Higher penetration of volatile renewable sources and increasing load demand are putting a strain on the current utility grid structure. Energy storage solutions are required to maintain grid stability and are vital components to future smart grid designs. Flywheel energy storage can be a strong part of the solution due to high cycle life capabilities and flexible design configurations that balance power and energy capacity. This dissertation focuses on developing design methodologies for advanced flywheel energy storage, with an emphasis on sizing flywheel energy storage and developing lumped parameter modeling techniques for low loss, high temperature superconducting. The first contribution of this dissertation presents a method for using an optimal control law to size flywheel energy storage and develops a design space for potential power and energy storage combinations. This method is a data driven technique, that utilizes power consumption and renewable generation data from a particular location where the storage may be placed. The model for this sizing technique includes the spinning losses, that are unique to flywheel energy storage systems and have limited this technology to short term storage applications, such as frequency and voltage regulation. For longer term storage solutions, the spinning losses for flywheels must be significantly reduced. One potential solution is to use high temperature superconducting bearings, that work by the stable levitation of permanent magnet materials over bulk superconductors. These advanced bearing systems can reduce losses to less than 0.1% stored energy per hour. In order to integrate high temperature superconducting bearings into flywheel system designs, accurate and reduced order models are needed, that include the losses and emulate the hysteretic, non-linear behavior of superconducting levitation. The next two contributions of this dissertation present a lumped parameter axissymmetric model and a 3-D lumped parameter transverse model, which can be used to evaluate bearing lifting capabilities and transverse stiffness for flywheel rotor designs. These models greatly reduce computational time, and were validated against high level finite element analysis, and dynamic experimental tests. The validation experiments are described in detail. / text