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This chapter is devoted to markovian approaches to model first the wind speed in a given site starting from experimental results and, then, power availability of a wind turbine installed in assigned wind conditions. The chapter organization is as follows: section 2 is devoted to wind data and their treatment; section 3 presents two wind models with different accuracy; section 4 describes produced power models for wind turbines, first in hypotheses of ideal failure-free turbine and, then, accounting for a real behaviour; section 5 is devoted to model analytical solutions; section 6 reports the results of numerical examples developed for a very simple case-study; section 7 describes some possible model applications; section 8 concludes the chapter; section 9 is constituted of an appendix on the basic Markov model concepts. A significant part of the chapter content derives from references (Manco & Testa, 2007 and to other references of the chapters’ authors reported in Section 10).

A general probabilistic model is presented of an electrical system node capable of unifying supply reliability (SR) and voltage quality (VQ) from the point of view of a sensitive user. It is a discrete state model based on the classification characteristics of measurement results, as recommended by the SR/VQ standards. It makes it possible to take into account: 1) the user's sensitivity, simply by drawing border lines between the states whose effects cause malfunctions and the other states, and 2) the uncertainty related to the random nature of the phenomena involved and of the equipment sensitivities. The authors use the Markov process theory to develop and solve the model, taking advantage of the so-called device of stages extension to represent the nonexponential nature of voltage dip durations and the recovery times consequent to long and short interruptions. In order to demonstrate the usefulness of the proposed model and the importance of the recovery time probability distribution, a representative case study is also discussed.

SUMMARY A model of an electrical system node is presented. It allows predicting the effects of long and short interruptions as well as of voltage dips on final users starting from statistical input data. The model is developed using an extension of the homogeneous multi-state Markov process to take into account the non exponential nature of the failure-repair process. Case studies demonstrate the usefulness of the model for practical applications.