Evaluation of the probability density functions of distribution system reliability indices with a characteristic functions-based approach

In reliability analysis of distribution systems, random events like the occurrence of a fault or the time to restore the service after a fault are represented by using random variables (RVs), so that the reliability indices built on the basis of these RVs also become RVs. Existing techniques for the evaluation of the probability distributions of reliability indices are typically based on Monte Carlo and analytical simulations. This paper presents a new method for computing the probability distribution of reliability indices. The random sums introduced by the randomness of the number of fault occurrences in the time interval of analysis are handled by using a characteristic functions-based approach. The direct convolution of the probability density functions is avoided by resorting to the properties of the compound Poisson process. In addition, the direct and inverse discrete Fourier transforms are used to allow for handling any type of probability distribution. The proposed method is an effective alternative to the existing methods, providing a fast and simple computation of probability distributions and moments for local and global reliability indices. Results obtained for large real urban distribution systems are presented.

[1]  R. Billinton,et al.  Distributional Variation of Distribution System Reliability Indices , 1985, IEEE Power Engineering Review.

[2]  A. Papoulis.  Signal Analysis , 1977 .

[3]  E. N. Dialynas,et al.  Evaluating the approximate probability distributions of load point reliability indices in power distribution networks , 1990 .

[4]  L. Goel,et al.  Using Monte Carlo simulation for overall distribution system reliability worth assessment , 1999 .

[5]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[6]  Wolfram H. Wellssow,et al.  IDENTIFICATION OF PROBABILITY DISTRIBUTIONS OF PROBABILISTIC RELIABILITY INDICES FOR MONETARY EVALUATION AND RISK ASSESSMENT , 2002 .

[7]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[8]  Roy Billinton,et al.  Distribution system reliability performance and evaluation , 1988 .

[9]  R. Billinton,et al.  An Analytical Approach to Evaluate Probability Distributions Associated with the Reliability Indices of Electric Distribution Systems , 1986, IEEE Power Engineering Review.

[10]  Enrico Carpaneto,et al.  Tools for optimal operation and planning of urban distribution systems , 2001 .

[11]  Wenyuan Li,et al.  Reliability Assessment of Electric Power Systems Using Monte Carlo Methods , 1994 .

[12]  I. Miller.  Probability, Random Variables, and Stochastic Processes , 1966 .

[13]  W. G. Watson,et al.  Reliability Modeling in Electric Power Systems , 1979 .

[14]  Roy Billinton,et al.  Reliability evaluation of power systems , 1984 .

[15]  A. P. Hanson,et al.  Impact of Two-Stage Service Restoration on Distribution Reliability , 2001, IEEE Power Engineering Review.

[16]  P. Hughett.  Error Bounds for Numerical Inversion of a Probability Characteristic Function , 1998 .

[17]  K. Sand,et al.  RELRAD-an analytical approach for distribution system reliability assessment , 1991, Proceedings of the 1991 IEEE Power Engineering Society Transmission and Distribution Conference.

[18]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[19]  J. Hammersley.  SIMULATION AND THE MONTE CARLO METHOD , 1982 .

[20]  S. Asgarpoor,et al.  Reliability evaluation of distribution systems with nonexponential down times , 1997 .

[21]  M. Schmieg,et al.  Reliability assessment in electrical power systems: the Weibull-Markov stochastic model , 1999, 1999 IEEE Industrial and Commercial Power Systems Technical Conference (Cat. No.99CH36371).

[22]  Enrico Carpaneto,et al.  Analytical evaluation of the probability distributions of reliability indices for large distribution systems , 2002 .