As renewable energy is gaining an increasing attention due to global warming, traditional grids are facing a radical change and a modernization process. A combination of different technologies is essential to ensure energy security and equity, while maintaining a valuable level of environmental sustainability. Energy storage devices will play a key role at different levels of the electrical grids for maintaining a stable supply of energy, both in a short- and long-term context. As storage can provide a wide variety of services to the grid, an accurate regulatory framework is necessary for a detailed consideration of its benefits. In this thesis, after introducing the basics of mathematical optimization and power system analysis, a discussion on the role and consideration of storage devices in electrical grids is presented.