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Virtual Inertia Placement in Electric Power Grids

Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 162)

Abstract

The past few years have witnessed a steady shift in the nature of power generation worldwide. While the share of renewable-based distributed generation has been on the rise, there has also been a decline in the conventional synchronous-based generation. The renewable-based power generation interfaced to the grid via power-electronic converters, however, does not provide rotational inertia, an inherent feature of synchronous machines. This absence of inertia has been highlighted as the prime source for the increasing frequency violations and severely impacting grid stability. As a countermeasure, virtual or synthetic inertia and damping emulated by advanced control techniques have been proposed. In this chapter, we study the optimal placement and tuning of these devices. We discuss two approaches based on the control notion of \(\mathcal H_2\) system gain characterizing the amplification of a disturbance and the spectral notion of pole-placement. A comprehensive analysis accompanied by iterative gradient-based algorithms is presented for both the approaches and validated on a three-area test case for comparison.

References

  1. 1.
    AEMO (2016) Update report—black system event in South Australia on 28 September 2016. Tech. rep.Google Scholar
  2. 2.
    Anaya-Lara O, Hughes F, Jenkins N, Strbac G (2006) Contribution of DFIG-based wind farms to power system short-term frequency regulation. IEE Proc Gener Transm Distrib 153(2):164–170CrossRefGoogle Scholar
  3. 3.
    Bergen AR, Hill DJ (1981) A structure preserving model for power system stability analysis. IEEE Trans Power Apparatus Syst 100(1):25–35CrossRefGoogle Scholar
  4. 4.
    Bertsekas D (1995) Nonlinear programming. Athena Scientific, NashuaGoogle Scholar
  5. 5.
    Bevrani H, Ise T, Miura Y (2014) Virtual synchronous generators: a survey and new perspectives. Int J Electr Power Energy Syst 54:244-254CrossRefGoogle Scholar
  6. 6.
    Borsche TS, Dörfler F (2017) On placement of synthetic inertia with explicit time-domain constraints. IEEE Trans Power Syst, Submitted. Available at https://arxiv.org/abs/1705.03244
  7. 7.
    Borsche TS, Liu T, Hill DJ (2015) Effects of rotational inertia on power system damping and frequency transients. In: 54th IEEE conference on decision and controlGoogle Scholar
  8. 8.
    D’Arco S, Suul JA (2013) Virtual synchionous machines—classification of implementations and analysis of equivalence to droop controllers for microgrids. Proceedings of the IEEE Powertech conference, pp 1–7Google Scholar
  9. 9.
    Dörfler F, Bullo F (2013) Kron reduction of graphs with applications to electrical networks. IEEE Trans Circuits Syst Regul Pap 60(1):150–163MathSciNetCrossRefGoogle Scholar
  10. 10.
    Ekanayake J, Jenkins N (2004) Comparison of the response of doubly fed and fixed-speed induction generator wind turbines to changes in network frequency. IEEE Trans Energy Convers 19(4):800–802CrossRefGoogle Scholar
  11. 11.
    Ekanayake J, Holdsworth L, Jenkins N (2003) Control of DFIG wind turbines. Power Eng 17(1):28–32CrossRefGoogle Scholar
  12. 12.
    Groß D, Bolognani S, Poolla BK, Dörfler F (2017) Increasing the resilience of low-inertia power systems by virtual inertia and damping. In: Bulk power systems dynamics and control symposium (iREP)Google Scholar
  13. 13.
    Guggilam SS, Zhao C, Dall’Anese E, Chen YC, Dhople SV (2017) Engineering inertial and primary-frequency response for distributed energy resources. arXiv preprint arXiv:170603612Google Scholar
  14. 14.
    Hughes F, Anaya-Lara O, Jenkins N, Strbac G (2005) Control of DFIG-based wind generation for power network support. IEEE Trans Power Syst 20(4):1958–1966CrossRefGoogle Scholar
  15. 15.
    Jouini T, Arghir C, Dörfler F (2017, Submitted) Grid-forming control for power converters based on matching of synchronous machines. Available at https://arxiv.org/abs/1706.09495
  16. 16.
    Koller M, Borsche T, Ulbig A, Andersson G (2015) Review of grid applications with the Zurich 1 MW battery energy storage system. Electr Power Syst Res 120:128–135CrossRefGoogle Scholar
  17. 17.
    Lalor G, Ritchie J, Rourke S, Flynn D, O’Malley M (2004) Dynamic frequency control with increasing wind generation. In: IEEE power engineering society general meetingGoogle Scholar
  18. 18.
    Machowski J, Bialek J, Bumby J (2011) Power system dynamics: stability and control. Wiley, HobokenGoogle Scholar
  19. 19.
    Mešanović A, Münz U, Heyde C (2016) Comparison of H-, H-2, and pole optimization for power system oscillation damping with remote renewable generation. In: IFAC workshop on control of transmission and distribution smart grids, pp 103–108CrossRefGoogle Scholar
  20. 20.
    Milano F, Ortega A (2017) Frequency divider. IEEE Trans Power Syst 32(2):1493–1501Google Scholar
  21. 21.
    Morren J, de Haan S, Kling W, Ferreira J (2006) Wind turbines emulating inertia and supporting primary frequency control. IEEE Trans Power Syst 21(1):433–434CrossRefGoogle Scholar
  22. 22.
    Murthy DV, Haftka RT (1988) Derivatives of eigenvalues and eigenvectors of a general complex matrix. Int J Numer Methods Eng 26:293–311MathSciNetCrossRefGoogle Scholar
  23. 23.
    Pirani M, Hashemi E, Fidan B, Simpson-Porco JW (2016) H- robustness in mechanical and power networks. IFAC-PapersOnLine 50(1):5196–5201Google Scholar
  24. 24.
    Poolla BK, Bolognani S, Dörfler F (2017) Optimal placement of virtual inertia in power grids. IEEE Trans Autom Control 62(12):6209–6220MathSciNetCrossRefGoogle Scholar
  25. 25.
    Rakhshani E, Remon D, Cantarellas AM, Rodriguez P (2016) Analysis of derivative control based virtual inertia in multi-area high-voltage direct current interconnected power systems. IET Gener Transm Distrib 10(6):1458–1469CrossRefGoogle Scholar
  26. 26.
    Rautert T, Sachs EW (1997) Computational design of optimal output feedback controllers. SIAM J Optim 7(3):837–852MathSciNetCrossRefGoogle Scholar
  27. 27.
    RG-CE System Protection & Dynamics Sub Group (2016) Frequency stability evaluation criteria for the synchronous zone of continental Europe. Tech. rep., ENTSO-EGoogle Scholar
  28. 28.
    Sauer PW, Pai M (1997) Power system dynamics and stability. Urbana 51:61,801Google Scholar
  29. 29.
    Slootweg J, Kling W (2002) Impacts of distributed generation on power system transient stability. In: Proceedings of IEEE power engineering society summer meetingGoogle Scholar
  30. 30.
    Soni N, Doolla S, Chandorkar MC (2013) Improvement of transient response in microgrids using virtual inertia. IEEE Trans Power Delivery 28(3):1830–1838CrossRefGoogle Scholar
  31. 31.
    Svenska kraftnät, Statnett, Fingrid and Energinetdk (2016) Challenges and opportunities for the nordic power system. Tech. rep.Google Scholar
  32. 32.
    Torres M, Lopes LA (2009) Virtual synchronous generator control in autonomous wind-diesel power systems. In: Proceedings of IEEE electrical power & energy conferenceGoogle Scholar
  33. 33.
    Ulbig A, Borsche TS, Andersson G (2014) Impact of low rotational inertia on power system stability and operation. In: Proceedings of 19th IFAC world congressCrossRefGoogle Scholar
  34. 34.
    Vournas CD, Papadias BC (1987) Power system stabilization via parameter optimization-application to the Hellenic interconnected system. IEEE Trans Power Syst 2(3):615–622CrossRefGoogle Scholar
  35. 35.
    Vu Van T, Visscher K, Diaz J, Karapanos V, Woyte A, Albu M, Bozelie J, Loix T, Federenciuc D (2010) Virtual synchronous generator: an element of future grids. In: IEEE PES innovative smart grid technologies conference EuropeGoogle Scholar
  36. 36.
    Wang S, Hu J, Yuan X (2015) Virtual synchronous control for grid-connected DFIG-based wind turbines. IEEE J Emerging Sel Top Power Electron 3(4):932–944CrossRefGoogle Scholar
  37. 37.
    Zhong QC, Weiss G (2011) Synchronverters: inverters that mimic synchronous generators. IEEE Trans Ind Electron 58(4):1259–1267CrossRefGoogle Scholar
  38. 38.
    Zhou K, Doyle JC, Glover K (1996) Robust and optimal control. Prentice-Hall, Upper Saddle RiverzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.ETH ZurichZurichSwitzerland

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