Storage Technology for Renewable and Green Energy Act of 2013 or the STORAGE 2013 Act - Amends the Internal Revenue Code to: (1) allow, through 2020, a 20% energy tax credit for investment in energy storage property that is directly connected to the electrical grid (i.e., a system of generators, transmission lines, and distribution facilities) and that is designed to receive, store, and convert energy to electricity, deliver it for sale, or use such energy to provide improved reliability or economic benefits to the grid; (2) make such property eligible for new clean renewable energy bond financing; (3) allow a 30% energy tax credit for investment in energy storage property used at the site of energy storage; and (4) allow a 30% nonbusiness energy property tax credit for the installation of energy storage equipment in a principal residence.