A Bayes Inference Method for Probabilistic Transient Stability Assessment of Power Systems

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A Bayesian inference approach is proposed for power systems transient stability assessment. Such assessment is crucial for modern power systems, which must often operate close to their stability limits, and are facing increasing levels of uncertainty. In particular, the estimation of the transient instability probability of a system is discussed in the paper, with some hints to interval estimation. First, the theoretical foundations of probabilistic stability assessment are reviewed according to already established models, which allow an analytical formulation of the instability probability in terms of the basic random variables affecting stability, such as the fault clearing time and the critical clearing time. Then, the novelty of the paper is illustrated, consisting in the above estimation, motivated by the observation that the parameters of the basic random variables (e.g. the expected values of the clearing times), being unknown in practice, have to be estimated. A large series of numerical simulations show that the proposed estimation method constitutes a very efficient method. Moreover, other numerous simulations have been performed for the purpose of a robustness analysis, showing that the methodology efficiency appears to hold also when departing from the assumptions made on prior parameter distributions and also on basic model distributions
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Bayesian Inference; Lognormal Distribution; Power Systems; Probability Theory; Transient Stability

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P. Kundur, Power System Stability and Control, Electric Power System Research, Power System Engineering Series, McGraw-Hill, 1993.

M. Pavella, P.G. Murthy, Transient stability of power systems. Theory and Practice, John Wiley & Sons, 1994.

M.A. Pai, Power system stability analysis by the direct method of Lyapunov, North Holland Publishing Company, 1981.

A.A.Fouad, V. Vittal, Power system transient stability analysis using the transient energy function method, Pearson Education, 1991.

E. Chiodo, D. Lauria, Probabilistic Transient Stability Assessment and on-line Bayes Estimation, in: G. Anders and A.Vaccaro (eds), Innovations in Power Systems Reliability, p. 259-312, Springer-Verlag, London 2011.

F. Allella, D. Lauria, A fast optimal dispatch with global transient stability constraint, IEE Proceedings - Generation, Transmission and Distribution, vol. 148, n.5, 2001, pp. 471-476.

N.G. Bretas, L.F.C. Alberto, Transient Stability of Power Systems: Robustness with Respect to Parameter Uncertainties, Proc. IEEE Power Engineering Society Winter Meeting, 2, 2002, pp. 1105-1112.

G.M. Huang, Y. Li, Power Systems Reliability Indices To Measure Impacts Caused by Transient Stability Crises, Proc. IEEE Power Engineering Society Winter Meeting, 2002, pp. 766-771.

D. Lauria, C. Pisani, D. Villacci, Probabilistic transient stability margins assessment based upon quadratic stability region approximation, Proc. IEEE International Energy Conference and Exhibition (ENERGYCON 2012), Florence; Italy; 9-12 September 2012, pp. 439-444.

Lauria, D., Pisani, C., Transient stability assessment based upon differential transform method, (2012) International Review of Electrical Engineering (IREE), 7 (4), pp. 4925-4935.

M. Abapour, M.-R. Haghifam, Probabilistic transient stability assessment for on-line applications, International Journal of Electrical Power and Energy Systems, vol. 42, n. 1,, 2012, pp. 627-634.

M. Abapour, M.R. Haghifam, On-line assessment of the transient instability risk, IET Generation, Transmission & Distribution, vol. 7, n. 6, 2013, pp. 602-612.

Chiodo, E., Lauria, D., Pisani, C., Villacci, D., Transient stability margins evaluation based upon probabilistic approach, (2013) International Review of Electrical Engineering (IREE), 8 (2), pp. 752-761.

R. Billinton, P.R.S. Kuruganty, Probabilistic assessment of transient stability, IEEE Transactions on PAS, vol. 100, n. 5, 1981, pp. 2163-2170.

R. Billinton, P.R.S. Kuruganty, Probabilistic assessment of transient stability in a practical multimachine system, IEEE Trans. on PAS, vol. 100, n. 5, 1981, pp. 3634-3641.

R. Billinton, P.R.S. Kuruganty, Protection system modelling in a probabilistic assessment of transient stability, IEEE Trans. on PAS, vol. 100, n. 7, 1981, pp. 3664-3641.

P.M. Anderson, A. Bose, A probabilistic approach to power system stability analysis, IEEE Trans. on PAS, Vol 102, n. 4, 1983, pp. 2430-2439.

Y.Y. Hsu, C.L. Chang, Probabilistic transient stability studies using the conditional probability approach, IEEE Trans. on PAS, Vol. 3, n. 4., 1988, pp. 1565-1572.

G.J. Anders, Probability Concepts in Electric Power Systems, John Wiley, New York, 1990.

E. Chiodo, F. Gagliardi, D. Lauria, A probabilistic approach to transient stability evaluation, IEE Proceedings - Generation, Transmission and Distribution, vol. 141, n. 5, 1994, pp. 537-544.

E. Chiodo, D. Lauria, Transient stability evaluation of multimachine power systems: a probabilistic approach based upon the Extended Equal Area Criterion, IEE Proceedings - Generation, Transmission and Distribution, vol. 141, n. 6, 1994, pp. 545-553.

E. Chiodo, D. Lauria, G. Mazzanti, S. Quaia, Technical Comparison among Different Solutions for Overhead Power Transmission Lines, Proc. International Symposium on Power Electronics, Electrical Drives, Automation and Motion”, (Speedam 2010), Pisa (Italy), 14-16 June 2010, pp. 68 – 73.

F. Allella, E. Chiodo, D. Lauria, Transient Stability Probability Assessment and Statistical Estimation, Electric Power Systems Research, vol. 67, n. 1, 2003, pp. 21-33.

S. Ayasun, Y. Liang, C.O. Nwankpa, A sensitivity approach for computation of the probability density function of critical clearing time and probability of stability in power system transient stability analysis, Applied Mathematics and Computation, 176, 2006, pp. 563–576.

H. Kim, C. Singh, Power system probabilistic security assessment using Bayes classifier, Electric Power Systems Research, 74, 2005, pp. 157–165.

L. Battistelli, E. Chiodo, D. Lauria, A New Methodology for Uncertainty Evaluation in Risk Assessment. Bayesian Estimation of a Safety Index Based upon Extreme Values, Proc. International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM 2008), Ischia (Italy), June 11-13, 2008, pp. 439-444

E. Chiodo, G. Velotto, Bayes Inference in Multicriteria Analysis for Hybrid Electrical Transportation Systems Design, Journal of Fuel Cell Science and Technology, vol. 4, n. 4, November 2007, p. 450-458.

E. Chiodo, L. P. Di Noia, R. Rizzo, The Application of Bayes Inference in Multicriteria Analysis to Design Energy Storage Systems in Renewable Power Generation, Proc. IEEE International Conference on Clean Electrical Power Renewable Energy Resources Impact (ICCEP 2013), Alghero, Italy, June 11-13, 2013.

L. Gong, S. Jing, Applications of Bayesian Methods in Wind Energy Conversion Systems, Renewable Energy, vol. 43, July 2012, pp. 1-8.

Chiodo, E., The burr XII model and its bayes estimation for wind power production assessment, (2013) International Review of Electrical Engineering (IREE), 8 (2), pp. 737-751.

Battistelli, L., Chiodo, E., Lauria, D., Posterior distributions for bayes assessment of photovoltaic inverter reliability and availability, (2012) International Review of Electrical Engineering (IREE), 7 (5), pp. 5808-5817.

T.R. Ayodele, A.A. Jimoh, J.L. Munda, J.T. Agee, The impact of wind power on power system transient stability based on probabilistic weighting method, Journal of Renewable and Sustainable Energy, vol. 4, n. 6, 2012.

R. A. Johnson, Stress-Strength Models for Reliability, in Krishnaiah P.R., Rao C. R. (ed.) Handbook of Statistics, Vol. 7, Quality Control and Reliability, North Holland, Amsterdam, 1988.

S. Kotz, Y. Lumelskii, M. Pensky, The Stress-Strength Model and Its Generalizations: Theory and Applications, Imperial College Press, London, UK, 2003.

E. Chiodo, G. Mazzanti, Theoretical and Practical Aids for the Proper Selection of Reliability Models for Power System Components, International Journal of Reliability and Safety, vol. 2, n. 1/2, 2008, pp. 99-128.

E. Chiodo, G. Mazzanti, New Models for Reliability Evaluation of Power System Components Subjected to Transient Overvoltages, Proceedings of 2006 IEEE PES General Meeting. Montreal, Montreal (Canada), June 18-22 2006.

E. Chiodo, G. Mazzanti, Bayesian Reliability Estimation Based on a Weibull Stress-Strength Model for Aged Power System Components Subjected to Voltage Surges, IEEE Trans. on Dielectrics and Electrical Insulation, vol.13, n. 1, 2006, pp. 146-159

A. Papoulis, Probability, Random Variables, Stochastic Processes, Mc Graw Hill, N.Y, 2002.

G. Carpinelli, E. Chiodo, D. Lauria, Indices for the characterisation of bursts of short-duration waveform distortion, IET Generation, Transmission & Distribution, vol. 1, n.1, January 2007, p. 170-175.

A.M. Breipohl, F.N. Lee, A Stochastic Load Model for Use in Operating Reserve Evaluation, Proc. 3rd International Conference on Probabilistic Methods Applied to Electric Power Systems, London 3-5 July 1991, IEE Publishing, London

N.L. Johnson, S. Kotz, N. Balakrishnan, Continuous univariate distributions, 2nd edn. J. Wiley, New York, 1995.

H.F. Martz, R.A.Waller, Bayesian reliability analysis. Krieger Publishing, Malabar, Florida, 1991.

S.J. Press, Subjective and Objective Bayesian Statistics: Principles, Models, and Applications, J. Wiley, N.Y, 2002.

C.P. Robert Bayesian Core: A Practical Approach to Computational Bayesian Statistics, Springer Verlag, 2007.

S. Weerahandi, R.A. Johnson, Testing Reliability in a Stress-Strength Model When X and Y are Normally Distributed, Technometrics, Vol. 34, n.1, 1992, pp. 83-91.

H. Guo, K. Krishnamoorthy, New approximate inferential methods for the reliability parameter in a stress–strength model: The normal case, Communications in Statistics – Theory and Methods, Vol. 33, n.7, 2004, pp.1715–1731.

A. Barbiero, Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case, Communications in Statistics - Simulation and Computation, vol.40, n. 6, 2011, pp. 907-925.

V.K. Rohatgi, Statistical Inference, J. Wiley & Sons, N.Y., 1984.

D.Z. Fang, L. Jing, T.S. Chung, Corrected transient energy function-based strategy for stability probability assessment of power systems, IET Generation, Transmission & Distribution, vol.2 , n. 3, May 2008, pp. 424 – 432.


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