Energy storage technologies are of great practical importance in electrical grids where renewable energy sources are becoming a significant component in the energy generation mix. Here, we focus on some of the basic properties of flywheel energy storage systems, a technology that becomes competitive due to recent progress in material and electrical design. While the description of the rotation of rigid bodies about a fixed axis is classical mechanics textbook material, all its basic aspects pertinent to flywheels, like, e.g., the evaluation of stress caused by centripetal forces at high rotation speeds, are either not covered or scattered over different sources of information; so it is worthwhile to look closer at the specific mechanical problems for flywheels, and to derive and clearly analyse the equations and their solutions. The connection of flywheels to electrical systems impose particular boundary conditions due to the coupling of mechanical and electrical characteristics of the system. Our report thus deal with the mechanical design in terms of stresses in flywheels, particularly during acceleration and deceleration, considering both solid and hollow disks geometries, in light of which we give a detailed electrical design of the flywheel system considering the discharge-stage dynamics of the flywheel. We include a discussion on the applicability of this mathematical model of the electrical properties of the flywheel for actual settings. Finally, we briefly discuss the relative advantages of flywheels in electrical grids over other energy storage technologies.
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