Stochastic Extreme Wind Speed Modeling and Bayes Estimation under the Inverse Rayleigh Distribution

Abstract

Inverse Rayleigh probability distribution is shown in this paper to constitute a valid model for characterization and estimation of extreme values of wind speed, thus constituting a useful tool of wind power production evaluation and mechanical safety of installations. The first part of this paper illustrates such a model and its validity to interpret real wind speed field data. The inverse Rayleigh model is then adopted as the parent distribution for assessment of a dynamical “risk index” defined in terms of a stochastic Poisson process, based upon crossing a given value with part of the maximum value of wind speed on a certain time horizon. Then, a novel Bayes approach for the estimation of such an index under the above model is proposed. The method is based upon assessment of prior information in a novel way which should be easily feasible for a system engineer, being based upon a model quantile (e.g., the median value) or, alternatively, on the probability that the wind speed is greater than a given value. The results of a large set of numerical simulation—based upon typical values of wind-speed parameters—are reported to illustrate the efficiency and the precision of the proposed method, also with hints to its robustness. The validity of the approach is also verified with respect to the two different methods of assessing the prior information.

The Compound Inverse Rayleigh as an Extreme Wind Speed Distribution and Its Bayes Estimation

“…Moreover, as discussed in [16], the randomness of WS also has a great impact on the mechanical reliability of wind power systems, since extreme values of wind speed (EWS) may damage sensible components of the structures, such as towers and wind blades, so that EWS characterization also constitutes a basic tool for an efficient wind turbine design. In [17][18][19][20][21], the theory of extreme value distributions is adopted for studying such aspects Furthermore, as also pointed out in [20], values of WS that are greater than the "cut-off" value of the wind generator are generally undesirable, since the electric generator has to be disconnected from the wind turbine to avoid damages to the electrical section of the wind power system; consequently, the "cut off" value of the generator must be chosen according to the characterization of EWS in the particular location, since it has a great impact on aggregate power production [21][22][23]. So, EWS is also indirectly related to the electricity production, as discussed in [4], although the paper is primarily devoted to the issue of mechanical safety.…”

“…With this aim, a new model, the Compound Inverse Rayleigh (CIR) distribution, is proposed and illustrated in the paper, as this is a particularly valid model for extreme wind speeds. This CIR model takes its name (as well as its derivation) from the more popular Inverse Rayleigh distribution [20,[33][34][35], which was proposed a few decades ago for the purpose of modeling positive random variables, and especially for its applications in reliability and survival time studies. This model also constitutes a particular case of the Inverse Weibull distribution [33] which, which-apart from being rather popular for its reliability applications [36][37][38]-has been also adopted as a valid model for the characterization and estimation of EWS [6][7][8][9][10][11]23].…”

The Compound Inverse Rayleigh as an Extreme Wind Speed Distribution and its Bayes Estimation

“…Moreover, as discussed in [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], the randomness of WS also has a great impact on the mechanical reliability of wind power systems, since extreme values of wind speed (EWS) may damage sensible components of the structures, such as towers and wind blades, so that EWS characterization also constitutes a basic tool for an efficient wind turbine design. Furthermore, as also pointed out in [15][16][17][18][19], values of WS that are greater than the "cut-off" value of the wind generator are generally undesirable, since the electric generator has to be disconnected from the wind turbine to avoid damages to the electrical section of the wind power system; consequently, the "cut off" value of the generator must be chosen according to the characterization of EWS in the particular location, since it has a great impact on aggregate power production [1][2][3][4][21][22][23]. So, EWS is also indirectly related to the electricity production, as discussed in [4], although the paper is primarily devoted to the issue of mechanical safety.…”

“…With this aim, a new model, the Compound Inverse Rayleigh (CIR) distribution, is illustrated and proposed in the paper as valid model for extreme wind speeds. Such CIR model takes its name (as well as its derivation) from the more popular Inverse Rayleigh distribution [19,[33][34][35], which was proposed since a few decades for the purpose of modeling positive random variables, and especially for its applications in reliability and survival times studies. Such model also constitutes a particular case of the Inverse Weibull distribution [33] which, which -apart being rather popular for its reliability applications [36][37][38] -has been also adopted as a valid model for the characterization and estimation of EWS [6][7][8][9][10][11]23].…”

“…Such model also constitutes a particular case of the Inverse Weibull distribution [33] which, which -apart being rather popular for its reliability applications [36][37][38] -has been also adopted as a valid model for the characterization and estimation of EWS [6][7][8][9][10][11]23]. The IR model is studied in this paper in relation to applications to EWS data analysis, by extending a similar approach promoted by some of the authors in a previous paper on the subject [19].…”