Mathematical And Physical Properties Of Reliability Models In View Of Their Application To Modern Power System Components

This chapter has a twofold purpose. The first is to present an up-to-date review of the basic theoretical and practical aspects of the main reliability models, and of some models that are rarely adopted in literature, although being useful in the authors’ opinion; some very new models, or new ways to justify their adequacy, are also presented. The above aspects are illustrated from a general, meth-odological, viewpoint, but with an outlook to their application to power system component characterization, aiming at contributing to a rational model selection. Such selection should be based upon a full insight into the basic consequences of assuming – sometimes with insufficient information – a given model. The second purpose of this chapter, closely related to the first, is to highlight the rationale behind a proper and accurate selection of a reliability model for the above devices, namely a selection which is based on phenomenological and physical models of aging, i.e. on the probabilistic laws governing the process of stress and degradation acting on the device. This “technological” approach, which is also denoted in the recent literature as an “indirect reliability assessment”, might be in practice the only feasible in the presence of a limited amount of data, as typically occurs in the field of modern power system. Although the present contribution does not address, for reasons of brevity, the topic of model or parameter statistical estimation, the development of the indirect reliability assessment is perfectly coherent – from a “philosophical” point of view – with the recent success and fast-growing adoption of the Bayesian estima-tion methodology in reliability, as proved by the ever-increasing number of papers devoted to such methodology, in particular in the field of electric and electronic engineering. In the framework of the investigation of innovations in reliability analyses regarding modern power systems, the present chapter takes its stimulus from the observation that the modern, deregulated, electrical energy market, striving towards higher system availability at lower costs, requires an accurate reliabil-ity estimation of electrical components. As witnessed by many papers appearing on the subject in literature, this is becoming an increasingly important, as well as difficult, task. This chapter gives theoretical and practical aids for the proper selection of reliability models for power system components. Firstly, the most adopted reliability models in the literature about electrical components are synthetically reviewed from the viewpoint of the classical “direct reliability assessment”, i.e. a reliability assessment via statistical fitting directly from in-service failure data of components. The properties of these models, as well as their practical consequences, are discussed and it is shown that direct fitting of failure data may result poor or uncertain due to the limited number of data. Thus, practical aids for reliability assessment can be given by the knowledge of the degradation mechanisms responsible for component aging and failure. Such aging and life models, when inserted in a probabilistic framework, lead to “physical reliability models” that are employed for the above-mentioned indirect reliability assessment: in this respect, a key role is played by “Stress-Strength” models, whose properties are discussed in detail in the chapter. While the above part is essentially methodological and might be of interest even for non-electrical devices (e.g., Stress-Strength models were originally derived in mechanical engineering), very useful models can be deduced in the framework of indirect reliability assessment, that are useful both in the evaluation and at the design stage of components such as switchgears, insulators, cables, capacitors, trans-formers and rotating electrical machines. Then, since insulation is the weakest part of most electrical devices –particularly in medium voltage and high voltage...