Master training period

Optimal placement of dispersed generators on a Grenoble distribution network

Location : Univ. Grenoble Alpes and INSA de Rouen

Salary : legal french gratification  ( 550 Euros per month )

Duration : 6 months starting in September, 2018


The training period will take place at the G2elab of Univ. Grenoble Alpes and Laboratoire de Mathématiques de l’INSA de Rouen within the Agence Nationale de la Recherche (ANR) project “Fractal grid”. In Fractal grid we study the design of resilient and agile architectures for the optimization of Smart Grids operations. Specifically, in G2Elab, the theory and application of smart grids is studied and in LMI, the theory of networks and optimization is analyzed. Within Fractal grid, the training period will address the optimal placement of dispersed generators (mainly PV units) on a distribution network.


In harmonic regime, electrical networks are governed by non-linear equations so called “load-flow” which describe the power flows from one node to another. In some limits, these equations can be reduced to a singular linear system involving the graph Laplacian matrix. Using the spectral decomposition of the Laplacian matrix, we obtained a quadratic expression for the voltage drops across the lines [ckr17]. We can then optimize the location of dispersed generators to alleviate the most critical lines. Another direction is to choose which loads to disconnect. We propose to apply these new ideas to the distribution network of the city of Grenoble-France.

In the first half of the training period, the student will be hosted at G2elab. He will work on the modeling of Grenoble’s network and perform some load-flow computations. The second part of the training period will be dedicated to the optimization formulation and solving.

The training period will be mentored by Nicolas Retière at G2Eeab and Jean-Guy Caputo and Arnaud Knippel at the Laboratoire de Mathématiques de l’INSA de Rouen.

Profile of the candidate :

Finishing master student in electrical engineering or applied mathematics. The candidate should know well optimisation and graph theory and have good computing abilities.


Send your application with a vitae to Nicolas Retière ( and Jean-Guy Caputo (

[ckr17] J. G. Caputo, A. Knippel et N. Retière, « Spectral analysis of transmission networks », internal report 2017.