous behavior of the synchronization stability on power-grid networks
- 3. synchronization dynamics i j Power plant (P>0) Power plant (P>0) Consumer (P<0) the phase angle of voltage at node i i’s angular velocity (frequency) adjacency matrix the power input (P>0) or output (P<0) the dissipation constant the transmission capacity θi ωi Aij Pi α K !ωi = Pi −α !θi − K Aij sin(θi −θj )∑ !θi = ωi Reference frameNode jNode i G. Filatrella, A. H. Nielsen, and N. F. Pedersen, Eur. Phys. J. B 61, 485 (2008). P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nat Phys 9, 89 (2013). Basin stability of a node ∈ [0,1] Kumamoto-type model Synchronization [Basin] stability The proportion of initial points among a given phase space, where the oscillation results in synchrony.
- 4. Synchronization of power-grid P. J. Menck, J. Heitzig, J. Kurths, and H. Joachim Schellnhuber, Nat Comms 5, 3969 (2014). P. Schultz, J. Heitzig, and J. Kurths, New J. Phys. 16, 125001 (2014). A. van Kan, J. Jegminat, J. F. Donges, and J. Kurths, Phys Rev E 93, 042205 (2016). P. Ji and J. Kurths, Eur. Phys. J. Spec. Top. 223, 2483 (2014). <Northern European power grid> degree is unlikely to be connected increase of the curves in Fig. 2c,d. Case study. Do these results from carry over to real-world topologies? of the Northern European power g with N ¼ 236 nodes and E ¼ 320 co (see Methods and Supplementary to concentrate on the effects of th other transmission and generatio N/2 net generators (with Pi ¼ þ (with Pi ¼ À P) and perform nu coarse-grained model equations (7 a basin stability Si for every node ( Table 1). What we find is in line w grid’s synchronous state is especial turbations hitting nodes adjacent dead trees. For example, observe the 3 2 14 6 7 5 Increasing S Generator 0 P Consumer Non-adjacent〈S〉 Adjacent d 1 2 3 4 2 3 4 5 6 7 8 1 0.75 0.50 0.25 0 – NATURE COMMUNICATIONS | DOI: 10.1038/ncomms4969 1 I 2 Finland Sweden Norway Denmark II III 3 4 Increasing S ConsumerGenerator Figure 4 | Northern European power grid. The grid has N ¼ 236 nodes and E ¼ 320 transmission lines. The load scenario was chosen rand squares (circles) depicting N/2 net consumers with Pi ¼ À P (net generators with Pi ¼ þ P). The colour scale indicates how large a node’s bas is. Insets I–III show that re-computed basin stability values after 27 lines have been added in order to ‘heal’ dead trees. New lines are colou simulation parameters, a ¼ 0.1, P ¼ 1 and K ¼ 8, imply the simplifying assumptions that all generators in the grid are of the same making an transmission lines are of the same voltage and impedance. These assumptions enable us to focus on the effects of the (unweighted) topology ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/n
- 5. Previous study 1 0 Community consistency 1 0 ∆K/∆Kmax Φ: community consistency k: degree C: clustering coefficient F: current flow betweenness centrality. Table 1. Pearson correlation coefficient r of ΔK versus community consistency (Φ), degree (k), clustering coeffi- cient (C), and current flow betweenness (F) centrality. Φ k C F r −0.581 0.033 −0.054 0.072 p-value < 10−3 0.500 0.266 0.139
- 6. Stability transition Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 <Synchronization stability analysis on a toy model> H. Kim, S. H. Lee, and P. Holme, New J. Phys. 17, 113005 (2015). H. Kim, S. H. Lee, and P. Holme, Phys Rev E 93, 062318 (2016). Consumer Producer
- 7. Stability transition Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 <Synchronization stability analysis on a toy model>
- 8. Stability transition Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 Node 7 Node 4 Node 8 Node 9 Node 12 Node 16Node 2 Node 3 Node 10 Node 11 Node 17Node 1 Node 18 0 1 0 25 Basin stability K Node 6 Node 5 Node 14 Node 13 Node 15 <Synchronization stability analysis on a toy model>
- 9. Stability transition � ��� ��� ��� ��� � � �� �� �� �� 0 1 0 20 40 B K Producer Consumer 1300 400 H. Kim, S. H. Lee, and P. Holme, Phys Rev E 93, 062318 (2016). Legend
- 10. Phase diagram of dynamics e5n1k14 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k7 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k21 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k28 -π -π/2 0 π/2 π -100 -50 0 50 100 ω � ��� ��� ��� ��� � � �� �� �� �� K=7.0 K=14.0 K=28.0K=21.0 Achieve sync Fail to sync ω K B
- 11. Phase diagram of dynamics e5n1k14 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k125 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k7 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k15 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k17 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k21 -π -π/2 0 π/2 π -100 -50 0 50 100 ω e5n1k28 -π -π/2 0 π/2 π -100 -50 0 50 100 ω � ��� ��� ��� ��� � � �� �� �� �� K=7.0 K=14.0 K=28.0 K=12.5 K=15.0 K=17.0 K=21.0 Achieve sync Fail to sync ω e5n1k13 -π -π/2 0 π/2 π -100 -50 0 50 100 ω K=13.0 K B
- 12. Oscillation trajectory K=15 K=17 K=18 K=28K=16 -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) -13 0 13 495 500 ω Time(s) K=7 K=12K=11K=10 � ��� ��� ��� ��� � � �� �� �� �� K Bω1=17 θ1=0 ω2,3,4=0 θ2,3,4=0
- 13. Anomalous behaviour of the synchronization stability on power-grid networks Kim Heetae1 , Lee Sang Hoon2 , Son Seung-Woo3 Asia Pacific Center for Theoretical Physics School of Physics, Korea Institute for Advanced Study Department of Applied Physics, Hanyang University Anomalous behavior of the synchronization stability on power-grid networks 19 Oct. 2016 KPS 2016 Fall meeting, Kimdaejung Convention Center, Gwangju, South Korea
- 14. Chilean power-grid network • 420 Nodes ↳129 power plants 291 substations • 543 Links • 1252 Nodes ↳285 power plants 967 substations • 961 Links Chilean power-grid network
- 15. Raw data collection <Activity data with time series> A g g r e g a te d a c tiv ity t=1 t=2 …
- 16. Raw data collection <Field trip>
- 17. Raw data collection <Grid circuit map>
- 18. San Andres Robleria Rapel Pangue Total Chilean power grid Various patterns
- 19. Campiche Candelaria RecaRio Tureno Eolica Los Cururos Eolica Punta Palmeras Solar Llano Llampos Solar Santa Cecilia The Various Duration of Activity The Pattern of Hydro Power The Pattern of Wind Power The Pattern of Solar Power
- 20. Conclusions Stability analysis: Second order Kuramoto-type model Meso-scale: community characteristics ✓ Micro-scale: motif study ✓ Observed: Anomalous peak in stability transition Data: Chilean power-grid network with richer information Theoretical side Application side
- 21. Acknowledgement Prof. Claudio Tenreiro Prof. Eduardo Álvarez-Miranda David Olave Rojas
- 22. Acknowledgement Thank you for your attention sincerely appreciate your being my neighbour node. and