| Popis: |
In the scope of operating safety in electrical substations, EDF is brought to perform reliability and availability computations. These computations declined on the substation performance are used to estimate non-quality indicators. However, these different computations use models which rely on simplifying assumptions of functioning and dysfunctioning probabilistic data. Generally, the main assumption retained in order to evaluate reliability and availability parameters is that failure and repair rates of the components are time-constant. This is the case of time-homogeneous Markov systems. The above assumption allows to use traditional models to evaluate reliability and availability parameters, such as Markovian graphs or fault trees. Therefore, in these models, we use mean values for the failure rates and the repair rates. In the same way, certain parameters involving the system performance are computed with mean values (mean value of an electrical substation load). However, for electrical power systems, many parameters may vary with time, especially on the hour of the day and the period of the year. As a consequence, if we take into account hazard rate time variation, the traditional models are no longer valid for this kind of problems. This dependence of the hazard rate function with time leads us, naturally, to investigate non-homogeneous Markov models. In this paper, we first define and give basic developments of transient analysis of non-homogeneous Markov chains then we provide a new formulation for reliability and performability indicators. This new formulation naturally includes state probabilities, reliability, availability, maintainability but also some useful performance indicators that are more dedicated to power systems such as expected energy not supplied on a time interval. Finally a numerical application is solved to illustrate this method. In this example, we highlight the differences in the results obtained by classical and new modelling but also the new information we can access. |
