Optimal operation of building micro-grids, comparison for both mixed linear integer and continuous non-linear approaches

International audience; This paper presents two mathematical models to solve the Energy Management problem of a building microgrid. In particular, it proposes a deterministic Mixed Integer Linear Programming and Non-Linear Programming formulations. This article focuses on the modelling process and the optimization performances for both approaches regarding optimal operation of near zero energy buildings connected to an electric microgrid with a 24 hours time horizon. For that purpose, a general architecture of a microgrid is detailed, involving energy storage systems, distributed generation and a thermal reduced-model of the grid-connected building. A continuous non-linear model is detailed along with linearisations for the mixed-integer liner formulation. Multi-physic, non-linear and non-convex phenomenon are detailed, such as ventilation and air quality models. Results show that both approaches are relevant for solving the energy management problem of the building microgrid.