Tokamaks are a very promising option to exploit nuclear fusion as a programmable and safe energy source. A very critical issue for the practical use of tokamaks consists of the power flow required to initiate and sustain the fusion process, in particular in the poloidal field coils. This flow can be managed by introducing a DC energy storage based on supercapacitors. Because such storage may be the most expensive and largest part of the poloidal power supply system, an excessive size would cancel its potential advantages. This paper presents innovative strategies to optimize the DC storage in poloidal power supply systems. The proposed solution involves the sharing of the DC storage between different coil circuits. The study is supported by novel analytical formulas and by a circuital model developed for this application. The obtained results show that this method and the related algorithms can noticeably reduce the overall size of the storage and the power exchange with the grid, providing a practical contribution toward the feasibility and the effectiveness of nuclear fusion systems.