According to the European Hydrogen Strategy, hydrogen will solve many of the problems with energy storage for balancing variable renewable energy sources (RES) supply and demand. At the same time, we can see increasing popularity of the so-called energy communities (e.g., cooperatives) which (i) enable groups of entities to invest in, manage, and benefit from shared RES energy infrastructure; (ii) are expected to increase the energy independence of local communities from large energy corporations and increase the share of RES. Analyses were conducted on 2000 randomly selected energy cooperatives and four energy cooperatives formed on the basis of actual data. The hypotheses assumed in the research and positively verified in this paper are as follows: (i) there is a relationship between hydrogen storage capacity and the power of RES, which allows an energy community to build energy independence; (ii) the type of RES generating source is meaningful when optimizing hydrogen storage capacity. The paper proves it is possible to build “island energy independence” at the local level using hydrogen storage and the efficiency of the power-to-power chain. The results presented are based on simulations carried out using a dedicated optimization model implemented by mixed integer programming. The authors’ next research projects will focus on optimizing capital expenditures and operating costs using the Levelized Cost of Electricity and Levelized Cost of Hydrogen methodologies.