Bayesian Hidden Markov Models for Performance-Based Regulation of Continuity of Electricity Supply

A fundamental aspect in the regulation of the continuity of electricity supply is the identification of faults that could be caused by an exceptional event and, therefore, that are outside the utility control and responsibility. Different methods have been proposed during the years: the interpretation of the observed faults as a signal of an underlying system naturally leads to the analysis of the problem by means of a hidden Markov model. These models, in fact, are widely used for introducing dependence in data and/or for modeling observed phenomena depending on hidden processes. The application of this method shows that the model is able to identify exceptional events; moreover, the study of the estimated model parameters gives rise to reality-linked considerations.

[1]  E. Fumagalli,et al.  Service Quality Regulation in Electricity Distribution and Retail , 2007 .

[2]  Sylvia Frühwirth-Schnatter,et al.  Finite Mixture and Markov Switching Models , 2006 .

[3]  Lain L. MacDonald,et al.  Hidden Markov and Other Models for Discrete- valued Time Series , 1997 .

[4]  R. D. Christie,et al.  Classification of major event days , 2003, 2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491).

[5]  John M. Olin Calculating posterior distributions and modal estimates in Markov mixture models , 1996 .

[6]  C. Robert,et al.  Bayesian estimation of hidden Markov chains: a stochastic implementation , 1993 .

[7]  Mitchell J. Mergenthaler Nonparametrics: Statistical Methods Based on Ranks , 1979 .

[8]  E. Fumagalli,et al.  Statistical identification of major event days: an application to continuity of supply regulation in Italy , 2006, IEEE Transactions on Power Delivery.

[9]  C. Robert,et al.  Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method , 2000 .

[10]  Eric Moulines,et al.  Inference in hidden Markov models , 2010, Springer series in statistics.

[11]  S. L. Scott Bayesian Methods for Hidden Markov Models , 2002 .

[12]  D. Titterington,et al.  Bayesian inference in hidden Markov modelsthrough reversible jump Markov chain Monte , 2022 .

[13]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001 .

[14]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

[15]  L. Baum,et al.  A Maximization Technique Occurring in the Statistical Analysis of Probabilistic Functions of Markov Chains , 1970 .

[16]  Anna Maria Paganoni,et al.  Statistical analyses of exceptional events: the Italian experience , 2008 .

[17]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[18]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[19]  P. Rousseeuw Silhouettes: a graphical aid to the interpretation and validation of cluster analysis , 1987 .

[20]  Paul R. Cohen,et al.  Bayesian Clustering by Dynamics Contents 1 Introduction 1 2 Clustering Markov Chains 2 , 2022 .

[21]  Ali S. Hadi,et al.  Finding Groups in Data: An Introduction to Chster Analysis , 1991 .

[22]  W. Marsden I and J , 2012 .

[23]  Van Nostrand,et al.  Error Bounds for Convolutional Codes and an Asymptotically Optimum Decoding Algorithm , 1967 .

[24]  Leo Breiman,et al.  Statistical Modeling: The Two Cultures (with comments and a rejoinder by the author) , 2001, Statistical Science.

[25]  R. D. Christie Statistical Classifitcation of Major Event Days in Distribution System Reliability , 2002, IEEE Power Engineering Review.

[26]  E. Fumagalli,et al.  Statistical Analysis of Exceptional Events: The Italian Regulatory Experience , 2009, IEEE Transactions on Power Delivery.