Electromagnetic Time Reversal: Theory, Application to Fault Location in Power Networks and Experimental Validation

The time-reversal invariance is readily described and universally embodied in most laws of nature, either in a strict or in a soft sense. Based on this underlying physical principle, time-reversal theory has been theoretically and experimentally studied in the field of acoustics first, and later introduced into electromagnetism, under the general denomination of Electromagnetic Time Reversal (EMTR). With the development of modern power system, especially represented by the technology of Smart Grids and Active Distribution Networks (ADNs), a reliable and efficient fault detection and location functionality is increasingly required to ensure the security and quality of supply. It has recently been shown that an EMTR-based fault location technique can provide superior performance with respect to existing techniques in terms of location accuracy and robustness against uncertainties. At the same time, several theoretical and technological challenges have to be addressed before such a technique can be used in real-world applications. The present work aims at addressing these challenges, which are summarized hereunder. Time reversal cavity applied to power networks. The concept of the time-reversal cavity was proposed by Cassereau and Fink for acoustic waves and later extended to electromagnetic waves. It is accepted that a time-reversal cavity is a theoretical concept and cannot be realized experimentally because it requires in principle an infinite number of transducers covering a closed surface around the medium to obtain information about all wavefronts propagating in all directions. Although this is true in a 3D situation, we believe that in the case of power networks in which waves are confined in a specific region of the space and propagate along the longitudinal direction of the lines (1D situation), such a time-reversal cavity is realizable. We propose to design, simulate, and experimentally validate such a cavity for the case of inhomogeneous power networks. Improving the performance of EMTR-based fault locating techniques. The currently-developed EMTR-based technique requires multiple simulations to identify the location of the fault. We will investigate possible ways of reducing the number of required simulation runs. Practical implementation of an EMTR-based fault locator. The EMTR-based method technologically requires the use of a hardware platform, such as a Field Programmable Gate Array (FPGA), capable of performing Electromagnetic Transient (EMT) simulations and post Digital Signal Processing (DSP). In order to address constraints of application in real-world power networks and robustness requirements, further improvement and optimization will be considered, namely, the determination of the minimum time-reversal window required to achieve a certain location accuracy, the development of a library of transmission lines and cables commonly used in power networks, analysis of the location error caused either by incomplete knowledge of the network, or other disturbances such as those originated by lightning, as well as limitations associated with the measurement. The final aim of the thesis is to further develop a fault location hardware platform integrating EMTR theory with numerous functionalities, like EMT simulations, DSP, interactive communication. Its performance will be verified by hardware-in-the-loop tests, and eventually by live tests in real power networks.

A Closed Time-Reversal Cavity for Electromagnetic Waves in Transmission Line Networks

Mario Paolone, Reza Razzaghi, Marcos Rubinstein, Zhaoyang Wang

A closed time-reversal (TR) cavity has been considered a purely theoretical concept whose experimental realization was assumed to be impossible. In this article, we demonstrate that it is, in fact, possible to realize a closed TR cavity using a network of transmission lines. The network is excited by either lumped voltage or current sources at arbitrary locations, and it is terminated on matched impedances. This system is an exact closed TR cavity in the sense that, in the backward-propagation stage, by back-injecting time-reversed measured responses (voltage or current) generated by a source at each line terminal, a time-reversed copy of the current and voltage distribution in the forward-propagation stage is obtained. We report for the first time an experimental realization of a TR cavity formed by a network of inhomogeneous transmission lines, in which the spatial and temporal signal distribution along the network is reproduced as in a sequence of the system state (i.e., voltages and or current along the lines) being played in reverse. We also discuss the interfering effect of the so-called diverging wave for observation points in the vicinity of the source. An active realization of a TR sink is proposed to effectively overcome the interfering effect caused by the diverging waves.

2021

Dynamic triangulations for efficient 3D simulation of granular materials

Jean-Albert Ferrez

Granular materials are omnipresent in many fields ranging from civil engineering to food, mining and pharmaceutical industries. Often considered a fourth state of matter, they exhibit specific phenomena such as segregation, arching effects, pattern formation, etc. Due to its potential capability of realistically rendering these behaviors, the Distinct Element Method (DEM) is a very enticing simulation technique. Indeed it makes it possible to analyze and observe phenomena that are barely if at all accessible experimentally. DEM works by tracking every particle in the system individually, maintaining for each a trajectory influenced by external factors such as gravitation or contacts with boundary objects and by the interactions with other grains. The mathematical problem of identifying pairs of grains that interact and locating precisely where the contact occurs is highly dependent on the shape of the grains. We focus in this thesis on 3D spherical grains and use dynamic weighted Delaunay triangulations to track the collisions. The triangulation is built on the centers of the grains and evolves to follow their motion. We prove that all potentially colliding pairs of spheres are adjacent in the triangulation. As there are 6n to 8n edges for n spheres in most practical cases, the complexity of the collision detection becomes linear instead of quadratic in the number of particles, with a small overhead in maintaining the triangulation with efficient local operations. For the physical problem of realistically rendering the collision in a numerical contact model suitable for computer simulation, we have used widely accepted theories such as the viscoelastic model of Cundall, but have also tested some recent, more sophisticated developments in the field. The collision detection and contact models have been implemented in a modular DEM simulation code with advanced features in data structures storing the triangulation, in numerical robustness of the geometric computations, and in parallel processing on shared memory computers. Optimal packing of powders is important in many industrial processes, yet no theoretical result exists when dealing with grains of different sizes. We have performed simulations of such cases and could compare our results with experimental data. Preliminary results have been obtained regarding the relation between the size and proportion of grains and the density of the packing. Other simulations have also been performed, such as the granular flow through an hourglass. As no efficient simulation method is currently known for non-spherical 3D grains, we propose an intermediate approach of gluing spheres together into arbitrary shaped clusters and show some examples based on this approach.

EPFL2001

Bayesian risk analysis of financial time series

Christophe Osinski

This thesis is a contribution to financial statistics. One of the principal concerns of investors is the evaluation of portfolio risk. The notion of risk is vague, but in finance it is always linked to possible losses. In this thesis, we present some measures allowing the valuation of risk with the help of Bayesian methods. An exploratory analysis of data is presented to describe the sampling properties of financial time series. This analysis allows us to understand the origins of the daily returns studied in this thesis. Moreover, a discussion of different models is presented. These models make strong assumptions on investor behaviour, which are not always satisfied. This exploratory analysis shows some differences between the behaviour anticipated under equilibrium models, and that of real data. The Bayesian approach has been chosen because it allows one to incorporate all the variability, in particular that associated with model choice. The models studied in this thesis allow one to take heteroskedasticity into account, as well as particular shapes of the tails of returns. ARCH type models and models based on extreme value theory are studied. One original aspect of this thesis is its use of Bayesian analysis to detect change points in financial time series. We suppose that a market has two phases, and that it switches from a state to the other at random. Another new contribution is a model integrating heteroskedasticity and time dependence of extreme values, by superposition of the model proposed by Bortot and Coles (2003) and a GARCH process. This thesis uses simulation intensively for the estimation of risk measures. The drawback of simulation is the amount of time needed to obtain accurate estimates. However, simulation allows one to produce results when direct calculation is not feasible. For example, simulation allows one to compute risk estimates for time horizons greater than one day. The methods presented in this thesis are illustrated on simulated data, and on real data from European and American markets. This thesis involved the construction of a library containing C and S code to perform risk analysis using GARCH and extreme value theory models. The results show that model uncertainty can be incorporated, and that risk measures for time horizons greater than one can be obtained by simulation. The methods presented in this thesis have a natural representation involving conditioning. Thus, they permit the computation of both conditional and unconditional risk estimates. Three methods are described: the GARCH method; the two-state GARCH method; and the HBC method. Unconditional risk estimation using the GARCH method is satisfactory on data which seem stationary, but not reliable on data which are non-stationary, such as data with change points. The two-state GARCH model does a little better, but gives very satisfactory results when the risk is estimated conditionally on time. The HBC method does not give satisfactory results.