## Postdoc at École Polytechnique

### Computer Science department (LIX)

"SOGRID" project on monitoring in smart grids.

In order to ensure continuous reliabilty and quality of services to customers, an electrical distribution network must be stringly controled. This can be done by real time monitoring of the state of the network using measurement and control tools.

SOGRID project aims to test in real condition a communication architecture G3-PLC (Power line current) from domestic meters to source stations. Hence, several electrical measurement devices are designed, developed and deployed in order to control in real time medium and low voltage electrical networks. Our objective within this project is to determine the number and location of measurement devices in medium network that minimizes the total measurement cost and ensures the convergence of the state estimation function.

We first consider the full observability of the network whit only zero injection nodes. Modelling the network by a graph, the problem, called Power Edge Set, is to find the minimum number of devices to install on the edges of the graph such that all the nodes are observed. The observability is defined by these two rules: (i) if a device is istalled on an edge then both its extrimity nodes are observed; (ii) if an observed node has all its neighbours observed, except one, then this node is also observed. We proved that this problem is NP-hard to approximate within 1.12-epsilon, for any epsilon>0, unless P=NP and polynomial for trees and grids. We also proposed two mathematical models: an itrative model modelling the observability propagation process and is given by a binary linear program, and a bilevel binary linear program that is inferred from the former model by means of a fixed-point approach. We showed that the bilevel model can be transform to a single level mixed integer linear program (MILP). We also proposed a cutting plane algorithm to solve the bilevel model directly. To the best of our knowledge, no such algorithm has been proposed to solve this kind of problems. We implemented these two models and the cutting plane algorithm using CPLEX and tested on different graphs. The results showed that only cutting plane algorithm can handle large size instances.

The bilevel model proposed is more appropriate to transport network and allows its full observability. For distribution networks, we consider an observability based on a state estimation function. We proposed a non linear bilevel model to determine the optimal placement of measurement devices that ensures the convergence of the state estimator and satisfy telecom, G3-PLC and structural constraints. We proposed a cutting plane algorithm to solve this model.

Tools: Bilevel models, Mathematical programming, Combinatorial optimisation, Graph theory, Optimisation solver: CPLEX via Jump

## Postdoc at University College London

### Departement of Security and Crime Science

"Risilience Infrastructure and Building Security (RIBS)" - EU FP7 Security Project

Dans un contexte mondial où les intérêts nationaux sont de plus en plus interdépendants, les infrastructures les plus vulnérables en Europe, et en particulier les plus critiques, sont les principales cibles pour les terroristes. De nos jours, des attaques, menées sous la bannière nationale, politique ou religieuse, frappent régulièrement dans nos villes, faisant des morts, des dégâts et des perturbations sur une échelle sans précédent. Le projet RIBS vise à modéliser des mesures de sécurité effectives et viables afin de protéger les infrastructures sans impacter sur la dynamique de leur business. Dans le cadre de ce projet, les attaques terroristes incluant les explosifs, produits chimiques et biologiques ont été considérées.

In order to evaluate the ability of a given infrastructure security system to mitigate the risk of terrorist attacks, an integrated model allowing a dynamic generation of attack scenarios has been proposed. The approach consists in modelling the environment and its occupants, building an event tree representing the different attack scenarios (sequences of events) and assessing the states of all the entities during each scenario. Hence, assessing the risk of these scenarios allows to determine the weeknesses of the security system, the fragility of critical infrastructure entities and the accessibility of the target. New security measures and technologies can then be implemented in order to reduce the risk.

### Contributions

• Vulnerability analysis of critical infrastructures to assess the ability of security system to mitigate the risk of terrorist attacks
• Infrastructure graph modelling
• Complex analysis of terrorist threats
• Probabilistic risk assessment for modelling terrorist attack occurring within critical infrastructure
• Dynamic generation of attack scenarios (Event tree)
• Procurement and evaluation of new security systems to mitigate the risk of terrorist attacks

Tools: Risk analysis, Combinatorial optimisation, Graph theory, Graph modelling, Operational Research and Multi-Criteria Decision Making

## PhD in Computer Science and Combinatorial Optimisation

### Paris-Dauphine University- LAMSADE laboratory

Title: Determination of the most vital elements for graph problems (Détermination des éléments les plus vitaux pour des problèmes de graphes)

Supervisors: Profs. Cristina Bazgan et Daniel Vanderpoten.

An abstract is available here.