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Time delay effects in the control of synchronous electricity grids. (English) Zbl 1431.34062
Summary: The expansion of inverter-connected generation facilities (i.e., wind and photovoltaics) and the removal of conventional power plants is necessary to mitigate the impacts of climate change, whereas conventional generation with large rotating generator masses provides stabilizing inertia, inverter-connected generation does not. Since the underlying power system and the control mechanisms that keep it close to a desired reference state were not designed for such a low inertia system, this might make the system vulnerable to disturbances. In this paper, we will investigate whether the currently used control mechanisms are able to keep a low inertia system stable and how this is affected by the time delay between a frequency deviation and the onset of the control action. We integrate the control mechanisms used in Continental Europe into a model of coupled oscillators which resembles the second order Kuramoto model. This model is then used to investigate how the interplay of changing inertia, network topology, and delayed control affects the stability of the interconnected power system. To identify regions in the parameter space that make stable grid operation possible, the linearized system is analyzed to create the system’s stability chart. We show that lower and distributed inertia could have a beneficial effect on the stability of the desired synchronous state.
©2020 American Institute of Physics
MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
34H05 Control problems involving ordinary differential equations
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[1] Sims, R. E., Renewable energy: A response to climate change, Solar Energy, 76, 9-17 (2004)
[2] Stappel, M., Gerlach, A.-K., Scholz, A., and Pape, C., “The European power system in 2030: Flexibility challenges and integration benefits. An analysis with a focus on the pentalateral energy forum region,” (Agora Energiewende, 2015).
[3] Wu, D.; Javadi, M.; Jiang, J. N., A preliminary study of impact of reduced system inertia in a low-carbon power system, J. Mod. Power Syst. Clean Energy, 3, 82-92 (2015)
[4] Tielens, P.; Van Hertem, D., The relevance of inertia in power systems, Renew. Sustainable Energy Rev., 55, 999-1009 (2016)
[5] Filatrella, G.; Nielsen, A. H.; Pedersen, N. F., Analysis of a power grid using a Kuramoto-like model, Eur. Phys. J. B Condens. Matter Complex Syst., 61, 485-491 (2008)
[6] Rohden, M.; Sorge, A.; Timme, M.; Witthaut, D., Self-organized synchronization in decentralized power grids, Phys. Rev. Lett., 109, 064101 (2012)
[7] Witthaut, D.; Timme, M., Braess’s paradox in oscillator networks, desynchronization and power outage, New J. Phys., 14, 083036 (2012)
[8] Rohden, M.; Sorge, A.; Witthaut, D.; Timme, M., Impact of network topology on synchrony of oscillatory power grids, Chaos, 24, 013123 (2014) · Zbl 1374.05220
[9] Witthaut, D.; Rohden, M.; Zhang, X.; Hallerberg, S.; Timme, M., Critical links and nonlocal rerouting in complex supply networks, Phys. Rev. Lett., 116, 138701 (2016)
[10] Tchuisseu, E. B. T.; Gomila, D.; Colet, P.; Witthaut, D.; Timme, M.; Schäfer, B., Curing Braess’ paradox by secondary control in power grids, New J. Phys., 20, 083005 (2018)
[11] Skardal, P. S.; Taylor, D.; Sun, J.; Arenas, A., Collective frequency variation in network synchronization and reverse pagerank, Phys. Rev. E, 93, 042314 (2016)
[12] Jacquod, P. and Pagnier, L., “Optimal placement of inertia and primary control in high voltage power grids,” in 2019 53rd Annual Conference on Information Sciences and Systems (CISS) (IEEE, 2019), pp. 1-6.
[13] Schäfer, B.; Matthiae, M.; Timme, M.; Witthaut, D., Decentral smart grid control, New J. Phys., 17, 015002 (2015)
[14] Schäfer, B.; Grabow, C.; Auer, S.; Kurths, J.; Witthaut, D.; Timme, M., Taming instabilities in power grid networks by decentralized control, Eur. Phys. J. Spec. Top., 225, 569-582 (2016)
[15] Otto, A.; Just, W.; Radons, G., Nonlinear dynamics of delay systems: An overview, Philos. Trans. R. Soc. A, 377, 20180389 (2019)
[16] Sipahi, R.; Niculescu, S.; Abdallah, C. T.; Michiels, W.; Gu, K., Stability and stabilization of systems with time delay, IEEE Control Syst. Mag., 31, 38-65 (2011) · Zbl 1395.93271
[17] Olgac, N.; Sipahi, R., An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems, IEEE Trans. Automat. Contr., 47, 793-797 (2002) · Zbl 1364.93576
[18] Lakshmanan, M.; Senthilkumar, D. V., Dynamics of Nonlinear Time-Delay Systems (2011), Springer Science and Business Media
[19] Bokharaie, V., Sipahi, R., and Milano, F., “Small-signal stability analysis of delayed power system stabilizers,” in Power Systems Computation Conference (PSCC) (IEEE, 2014), pp. 1-7.
[20] Machowski, J.; Bialek, J.; Bumby, J., Power System Dynamics: Stability and Control (2011), Wiley
[21] UCTE Operation Handbook, “Policy 1: Load-frequency control and performance,” Technical Report (UCTE, OH, 2009).
[22] Andersson, G., “Dynamics and Control of Electric Power Systems, Lecture Notes Vol. 227 (ETH Zürich, 2012), p. 0528.
[23] UCTE Operation Handbook, “Policy 1: Load-frequency control and performance,” Technical Report (UCTE, OH, 2004).
[24] UCTE Operation Handbook, “Appendix 1: Load-frequency-control and performance,” Technical Report (UCTE, Brussels, 2004).
[25] Kundur, P.; Balu, N. J.; Lauby, M. G., Power System Stability and Control (1994), McGraw-Hill: McGraw-Hill, New York
[26] Ulbig, A.; Borsche, T. S.; Andersson, G., Impact of low rotational inertia on power system stability and operation, IFAC Proc. Vol., 47, 7290-7297 (2014)
[27] Kurth, M.; Welfonder, E., Importance of the self-regulating effect within power systems, IFAC Proc. Vol., 39, 345-352 (2006)
[28] Rodrigues, F. A.; Peron, T. K. D.; Ji, P.; Kurths, J., The Kuramoto model in complex networks, Phys. Rep., 610, 1-98 (2016) · Zbl 1357.34089
[29] Schavemaker, P.; Van der Sluis, L., Electrical Power System Essentials (2017), John Wiley & Sons
[30] Kettemann, S., Delocalization of disturbances and the stability of ac electricity grids, Phys. Rev. E, 94, 062311 (2016)
[31] Tamrakar, S.; Conrath, M.; Kettemann, S., Propagation of disturbances in ac electricity grids, Sci. Rep., 8, 6459 (2018)
[32] Haehne, H.; Schottler, J.; Waechter, M.; Peinke, J.; Kamps, O., The footprint of atmospheric turbulence in power grid frequency measurements, EPL (Europhys. Lett.), 121, 30001 (2018)
[33] Haehne, H.; Schmietendorf, K.; Tamrakar, S.; Peinke, J.; Kettemann, S., Propagation of wind-power-induced fluctuations in power grids, Phys. Rev. E, 99, 050301 (2019)
[34] Wolff, M. F.; Schmietendorf, K.; Lind, P. G.; Kamps, O.; Peinke, J.; Maass, P., Heterogeneities in electricity grids strongly enhance non-Gaussian features of frequency fluctuations under stochastic power input, Chaos, 29, 103149 (2019)
[35] Asal, H., Madsen, B., Weber, H., and Grebe, E., “Development in power-frequency characteristic and droop of the UCPTE power system and proposals for new recommendations for primary control,” in Proceedings of 37 CIGRE Session, 28.08 (cigre, 1998), pp. 39-115.
[36] Zhang, X.; Hallerberg, S.; Matthiae, M.; Witthaut, D.; Timme, M., Fluctuation-induced distributed resonances in oscillatory networks, Sci. Adv., 5, eaav1027 (2019)
[37] Tyloo, M.; Coletta, T.; Jacquod, P., Robustness of synchrony in complex networks and generalized Kirchhoff indices, Phys. Rev. Lett., 120, 084101 (2018)
[38] Amann, A.; Schöll, E.; Just, W., Some basic remarks on eigenmode expansions of time-delay dynamics, Phys. A Stat. Mech. Appl., 373, 191-202 (2007)
[39] Michiels, W.; Niculescu, S., Stability, Control, and Computation for Time-Delay Systems: An Eigenvalue-Based Approach (2014), Cambridge University Press
[40] Jarlebring, E.
[41] Altintas, Y.; Weck, M., Chatter stability of metal cutting and grinding, CIRP Ann., 53, 619-642 (2004)
[42] Otto, A.; Rauh, S.; Kolouch, M.; Radons, G., Extension of Tlusty’s law for the identification of chatter stability lobes in multi-dimensional cutting processes, Int. J. Mach. Tools Manuf., 82, 50-58 (2014)
[43] Balanov, A. G.; Janson, N. B.; Schöll, E., Delayed feedback control of chaos: Bifurcation analysis, Phys. Rev. E, 71, 016222 (2005)
[44] The authors thank Eckehard Schöll for hints in this direction.
[45] Löser, M.; Otto, A.; Ihlenfeldt, S.; Radons, G., Chatter prediction for uncertain parameters, Adv. Manuf., 6, 319-333 (2018)
[46] Ramírez, A.; Koh, M. H.; Sipahi, R., An approach to compute and design the delay margin of a large-scale matrix delay equation, Int. J. Robust Nonlinear Control, 29, 1101-1121 (2019) · Zbl 1418.93091
[47] Breda, D.; Maset, S.; Vermiglio, R., Pseudospectral differencing methods for characteristic roots of delay differential equations, SIAM J. Sci. Comput., 27, 482-495 (2005) · Zbl 1092.65054
[48] Trefethen, L. N., Spectral Methods in MATLAB (2000), SIAM · Zbl 0953.68643
[49] See for “Entso-e transparency platform” (2019).
[50] Ansmann, G., Efficiently and easily integrating differential equations with JiTCODE, JiTCDDE, and JiTCSDE, Chaos, 28, 043116 (2018) · Zbl 1390.34005
[51] Zatarain, M.; Bediaga, I.; Muñoa, J.; Insperger, T., Analysis of directional factors in milling: Importance of multi-frequency calculation and of the inclusion of the effect of the helix angle, Int. J. Adv. Manuf. Techn., 47, 535-542 (2010)
[52] Zappa, W.; van den Broek, M., Analysing the potential of integrating wind and solar power in Europe using spatial optimisation under various scenarios, Renew. Sustainable Energy Rev., 94, 1192-1216 (2018)
[53] Kohler, S., Seidel, H.et al., “Dena grid study II: Integration of renewable energy sources in the German power supply system from 2015-2020 with an outlook to 2025,” Dena-Deutsche-Energie-Agentur (2010).
[54] Matke, C., Medjroubi, W., and Kleinhans, D., “SciGRID—An open source reference model for the European transmission network (v0.2)” (2016).
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