Probabilistic Assessment and Sensitivity Analysis in Stability Studies

Part of the Springer Theses book series (Springer Theses)


This chapter discusses the overall approach used for load model parameter ranking comprising three essential parts, namely, probabilistic assessment, sensitivity analysis, and stochastic dependence. The chapter discusses each of them and how they were implemented. More specifically, the probabilistic assessment method is used for determining the required accuracy levels of different load model parameters, the sensitivity analysis techniques are used for ranking power system load model parameters, and the stochastic dependence is used to investigate the influence of correlation between load model parameters.


  1. 1.
    Sarić AT, Stankovic AM (2005) Model uncertainty in security assessment of power systems. Power Syst IEEE Trans 20:1398–1407CrossRefGoogle Scholar
  2. 2.
    Zhao JH, Dong ZY, Lindsay P, Wong KP (2009) Flexible transmission expansion planning with uncertainties in an electricity market. Power Syst IEEE Trans 24:479–488CrossRefGoogle Scholar
  3. 3.
    Soroudi A, Aien M, Ehsan M (2012) A probabilistic modeling of photo voltaic modules and wind power generation impact on distribution networks. Syst J IEEE 6:254–259CrossRefGoogle Scholar
  4. 4.
    Zou K, Agalgaonkar AP, Muttaqi KM, Perera S (2012) Distribution system planning with incorporating DG reactive capability and system uncertainties. Sustain Energy IEEE Trans 3:112–123CrossRefGoogle Scholar
  5. 5.
    Aien M, Fotuhi-Firuzabad M, Aminifar F (2012) Probabilistic load flow in correlated uncertain environment using unscented transformation. Power Syst IEEE Trans 27:2233–2241CrossRefGoogle Scholar
  6. 6.
    Zhang JF, Tse C, Wang K, Chung C (2009) Voltage stability analysis considering the uncertainties of dynamic load parameters. Gener Transm Distrib IET 3:941–948CrossRefGoogle Scholar
  7. 7.
    Valverde G, Saric AT, Terzija V (2013) Stochastic monitoring of distribution networks including correlated input variables. IEEE Trans Power Deliv 28:246–255CrossRefGoogle Scholar
  8. 8.
    Evangelopoulos VA, Georgilakis PS (2014) Optimal distributed generation placement under uncertainties based on point estimate method embedded genetic algorithm. Gener Transm Distrib IET 8:389–400Google Scholar
  9. 9.
    Ahmadi H, Ghasemi H (2012) Maximum penetration level of wind generation considering power system security limits. Gener Transm Distrib IET 6:1164–1170CrossRefGoogle Scholar
  10. 10.
    Faried SO, Billinton R, Aboreshaid S (2009) Probabilistic evaluation of transient stability of a wind farm. Energy Convers IEEE Trans 24:733–739CrossRefGoogle Scholar
  11. 11.
    Li Y, Li W, Yan W, Yu J, Zhao X (2014) Probabilistic optimal power flow considering correlations of wind speeds following different distributions. Power Syst IEEE Trans 29:1847–1854CrossRefGoogle Scholar
  12. 12.
    Zhao X, Zhou J (2010) Probabilistic transient stability assessment based on distributed DSA computation tool. In: 2010 IEEE 11th international conference on probabilistic methods applied to power systems (PMAPS). pp 685–690Google Scholar
  13. 13.
    Chiodo E, Gagliardi F, La Scala M, Lauria D (1999) Probabilistic on-line transient stability analysis. In: IEEE proceedings on generation, transmission and distribution. pp 176–180Google Scholar
  14. 14.
    Helton JC, Davis FJ (2003) Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliab Eng Syst Saf 81:23–69CrossRefGoogle Scholar
  15. 15.
    Fishman G (2013) Monte Carlo: concepts, algorithms, and applications. Springer Science & Business MediaGoogle Scholar
  16. 16.
    Preece R, Huang K, Milanovic JV (2014) Probabilistic small-disturbance stability assessment of uncertain power systems using efficient estimation methods. Power Syst IEEE Trans 29:2509–2517CrossRefGoogle Scholar
  17. 17.
    Valenzuela J, Mazumdar M (2001) Monte Carlo computation of power generation production costs under operating constraints. Power Syst IEEE Trans 16:671–677CrossRefGoogle Scholar
  18. 18.
    El-Khattam W, Hegazy Y, Salama M (2006) Investigating distributed generation systems performance using Monte Carlo simulation. IEEE Trans Power Syst 21:524–532CrossRefGoogle Scholar
  19. 19.
    Martinez JA, Guerra G (2014) A parallel Monte Carlo method for optimum allocation of distributed generation. Power Syst IEEE Trans 29:2926–2933CrossRefGoogle Scholar
  20. 20.
    Midence D (2008) Distribution system planning considering the social balance of supply quality. Ph.D. Dissertation. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía EléctricaGoogle Scholar
  21. 21.
    Rueda JL, Colomé DG, Erlich I (2009) Assessment and enhancement of small signal stability considering uncertainties. Power Syst IEEE Trans 24:198–207CrossRefGoogle Scholar
  22. 22.
    Saltelli A, Chan K, Scott EM (2000) Sensitivity analysis, vol 1. Wiley, New YorkzbMATHGoogle Scholar
  23. 23.
    Song X, Zhang J, Zhan C, Xuan Y, Ye M, Xu C (2015) Global sensitivity analysis in hydrological modeling: review of concepts, methods, theoretical framework, and applications. J Hydrol 523:739–757CrossRefGoogle Scholar
  24. 24.
    Iooss B, Lemaître P (2015) A review on global sensitivity analysis methods. In: Uncertainty management in simulation-optimization of complex systems. Springer, pp 101–122Google Scholar
  25. 25.
    Hasan K, Preece R, Milanović J (2016) Efficient identification of critical parameters affecting the small-disturbance stability of power systems with variable uncertainty. Power Energy Soc General Meet (PESGM) 2016:1–5Google Scholar
  26. 26.
    Ruano M, Ribes J, Ferrer J, Sin G (2011) Application of the Morris method for screening the influential parameters of fuzzy controllers applied to wastewater treatment plants. Water Sci Technol 63:2199–2206CrossRefGoogle Scholar
  27. 27.
    Bettonvil B, Kleijnen JP (1997) Searching for important factors in simulation models with many factors: sequential bifurcation. Eur J Oper Res 96:180–194CrossRefzbMATHGoogle Scholar
  28. 28.
    Papaefthymiou G, Kurowicka D (2009) Using copulas for modeling stochastic dependence in power system uncertainty analysis. IEEE Trans Power Syst 24:40–49CrossRefGoogle Scholar
  29. 29.
    Park H, Baldick R, Morton DP (2015) A stochastic transmission planning model with dependent load and wind forecasts. IEEE Trans Power Syst 30:3003–3011CrossRefGoogle Scholar
  30. 30.
    Zhang N, Kang C, Singh C, Xia Q (2016) Copula based dependent discrete convolution for power system uncertainty analysis. IEEE Trans Power Syst 31:5204–5205CrossRefGoogle Scholar
  31. 31.
    Wu W, Wang K, Han B, Li G, Jiang X, Crow ML (2015) A versatile probability model of photovoltaic generation using pair copula construction. IEEE Transactions on Sustainable Energy 6:1337–1345CrossRefGoogle Scholar
  32. 32.
    Li P, Guan X, Wu J, Zhou X (2015) Modeling dynamic spatial correlations of geographically distributed wind farms and constructing ellipsoidal uncertainty sets for optimization-based generation scheduling. IEEE Trans Sustainable Energy 6:1594–1605CrossRefGoogle Scholar
  33. 33.
    Haghi HV, Lotfifard S (2015) Spatiotemporal modeling of wind generation for optimal energy storage sizing. IEEE Trans Sustainable Energy 6:113–121CrossRefGoogle Scholar
  34. 34.
    Bina MT, Ahmadi D (2015) Stochastic modeling for the next day domestic demand response applications. IEEE Trans Power Syst 30:2880–2893CrossRefGoogle Scholar
  35. 35.
    Moriya N (2008) Noise-related multivariate optimal joint-analysis in longitudinal stochastic processes. In: Progress in applied mathematical modeling. p 223Google Scholar
  36. 36.
    Cohen J (1988) Statistical power analysis for the behavioral sciences, 2nd edn. Erlbaum, Hillsdale, NJzbMATHGoogle Scholar
  37. 37.
    Buda A, Jarynowski A (2010) Life time of correlations and its applications. Andrzej Buda Wydawnictwo NiezaleĹĽneGoogle Scholar
  38. 38.
    Parzen E (1962) On estimation of a probability density function and mode. Ann Math Stat 33:1065–1076CrossRefMathSciNetzbMATHGoogle Scholar
  39. 39.
    Wand MP, Jones MC (1994) Kernel smoothing. Chapman and Hall/CRCGoogle Scholar
  40. 40.
    Epanechnikov VA (1969) Non-parametric estimation of a multivariate probability density. Theor Probab Appl 14:153–158CrossRefMathSciNetGoogle Scholar
  41. 41.
    Park BU, Marron JS (1990) Comparison of data-driven bandwidth selectors. J Am Stat Assoc 85:66–72CrossRefGoogle Scholar
  42. 42.
    Park B, Turlach B (1992) Practical performance of several data driven bandwidth selectors. Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)Google Scholar
  43. 43.
    Cao R, Cuevas A, Manteiga WG (1994) A comparative study of several smoothing methods in density estimation. Comput Stat Data Anal 17:153–176CrossRefzbMATHGoogle Scholar
  44. 44.
    Jones MC, Marron JS, Sheather SJ (1996) A brief survey of bandwidth selection for density estimation. J Am Stat Assoc 91:401–407CrossRefMathSciNetzbMATHGoogle Scholar
  45. 45.
    Hentati R, Prigent J-L (2010) Chapter 4 Copula theory applied to hedge funds dependence structure determination. In: Nonlinear modeling of economic and financial time-series. Emerald Group Publishing Limited, pp 83–109Google Scholar
  46. 46.
    Cai D, Shi D, Chen J (2014) Probabilistic load flow computation using Copula and Latin hypercube sampling. IET Gener Transm Distrib 8:1539–1549CrossRefGoogle Scholar
  47. 47.
    Saadat N, Choi SS, Vilathgamuwa DM (2015) A statistical evaluation of the capability of distributed renewable generator-energy-storage system in providing load low-voltage ride-through. IEEE Trans Power Delivery 30:1128–1136CrossRefGoogle Scholar
  48. 48.
    Zhang N, Kang C, Xia Q, Liang J (2014) Modeling conditional forecast error for wind power in generation scheduling. IEEE Trans Power Syst 29:1316–1324CrossRefGoogle Scholar
  49. 49.
    Park H, Baldick R (2015) Stochastic generation capacity expansion planning reducing greenhouse gas emissions. IEEE Trans Power Syst 30:1026–1034CrossRefGoogle Scholar
  50. 50.
    Hasan KN, Preece R (2017) Influence of stochastic dependence on small-disturbance stability and ranking uncertainties. IEEE Trans Power SystGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.State Grid Corporation of ChinaShanghaiChina

Personalised recommendations