Antonio Pievatolo

Semi-Markov Processes for power system reliability assessment with application to uninterruptible power supply

We propose a state space model for electrical power systems made by independent semi-Markov components, in which restoration times can have a nonexponential distribution, thus obtaining a more realistic reliability characterization, especially regarding the outage duration distribution. We also propose a model for an energy storage unit, assuming that the storage is fully charged when it begins to deliver power. An approximate analytical evaluation based on the minimal cut sets for the outage allows to surmount the shortcomings of the Monte Carlo approach. The application of the model for an uninterruptible power supply (UPS) system shows that the autonomy of the storage plays a key role, not only for the frequency of the load point voltage failures, but also for their duration distribution.

Bayesian density estimation and model selection using nonparametric hierarchical mixtures

A class of nonparametric hierarchical mixtures is considered for Bayesian density estimation. This class, namely mixtures of parametric densities on the positive reals with a normalized generalized gamma process as mixing measure, is very flexible in the detection of clusters in the data. With an almost sure approximation of the posterior trajectories of the mixing process a Markov chain Monte Carlo algorithm is run to estimate linear and nonlinear functionals of the predictive distributions. The best-fitting mixing measure is found by minimizing a Bayes factor for parametric against nonparametric alternatives. Simulated and historical data illustrate the method, finding a trade-off between the best-fitting model and the correct identification of the number of components in the mixture.

A Bayesian hidden Markov model for imperfect debugging

In this paper we present a new model to describe software failures from a debugging process. Our model allows for the imperfect debugging scenario by considering potential introduction of new bugs to the software during the development phase. Since the introduction of bugs is an unobservable process, latent variables are introduced to incorporate this property via a hidden Markov model. We develop a Bayesian analysis of the model and discuss its extensions. We also consider how to infer the unknown number of states of the hidden Markov model. The model and the Bayesian analysis are implemented to actual software failure data.

Distributed Interruptible Load Shedding and Micro-Generator Dispatching to Benefit System Operations

A blackout is the worst end result of a significant difference between generation and absorption of power. Therefore, distribution network operators (DNO) need to know and control the load and generation profiles in advance to run an electric power network well, especially when distributed generation is present, as in the smart grid of the future. The combination of distributed interruptible load shedding and dispatched microgenerators provides the DNO with an interesting opportunity for power network emergency management. In this paper, a proposal to approach this problem and some test results are presented using probabilistic methods for a small low-voltage network with interruptible loads and combined heat and power (μCHP) generators.

An Overview of Control Charts for High-quality Processes

Major difficulties in the study of high-quality processes with traditional process monitoring techniques are a high false alarm rate and a negative lower control limit. The purpose of time-between-events control charts is to overcome existing problems in the high-quality process monitoring setup. Time-between-events charts detect an out-of-control situation without great loss of sensitivity as compared with existing charts. High-quality control charts gained much attention over the last decade because of the technological revolution. This article is dedicated to providing an overview of recent research and presenting it in a unifying framework. To summarize results and draw a precise conclusion from the statistical point of view, cross-tabulations are also given in this article. Copyright

Optimal Storage Scheduling Using Markov Decision Processes

The paper presents a method based on Markov decision processes to optimally schedule energy storage devices in power distribution networks with renewable generation. The time series of renewable generation is modeled as a Markov chain which allows for the implementation of a stochastic dynamic programming algorithm. The output of this algorithm is an optimal scheduling policy for the storage device achieving the minimization of an objective function including cost of energy and network losses. Besides this, other properties, such as energy storage placement and size, can be assessed and compared in optimized systems with different layouts.

UPS reliability analysis with non-exponential duration distribution

Abstract In this paper, the reliability performance of uninterruptible power systems is studied. After the description of the protection system against anomalous conditions, a brief failure mode analysis is performed in order to define the fault tree referring to compensator output voltage. An analytical model able to deal with non-exponential life and repair time distributions is developed, using semi-Markov processes and assuming stochastic independence for the components of the system under study. The mean time between failure (MTBF) and the mean time to restoration of the compensator output voltage are then calculated exactly. Finally a mechanical bypass switch, which connects the load to the mains directly during long failures, is taken into account in the MTBF calculation via a simple approximation. Monte Carlo simulations are performed to validate the results of the analytical model and of the approximation.

Statistical rehabilitation of improper correlation matrices

The simplest way to describe the dependence for a set of financial assets is their correlation matrix. This correlation matrix can be improper when it is specified element-wise. We describe a new method for obtaining a positive definite correlation matrix starting from an improper one. The experts opinion and trust in each pairwise correlation is described by a beta distribution. Then, by combining these individual distributions, a joint distribution over the space of positive definite correlation matrices is obtained using Cholesky factorization, and its mode constitutes the new proper correlation matrix. The optimization is complemented by a visual representation of the entries that were most affected by the legalization procedure. We also sketch a Bayesian approach to the same problem.

Multilevel Functional Principal Component Analysis of Façade Sound Insulation Data

This work analyzes data from an experimental study on facade sound insulation, consisting of independent repeated measurements executed by different laboratories on the same residential building. Mathematically, data can be seen as functions describing an acoustic parameter varying with frequency. The aim of this study is twofold. On one hand, considering the laboratory as the grouping variable, it is important to assess the within-group and between-group variability in the measurements. On the other hand, in building acoustics, it is known that sound insulation is more variable at low frequencies (from 50 to 100Hz), compared with higher frequencies (up to 5000Hz), and therefore, a multilevel functional model is employed to decompose the functional variance both at the measurement level and at the group level. This decomposition also allows for the ranking of the laboratories on the basis of measurement variability and performance at low frequencies (relative high variability) and over the whole spectrum. The former ranking is obtained via the principal component scores and the latter via an original Bayesian extension of the functional depth. Copyright

More Accurate Prediction Intervals for Exponential Smoothing with Covariates with Applications in Electrical Load Forecasting and Sales Forecasting

The most widely used prediction intervals in empirical time series analysis are of plug-in type; that is, the empirical estimates of model parameters are inserted into formulae for prediction intervals that are obtained from a theoretical analysis of the time series model. Several authors have pointed out that such model-based prediction intervals are too narrow, that is, that the actual confidence level is smaller than the nominal confidence level. The reason is that the uncertainty contained in the parameter estimates is not taken into account in the prediction interval. We investigate this problem for exponential smoothing under covariates with additive trend and additive season. We determine alternative prediction intervals by analysing a linearisation of the underlying model with linear model methods. Two simulation studies based on electricity load data and on sales data confirm the reservations about the plug-in prediction intervals, whereas the intervals based on the linearisation approach are significantly better, and perform very well, with actual confidence levels close to the nominal. Copyright