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## Section: New Results

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

#### Modeling of electric transmission networks

Participants : Mohamed Oumri, Michel Sorine, 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 algorithms for fault diagnosis. The well known Baum-Liu-Tesche (BLT) equation is a powerful model for describing quite general networks and allows to compute the current and voltage waves at the nodes of a network from the specifications of its nodes and connecting cables [63] . This year we have studied the inverse problem: what can we know about the properties of the cables connecting the nodes of a network from experiments made at the nodes of the network? A convenient model for this purpose is formulated with admittance matrices. It is essentially equivalent to the BLT equation, hence can describe quite general networks. The inverse problem is then solved through a decomposition of the admittance matrix of the entire network.

#### Diagnosis of insulator degradation in long electric cables

Participants : Leila Djaziri, Michel Sorine, 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. One of them is based on the analysis of the sensitivity of the wave phase shift to the shunt conductance. The efficiency of this method has been demonstrated through extensive tests on cables of SNCF (Société Nationale des Chemins de Fer français). Another method 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. The results of this method evaluated by numerical simulations have been reported at the 16th IFAC Symposium on System Identification [68] .