In power system planning and operation studies, conventional methodologies are still largely used for small-signal stability analysis under the deterministic framework. Nevertheless, no information concerning the small-signal instability risk can be derived and the obtained results are too conservative since deterministic approaches are unable to properly reflect the existing uncertainties in real power systems. Hence, there is a need to develop new approaches which can handle a wider range of operating conditions and consequently capture all of the possible scenarios that may lead to insecure conditions. The present paper explores relevant issues associated with the conditions for application of the Monte Carlo method (MC) in probabilistic eigenanalysis (PE), namely the selection of: a suitable sampling technique for MC-based PE; and a stopping rule which is sufficient to achieve some specified confidence level. The proposed MC-based PE approach provides probabilistic indexes for small-signal stability assessment and enhancement. Several power systems of different sizes and with different small-signal stability performances are used to investigate the feasibility of the probabilistic indexes as well as to compare MC-based PE with an analytical probabilistic approach based on the two-point estimation method (TPE).
AllenE.KeriA.DeGroffA.KosterevD.TatroP.Importance of dynamic stability phenomena in power system planning. In Proceedings of the IEEE Power and Energy Society General Meeting, Calgary, Canada, 2009, pp. 1–6.
2.
ZhuS.ZhangY.LeD.ChowdhuryA. A.Understanding stability problems in actual system – case studies. In Proceedings of the IEEE Power and Energy Society General Meeting, Minneapolis, USA, 2010, pp. 1–6.
3.
MachowskiJ.BialekJ.BumbyJ.Power system dynamics: Stability and control, 2008 (John Wiley & Sons, New York, New York).
4.
CIGRE Task Force 38.01.07. Analysis and control of power system oscillations, CIGRE technical brochure, December1996.
5.
BurchettR. C.HeydtG. T.Probabilistic methods for power system dynamic stability studies. IEEE Trans. Power Apparatus Syst., 1978, PAS-97(3), 695–702.
6.
WangK. W.ChungC. Y.TseC. T.TsangK. M.Improved probabilistic method for power system dynamic stability studies. IEE Proc. Generat. Transm. Distrib., 2000, 147(1), 37–43.
7.
YiH.-Q.HouY.-H.ChengS.-J.ZhouH.CG.-G.Power system probabilistic small signal stability analysis using two point estimation method. In Proceedings of the 42nd International Universities Power Engineering Conference, Brighton, UK, September 2007, pp. 402–407.
8.
CaoY.WangC.ChengS.New algorithms for power system steady state stability probability evaluation. Dianli Xitong Zidonghue/Autom. Elec. Power Syst., 1997, 21(6), 13–18.
9.
BrucoliM.TorelliF.TrovatoM.Probabilistic approach for power system dynamic stability studies. IEE Proc. Generat. Transm. Distrib., 1981, 128(5), 295–301.
10.
TakahataA. Y.TarantoG. N.SchillingM. Th.Dynamic analysis of power systems under small disturbances considering uncertainties. In Proceedings of X Symposium of Specialists in Electric Operational and Expansion Planning, Florianopolis, Brazil, May 2006, paper SP-069.
11.
XuZ.DongZ.Y.ZhangP.Probabilistic small signal analysis using Monte Carlo simulation. In Proceedings of IEEE Power Engineering Society General Meeting, San Francisco, USA, June 2005, vol. 2, pp. 1658–1664.
12.
MeiyanL.JinM.DongZ. Y.Uncertainty analysis of load models in small signal stability. In Proceedings of the International Conference on Sustainable Power Generation and Supply, Nanjing, China, 2009, pp. 1–6.
13.
ReiA. M.SchillingM. T.Reliability assessment of the Brazilian power system using enumeration and Monte Carlo. IEEE Trans. Power Syst., 2008, 23(N), 1480–1487.
14.
HockenberryJ. R.LesieutreB. C.Evaluation of uncertainty in dynamic simulations of power system models: the probabilistic collocation method. IEEE Trans. Power Syst., 2004, 19(3), 1483–1491.
15.
SchillingM. T.Stacchini de SouzaJ. C.Do Coutto FilhoM. B.Power system probabilistic reliability assessment: current procedures in Brazil. IEEE Trans. Power Syst., 2008, 23(3), 868–876.
16.
RuedaJ. L.ColoméD. G.ErlichI.Assessment and enhancement of small signal stability considering uncertainties. IEEE Trans. Power Syst., 2009, 24(1), 198–207.
17.
RuedaJ. LColoméD. G.Probabilistic performance indexes for small signal stability enhancement in weak wind–hydro-thermal power systems. IET Generat. Transm. Distrib., 2009, 3(8), 733–747.
18.
Leite da SilvaA. M.RibeiroS. M. P.ArientiV. L.AllanR. N.Do Coutto FilhoM. B.Probabilistic load flow techniques applied to power system expansion planning. IEEE Trans. Power Syst., 1990, 5(4), 1047–1053.
19.
BillintonR.LiW.Reliability assessment of electric power systems using Monte Carlo methods, 1994 (Plenum Press, New York, New York).
20.
MoriH.OhmiM.Probabilistic short-term load forecasting with Gaussian processes. In Proceedings of the 13th International Conference on Intelligent Systems Application to Power Systems, Arlington, Virginia, November 2005, pp. 1–6.
21.
HeltonJ. C.DavisF. J.Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab. Engng Syst. Saf., 2003, 81(1), 23–69.
22.
McKayM. D.BeckmanR. J.ConoverW. J.A comparison of three methods for selecting input variables in the analysis of output from a computer code. Technometrics, 1979, 42(1), 55–64.
23.
GlassermanP.Monte Carlo methods in financial engineering, 2004 (Springer Verlag, New York, New York).
24.
SteinM.Large sample properties of simulations using Latin hypercube sampling. Technometrics, 1987, 29(2), 143–151.
25.
HoshinoN.TakemuraA.On reduction of finite sample variance by extended Latin hypercube sampling. Bernoulli, 2000, 6(6), 1035–1050.
26.
JirutitijaroenP.SinghC.Comparison of simulation methods for power system reliability indexes and their distributions. IEEE Trans. Power Syst., 2008, 23(2), 486–493.
DrewS. S.Homem-de-MelloT.Some large deviations results for Latin hypercube sampling. In Proceedings of the Winter Simulation Conference, 2005, pp. 673–681.
29.
HeltonJ. C.DavisF. J.JohnsonJ. D.A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling. Reliab. Engng Syst. Saf., 2005, 89(3), 305–330.
30.
ErlichI.FischerA.Fast assessment of small-signal oscillatory stability in large interconnected power systems. In Proceedings of the Balkan Power Conference, Belgrade, June 2002.
31.
TeeuwsenS. P.ErlichI.El-SharkawiM. A.Small-signal stability assessment for large power systems using computational intelligence. In Proceedings of the IEEE Power Engineering Society General Meeting, San Francisco, USA, June 2005, vol. 3, pp. 2661–2668.
32.
OurariM. L.DessaintL.-A.Van-QueDo. Dynamic equivalent modeling of large power systems using structure preservation technique. IEEE Trans. Power Syst., 2006, 21(3), 1284–1295.
33.
ZhaohongB.XifanW.Studies on variance reduction technique of Monte Carlo simulation in composite system reliability evaluation. Elec. Power Syst. Res., 2002, 63(1), 59–64.
34.
MurthyK. P. N.Montecarlo basics, Technical report no. ISRP-TD-3, Indian Society for Radiation Physics, January2000 (Kalpakkam, India).
35.
JirutitijaroenP.SinghC.Reliability constrained multi-area adequacy planning using stochastic programming with sample-average approximations. IEEE Trans. Power Syst., 2008, 23(2), 504–513.
36.
LindnerD. K.BabendreierJ.HamdanA. A.Measures of controllability and observability and residues. IEEE Trans. Autom. Contr., 1989, 34(6), 648–650.
37.
HenicheA.KamwaI.Assessment of two methods to select wide-area signals for power system damping control. IEEE Trans. Power Syst., 2008, 23(2), 572–581.
38.
MendoncaA.LopesJ. A. P.Impact of large scale wind power integration on small signal stability. In Proceedings of the International Conference on Future Power Systems, Amsterdam, Netherlands, November 2005, pp. 1–5.
39.
JuárezC. A.RuedaJ. L.ErlichI.ColoméD. G.Probabilistic approach-based wide-area damping controller for small-signal stability enhancement of wind–thermal power systems. In Proceedings of the IEEE Power and Energy Society General Meeting, Detroit, USA, 2011.
40.
WangL.HowellF.KundurP.ChungC. Y.XuW.A tool for small-signal security assessment of power systems. In Proceedings of the 2nd IEEE Power Engineering Society International Conference on Power Industry Computer Applications: Innovative Computing for Power – Electric Energy Meets the Market, Sydney, Australia, May 2001, pp. 246–252.
