Promoting Hydropower Development at Existing Nonpowered Dams Act This bill amends the Federal Power Act to authorize the Federal Energy Regulatory Commission (FERC) to establish an expedited process for issuing and amending licenses and preliminary permits for new hydropower facilities at existing nonpowered dams. Before licensing the hydropower facility, FERC must assess the safety of existing nonfederal dams and other nonfederal structures. Licensees of hydropower facility are not required to pay an annual charge for administrative expenses until construction commences.