# [BCP12] Robust optimal sizing of an hybrid energy stand-alone system

**Conférence Internationale avec comité de lecture : **
21st International Symposium on Mathematical Programming (ISMP 2012) and ROADEF 2012,
August 2012,

pp.191,
Berlin,
Germany,

**Mots clés: ** robust combinatorial optimization, renewable energy

**Résumé: **
The development of renewable energy brought new complex combinatorial optimization problems as the one studied here: the conception of an autonomous hybrid energy system. The study is made considering a finite time horizon divided into periods where an energy demand has to be fulfilled. An auxiliary fuel generator guarantees to meet the demand in every case but its use induces important costs. The aim is to determine the optimal number of photovoltaic panels, wind turbines and batteries while minimizing the total cost of investment and use. We first propose a mixed integer linear model for the problem without uncertainty. However, the stochastic behavior of both solar and wind energy and of the demand needs to be taken into account for a robust solution: here, we only consider the variation of the demands. We will focus on an approach where we assume that the total variation of the demands is bounded. The problem is modeled as a two stage optimization program where the decision variables are integer while the recourse problem is a quadratic continuous program. We show that it can be linearized, which allows us to solve the global robust problem with a constraint generation algorithm.