Comparison of Sub-Gramian Analysis with Eigenvalue Analysis for Stability Estimation of Large Dynamical System

 
PIIS000523100001870-1-1
DOI10.31857/S000523100001870-1
Publication type Article
Status Published
Authors
Affiliation:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Skolkovo Institute of Science and Technology, Center for Research, Innovation, and Education for Energy Systems
Address: Russian Federation, Moscow
Affiliation:
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences
Skolkovo Institute of Science and Technology, Center for Research, Innovation, and Education for Energy Systems
Address: Russian Federation, Moscow
Journal nameAvtomatika i Telemekhanika
EditionIssue 10
Pages39-54
Abstract

        

Keywords
Received21.10.2018
Publication date25.10.2018
Number of characters852
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1. Simonchini V. Computational methods for Linear Matrix Equations // SIAM Rev. 2014. V. 58. No. 3. P. 377–441.

2. Polyak B.T., Scherbakov P.S. Robastnaya ustojchivost' i upravlenie. M.: Nauka, 2002.

3. Lancaster P. Explicit Solution of Linear Matrix Equations // SIAM Rev. 1970. V. 12. No. 4. P. 544–566.

4. Sylvester J. Sur l’´equation en matrices px=xq // Comptes Rendus de l’Acad. Sci. 1884. P. 67–71.

5. Lyapunov A. Probl`eme G´en´eral de la Stabilit´e du Mouvement // Commun. Soc. Math. Kharkov, 1893. Reprinted in: Ann. of Math. Studies. V. 17. Princeton Univer. Press, USA, 1949.

6. Talbot A. The evaluation of integrals of products of linear systems responses // Quart. J. Mech. Appl. Math. 1959. V. 12. No. 4. P. 488–503.

7. Daletskij Yu.L., Krejn M.G. Ustojchivost' reshenij differentsial'nykh uravnenij v banakhovom prostranstve. M.: Nauka, 1970.

8. Godunov S.K. Lektsii po sovremennym aspektam linejnoj algebry. Novosibirsk: Nauch. kniga, 2002.

9. Demidenko G.V. Matrichnye uravneniya. Novosibirsk: Izd-vo NGU, 2009.

10. Yadykin I.B. On Properties of Gramians of Continuous Control Systems // Autom. Remote Control. 2010. V. 71. No. 6. P. 1011–1021.

11. Yadykin I.B., Iskakov A.B., Akhmetzyanov A.V. Stability analysis of large-scale dynamical systems by sub-Gramian approach // Int. J. Robust Nonlin. Control. 2014. V. 24. No. 8–9. P. 1361–1379.

12. Yadykin I.B. O spektral'nykh razlozheniyakh reshenij diskretnykh uravnenij Lyapunova // DAN. 2016. T. 468. № 3. S. 264–267.

13. Yadykin I.B., Kataev D.E., Iskakov A.B., Shipilov V.K. Characterization of power systems near their stability boundary using the sub-Gramian method // Control Eng. Practice. 2016. V. 53. P. 173–183.

14. Yadykin I.B., Iskakov A.B. Energy Approach to Stability Analysis of the Linear Stationary Dynamic Systems // Autom. Remote Control. 2016. V. 77. No. 12. P. 2132–2149.

15. Benner P., Damm T. Lyapunov equations, energy functionals, and model order reduction of bilinear and stochastic systems // SIAM J. Control Optim. 2011. V. 49. No. 2. P. 686–711.

16. Barinov V.A., Sovalov S.A. Rezhimy ehnergosistem: metody analiza i upravleniya. M: Ehnergoatomizdat, 1990.

17. Voropaj N.I. Uproschenie matematicheskikh modelej dinamiki ehlektroehnergeticheskikh sistem. Novosibirsk: Nauka, Sib. otdelenie, 1981.

18. Kundur P. Power Systems Stability and Control. New York: McGrow-Hill, 1994.

19. Rogers M.G. Power Systems Oscillations. Norwell, MA: Kluwer, 2000.

20. Klein M., Rogers G.J., Kundur P. A fundamental study of inter-area oscillations in power systems // IEEE Trans. Power Syst. 1991.V. 6. No. 3. P. 914–921.

21. Bialek J.W. Why has it happened again? Comparison between the UCTE blackout in 2006 and blackouts of 2003 // Proc. IEEE Lausanne Power Tech Int. Conf., Lausanne, Switzerland, 2007.

22. Neuman P. Island Operations of Parallel Synchronous Generators – Simulators Case Study for Large Power Plants // IFAC-PapersOnLine. 2016. V. 49. No. 27. P. 164–169.

23. Weber H., Al Ali S. Influence of huge renewable Power Production on Inter Area Oscillations in the European ENTSO-E-System // IFAC-PapersOnLine. 2016. V. 49. No. 27. P. 12–17.

24. Ruhle O. Eigenvalue Analysis – All Information on Power System Oscillation Behavior Rapidly Analyzed / Siemens PTI. Newsletter. Is. 99. 2006. https://w3.usa.siemens.com/datapool/us/SmartGrid/docs/pti/2006June/Eigenvalue_Analysis.pdf

25. Yadykin I.B., Iskakov A.B. Spektral'nye razlozheniya dlya reshenij uravnenij Sil'vestra – Lyapunova – Krejna // DAN. 2017. T. 472. № 4. S. 388–392.

26. Polyak B.T., Tremba A.A. Analiticheskoe reshenie linejnogo differentsial'nogo uravneniya s odinakovymi kornyami kharakteristicheskogo polinoma // Tr. XII Vseross. sov. po probl. upravleniya, VSPU-2014.M.: IPU RAN, 2014. C. 212–217.

27. Antoulas A.C. Approximation of Large-Scale Dynamical Systems. Philadelphia: SIAM, 2005.

28. Gradshtejn I.S., Ryzhik I.M. Tablitsy integralov, summ, ryadov i proizvedenij. M.: Gos. izd-vo fiz.-mat. lit-ry, 1963.

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