Section: New Results

Observation, control and traveling waves in systems modeled by partial differential equations

Inverse scattering for soft fault diagnosis in electric transmission lines

Participants : Michel Sorine, Huaibin Tang, Qinghua Zhang.

The inverse scattering theory is helpful for efficient use of the reflectometry technology in the field of electric transmission line fault diagnosis. Our recent studies on this topic have been published in [35] , [33] , [32] . The main progress of this year in our study has been the experimental validation of the inverse scattering-based method for soft fault diagnosis. In collaboration with Florent Loete of LGEP (Laboratoire de Génie Electrique de Paris), we have tested the inverse scattering-based method on cables used in Trucks. By slightly separating the two wires of a twisted pair following a predefined spatial profile, a soft fault in the cable is physically simulated. The spatially smoothly varying characteristic impedance of the cable is computed from the physical and geometrical parameters of the cable, and also computed from the reflection coefficient measured with a network analyzer at one end of the cable. The two results are close enough to clearly detect and to locate the physically simulated soft fault from the measured reflection coefficient. A demonstration software has been developed and registered at Agence pour la Protection des Programmes (APP). See Section  5.2 .

Modeling of electric transmission networks

Participants : Mohamed Oumri, Michel Sorine, Filippo Visco Comandini, Qinghua Zhang.

The increasing number and complexity of wired electric networks in modern engineering systems is amplifying the importance of the reliability of electric connections. In the framework of the ANR 0-DEFECT project, we have studied mathematical models of complex electric networks with the aim of designing an algorithm for fault diagnosis (see [34] , [20] for some theoretical results). A generalization of the Baum-Liu-Tesche (BLT) equation to the case of inhomogeneous transmission lines has been developed this year. Efforts have been made in particular to elaborate a fully automatized method for numerical simulation of complex networks with inhomogeneous transmission lines. An efficient method has been designed for the computation of the propagation matrix of each inhomogeneous transmission line and also for the computation of the scattering matrix at each network node. The implemented numerical simulator is based on these propagation and scattering matrices associated to the BLT equation, and on a numerical solution of this equation.

Diagnosis of insulator degradation in long electric cables

Participants : Leila Djaziri, Michel Sorine, Huaibin Tang, Qinghua Zhang.

For the diagnosis of insulator degradation in long electric cables, the estimation of the shunt conductance of such cables have been studied, in the framework of the ANR INSCAN project. The shunt conductance of a healthy electric cable is usually very weak. Even when the insulator in the cable is significantly degraded, the shunt conductance can still remain at a quite low level. The main difficulty in this study is due to the fact that the measurements made at the ends of a cable are hardly sensitive to the variations of the shunt conductance. To overcome this difficulty, two methods have been studied. The first one is based on the processing of long time data records. It is designed for the estimation of distributed shunt conductance, in order to detect and to locate inhomogeneous degradation of the insulator. The main idea of this method is to compensate the weak sensitivity of the measurement by long time data records. Numerical simulations have confirmed its feasibility. The second method aims at assessing the average shunt conductance along a cable. It is based on the analysis of the sensitivity of the wave propagation velocity to the shunt conductance. This method is currently tested through experiments made on cables of SNCF (Société Nationale des Chemins de Fer français).