E. Chiodo

Bayesian reliability estimation based on a Weibull stress-strength model for aged power system components subjected to voltage surges

For original article by E. Chiodo, G. Mazzanti, see ibid., vol.13, no.1, p.146-59, February 2006

Negative Log‐Gamma distribution for data uncertainty modelling in reliability analysis of complex systems ‐ Methodology and robustness

In the paper, the problem of uncertain data in reliability analysis of complex systems is examined. The analysis is addressed to system reliability assessment with imprecise knowledge of component reliabilities, an item becoming more and more important for systems affected by considerable technological change. Starting from component uncertain data, a new method for the whole system reliability uncertainty description, based upon a Bayesian approach and not depending on the reliability model of each component, is proposed. The reliability value of each component is considered as a random variable described by a Negative Log‐Gamma distribution. The proposed methodology makes it possible to compute the features of system reliability uncertainty (i.e. reliability distribution, confidence intervals, etc.) as functions of component uncertain data, thus characterizing the propagation of uncertainty from the components to the system. Numerical applications, related to a test system, are presented to show the validity of the method and its “robustness”, i.e. it is shown that it yields satisfactory results also when component reliabilities are not Negative Log‐Gamma but Beta distributed.

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.

Some Basic Properties of the Failure Rate of Redundant Reliability Systems in Industrial Electronics Applications

This paper discusses some common reliability architectures, such as “parallel” and “k out of n” systems, adopted to add redundancy in many modern industrial systems, such as parallel-inverter systems. The focus is on some crucial properties of the failure rate (FR) of such systems, motivated by the fact that, in applied literature, the system FR is often simply evaluated as the reciprocal of the “Mean Time To Failure” of the system. However, this relationship is valid if, and only if, the system has a “series” reliability architecture. This is indeed the only case in which also the system has a constant FR, i.e., an Exponential lifetime distribution. Instead, the system FR of redundant systems is a function of time, which can never be constant. It is simply shown indeed that the FR of a parallel system with constant FR components is an increasing, or “first increasing, then decreasing” function of time, eventually reaching the value of the smallest FR. These results are extended to k out of n reliability systems, and also to more general reliability models with nonconstant FR, such as the Weibull or the “bathtub” model.

Reliability aspects in wind farms design

Wind park design is not a straightforward task because it involves many heterogeneous aspects to handle in integrated and systemic way. Historically, the reliability issue has often been neglected in favor of economic issue in power systems design. By following the modern tendency of the power system literature, the reliability constraints have to be satisfied a priori, for sake of power system security and safety. For this reason, a rationale procedure is developed in the paper for suitably comparing various alternatives, at the aim of identifying the optimal candidate to be realized. In the work, a specific objective function is proposed in order to select the better wind farm configuration. It is constituted by some terms which basically compare the profits related to the economic trading in the deregulated electric market and the costs due to the investment, operation & management and to system unavailability. This objective function is accurately investigated as a function of the turbines number in order to derive the most convenient alternative, this implying also the optimal choice of the single wind generators size. The ranking coming out from this assessment is then compared with that one which establishes a preferability in terms of expected load not supplied (ELNS). A compromise choice, between the best alternatives provided by the two criteria has finally to be adopted. A simple numerical application is reported in the last part of the paper for testing the validity of the proposed approach.

Transient stability probability assessment and statistical estimation

Abstract In the paper, a general analytical method for the probabilistic evaluation of power system transient stability is discussed and a new statistical inference approach for this evaluation is proposed. In particular, the transient stability probability (TSP) is defined and evaluated by taking into account the random nature of both the system loads and the fault clearing times (FCT). The paper is focused upon the aspect of statistical estimation of the TSP—a topic generally neglected in literature—on the basis of the obvious consideration that the parameters affecting the TSP (e.g. mean value and variance of loads, FCTs, etc.) are not known, but must be estimated. New properties of point and interval estimations of the TSP are derived and, in particular, an efficient “lower confidence bound” for the TSP estimation is proposed, based upon a suitable Beta probability distribution. In order to show the feasibility of the proposed approach, a numerical application to the Cigre test network is illustrated. Moreover, extensive Monte Carlo simulations to evaluate the estimator efficiency are performed. In the final part of the paper, also a practical example of possible application to the optimization of system design is illustrated. The application of the method is illustrated and performed by using the potential energy boundary surface method, but the estimation results hold their validity irrespective of the method adopted for the transient stability problem formulation and resolution.

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.

Parameter estimation of mixed Weibull probability distributions for wind speed related to power statistics

Estimation of wind-speed statistics is essential for an efficient assessment of wind power generation, and thus for any rational decision upon the installation and operation of a wind farm. Most existing methods for the above estimation are based upon the popular Weibull distribution. However, a few recent papers have pointed out, based upon field data analysis, some drawback of the above model. Such data show indeed significant “heavy tails” in wind-speed probabilistic distribution for large wind speed values, constituting a crucial aspect for wind power estimation. Alternative models for such distribution, such as the Log-logistic (as discussed in a previous paper) or the Burr model, appear to be natural candidates for the wind statistics modeling, also on theoretical grounds. In particular, the Burr model is analyzed in the paper, based on a proper “mixture” of Weibull probability distributions. After illustrating such derivation, a suitable Bayes approach for the estimation of the Burr model (also including the Log-logistic model as a particular case) is proposed. The method, whose simplicity and efficiency is shown by means of a numerical application, is based upon the transformation of a Gamma distribution for converting prior information in a novel way which should be very practical for the system engineer.

Probabilistic characterization of uncertainty in the photovoltaic cell modeling

In the paper the uncertainty of the photovoltaic (PV) cell model, by properly deriving the probability density function of the interest parameters, is characterized. This issue is crucial for predicting the capability of the photovoltaic source in producing electrical energy, but also for the control aspects of designing an efficient Maximum Power Point Tracker (MPPT). The PV source is modeled by means of a five parameters model: Iph, I0, VT, Rs and Rsh. The probabilistic approach is based upon the knowledge of the cell datasheet. The shunt resistance Rsh, in absence of information, is characterized by a Gamma distribution. A statistical analysis, based upon Monte Carlo simulation, is performed for verify how the other parameters can be affected by the stochastic nature of the random variable. In the final part of the paper, the uncertainty of the datasheet values is also introduced. A case study is reported and the numerical results are discussed in detail.

Human reliability analyses by random hazard rate approach

The aim of this paper is to show the connections among uncertainty, information and human knowledge to develop methodologies able to support actions for measure and control of complex processes, and to propose new model to represent human hazard rate. The interest to human reliability analyses (HRA) arose for nuclear applications, observing that 50‐70 per cent of reported failures on operating systems were human‐induced. Since the middle of 1980, methods and tools of HRA have been transferred former to military weapons systems, latter to aviation designs and operations. At present, HRA, which consider human performance and human reliability knowledge, must be an integral element of complex system design and development. In this paper, system reliability function is carried out as a function of technological, information and human components, evidencing how human element affects the whole system reliability. On the basis of consideration that human errors are often the most unexpected and then the least protected, and subject to many random factors, an analytical model is proposed, based on a conditional Weibull hazard rate with a random scale parameter, for whose characterization the log‐normal, gamma and the inverse Gaussian distributions are considered. The aim of this model is to take into account random variability of human performances by introducing a random hazard rate.