Mathematical Models for Improving Flexibility within the Smart Grid domain

One of the most important topics of the last decades has been finding energy sources who can replace fossil fuels. Renewable energy is a good candidate, being virtually inexhaustible and more environment-friendly. In order to allow for this transition, electric energy grids have evolved and have become new objects, called \emph{smart grids}. However, the complexity of this new type of grid brings new issues and challenges, which are currently object of study for many researchers. The purpose of this thesis is to showcase some of these problems, and to build mathematical models and algorithms in order to solve them, by leveraging a new property relative to energy loads: flexibility. Since smart devices are becoming more common and they can be remotely controlled, manipulation of energy profiles is possible, and this is a powerful tool for the management of smart grids. Going more into detail, a framework for managing demand response, peak shaving and energy trading has been designed by the means of a combinatorial approach, and it has been enhanced by exploitation of parallel computing. Moreover, an incentive mechanism for usage of renewable energy has been analyzed and improved, by changing some functions which define its behavior. This mechanism has also been examined from a game-theoretic point of view, and it has been further improved in order to always guarantee an agreement between users for flexibility usage. Finally, a decentralized, multi-agent system approach has been used to solve the problems of cost optimization and congestion management. Most of the content of this thesis derives from research works published in journals and conferences.