Structural Limitations of Energy Storage Systems Based on the Virial Theorem

Based on the virial theorem, the structural limitations are compared among superconducting magnetic energy storage (SMES), flywheels, and capacitors. The conventional SMES coils such as toroidal field coils (TFCs) and solenoids and the capacitor generate the compressive stresses. Due to this, the ratio of the stored energy to the required mass of the structure (U/M ratio) is lower than that of the flywheel. The flywheel almost achieves the uniform tensile stress distribution to support the centrifugal force and enables the enhancement of the U/M ratio. Based on the development status, the superconducting coils and the conventional flywheels composed of steel metals achieve almost 12 kJ/kg of the U/M ratio. Especially, using carbon fiber reinforced plastic, the flywheel can increase the U/M ratio to 90 kJ/kg. The force-balanced coils (FBCs) are helically wound hybrid coils of TFCs and a solenoid and become one of the feasible options for the SMES coils. The FBCs remove the compressive stresses by balancing the electromagnetic forces and have a potential for the improvement of the U/M ratio of SMES coils by the effect of the uniform tensile stress distribution. The theoretical limitation of the U/M ratio is more than twice of that in the flywheel case for the same structural materials.