Giovanni Mazzanti

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, methodological, 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” (IRA), 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, which is well covered in reliability literature, we believe that the development of the IRA is perfectly coherent—from a “philosophical” point of view—with the recent success and fast-growing adoption of the Bayesian estimation methodology in reliability. This success is proved by the ever-increasing number of papers devoted to such methodology, in particular, in the field of electric and electronic engineering. Indeed, the Bayesian approach makes use of prior information, which in such kind of analyses is provided by technological information available to the engineer, and—as well known—proves to be very efficient in the presence of data scarcity. Loosely speaking, IRA is a way of using prior information not (only) for random parameter assessment, but for a rational “model assessment”. 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 toward higher system availability at lower costs, requires an accurate reliability 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. Indeed, utilities have to face on one hand the progressive aging of many power system devices and on the other hand the high-reliability of such devices, for which only a small number of lifetime values are observed. This chapter gives theoretical and practical aids for the proper selection of reliability models for power system components. First, 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 IRA: 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), a wide range of models can be deduced in the framework of IRA, that are useful for describing the reliability of electrical components such as switchgears, insulators, cables, capacitors, transformers and rotating electrical machines. Then, since insulation is the weakest part of most electrical devices—particularly in medium voltage and high voltage systems—phenomenological and physical models are developed over the years for the estimation of insulation aging and life is illustrated in this framework. Actually, in this kind of application the prior knowledge could be very fruitfully exploited within a “Stress-Strength” model, since Stress and Strength are clearly identifiable (mostly being applied voltage and dielectric Strength, respectively) and often measurable. By means of this approach, new derivations of the log-logistic distribution and of the “Inverse power model”, widely adopted for insulation applications, are shown among the others. Finally, the chapter shows by means of numerical and graphical examples that seemingly similar reliability models can possess very different lifetime percentiles, hazard rates and conditional (or “Residual”) reliability function values (and, thus, mean residual lives). This is a very practical consequence of the model selection which is generally neglected, but should be carefully accounted for, since it involves completely different maintenance actions and costs.

Four-Phase AC Connections: An Alternative Possibility for the Expansion of Transmission Grids

This paper investigates the economical feasibility of four-phase (4P) overhead transmission lines, considered as a possible alternative to the traditional three-phase (3P) connections. The paper performs an economical comparison between innovative 4P transmission lines and traditional 3P lines, with the goal of evaluating the contests where a 4P connection could become convenient, accounting for different reliability, land occupation, visual impact, energy losses and investment costs.

Technical comparison among different solutions for overhead power transmission lines

The goal of this paper is to develop a technical comparison among different possible solutions for overhead transmission lines. These include both traditional and innovative solutions: the former are usual three-phase AC lines and HVDC lines, the latter are four-phase AC lines and combined AC-DC lines. A technical-economical comparison between aerial standard three-phase AC and innovative four-phase AC lines has been already developed in, where the possible scope of convenience of the four-phase solution has been individuated. This paper first illustrates the main characteristics of the four considered solutions, pointing out the technical advantages provided by each one. Secondly, the paper performs a more detailed comparison based on a probabilistic analysis of the transient stability performances of the considered alternatives.

The application of the enlargement law to HVDC cable lines

In this paper the traditional enlargement law for AC cables - based on the so-called “volume effect” - is extended to DC cables via an innovative theoretical approach, that takes into account some aspects peculiar of HVDC cables, i.e. the dependence of the electric field profile on volume electrical resistivity of the insulation, the associated dependence of volume resistivity on electric field and temperature, the role played by the heat dissipated through the cable layers and by the thermal resistivity of the insulation. An application of the novel enlargement law developed is given in the paper considering real HVDC cables and examining the influence of some of the many parameters appearing in the model.

Toward a BITE for Real-Time Life Estimation of Capacitors Subjected to Thermal Stress

The use of a built-in test equipment (BITE) that is able to provide a real-time diagnostic of a monitored device allows increasing reliability and decreasing costs. The BITE operation can be based on a suitable life model of the device that must relate the time to failure to the “stress history” of the component. The life model is developed by exploiting the results of a proper measurement campaign. This paper investigates a life model for capacitors subjected to both constant and time-varying temperatures by illustrating the test system and discussing the achieved results.

A test set for LEDs life model estimation

Life models relate the time to failure to the applied stress. They can be derived starting from knowledge of chemical/physical phenomena involved in the ageing process caused by the stress or by means of regressive techniques on data acquired in ALT-based procedure. Anyway, experimental tests are needed. This paper deals with a test system implemented to estimate a life model for LEDs where the forward current is considered as stress.

A Simple Innovative Method to Calculate the Magnetic Field Generated by Twisted Three-Phase Power Cables

This paper firstly examines the consolidated analytical methodologies available in literature for the calculation of the magnetic field generated by a twisted three-phase conductor arrangement carrying balanced three-phase currents. Such literature methodologies consist of an exact analytical expression of the RMS magnetic induction given in the form of complicated Bessel-function series and of an approximation of such exact expression where only the first term of the series is considered. Subsequently, a simple innovative approximated formula for the RMS magnetic induction generated by twisted three-phase power cables is obtained by means of an heuristic procedure. This formula results a good approximation of the rigorous analytical one and at the same time is much more accurate than the approximated formula found in literature, as demonstrated by the case of a twisted three-phase power cable used for power distribution at the medium voltage level.

Evaluation of Continuous Exposure to Magnetic Field From AC Overhead Transmission Lines Via Historical Load Databases: Common Procedures and Innovative Heuristic Formulas

Public concern about electromagnetic fields from power systems calls for a proper evaluation of continuous exposure of the population to power frequency magnetic fields, especially those from overhead transmission lines, felt as impacting human activities and the environment. Sophisticated measuring and computing tools now available for continuous exposure evaluation may be ineffective without a sound knowledge of power system theory and of typical line loads. In this perspective, the paper firstly recalls the fundamentals of power line magnetic field calculation and shows that a proper use of historical load databases is essential for associating residential magnetic fields with load diagrams of the lines. Then, innovative heuristic formulas for ac double-circuit overhead transmission lines with independent circuits are proposed, so that line databases can be used accounting for phase-shift effects between line currents in an easier and faster way. Such formulas provide a good approximation, via one single fixed-load calculation, of the median/mean magnetic field over a reference operational period of the line (e.g., one year) and are successfully applied to an existing line, resorting to a historical load database of the line recorded from 1994 to 2001.

The so-called “Conto Energia”: An effective incentive to the use of photovoltaic energy in Italy

The paper deals with the incentive mechanism of electrical energy produced via the photovoltaic source in Italy. This mechanism, called the “Conto Energia” (Energy Account), relies on a preferential tariff (or “feed-in tariff”) which is based on annual generation and has led to a steep increase of the photovoltaic energy produced during the last four years in our Country, thereby constituting - with its advantages, but also with its weak points - a significant paradigm on a global scale in the field of financing strategies for renewable sources. In the paper, the evolution of the “Conto Energia” is analyzed, which has undergone several updates over time, thereby giving rise to three different “versions”, referred to as, respectively, First, Second and Third “Conto Energia”. Finally, the results obtained by means of the “Conto Energia” are illustrated, with a final comment on the latest changes taking place and the future perspectives.

The economic feasibility of four-phase AC overhead connections

The goal of this paper is assessing the economic feasibility of four-phase AC overhead connections, i.e. the real chance that such lines have of being competitive with commonly-used solutions for power transmission. For this reason, the paper illustrates an economical comparison among innovative 325 kV four-phase ac lines, traditional 400 kV three-phase ac lines and increasingly-popular 500 kV HVDC lines. These systems are considered firstly in single-circuit and secondly in double-circuit overhead arrangement. The comparison is based on the main cost items that characterize these lines, namely investment costs, energy losses costs and reliability-related costs. The uncertainty of the relevant parameters, particularly significant as far as innovative four-phase ac lines are concerned, is also discussed.