How Price-Based Frequency Regulation Impacts Stability in Power Grids: A Complex Network Perspective

Peng Ji; Lipeng Zhu; Chao Lu; Sciprofile linkWei Lin; Jürgen Kurths

With the deregulation of modern power grids, electricity markets are playing a more and more important role in power grid operation and control. However, it is still questionable how the real-time electricity price-based operation affects power grid stability. From a complex network perspective, here we investigate the dynamical interactions between price-based frequency regulations and physical networks, which results in an interesting finding that a local minimum of network stability occurs when the response strength of generators/consumers to the varying price increases. A case study of the real world-based China Southern Power Grid demonstrates the finding and exhibits a feasible approach to network stability enhancement in smart grids. This also provides guidance for potential upgrade and expansion of the current power grids in a cleaner and safer way.

Библиографический список
  1. O. Edenhofer and R. Pichs-Madruga, IPCC Special Report on Renewable Energy Sources and Climate Change Mitigation, Cambridge University Press, Cambridge, UK, 2011.
  2. D. Butler, “Energy efficiency: super savers: meters to manage the future,” Nature, vol. 445, no. 7128, pp. 586–588, 2007.
  3. M. Amin, “Energy: the smart-grid solution,” Nature, vol. 499, no. 7457, pp. 145–147, 2013.
  4. B. Sch¨afer, M. Matthiae, M. Timme, and D. Witthaut, “Decentral smart grid control,” New Journal of Physics, vol. 17, no. 1, Article ID 015002, 2015.
  5. P. Kundur, J. Paserba, V. Ajjarapu et al., “Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions,” Power Systems, IEEE Transactions, vol. 19, no. 3, pp. 1387–1401, 2004.
  6. A. Arenas, A. D´ıaz-Guilera, J. Kurths, Y. Moreno, and C. Zhou, “Synchronization in complex networks,” Physics Reports, vol. 469, no. 3, pp. 93–153, 2008.
  7. F. A. Rodrigues, T. K. D. Peron, P. Ji, and J. Kurths, “.e kuramoto model in complex networks,” Physics Reports, vol. 610, pp. 1–98, 2016.
  8. J. A. Acebr´on, L. L. Bonilla, C. J. P´erez Vicente, F. Ritort, and R. Spigler, “.e kuramoto model: a simple paradigm for synchronization phenomena,” Reviews of Modern Physics, vol. 77, no. 1, pp. 137–185, 2005.
  9. T. Nishikawa and A. E. Motter, “Comparative analysis of existing models for power-grid synchronization,” New Journal of Physics, vol. 17, no. 1, Article ID 015012, 2015.
  10. F. D¨orfler and F. Bullo, “Synchronization in complex networks of phase oscillators: a survey,” Automatica, vol. 50, no. 6, pp. 1539–1564, 2014.
  11. D. J. Hill and G. Chen, “Power systems as dynamic networks,” in Proceedings of the 2006 IEEE International Symposium on Circuits and Systems, IEEE, Island of Kos, Greece, May 2006.
  12. M. Rohden, A. Sorge, M. Timme, and D. Witthaut, “Self-organized synchronization in decentralized power grids,” Physical Review Letters, vol. 109, no. 6, Article ID 064101, 2012.
  13. P. Ji, T. K. D. Peron, P. J. Menck, F. A. Rodrigues, and J. Kurths, “Cluster explosive synchronization in complex networks,” Physical Review Letters, vol. 110, no. 21, Article ID 218701, 2013.
  14. S. Olmi, A. Navas, S. Boccaletti, and A. Torcini, “Hysteretic transitions in the kuramoto model with inertia,” Physical Review E, vol. 90, no. 4, Article ID 042905, 2014.
  15. P. Ji, W. Lu, and J. Kurths, “Stochastic basin stability in complex networks,” EPL (Europhysics Letters), vol. 122, no. 4, p. 40003, 2018.
  16. F. Dai, S. Zhou, T. Peron, W. Lin, and P. Ji, “Interplay among inertia, time delay, and frustration on synchronization dynamics,” Physical Review E, vol. 98, no. 5, Article ID 052218, 2018.
  17. L. Chen, P. Ji, D. Waxman, W. Lin, and J. Kurths, “Effects of dynamical and structural modifications on synchronization,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 29, no. 8, Article ID 083131, 2019.
  18. P. J. Menck, J. Heitzig, N. Marwan, and J. Kurths, “How basin stability complements the linear-stability paradigm,” Nature Physics, vol. 9, no. 2, pp. 89–92, 2013.
  19. P. J. Menck, J. Heitzig, J. Kurths, and H. J. Schellnhuber, “How dead ends undermine power grid stability,” Nature Communications, vol. 5, 2014.
  20. B. K. Poolla, S. Bolognani, and F. Dorfler, “Optimal placement of virtual inertia in power grids,” IEEE Transactions on Automatic Control, vol. 62, no. 12, pp. 6209–6220, 2017.
  21. P. Kundu, P. Khanra, C. Hens, and P. Pal, “Transition to synchrony in degree-frequency correlated sakaguchi-kuramoto model,” Physical Review E, vol. 96, no. 5, Article ID 052216, 2017.
  22. P. Kundu, C. Hens, B. Barzel, and P. Pal, “Perfect synchronization in networks of phase-frustrated oscillators,” EPL (Europhysics Letters), vol. 120, no. 4, p. 40002, 2018.
  23. B. Sch¨afer, C. Beck, K. Aihara, D. Witthaut, and M. Timme, “Non-gaussian power grid frequency fluctuations characterized by l´evy-stable laws and superstatistics,” Nature Energy, vol. 3, no. 2, pp. 119–126, 2018.
  24. A. W. Berger and F. C. Schweppe, “Real time pricing to assist in load frequency control,” IEEE Transactions on Power Systems, vol. 4, no. 3, pp. 920–926, 1989.
  25. Y. G. Jin, S. Y. Lee, S. W. Kim, and Y. T. Yoon, “Designing rule for price-based operation with reliability enhancement by reducing the frequency deviation,” IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4365–4372, 2013.
  26. F. Alvarado, “.e stability of power system markets,” IEEE Transactions on Power Systems, vol. 14, no. 2, pp. 505–511, 1999.
  27. A. R. Bergen and V. Vittal, Power System Analysis, Prentice-Hall, Upper Saddle River, NJ, USA, 2nd edition. 2002.
  28. R. Baldick, “Electricity market equilibrium models: the effect of parametrization,” IEEE Transactions on Power Systems, vol. 17, no. 4, pp. 1170–1176, 2002.
  29. G. Filatrella, A. H. Nielsen, and N. F. Pedersen, “Analysis of a power grid using a kuramoto-like model,” 1e European Physical Journal B, vol. 61, no. 4, pp. 485–491, 2008.
  30. F. D¨orfler, M. Chertkov, and F. Bullo, “Synchronization in complex oscillator networks and smart grids,” Proceedings of the National Academy of Sciences, vol. 110, no. 6, pp. 2005–2010, 2013.
  31. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Westview Press, Boulder, CO, USA, 2014.
  32. J. Machowski, J. Bialek, and J. Bumby, Power System Dynamics: Stability and Control, John Wiley & Sons, Hoboken, NJ, USA, 2011.
  33. A. E. Motter and Y.-C. Lai, “Cascade-based attacks on complex networks,” Physical Review E, vol. 66, no. 6, Article ID 065102, 2002.
  34. S.-P. Zhang, Z.-G. Huang, J.-Q. Dong, D. Eisenberg, T. P. Seager, and Y.-C. Lai, “Optimization and resilience of complex supply-demand networks,” New Journal of Physics, vol. 17, no. 6, Article ID 063029, 2015.
  35. R. Cohen and S. Havlin, Complex Networks: Structure, Robustness and Function, Cambridge University Press, Cambridge, UK, 2010.
  36. J. Zhao, D. Li, H. Sanhedrai, R. Cohen, and S. Havlin, “Spatiotemporal propagation of cascading overload failures in spatially embedded networks,” Nature Communications, vol. 7, 2016.
  37. P. Milan, M. W¨achter, and J. Peinke, “Turbulent character of wind energy,” Physical Review Letters, vol. 110, no. 13, p. 138701, 2013.
  38. J. Zhang, C. Y. Chung, C. Lu, K. Men, and L. Tu, “A novel adaptive wide area PSS based on output-only modal analysis,” IEEE Transactions on Power Systems, vol. 30, no. 5, pp. 2633–2642, 2015.
  39. “World Energy Perspective,
  40. A. Jokic, E. H. M. Wittebol, and P. P. J. Van den Bosch, “Dynamic market behavior of autonomous network-based power systems,” European Transactions on Electrical Power, vol. 16, no. 5, pp. 533–544, 2006.
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