In this this paper, the optimal sizing of electric and thermal storage is applied to the novel definition of a net zero multi energy system (NZEMS). A NZMES is based on producing electricity exclusively from renewable energy sources (RES) and converting it into other energy forms to satisfy multiple energy needs of a community. Due to the intermittent nature of RES, storage resources are needed to increase the self-sufficiency of the system. Possible storage sizing choices are examined considering, on an annual basis, the solution of a predictive control problem aimed at optimizing daily operation. For each day of the year, a predictive control problem is formulated and solved, aimed at minimizing operating costs. Electric, thermal, and (electric) transportation daily curves and expected RES production are assessed by means of a model that includes environmental parameters. Test results, based on the energy model of a small rural village, show expected technical-economic performance of different planning solutions, highlighting how the renewable energy mix influences the choice of both thermal and electric storage, and how self-sufficiency can affect the overall cost of energy.