The diploma thesis describes and analyzes island operation of the residential building for a family with four members with the selection of the appropriate solar power plant, lithium-ion batteries and a diesel generator (off-grid system). In the diploma thesis we briefly presented the issue of the operations of the solar power plant, operations of the island system and the elements which are necessary for its operation, as well as the description and operations of the batteries. Furthermore, there is a description of equations for modeling of the components of the island system, according to which principle we also made the following calculations. At the end there is a discussion about the possible selections of the number of the batteries on the real example with regards to the pretentiousness of the user, where there are the results for different combinations presented graphically and descriptively. In conclusion the results of individual solutions are evaluated and the evaluation is given.