Abstract
Transient stability and steady-state (small signal) stability in power girds are reviewed. Transient stability concepts are illustrated with simple examples; in particular, we consider three methods for computing region of attraction: time-simulations, extended Lyapunov function, and sum of squares optimization method. We discuss steady state stability in power systems, and present an example of a feedback control via a communication network for the 10 Unit 39 Bus New England Test system.
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References
A.J. Wood, B.F. Wollenberg, Power generation, operation, and control (John Wiley & Sons, 2012)
P.W. Sauer, M. Pai, Power system dynamics and stability (Prentice Hall Upper Saddle River, NJ, 1998)
J. Machowski, J. Bialek, J. Bumby, Power system dynamics: stability and control (John Wiley & Sons, 2011)
F.P. Demello, C. Concordia, Power Apparatus and Systems, IEEE Trans. (4), 316 (1969)
J.L. Willems, M. Pandit, Systems, Man and Cybernetics, IEEE Trans. 1(4), (1971)
P. Kessel, H. Glavitsch, Power Delivery, IEEE Trans. 1(3), 346 (1986)
P. Sauer, M. Pai, Power Systems, IEEE Trans. 5(4), 1374 (1990)
P. Dash, S. Mishra, M. Salama, A. Liew, Power Delivery, IEEE Trans. 15(2), 472 (2000)
M. Rohden, A. Sorge, M. Timme, D. Witthaut, Phys. Rev. Lett. 109(6), 064101 (2012)
M. Rohden, A. Sorge, D. Witthaut, M. Timme, arXiv preprint [arXiv:1305.1634] (2013)
F. Dörfler, M. Chertkov, F. Bullo, Proc. National Acad. Sci. 110(6), 2005 (2013)
P.J. Menck, J. Heitzig, N. Marwan, J. Kurths, Nat. Phys. 9(2), 89 (2013)
P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, et al., Power Systems, IEEE Trans. 19(3), 1387 (2004)
Report by the federal network agency for electricity, gas, telecommunications, post and railways on the disturbance in the german and european power system on the 4th of november 2006, http://www.bundesnetzagentur.de/shareddocs/downloads/en/bnetza/areas/electricitygas/special%20topics/blackout2005/berichtenglischeversionid9347pdf.pdfl
J. Willems, J. Willems, Power Apparatus and Systems, IEEE Trans. (5), 795 (1970)
J. Willems, Automatic Control, IEEE Trans. 16(4), 332 (1971)
G. Shackshaft, O. Symons, J. Hadwick, Electrical Engineers, Proc. Instit. 124(8), 715 (1977)
J.J. Grainger, W.D. Stevenson, Power System Analysis, International edn. (McGraw-Hill, New York, 1994)
F. Dorfler, F. Bullo, Circuits and Systems I: Regular Papers, IEEE Trans. 60(1), 150 (2013)
K. Padiyar, K. Ghosh, Int. J. Electr. Power Energy Syst. 11(1), 47 (1989)
L. Dias, M. El-Hawary, Nonlinear parameter estimation experiments for static load modelling in electric power systems, in Generation, Transmission and Distribution, IEE Proc. C, Vol. 136 (IET, 1989), p. 68
A.R. Bergen, D.J. Hill, Power Apparatus and Systems, IEEE Trans. (1), 25 (1981)
T. Van Cutsem, M. Ribbens-Pavella, Structure preserving direct methods for transient stability analysis of power systems, in Decision and Control, 24th IEEE Conference, Vol. 24 (IEEE, 1985), p. 70
K. Padiyar, H. Sastry, Int. J. Electr. Power Energy Syst. 9(1), 9 (1987)
M. Ribbens-Pavella, D. Ernst, D. Ruiz-Vega, Transient Stability of Power Systems: A Unified Approach to Assessment and Control, Vol. 581 (Springer, 2000)
M. Pai, Energy function analysis for power system stability (Springer, 1989)
A.-A. Fouad, V. Vittal, Power system transient stability analysis using the transient energy function method (Pearson Education, 1991)
M. Ribens-Pavella, P.G. Murthy, Transient Stability of Power Systems: Theory and Practice (John Wiley and Sons, 1994)
H.-D. Chiang, Direct Methods for Stability Analysis of Electric Power Systems: Theoretical Foundation, BCU Methodologies, and Applications (Wiley, 2011)
C.-C. Chu, H.-D. Chiang, Boundary properties of the BCU method for power system transient stability assessment, in Circuits and Systems (ISCAS), Proc. 2010 IEEE International Symposium (IEEE, 2010), p. 3453
H.-D. Chang, C.-C. Chu, G. Cauley, Proc. IEEE 83(11), 1497 (1995)
M. Pai, Power system stability: analysis by the direct method of Lyapunov, Vol. 3 (North-Holland Publishing Company, 1981)
M. Ribbens-Pavella, F. Evans, Automatica 21(1), 1 (1985)
R. Genesio, M. Tartaglia, A. Vicino, Automatic Control, IEEE Trans. 30(8), 747 (1985)
R. Ortega, M. Galaz, A. Astolfi, Y. Sun, T. Shen, Automatic Control, IEEE Trans. 50(1), 60 (2005)
N.G. Bretas, L.F. Alberto, Power Systems, IEEE Trans. 18(2), 769 (2003)
G. Chesi, Automatica 45(6), 1536 (2009)
G. Chesi, Domain of attraction: analysis and control via SOS programming (Springer, 2011)
J. Anderson, A. Papachristodoulou, Automatic Control, IEEE Trans. 57(6), 1516 (2012)
M. Anghel, F. Milano, A. Papachristodoulou, Circuits and systems, Trans. 60(9), 155 (2013)
P. Aylett, Proceedings of the IEE-Part C: Monographs 105(8), 527 (1958)
M. Anghel, J. Anderson, A. Papachristodoulou, Stability analysis of power systems using network decomposition and local gain analysis, in Bulk Power System Dynamics and Control-IX Optimization, Security and Control of the Emerging Power Grid (IREP), IREP Symposium (IEEE, 2013), p. 1
A. Llamas, J. De La Ree Lopez, L. Mili, A. Phadke, J. Thorp, Power Systems, IEEE Trans. 10(1), 210 (1995)
P. Kundur, G. Rogers, D. Wong, L. Wang, M. Lauby, Power Systems, IEEE Trans. 5(4), 1076 (1990)
L. Wang, A. Semlyen, Application of sparse eigenvalue techniques to the small signal stability analysis of large power systems, in Power Industry Computer Application Conference, 1989, PICA'89, Conference Papers (IEEE, 1989), p. 358
N. Yadaiah, N. Venkata Ramana, Int. J. Elect. Power Energy Syst. 29(4), 297 (2007)
A.D. Dominguez-Garcia, Reliability modeling of cyber-physical electric power systems: A system-theoretic framework, in Power and Energy Society General Meeting, IEEE (IEEE, 2012), p. 1
J.P. Hespanha, IEE Proc. Control Theory Appl. 153(5), 520 (2006)
Y.C. Chen, A.D. Domínguez-García, Power Systems, IEEE Trans. 27(4), 1978 (2012)
S. Dhople, Y.C. Chen, L. DeVille, A.D. Dominguez-Garcia, Circuits and Systems I: Regular Papers, IEEE Trans. 60(13), 3341 (2012)
P. Hartman, Proc. Amer. Math. Soc. 14(4), 568 (1963)
V. Venikov, V. Stroev, V. Idelchick, V. Tarasov, Power Apparatus and Systems, IEEE Trans. 94(3), 1034 (1975)
A.D. Del Rosso, C.A. Cañizares, V.M. Dona, Power Systems, IEEE Trans. 18(4), 1487 (2003)
H.G. Kwatny, A. Pasrija, L. Bahar, Circuits and Systems, IEEE Trans. 33(10), 981 (1986)
H. Li, Z. Han, Synchronization of power networks without and with communication infrastructures, in Smart Grid Communications (SmartGridComm), IEEE International Conference (IEEE, 2011), p. 463
T. Athay, R. Podmore, S. Virmani, Power Apparatus and Systems, IEEE Trans. (2), 573 (1979)
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Gajduk, A., Todorovski, M. & Kocarev, L. Stability of power grids: An overview. Eur. Phys. J. Spec. Top. 223, 2387–2409 (2014). https://doi.org/10.1140/epjst/e2014-02212-1
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DOI: https://doi.org/10.1140/epjst/e2014-02212-1